Advection diffusion model for particles deposition in Rayleigh-Benard turbulent flows

International Nuclear Information System (INIS)

Oresta, P.; Lippolis, A.; Verzicco, R.; Soldati, A.

2005-01-01

In this paper, Direct Numerical Simulation (DNS) and Lagrangian Particle Tracking are used to precisely investigate the turbulent thermally driven flow and particles dispersion in a closed, slender cylindrical domain. The numerical simulations are carried out for Rayleigh (Ra) and Prandtl numbers (Pr) equal to Ra = 2X10 8 and Pr = 0.7, considering three sets of particles with Stokes numbers, based on Kolmogorov scale, equal to St k 1.3, St k 0.65 and St k = 0.13. This data are used to calculate a priori the drift velocity and the turbulent diffusion coefficient for the Advection Diffusion model. These quantities are function of the Stokes, Froude, Rayleigh and Prandtl numbers only. One dimensional, time dependent, Advection- Diffusion Equation (ADE) is presented to predict particles deposition in Rayleigh-Benard flow in the cylindrical domain. This archetype configuration models flow and aerosol dynamics, produced in case of accident in the passive containment cooling system (PCCS) of a nuclear reactor. ADE results show a good agreement with DNS data for all the sets of particles investigated. (author)

Onset of Absolute Instability Induced by Viscous Dissipation in the Poiseuille-Darcy-Benard Convection of a Newtonian Fluid

International Nuclear Information System (INIS)

Brandão, P V; Alves, L S de B; Barletta, A

2014-01-01

The present paper investigates the transition from convective to absolute instability induced by viscous dissipation. As far as the authors are aware, this is the first time such a study is reported in the literature. Its framework is provided by the Poiseuille-Darcy-Benard convection of a Newtonian fluid. We found the same behaviour observed in the absence of viscous dissipation whenever the Gebhart number is smaller than Ge < 0.95, which is the stabilising effect of the cross flow. When 0.95 < Ge < 4.31, weak cross flows still stabilise the onset of absolute instability but stronger cross flows destabilise it. For a stronger viscous dissipation, i.e. Ge > 4.31, the cross flow always destabilises this onset. The latter two conditions create a scenario where viscous dissipation is capable of inducing a transition to absolute instability in the absence of wall heating, i.e. with a zero Rayleigh number

Benard convection in liquid sodium layers

International Nuclear Information System (INIS)

Kek, V.

1989-08-01

In a sodium layer heated from below and cooled from above, the integral Nusselt numbers are determined in a range of Rayleigh numbers 1.5x10 3 5 . The experiments are performed in containers with dimensions of 500 mm in diameter and 15 mm and 45 mm in height. The relevant quantities are evaluated from measured temperature and heating power data. The experiments show that the heat transfer across the layer is determined mainly by heat conduction up to Rayleigh number Ra ≅ 10 4 . Beyond this value a significant increase of the convective heat transport is observed. At a Rayleigh number of 4x10 4 the Nusselt number achieves the value Nu = 1.7. This result differs from values given by Nusselt-Rayleigh number correlations reported in the literature for liquids with higher Prandtl number. A regression analysis of the experimental data results empirical correlations for the Nusselt number. A time series analysis of the time dependent temperature signals shows that the measured temperature fluctuations exhibit predominantly stochastic features. However, in the lower range of Rayleigh numbers 1.5x10 3 4 certain regular frequencies can be identified from peaks in broadband power density spectra. These frequencies correspond to fluctuations of a period of 80 to 200 seconds. These regular frequencies are explained by instabilities of the cellular pattern in the convection layer reported in the literature. (orig./HP) [de

Non-Oberbeck-Boussinesq effects in two-dimensional Rayleigh-Bénard convection in glycerol

NARCIS (Netherlands)

Sugiyama, K.; Calzavarini, E.; Grossmann, S.; Lohse, Detlef

2007-01-01

We numerically analyze Non-Oberbeck-Boussinesq (NOB) effects in two-dimensional Rayleigh-Benard flow in glycerol, which shows a dramatic change in the viscosity with temperature. The results are presented both as functions of the Rayleigh number Ra up to 108 (for fixed temperature difference �

Rayleigh-Bénard convection instability in the presence of temperature variation at the lower wall

Directory of Open Access Journals (Sweden)

Jovanović Miloš M.

2012-01-01

Full Text Available This paper analyzes the two-dimensional viscous fluid flow between two parallel plates, where the lower plate is heated and the upper one is cooled. The temperature difference between the plates is gradually increased during a certain time period, and afterwards it is temporarily constant. The temperature distribution on the lower plate is not constant in x-direction, and there is longitudinal sinusoidal temperature variation imposed on the mean temperature. We investigate the wave number and amplitude influence of this variation on the stability of Rayleigh-Benard convective cells, by direct numerical simulation of 2-D Navier-Stokes and energy equation.

Stability of impulsively-driven natural convection with unsteady base state: implications of an adiabatic boundary

International Nuclear Information System (INIS)

Ihle, Christian F.; Nino, Yarko

2011-01-01

Stability conditions of a quiescent, horizontally infinite fluid layer with adiabatic bottom subject to sudden cooling from above are studied. Here, at difference from Rayleigh-Benard convection, the temperature base state is never steady. Instability limits are studied using linear analysis while stability is analyzed using the energy method. Critical stability curves in terms of Rayleigh numbers and convection onset times were obtained for several kinematic boundary conditions. Stability curves resulting from energy and linear approaches exhibit the same temporal growth rate for large values of time, suggesting a bound for the temporal asymptotic behavior of the energy method. - Highlights: → Non-penetrative convection appears after a time-evolving temperature base state. → Global stability and instability limits were analyzed. → Critical Rayleigh numbers were computed for different kinematic boundary conditions. → Adiabatic, bottom boundary was found to have a de-stabilizing effect. → System is less stable than in Benard convection.

On the structure of cellular solutions in Rayleigh-Benard-Marangoni flows in small-aspect-ratio containers

Science.gov (United States)

Dijkstra, Henk A.

1992-01-01

Multiple steady flow patterns occur in surface-tension/buoyancy-driven convection in a liquid layer heated from below (Rayleigh-Benard-Marangoni flows). Techniques of numerical bifurcation theory are used to study the multiplicity and stability of two-dimensional steady flow patterns (rolls) in rectangular small-aspect-ratio containers as the aspect ratio is varied. For pure Marangoni flows at moderate Biot and Prandtl number, the transitions occurring when paths of codimension 1 singularities intersect determine to a large extent the multiplicity of stable patterns. These transitions also lead, for example, to Hopf bifurcations and stable periodic flows for a small range in aspect ratio. The influence of the type of lateral walls on the multiplicity of steady states is considered. 'No-slip' lateral walls lead to hysteresis effects and typically restrict the number of stable flow patterns (with respect to 'slippery' sidewalls) through the occurrence of saddle node bifurcations. In this way 'no-slip' sidewalls induce a selection of certain patterns, which typically have the largest Nusselt number, through secondary bifurcation.

Surfactant-Enhanced Benard Convection on an Evaporating Drop

Science.gov (United States)

Nguyen, Van X.; Stebe, Kathleen J.

2001-11-01

Surfactant effects on an evaporating drop are studied experimentally. Using a fluorescent probe, the distribution and surface phase of the surfactant is directly imaged throughout the evaporation process. From these experiments, we identify conditions in which surfactants promote surface tension-driven Benard instabilities in aqueous systems. The drops under study contain finely divided particles, which act as tracers in the flow, and form well-defined patterns after the drop evaporates. Two flow fields have been reported in this system. The first occurs because the contact line becomes pinned by solid particles at the contact line region. In order for the contact line to remain fixed, an outward flow toward the ring results, driving further accumulation at the contact ring. A ‘coffee ring’ of particles is left as residue after the drop evaporates[1]. The second flow is Benard convection, driven by surface tension gradients on the drop[2,3]. In our experiments, an insoluble monolayer of pentadecanoic acid is spread at the interface of a pendant drop. The surface tension is recorded, and the drop is deposited on a well-defined solid substrate. Fluorescent images of the surface phase of the surfactant are recorded as the drop evaporates. The surfactant monolayer assumes a variety of surface states as a function of the area per molecule at the interface: surface gaseous, surface liquid expanded, and surface liquid condensed phases[4]. Depending upon the surface state of the surfactant as the drop evaporates, transitions of residue patterns left by the particles occur, from the coffee ring pattern to Benard cells to irregular patterns, suggesting a strong resistance to outward flow are observed. The occurrence of Benard cells on a surfactant-rich interface occurs when the interface is in LE-LC coexistence. Prior research concerning surfactant effects on this instability predict that surfactants are strongly stabilizing[5]. The mechanisms for this change in behavior

Active control of convection

Energy Technology Data Exchange (ETDEWEB)

Bau, H.H. [Univ. of Pennsylvania, Philadelphia, PA (United States)

1995-12-31

Using stability theory, numerical simulations, and in some instances experiments, it is demonstrated that the critical Rayleigh number for the bifurcation (1) from the no-motion (conduction) state to the motion state and (2) from time-independent convection to time-dependent, oscillatory convection in the thermal convection loop and Rayleigh-Benard problems can be significantly increased or decreased. This is accomplished through the use of a feedback controller effectuating small perturbations in the boundary data. The controller consists of sensors which detect deviations in the fluid`s temperature from the motionless, conductive values and then direct actuators to respond to these deviations in such a way as to suppress the naturally occurring flow instabilities. Actuators which modify the boundary`s temperature/heat flux are considered. The feedback controller can also be used to control flow patterns and generate complex dynamic behavior at relatively low Rayleigh numbers.

Dynamics of a secondary instability in Benard-Marangoni convection with unidimensional heating

International Nuclear Information System (INIS)

Burguete, J.; Mancini, H.L.; Perez-Garcia, C.

1993-01-01

The dynamics of Benard-Marangoni convection with unidimensional heating in a pure fluid is studied experimentally. Convection begins with rolls parallel to the heater. The characteristics of these primary rolls have been determined. When the temperature difference across the liquid layer is increased beyond a critical value a secondary instability appears. Motions transverse to the heater with a definite wavelength can be seen. Moreover, for small angles between the heater and the fluid surface, the pattern drifts along the heater with a velocity that depends almost linearly on the inclination. A phenomenological phase equation is proposed to interpret this observation. (orig.)

Efficiency of Heat Transfer in Turbulent Rayleigh-Benard Convection

Czech Academy of Sciences Publication Activity Database

Urban, Pavel; Musilová, Věra; Skrbek, L.

2011-01-01

Roč. 107, č. 1 (2011), 014302:1-4 ISSN 0031-9007 R&D Projects: GA AV ČR KJB200650902 Institutional research plan: CEZ:AV0Z20650511 Keywords : natural convection * thermal convection Subject RIV: BK - Fluid Dynamics Impact factor: 7.370, year: 2011

Modulated convection at high frequencies and large modulation amplitudes

International Nuclear Information System (INIS)

Swift, J.B.; Hohenberg, P.C.

1987-01-01

Modulated Rayleigh-Benard convection is analyzed for high frequencies and large modulation amplitudes. The linear theory of Gershuni and Zhukhovitskii is generalized to the nonlinear domain, and a subcritical bifurcation to convection is found in agreement with the experiments of Niemela and Donnelly. The crossover between the high-frequency (''Stokes layer'') regime and the low-frequency regime studied previously is analyzed

Effects of modulation on Rayleigh-Benard convection. Part I

Directory of Open Access Journals (Sweden)

B. S. Bhadauria

2004-01-01

Full Text Available The linear stability of a horizontal layer of fluid heated from below and above is considered. In addition to a steady temperature difference between the walls of the fluid layer, a time-dependent periodic perturbation is applied to the wall temperatures. Only infinitesimal disturbances are considered. Numerical results for the critical Rayleigh number are obtained at various Prandtl numbers and for various values of the frequency. Some comparisons have been made with the known results.

Lattice BGK simulation of natural convection

International Nuclear Information System (INIS)

Chen, Yu; Ohashi, Hirotada; Akiyama, Mamoru

1995-01-01

Recently a new thermal lattice Bhatnagar-Gross-Krook fluid model was suggested by the authors. In this study, this new model was applied into the numerical simulation of natural convection, namely the Rayleigh Benard flow. The critical number for the onset of convective phenomenon was numerically measured and compared with that of theoretical prediction. A gravity dependent deviation was found in the numerical simulation, which is explained as an unavoidable consequence of the incorporation of gravity force in the lattice BGK system. (author)

The convection patterns in microemulsions

International Nuclear Information System (INIS)

Korneta, W.; Lopez Quintela, M.A.; Fernandez Novoa, A.

1991-07-01

The Rayleigh-Benard convection in the microemulsion consisting of water (7.5%), cyclohexan (oil-61.7%) and diethylenglycolmonobutylether (surfactant-30.8%) is studied from the onset of convection to the phase separation. The five classes of convection patterns are observed and recorded on the video: localized travelling waves, travelling waves, travelling waves and localized steady rolls, steady rolls and steady polygons. The Fourier transforms and histograms of these patterns are presented. The origin of any pattern is discussed. The intermittent behaviour close to the phase separation was observed. Possible applications of the obtained results are suggested. (author). 6 refs, 4 figs

GPU Implementation of High Rayleigh Number Three-Dimensional Mantle Convection

Science.gov (United States)

Sanchez, D. A.; Yuen, D. A.; Wright, G. B.; Barnett, G. A.

2010-12-01

Although we have entered the age of petascale computing, many factors are still prohibiting high-performance computing (HPC) from infiltrating all suitable scientific disciplines. For this reason and others, application of GPU to HPC is gaining traction in the scientific world. With its low price point, high performance potential, and competitive scalability, GPU has been an option well worth considering for the last few years. Moreover with the advent of NVIDIA's Fermi architecture, which brings ECC memory, better double-precision performance, and more RAM to GPU, there is a strong message of corporate support for GPU in HPC. However many doubts linger concerning the practicality of using GPU for scientific computing. In particular, GPU has a reputation for being difficult to program and suitable for only a small subset of problems. Although inroads have been made in addressing these concerns, for many scientists GPU still has hurdles to clear before becoming an acceptable choice. We explore the applicability of GPU to geophysics by implementing a three-dimensional, second-order finite-difference model of Rayleigh-Benard thermal convection on an NVIDIA GPU using C for CUDA. Our code reaches sufficient resolution, on the order of 500x500x250 evenly-spaced finite-difference gridpoints, on a single GPU. We make extensive use of highly optimized CUBLAS routines, allowing us to achieve performance on the order of O( 0.1 ) µs per timestep*gridpoint at this resolution. This performance has allowed us to study high Rayleigh number simulations, on the order of 2x10^7, on a single GPU.

The structure and dynamics of patterns of Benard convection cells

International Nuclear Information System (INIS)

Rivier, N.; Imperial Coll. of Science and Technology, London; Lausanne Univ.

1990-08-01

Benard-Marangoni convection, in containers with large aspect ratio, exhibits space-filling cellular structures, highly deformable, but crystallized. They contain dislocations and grain boundaries generated and moved by elementary topological transformations, and are subjected to a weak shear stress due to the earth's rotation. The cellular structure and its fluctuations are analyzed from a crystallographic viewpoint, by using two complementary approaches. One is a global analysis of cellular structures in cylindrical symmetry. Their structural stability and defect pattern are obtained as topological mode-locking of a continuous structural parameter. The other, a local, molecular dynamics of the cells, gives a realistic parametrization of the forces and the transformations by generalizing the Voronoi cell construction in one extra dimension. 23 refs., 8 figs

Plume structure in high-Rayleigh-number convection

Science.gov (United States)

Puthenveettil, Baburaj A.; Arakeri, Jaywant H.

2005-10-01

Near-wall structures in turbulent natural convection at Rayleigh numbers of 10^{10} to 10^{11} at A Schmidt number of 602 are visualized by a new method of driving the convection across a fine membrane using concentration differences of sodium chloride. The visualizations show the near-wall flow to consist of sheet plumes. A wide variety of large-scale flow cells, scaling with the cross-section dimension, are observed. Multiple large-scale flow cells are seen at aspect ratio (AR)= 0.65, while only a single circulation cell is detected at AR= 0.435. The cells (or the mean wind) are driven by plumes coming together to form columns of rising lighter fluid. The wind in turn aligns the sheet plumes along the direction of shear. the mean wind direction is seen to change with time. The near-wall dynamics show plumes initiated at points, which elongate to form sheets and then merge. Increase in rayleigh number results in a larger number of closely and regularly spaced plumes. The plume spacings show a common log normal probability distribution function, independent of the rayleigh number and the aspect ratio. We propose that the near-wall structure is made of laminar natural-convection boundary layers, which become unstable to give rise to sheet plumes, and show that the predictions of a model constructed on this hypothesis match the experiments. Based on these findings, we conclude that in the presence of a mean wind, the local near-wall boundary layers associated with each sheet plume in high-rayleigh-number turbulent natural convection are likely to be laminar mixed convection type.

Boundary layers and scaling relations in natural thermal convection

Science.gov (United States)

Shishkina, Olga; Lohse, Detlef; Grossmann, Siegfried

2017-11-01

We analyse the boundary layer (BL) equations in natural thermal convection, which includes vertical convection (VC), where the fluid is confined between two differently heated vertical walls, horizontal convection (HC), where the fluid is heated at one part of the bottom plate and cooled at some other part, and Rayleigh-Benard convection (RBC). For BL dominated regimes we derive the scaling relations of the Nusselt and Reynolds numbers (Nu, Re) with the Rayleigh and Prandtl numbers (Ra, Pr). For VC the scaling relations are obtained directly from the BL equations, while for HC they are derived by applying the Grossmann-Lohse theory to the case of VC. In particular, for RBC with large Pr we derive Nu Pr0Ra1/3 and Re Pr-1Ra2/3. The work is supported by the Deutsche Forschungsgemeinschaft (DFG) under the Grant Sh 405/4 - Heisenberg fellowship.

Comparison of entropy production rates in two different types of self-organized flows: Benard convection and zonal flow

International Nuclear Information System (INIS)

Kawazura, Y.; Yoshida, Z.

2012-01-01

Two different types of self-organizing and sustaining ordered motion in fluids or plasmas--one is a Benard convection (or streamer) and the other is a zonal flow--have been compared by introducing a thermodynamic phenomenological model and evaluating the corresponding entropy production rates (EP). These two systems have different topologies in their equivalent circuits: the Benard convection is modeled by parallel connection of linear and nonlinear conductances, while the zonal flow is modeled by series connection. The ''power supply'' that drives the systems is also a determinant of operating modes. When the energy flux is a control parameter (as in usual plasma experiments), the driver is modeled by a constant-current power supply, and when the temperature difference between two separate boundaries is controlled (as in usual computational studies), the driver is modeled by a constant-voltage power supply. The parallel (series)-connection system tends to minimize (maximize) the total EP when a constant-current power supply drives the system. This minimum/maximum relation flips when a constant-voltage power supply is connected.

Penetrative convection at high Rayleigh numbers

Science.gov (United States)

Toppaladoddi, Srikanth; Wettlaufer, John S.

2018-04-01

We study penetrative convection of a fluid confined between two horizontal plates, the temperatures of which are such that a temperature of maximum density lies between them. The range of Rayleigh numbers studied is Ra=[0.01 ,4 ]106,108 and the Prandtl numbers are Pr=1 and 11.6. An evolution equation for the growth of the convecting region is obtained through an integral energy balance. We identify a new nondimensional parameter, Λ , which is the ratio of temperature difference between the stable and unstable regions of the flow; larger values of Λ denote increased stability of the upper stable layer. We study the effects of Λ on the flow field using well-resolved lattice Boltzmann simulations and show that the characteristics of the flow depend sensitively upon it. For the range Λ = , we find that for a fixed Ra the Nusselt number, Nu, increases with decreasing Λ . We also investigate the effects of Λ on the vertical variation of convective heat flux and the Brunt-Väisälä frequency. Our results clearly indicate that in the limit Λ →0 the problem reduces to that of the classical Rayleigh-Bénard convection.

Feedback control and heat transfer measurements in a Rayleigh-Bénard convection cell

Science.gov (United States)

Vial, M.; Hernández, R. H.

2017-07-01

We report experimental results on the heat transfer and instability onset of a Rayleigh-Bénard convection cell of aspect ratios 6:3:1 filled with a high Prandtl aqueous solution of glycerol under feedback control. We investigate the transient and stationary response of both local temperature readings and heat transfer fluxes on the Rayleigh Bénard cell in both conductive and convective states when we perform two independent feedback control actions on both hot and cold walls. We evaluate the performance of both controllers to maintain a temperature gradient independently if the system is below or above the convection threshold. As the convection cell can be rotated at 180° about the shorter axis of the cell, it was possible to perform transitions between thermal conduction and convection regimes and vice versa under a constant temperature difference maintained by both independent controllers. The experimental setup provided an accurate measurement of the critical Rayleigh number and the evolution of the Nusselt number as a function of the Rayleigh number in the moderately supercritical regime (R a cellular convection pattern formed by 6 transverse rolls throughout the range of Rayleigh numbers.

Boundary layers in turbulent convection for air, liquid gallium and liquid sodium

Science.gov (United States)

Scheel, Janet; Schumacher, Joerg

2017-11-01

The scaling of physical quantities that characterize the shape and dynamics of the viscous and thermal boundary layers with respect to the Rayleigh number will be presented for three series of three-dimensional high-resolution direct numerical simulations of Rayleigh-Benard convection (RBC) in a closed cylindrical cell of aspect ratio one. The simulations have been conducted for convection in air at a Prandtl number Pr = 0.7, in liquid gallium at Pr = 0.021 and in liquid sodium at Pr = 0.005. Then we discuss three statistical analysis methods which have been developed to predict the transition of turbulent RBC into the ultimate regime. The methods are based on the large-scale properties of the velocity profile. All three methods indicate that the range of critical Rayleigh numbers is shifted to smaller magnitudes as the Prandtl number becomes smaller. This work is supported by the Priority Programme SPP 1881 of the Deutsche Forschungsgemeinschaft.

Boundary Layer Control of Rotating Convection Systems

Science.gov (United States)

King, E. M.; Stellmach, S.; Noir, J.; Hansen, U.; Aurnou, J. M.

2008-12-01

Rotating convection is ubiquitous in the natural universe, and is likely responsible for planetary processes such magnetic field generation. Rapidly rotating convection is typically organized by the Coriolis force into tall, thin, coherent convection columns which are aligned with the axis of rotation. This organizational effect of rotation is thought to be responsible for the strength and structure of magnetic fields generated by convecting planetary interiors. As thermal forcing is increased, the relative influence of rotation weakens, and fully three-dimensional convection can exist. It has long been assumed that rotational effects will dominate convection dynamics when the ratio of buoyancy to the Coriolis force, the convective Rossby number, Roc, is less than unity. We investigate the influence of rotation on turbulent Rayleigh-Benard convection via a suite of coupled laboratory and numerical experiments over a broad parameter range: Rayleigh number, 10310; Ekman number, 10-6≤ E ≤ ∞; and Prandtl number, 1≤ Pr ≤ 100. In particular, we measure heat transfer (as characterized by the Nusselt number, Nu) as a function of the Rayleigh number for several different Ekman and Prandtl numbers. Two distinct heat transfer scaling regimes are identified: non-rotating style heat transfer, Nu ~ Ra2/7, and quasigeostrophic style heat transfer, Nu~ Ra6/5. The transition between the non-rotating regime and the rotationally dominant regime is described as a function of the Ekman number, E. We show that the regime transition depends not on the global force balance Roc, but on the relative thicknesses of the thermal and Ekman boundary layers. The transition scaling provides a predictive criterion for the applicability of convection models to natural systems such as Earth's core.

Rayleigh-Taylor convective overturn in stellar collapse

International Nuclear Information System (INIS)

Bruenn, S.W.; Buchler, J.R.; Livio, M.

1979-01-01

Rayleigh--Taylor convective overturn in collapsing stellar cores is modeled with a one-dimensional parametrization. The results of a numerical hydrodynamic study are very encouraging and indicate that such an overturn could well be a dominant feature in the supernova explosion mechanism

The onset of nonpenetrative convection in a suddenly cooled layer of fluid

Energy Technology Data Exchange (ETDEWEB)

Ihle, Christian F. [Program in Fluid Dynamics, Facultad de Ciencias Fisicas y Matematicas, Universidad de Chile, Blanco Encalada 2002 Of. 327, Santiago (Chile); Nino, Yarko [Departamento de Ingenieria Civil, Division de Recursos Hidricos y Medio Ambiente, Universidad de Chile, Av. Blanco Encalada 2002, Santiago (Chile)

2006-04-15

Conditions for the onset of nonpenetrative convection in a horizontal Boussinesq fluid layer subject to a step change in temperature are studied using propagation theory. A wide range of Prandtl numbers and two different kinematic boundary conditions are considered. It is shown that for high Rayleigh numbers, critical conditions for the onset of convective motion reproduce exactly those for the unsteady Rayleigh-Benard instability. Present results extend those of previous research and show a tendency of the rigid-rigid and free-rigid critical curves to converge for low Prandtl numbers. Comparison between present and previously reported results on critical conditions for the onset of instabilities and onset time using different methods yields good agreement on a middle to high Prandtl number range. A ratio of 10 between experimentally measured and theoretically predicted onset times is suggested for stress-free bounded systems. (author)

Rotating thermal convection at very large Rayleigh numbers

Science.gov (United States)

Weiss, Stephan; van Gils, Dennis; Ahlers, Guenter; Bodenschatz, Eberhard

2016-11-01

The large scale thermal convection systems in geo- and astrophysics are usually influenced by Coriolis forces caused by the rotation of their celestial bodies. To better understand the influence of rotation on the convective flow field and the heat transport at these conditions, we study Rayleigh-Bénard convection, using pressurized sulfur hexaflouride (SF6) at up to 19 bars in a cylinder of diameter D=1.12 m and a height of L=2.24 m. The gas is heated from below and cooled from above and the convection cell sits on a rotating table inside a large pressure vessel (the "Uboot of Göttingen"). With this setup Rayleigh numbers of up to Ra =1015 can be reached, while Ekman numbers as low as Ek =10-8 are possible. The Prandtl number in these experiment is kept constant at Pr = 0 . 8 . We report on heat flux measurements (expressed by the Nusselt number Nu) as well as measurements from more than 150 temperature probes inside the flow. We thank the Deutsche Forschungsgemeinschaft (DFG) for financial support through SFB963: "Astrophysical Flow Instabilities and Turbulence". The work of GA was supported in part by the US National Science Foundation through Grant DMR11-58514.

Homogeneous purely buoyancy driven turbulent flow

Science.gov (United States)

Arakeri, Jaywant; Cholemari, Murali; Pawar, Shashikant

2010-11-01

An unstable density difference across a long vertical tube open at both ends leads to convection that is axially homogeneous with a linear density gradient. We report results from such tube convection experiments, with driving density caused by salt concentration difference or temperature difference. At high enough Rayleigh numbers (Ra) the convection is turbulent with zero mean flow and zero mean Reynolds shear stresses; thus turbulent production is purely by buoyancy. We observe different regimes of turbulent convection. At very high Ra the Nusselt number scales as the square root of the Rayleigh number, giving the so-called "ultimate regime" of convection predicted for Rayleigh-Benard convection in limit of infinite Ra. Turbulent convection at intermediate Ra, the Nusselt number scales as Ra^0.3. In both regimes, the flux and the Taylor scale Reynolds number are more than order of magnitude larger than those obtained in Rayleigh-Benard convection. Absence of a mean flow makes this an ideal flow to study shear free turbulence near a wall.

Nusselt-Rayleigh correlations for design of industrial elements: Experimental and numerical investigation of natural convection in tilted square air filled enclosures

International Nuclear Information System (INIS)

Bairi, A.

2008-01-01

Natural convection in air filled 2D tilted square cavities is experimentally and numerically studied. The hot and cold walls of the cavity are maintained isothermal at temperatures T h and T c , respectively, and the channel of the cavity is adiabatic. Measurements and simulations are performed for various geometrical and thermal configurations. Different values of the Rayleigh number Ra and the tilt angle α of the cavity are considered. The range of Ra covered in our work extends from 10 to 10 10 while α varies from 0 to 360 deg. This permits the analysis of several significant situations corresponding to vertical active walls (α 0 deg.), hot wall at the bottom (α = 90 deg.; Rayleigh-Benard convection) and hot wall at the top, pure conductive mode (α = 270 deg.). A computational 2D model based on the finite volume method is used for solving the mass, momentum and energy transfer governing equations. The simulation provides thermal and dynamic maps of the fluid for all configurations treated. The influence of Ra and α on the flow pattern and on the convective heat transfer are analysed and discussed. The thermal boundary distribution and the convective heat transfer calculated are, for most treated cases, close to those obtained experimentally by means of a simple bench specifically designed for this purpose. The maximum discrepancy between the simulations and measurements is relatively small, corresponding to the expected uncertainty of the model and measurements. The convective heat transfer is determined while calculating the radiative and conductive contributions to the global exchange. Radiation is determined by the radiosity method associated with the measured field of temperatures as well as to the global IR emissivities of all the internal elements of the cavity. The average Nusselt number Nu-bar is used to quantify the calculated convective contribution of the heat exchange within the cavity, and is compared with the measured value Nu-bar m . We

Turbulent boundary layer in high Rayleigh number convection in air.

Science.gov (United States)

du Puits, Ronald; Li, Ling; Resagk, Christian; Thess, André; Willert, Christian

2014-03-28

Flow visualizations and particle image velocimetry measurements in the boundary layer of a Rayleigh-Bénard experiment are presented for the Rayleigh number Ra=1.4×1010. Our visualizations indicate that the appearance of the flow structures is similar to ordinary (isothermal) turbulent boundary layers. Our particle image velocimetry measurements show that vorticity with both positive and negative sign is generated and that the smallest flow structures are 1 order of magnitude smaller than the boundary layer thickness. Additional local measurements using laser Doppler velocimetry yield turbulence intensities up to I=0.4 as in turbulent atmospheric boundary layers. From our observations, we conclude that the convective boundary layer becomes turbulent locally and temporarily although its Reynolds number Re≈200 is considerably smaller than the value 420 underlying existing phenomenological theories. We think that, in turbulent Rayleigh-Bénard convection, the transition of the boundary layer towards turbulence depends on subtle details of the flow field and is therefore not universal.

Ultimate regime of high Rayleigh number convection in a porous medium.

Science.gov (United States)

Hewitt, Duncan R; Neufeld, Jerome A; Lister, John R

2012-06-01

Well-resolved direct numerical simulations of 2D Rayleigh-Bénard convection in a porous medium are presented for Rayleigh numbers Ra≤4×10(4) which reveal that, contrary to previous indications, the linear classical scaling for the Nusselt number, Nu~Ra, is attained asymptotically. The flow dynamics are analyzed, and the interior of the vigorously convecting system is shown to be increasingly well described as Ra→∞ by a simple columnar "heat-exchanger" model with a single horizontal wave number k and a linear background temperature field. The numerical results are approximately fitted by k~Ra(0.4).

Cell structures caused by settling particles in turbulent Rayleigh-Bénard convection

Science.gov (United States)

Lee, Changhoon; Park, Sangro

2016-11-01

Turbulent thermal convection is an important phenomenon frequently found in nature and industrial processes, often with laden particles. In the last several decades, the vast majority of studies have addressed single phase convective flow with focus on the scaling relation of flow parameters associated with heat transfer. Particle-laden Rayleigh-Bénard convection, however, has not been sufficiently studied. In this study, modulation of cell structures by settling particles in turbulent Rayleigh-Bénard convection in a doubly periodic square channel is investigated using direct numerical simulation with a point particle approach. Flow parameters are fixed at Rayleigh number=106, Prandtl number=0.7, the aspect ratio=6, and Froude number=0.19. We report from the simulations that settling heavy particles modulate irregular large-scale thermal plume structures into organized polygonal cell structures. Different shapes of flow structures are obtained for different particle diameters and mass loadings. We found that polygonal cell structures arise due to asymmetric feedback force exerted by particles onto hot and cold plumes. Increasing the number of particles augments the asymmetry and the polygonal cell structures become smaller, eventually going to the hexagonal structures.

Rotating Rayleigh-Bénard convection at low Prandtl number

Science.gov (United States)

Aguirre Guzman, Andres; Ostilla-Monico, Rodolfo; Clercx, Herman; Kunnen, Rudie

2017-11-01

Most geo- and astrophysical convective flows are too remote or too complex for direct measurements of the physical quantities involved, and thus a reduced framework with the main physical constituents is beneficial. This approach is given by the problem of rotating Rayleigh-Bénard convection (RRBC). For large-scale systems, the governing parameters of RRBC take extreme values, leading to the geostrophic turbulent regime. We perform Direct Numerical Simulations to investigate the transition to this regime at low Prandtl number (Pr). In low- Pr fluids, thermal diffusivity dominates over momentum diffusivity; we use Pr = 0.1 , relevant to liquid metals. In particular, we study the convective heat transfer (Nusselt number Nu) as a function of rotation (assessed by the Ekman number Ek). The strength of the buoyant forcing (Rayleigh number Ra) is Ra = 1 ×1010 to ensure turbulent convection. Varying Ek , we observe a change of the power-law scaling Nu Ekβ that suggests a transition to geostrophic turbulence, which is likely to occur at Ek = 9 ×10-7 . The thermal boundary layer thickness, however, may suggest a transition at lower Ekman numbers, indicating that perhaps not all statistical quantities show a transitional behaviour at the same Ek .

A model for near-wall dynamics in turbulent Rayleigh Bénard convection

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Theerthan, S. Ananda; Arakeri, Jaywant H.

1998-10-01

Experiments indicate that turbulent free convection over a horizontal surface (e.g. Rayleigh Bénard convection) consists of essentially line plumes near the walls, at least for moderately high Rayleigh numbers. Based on this evidence, we propose here a two-dimensional model for near-wall dynamics in Rayleigh Bénard convection and in general for convection over heated horizontal surfaces. The model proposes a periodic array of steady laminar two-dimensional plumes. A plume is fed on either side by boundary layers on the wall. The results from the model are obtained in two ways. One of the methods uses the similarity solution of Rotem & Classen (1969) for the boundary layer and the similarity solution of Fuji (1963) for the plume. We have derived expressions for mean temperature and temperature and velocity fluctuations near the wall. In the second approach, we compute the two-dimensional flow field in a two-dimensional rectangular open cavity. The number of plumes in the cavity depends on the length of the cavity. The plume spacing is determined from the critical length at which the number of plumes increases by one. The results for average plume spacing and the distribution of r.m.s. temperature and velocity fluctuations are shown to be in acceptable agreement with experimental results.

Heat transfer and large scale dynamics in turbulent Rayleigh-Bénard convection

NARCIS (Netherlands)

Ahlers, Günter; Grossmann, Siegfried; Lohse, Detlef

2009-01-01

The progress in our understanding of several aspects of turbulent Rayleigh-Bénard convection is reviewed. The focus is on the question of how the Nusselt number and the Reynolds number depend on the Rayleigh number Ra and the Prandtl number Pr, and on how the thicknesses of the thermal and the

The multifractal nature of plume structure in high-Rayleigh-number convection

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Puthenveettil, Baburaj A.; Ananthakrishna, G.; Arakeri, Jaywant H.

2005-03-01

The geometrically different planforms of near-wall plume structure in turbulent natural convection, visualized by driving the convection using concentration differences across a membrane, are shown to have a common multifractal spectrum of singularities for Rayleigh numbers in the range 1010-1011 at Schmidt number of 602. The scaling is seen for a length scale range of 25 and is independent of the Rayleigh number, the flux, the strength and nature of the large-scale flow, and the aspect ratio. Similar scaling is observed for the plume structures obtained in the presence of a weak flow across the membrane. This common non-trivial spatial scaling is proposed to be due to the same underlying generating process for the near-wall plume structures.

Non-Oberbeck-Boussinesq Effects in Gaseous Rayleigh-Bénard Convection

NARCIS (Netherlands)

Ahlers, Günter; Fontenele Araujo Junior, F.; Funfschilling, Denis; Grossmann, Siegfried; Lohse, Detlef

2007-01-01

Non-Oberbeck-Boussinesq (NOB) effects are measured experimentally and calculated theoretically for strongly turbulent Rayleigh-Be´nard convection of ethane gas under pressure where the material properties strongly depend on the temperature. Relative to the Oberbeck-Boussinesq case we find a decrease

Thermal Rayleigh-Marangoni convection in a three-layer liquid-metal-battery model

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Köllner, Thomas; Boeck, Thomas; Schumacher, Jörg

2017-05-01

The combined effects of buoyancy-driven Rayleigh-Bénard convection (RC) and surface tension-driven Marangoni convection (MC) are studied in a triple-layer configuration which serves as a simplified model for a liquid metal battery (LMB). The three-layer model consists of a liquid metal alloy cathode, a molten salt separation layer, and a liquid metal anode at the top. Convection is triggered by the temperature gradient between the hot electrolyte and the colder electrodes, which is a consequence of the release of resistive heat during operation. We present a linear stability analysis of the state of pure thermal conduction in combination with three-dimensional direct numerical simulations of the nonlinear turbulent evolution on the basis of a pseudospectral method. Five different modes of convection are identified in the configuration, which are partly coupled to each other: RC in the upper electrode, RC with internal heating in the molten salt layer, and MC at both interfaces between molten salt and electrode as well as anticonvection in the middle layer and lower electrode. The linear stability analysis confirms that the additional Marangoni effect in the present setup increases the growth rates of the linearly unstable modes, i.e., Marangoni and Rayleigh-Bénard instability act together in the molten salt layer. The critical Grashof and Marangoni numbers decrease with increasing middle layer thickness. The calculated thresholds for the onset of convection are found for realistic current densities of laboratory-sized LMBs. The global turbulent heat transfer follows scaling predictions for internally heated RC. The global turbulent momentum transfer is comparable with turbulent convection in the classical Rayleigh-Bénard case. In summary, our studies show that incorporating Marangoni effects generates smaller flow structures, alters the velocity magnitudes, and enhances the turbulent heat transfer across the triple-layer configuration.

Experimental investigation of the influence of natural convection and end-effects on Rayleigh streaming in a thermoacoustic engine.

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Ramadan, Islam A; Bailliet, Hélène; Valière, Jean-Christophe

2018-01-01

The influence of both the natural convection and end-effects on Rayleigh streaming pattern in a simple standing-wave thermoacoustic engine is investigated experimentally at different acoustic levels. The axial mean velocity inside the engine is measured using both Laser Doppler Velocimetry and Particle Image Velocimetry. The mean flow patterns are categorized in three different regions referred to as "cold streaming" region, "hot streaming" region, and "end-effects" region. In the cold streaming region, the dominant phenomenon is Rayleigh streaming and the mean velocity measurements correspond well with the theoretical expectations of Rayleigh streaming at low acoustic levels. At higher acoustic levels, the measurements deviate from the theoretical expectations which complies with the literature. In the hot streaming region, temperature measurements reveal that the non-uniformity of the resonator wall temperature is the origin of natural convection flow. Velocity measurements show that natural convection flow superimposes on the Rayleigh streaming flow so that the measured mean velocity deviates from the theoretical expectations of Rayleigh streaming. In the last region, the measured mean velocity is very different from Rayleigh streaming due to the combined effects of both the flow disturbances generated near the extremity of the stack and the natural convection flow.

Mixed convection between horizontal plates and consequences for chemical vapor deposition flows

International Nuclear Information System (INIS)

Chiu, K.C.

1986-01-01

To simulate the fluid dynamics of VD systems, mixed convection between horizontal plates (AR = width/height = 10) heated from below was studied by laser Doppler anemometry in a range 1368 < Ra < 8300 and 15 < R3 < 170. The entrance effects were characterized by two lengths: one for the onset of bouyancy-driven instability, and one for the full development of longitudinal convection rolls. Explicit expressions for both entrance lengths are given in terms of Ra and Re. In addition, unsteady longitudinal convection rolls were observed. These are discussed in terms of the admixture of transverse convection rolls and/or contributions from upstream turbulence. For the fully developed region it is shown analytically that the transverse velocities of the longitudinal convection rolls, v and w, are independent of the forced flow and are identical to those of the two-dimensional Rayleigh-Benard convection rolls. These fundamental results serve as a base for the discussion of horizontal CVD flows. The entrance and sidewall effects are found to have pronounced influences on the flow patterns observed in CVD (AR = 2) reactors

Design Aspects of the Rayleigh Convection Code

Science.gov (United States)

Featherstone, N. A.

2017-12-01

Understanding the long-term generation of planetary or stellar magnetic field requires complementary knowledge of the large-scale fluid dynamics pervading large fractions of the object's interior. Such large-scale motions are sensitive to the system's geometry which, in planets and stars, is spherical to a good approximation. As a result, computational models designed to study such systems often solve the MHD equations in spherical geometry, frequently employing a spectral approach involving spherical harmonics. We present computational and user-interface design aspects of one such modeling tool, the Rayleigh convection code, which is suitable for deployment on desktop and petascale-hpc architectures alike. In this poster, we will present an overview of this code's parallel design and its built-in diagnostics-output package. Rayleigh has been developed with NSF support through the Computational Infrastructure for Geodynamics and is expected to be released as open-source software in winter 2017/2018.

Thermal convection at low Rayleigh number from concentrated sources in porous media

International Nuclear Information System (INIS)

Hickox, C.E.

1980-01-01

A simple mathematical theory is proposed for the analysis of natural convective motion, at low Rayleigh number, from a concentrated source of heat in a fluid-saturated porous medium. The theory consists of retaining only the leading terms of series expansions of the dependent variables in terms of the Rayleigh number, is thus linear, and is valid only in the limit of small Rayleigh number. Based on fundamental results for a variety of isolated sources, superposition is used to provide solutions for situations of practical interest. Special emphasis is given to the analysis of sub-seabed disposal of nuclear waste. 8 figures

Turbulence modeling of natural convection in enclosures: A review

International Nuclear Information System (INIS)

Choi, Seok Ki; Kim, Seong O

2012-01-01

In this paper a review of recent developments of turbulence models for natural convection in enclosures is presented. The emphasis is placed on the effect of the treatments of Reynolds stress and turbulent heat flux on the stability and accuracy of the solution for natural convection in enclosures. The turbulence models considered in the preset study are the two-layer k -ε model, the shear stress transport (SST) model, the elliptic-relaxation (V2-f) model and the elliptic-blending second-moment closure (EBM). Three different treatments of the turbulent heat flux are the generalized gradient diffusion hypothesis (GGDH), the algebraic flux model (AFM) and the differential flux model (DFM). The mathematical formulation of the above turbulence models and their solution method are presented. Evaluation of turbulence models are performed for turbulent natural convection in a 1:5 rectangular cavity ( Ra = 4.3x10 10 ) and in a square cavity with conducting top and bottom walls ( Ra =1.58x10 9 ) and the Rayleigh-Benard convection ( Ra = 2x10 6 ∼ Ra =10 9 ). The relative performances of turbulence models are examined and their successes and shortcomings are addressed

Apparatus for real-time acoustic imaging of Rayleigh-Bénard convection

Energy Technology Data Exchange (ETDEWEB)

Kuehn, Kerry, K.

2008-10-28

We have successfully designed, built and tested an experimental apparatus which is capable of providing the first real-time ultrasound images of Rayleigh-B\\'{e}nard convection in optically opaque fluids confined to large aspect ratio experimental cells. The apparatus employs a modified version of a commercially available ultrasound camera to capture images (30 frames per second) of flow patterns in a fluid undergoing Rayleigh Bénard convection. The apparatus was validated by observing convection rolls in 5cSt polydimethylsiloxane (PDMS) polymer fluid. Our first objective, after having built the apparatus, was to use it to study the sequence of transitions from diffusive to time--dependent heat transport in liquid mercury. The aim was to provide important information on pattern formation in the largely unexplored regime of very low Prandtl number fluids. Based on the theoretical stability diagram for liquid mercury, we anticipated that straight rolls should be stable over a range of Rayleigh numbers, between 1708 and approximately 1900. Though some of our power spectral densities were suggestive of the existence of weak convection, we have been unable to unambiguously visualize stable convection rolls above the theoretical onset of convection in liquid mercury. Currently, we are seeking ways to increase the sensitivity of our apparatus, such as (i) improving the acoustic impedance matching between our materials in the ultrasound path and (ii) reducing the noise level in our acoustic images due to turbulence and cavitation in the cooling fluids circulating above and below our experimental cell. If we are able to convincingly improve the sensitivity of our apparatus, and we still do not observe stable convection rolls in liquid mercury, then it may be the case that the theoretical stability diagram requires revision. In that case, either (i) straight rolls are not stable in a large aspect ratio cell at the Prandtl numbers associated with liquid mercury, or (ii

Prandtl-number Effects in High-Rayleigh-number Spherical Convection

Science.gov (United States)

Orvedahl, Ryan J.; Calkins, Michael A.; Featherstone, Nicholas A.; Hindman, Bradley W.

2018-03-01

Convection is the predominant mechanism by which energy and angular momentum are transported in the outer portion of the Sun. The resulting overturning motions are also the primary energy source for the solar magnetic field. An accurate solar dynamo model therefore requires a complete description of the convective motions, but these motions remain poorly understood. Studying stellar convection numerically remains challenging; it occurs within a parameter regime that is extreme by computational standards. The fluid properties of the convection zone are characterized in part by the Prandtl number \\Pr = ν/κ, where ν is the kinematic viscosity and κ is the thermal diffusion; in stars, \\Pr is extremely low, \\Pr ≈ 10‑7. The influence of \\Pr on the convective motions at the heart of the dynamo is not well understood since most numerical studies are limited to using \\Pr ≈ 1. We systematically vary \\Pr and the degree of thermal forcing, characterized through a Rayleigh number, to explore its influence on the convective dynamics. For sufficiently large thermal driving, the simulations reach a so-called convective free-fall state where diffusion no longer plays an important role in the interior dynamics. Simulations with a lower \\Pr generate faster convective flows and broader ranges of scales for equivalent levels of thermal forcing. Characteristics of the spectral distribution of the velocity remain largely insensitive to changes in \\Pr . Importantly, we find that \\Pr plays a key role in determining when the free-fall regime is reached by controlling the thickness of the thermal boundary layer.

Development of Rayleigh-Taylor and bulk convection instabilities in the dynamics of plasma liners and pinches

International Nuclear Information System (INIS)

Bud'ko, A.B.; Velikovich, A.L.; Liberman, M.A.; Felber, F.S.

1989-01-01

A solution is derived for the problem of the initial, linear stage of the growth of small perturbations in the course of the cylindrically symmetric compression and expansion of a plasma liner and a Z-pinch with a sharp boundary. In these systems, Rayleigh-Taylor instabilities localized near the plasma boundaries are the most dangerous. Bulk convective instabilities develop in addition to these Rayleigh-Taylor instabilities. The various instability modes, including local and global Rayleigh-Taylor modes, which grown in an accelerated plasma with distributed profiles of hydrodynamic variables, are classified. The spectra of the instability growth rates are calculated for plasma liners and Z-pinches. The shape of these spectra reveals an explanation of the stratification and filamentation of the plasma observed experimentally in pinches and liners. The imposition of a longitudinal magnetic field gives rise to a stability window in the space of the flow parameters. In this window, the Rayleigh-Taylor modes are suppressed completely by magnetic shear, while the bulk convective modes are suppressed to a significant extent

Rayleigh convective instability in the presence of phase transitions of water vapor. The formation of large-scale eddies and cloud structures

International Nuclear Information System (INIS)

Shmerlin, Boris Ya; Kalashnik, Maksim V

2013-01-01

Convective motions in moist saturated air are accompanied by the release of latent heat of condensation. Taking this effect into account, we consider the problem of convective instability of a moist saturated air layer, generalizing the formulation of the classical Rayleigh problem. An analytic solution demonstrating the fundamental difference between moist convection and Rayleigh convection is obtained. Upon losing stability in the two-dimensional case, localized convective rolls or spatially periodic chains of rollers with localized areas of upward motion evolve. In the case of axial symmetry, the growth of localized convective vortices with circulation characteristic of tropical cyclones (hurricanes) is possible at the early stages of development and on the scale of tornados to tropical cyclones. (methodological notes)

Horizontal structures of velocity and temperature boundary layers in two-dimensional numerical turbulent Rayleigh-Bénard convection

NARCIS (Netherlands)

Zhou, Quan; Sugiyama, K.; Stevens, Richard Johannes Antonius Maria; Grossmann, Siegfried; Lohse, Detlef; Xia, K.

2011-01-01

We investigate the structures of the near-plate velocity and temperature profiles at different horizontal positions along the conducting bottom (and top) plate of a Rayleigh-Bénard convection cell, using two-dimensional (2D) numerical data obtained at the Rayleigh number Ra = 108 and the Prandtl

Adapting a Fourier pseudospectral method to Dirichlet boundary conditions for Rayleigh-Bénard convection

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I. C. Ramos

2015-10-01

Full Text Available We present the adaptation to non-free boundary conditions of a pseudospectral method based on the (complex Fourier transform. The method is applied to the numerical integration of the Oberbeck-Boussinesq equations in a Rayleigh-Bénard cell with no-slip boundary conditions for velocity and Dirichlet boundary conditions for temperature. We show the first results of a 2D numerical simulation of dry air convection at high Rayleigh number (. These results are the basis for the later study, by the same method, of wet convection in a solar still. Received: 20 Novembre 2014, Accepted: 15 September 2015; Edited by: C. A. Condat, G. J. Sibona; DOI:http://dx.doi.org/10.4279/PIP.070015 Cite as: I C Ramos, C B Briozzo, Papers in Physics 7, 070015 (2015

Turbulent thermal superstructures in Rayleigh-Bénard convection

Science.gov (United States)

Stevens, Richard J. A. M.; Blass, Alexander; Zhu, Xiaojue; Verzicco, Roberto; Lohse, Detlef

2018-04-01

We report the observation of superstructures, i.e., very large-scale and long living coherent structures in highly turbulent Rayleigh-Bénard convection up to Rayleigh Ra=109 . We perform direct numerical simulations in horizontally periodic domains with aspect ratios up to Γ =128 . In the considered Ra number regime the thermal superstructures have a horizontal extend of six to seven times the height of the domain and their size is independent of Ra. Many laboratory experiments and numerical simulations have focused on small aspect ratio cells in order to achieve the highest possible Ra. However, here we show that for very high Ra integral quantities such as the Nusselt number and volume averaged Reynolds number only converge to the large aspect ratio limit around Γ ≈4 , while horizontally averaged statistics such as standard deviation and kurtosis converge around Γ ≈8 , the integral scale converges around Γ ≈32 , and the peak position of the temperature variance and turbulent kinetic energy spectra only converge around Γ ≈64 .

Numerical simulations of thermal convection in a rotating spherical fluid shell at high Taylor and Rayleigh numbers

International Nuclear Information System (INIS)

Sun, Z.; Schubert, G.

1995-01-01

In this study, we carry out numerical simulations of thermal convection in a rapidly rotating spherical fluid shell at high Taylor number Ta and Rayleigh number R with a nonlinear, three-dimensional, time-dependent, spectral-transform code. The parameters used in the simulations are chosen to be in a range which allows us to study two different types of convection, i.e., single column and multi-layered types, and the transition between them. Numerical solutions feature highly time-dependent north--south open columnar convective cells. The cells occur irregularly in longitude, are quasi-layered in cylindrical radius, and maintain alternating bands of mean zonal flow. The complex convective structure and the banded mean zonal flow are results of the high Taylor and Rayleigh numbers. The transition between the two types of convection appears to occur gradually with increasing Rayleigh and Taylor numbers. At a Taylor number of 10 7 the differential rotation pattern consists of an inner cylindrical region of subrotation and an outer cylindrical shell of superrotation manifest at the outer boundary as an equatorial superrotation and a high latitude subrotation. The differential rotation pattern is similar at Ta=10 8 and low Rayleigh number. Cylindrical shells of alternately directed mean zonal flow begin to develop at Ta=10 8 and R=50R c and at Ta=10 9 and R=25R c . This pattern is seen on the outer surface as a latitudinally-banded zonal flow consisting of an equatorial superrotation, a middle and high latitude subrotation, and a polar superrotation. At Ta=10 9 and R=50R c the differential rotation appears at the surface as a broad eastward flow in the equatorial region with alternating bands of westward and eastward flow at high latitudes. copyright 1995 American Institute of Physics

Thermal convection of a viscoplastic liquid with high Rayleigh and Bingham numbers

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Vikhansky, A.

2009-10-01

We consider the effect of yield stress on the Rayleigh-Bénard convection of a viscoplastic material. First we consider the model problem of convection in a differentially heated loop, which is described by the (modified) Lorenz equations. The presence of the yield stress significantly alters the dynamics of the system. In particular, the chaotic motion can stop suddenly (sometimes, after a period of chaotic oscillations). Guided by the model equations we performed direct numerical simulations of convection of the Bingham liquid in a square cavity heated from bellow. Our interest has been concentrated on the situation when both buoyancy and plastic forces are large. The obtained results are in a reasonable agreement with the predictions by the Lorenz equations.

Nusselt number and bulk temperature in turbulent Rayleigh-Bénard convection

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Bodenschatz, Eberhard; Weiss, Stephan; Shishkina, Olga; International CollaborationTurbulence Research Collaboration

2017-11-01

We present an algorithm to calculate the Nusselt number (Nu) in measurements of the heat transport in turbulent Rayleigh-Bénard convection under general non-Oberbeck-Boussinesq (NOB) conditions. We further critically analyze the different ways to evaluate the dependences of Nu over the Rayleigh number (Ra) and show the sensitivity of these dependences to the reference temperatures in the bulk, top and bottom boundary layers (BLs). Finally we propose a method to predict the bulk temperature and a way to calculate the reference temperatures of the top and bottom BLs and validate them against the Göttingen measurements. The work is supported by the Max Planck Society and the Deutsche Forschungsgemeinschaft (DFG) under the Grant Sh 405/4 - Heisenberg fellowship.

Heat Transport Enhancement of Turbulent Thermal Convection by Inserted Channels

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Xia, Ke-Qing; Zhang, Lu

2017-11-01

We report an experimental study on the heat transport properties of turbulent Rayleigh Benard Convection (RBC) in a rectangular cell with two types of 3D-printed structures inserted inside. The first one splits the original rectangular cell into 60 identical sub cells whose aspect ratio is 1:1:10 (length, width, height). The second one splits the cell into 30 sub cells, each with a 1:2:10 aspect ratio and a baffle in the center. We find that for large Rayleigh numbers (Ra), the Nusselt numbers (Nu) of both structures increase compared with that of the empty rectangular cell. An enhancement in Nu as much as 20% is found for the second type of insertion at Rayleigh number 2 ×109 . Moreover, the Nu-Ra scaling shows a transition with both geometries. The particle image velocimetry (PIV) measurement within a single sub unit indicates that the transition may be related to the laminar to turbulent transition in flow field. Direct numerical simulations (DNS) confirm the experimental results. Our results demonstrate the potential in using insertions to enhance passive heat transfer. This work was supported by the Research Grants Council (RGC) of HKSAR (Nos. CUHK404513 and CUHK14301115).

Time-stepping approach for solving upper-bound problems: Application to two-dimensional Rayleigh-Bénard convection

Science.gov (United States)

Wen, Baole; Chini, Gregory P.; Kerswell, Rich R.; Doering, Charles R.

2015-10-01

An alternative computational procedure for numerically solving a class of variational problems arising from rigorous upper-bound analysis of forced-dissipative infinite-dimensional nonlinear dynamical systems, including the Navier-Stokes and Oberbeck-Boussinesq equations, is analyzed and applied to Rayleigh-Bénard convection. A proof that the only steady state to which this numerical algorithm can converge is the required global optimal of the relevant variational problem is given for three canonical flow configurations. In contrast with most other numerical schemes for computing the optimal bounds on transported quantities (e.g., heat or momentum) within the "background field" variational framework, which employ variants of Newton's method and hence require very accurate initial iterates, the new computational method is easy to implement and, crucially, does not require numerical continuation. The algorithm is used to determine the optimal background-method bound on the heat transport enhancement factor, i.e., the Nusselt number (Nu), as a function of the Rayleigh number (Ra), Prandtl number (Pr), and domain aspect ratio L in two-dimensional Rayleigh-Bénard convection between stress-free isothermal boundaries (Rayleigh's original 1916 model of convection). The result of the computation is significant because analyses, laboratory experiments, and numerical simulations have suggested a range of exponents α and β in the presumed Nu˜PrαRaβ scaling relation. The computations clearly show that for Ra≤1010 at fixed L =2 √{2 },Nu≤0.106 Pr0Ra5/12 , which indicates that molecular transport cannot generally be neglected in the "ultimate" high-Ra regime.

Boundary-modulated Thermal Convection Model in the Mantle

Science.gov (United States)

Kurita, K.; Kumagai, I.

2008-12-01

Analog experiments have played an important role in the constructing ideas of mantle dynamics. The series of experiments by H. Ramberg is one of the successful examples. Recently, however the realm of the analog experiments seems to be overwhelmed by steady progress of computer simulations. Is there still room for the analog experiments? This might be a main and hidden subject of this session. Here we propose a working hypothesis how the convecting mantle behaves based on the analog experiments in the system of viscous fluid and particles. The essential part is the interaction of convecting flow with heterogeneities existing in the boundaries. It is proposed the preexisting topographical heterogeneity in the boundary could control the flow pattern of convecting fluid. If this kind of heterogeneity can be formed as a consequence of convective motion and mobilized by the flow, the convection also can control the heterogeneity. We can expect interactions in two ways, by which the system behaves in a self-organize fashion. To explore the mutual interactions between convection flow and heterogeneity the system of viscous fluid and particles with slightly higher density is selected as 2D Rayleigh-Benard type convection. The basic structure consists of a basal particulate layer where permeable convection transports heat and an upper viscous fluid layer. By reducing the magnitude of the density difference the convective flow can mobilize the particles and can erode the basal layer. The condition of this erosion can be identified in the phase diagram of the particle Shields"f and the Rayleigh numbers. At Ra greater than 107 the convection style drastically changed before and after the erosion. Before the erosion where the flat interface of the boundary is maintained small scaled turbulent convection pattern is dominant. After the erosion where the interface becomes bumpy the large scale convective motion is observed. The structure is coherent to that of the boundary. This

Growth of Rayleigh-Taylor and bulk convective instabilities in dynamics of plasma liners and pinches

International Nuclear Information System (INIS)

Bud'ko, A.B.; Velikovich, A.L.; Liberman, M.A.; Felber, F.S.

1989-01-01

Perturbation growth is studied for the initial, linear stage of an instability development in the course of a cylindrically-symmetric compression and expansion of plasma liners and Z-pinches with a sharp boundary. The hydrodynamic instabilities are Rayleigh-Taylor and bulk convective ones, the former being the most dengerous. Classification of the instability modes developing in accelerated plasmas, inclusing the local and global Rayleigh-Taylor modes, is given. The spectra of the instability growth rates are calculated for plasma liners and Z-pinches. The properties of the spectra appear to explain the filamentation and stratification of plasmas observed in the experiments with liners and Z-pinches. An axial magnetic field is shown to create a window of stability in the space of the flow parameters, where th Rayleigh-Taylor modes are fully suppressed by the magnetic shear, and the bulk convective ones - to a considerable extent. The axial magnetic field required to stabilize the implosion of a liner is estimated as B z0 =(10-30 kG)I(MA)/R 0 (cm), where I is the average current, R 0 - the initial radius of the liner

Study on the Instability of Two-Phase Flow in the Heat-Absorbing Tube of Trough Solar Collector

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Ying Zhang

2017-01-01

Full Text Available The Marangoni effect and Rayleigh-Benard effect in the two-phase region of solar trough heat-absorbing tube are simulated by FTM (front tracking method. Considering the Marangoni effect alone, although surface tension gradient and surface tension affect the interface wave, the two effects have different characteristics. The surface tension gradient caused by the temperature gradient is one of the factors that swing the interface. The amplitude attenuation of the interface wave decreases with the increase of the Marangoni number (Ma. In general, the surface tension gradient enhances the convection opposite to the temperature gradient. Under the gravity field, the Rayleigh-Benard effect influences the development of the vortex structure in the flow field, which in turn affects the velocity gradient near the interface to influence the evolution of the interface fluctuation. In a small Rayleigh number (Ra, the buoyancy convection reduces the velocity gradient, thus suppressing the evolution of the interfacial wave. In the range of Ra  4.0E4, the situation is just the opposite. The larger the Ra is, the stronger the promoting effect is.

Effect of periodic bottom plate heating on large scale flow in turbulent Rayleigh-Bénard convection

Czech Academy of Sciences Publication Activity Database

Kuqali, M.; Babuin, Simone; Niemela, J.J.

2015-01-01

Roč. 8, č. 3 (2015), 483-489 ISSN 1735-3572 Institutional support: RVO:68378271 Keywords : Rayleigh-Bénard convection * Reynolds number Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 0.888, year: 2015

Three-dimensional Rayleigh-Taylor convection of miscible fluids in a porous medium

Science.gov (United States)

Suekane, Tetsuya; Nakanishi, Yuji; Wang, Lei

2017-11-01

Natural convection of miscible fluids in a porous medium is relevant for fields, such as geoscience and geoengineering, and for the geological storage of CO2. In this study, we use X-ray computer tomography to visualize 3D fingering structures associated with the Rayleigh-Taylor instability between miscible fluids in a porous medium. In the early stages of the onset of the Rayleigh-Taylor instability, a fine crinkling pattern gradually appears at the interface. As the wavelength and amplitude increase, descending fingers form on the interface and extend vertically downward; moreover, ascending and highly symmetric fingers form. The adjacent fingers are cylindrical in shape and coalesce to form large fingers. Fingers appearing on the interface tend to become finer with increasing Rayleigh number, which is consistent with linear perturbation theory. If the Péclet number exceeds 10, the transverse dispersion increases the finger diameter and enhances finger coalescence, strongly impacting the decay in finger number density. When mechanical dispersion is negligible, the finger-extension velocity, the mass-transfer rate, and the onset time scale with Rayleigh number. Mechanical dispersion not only reduces the onset time but also enhances mass transport, which indicates that mechanical dispersion influences the long-term dissolution process of CO2 injected into aquifers.

Numerical simulation of helical-vortex effects in Rayleigh-Bénard convection

Directory of Open Access Journals (Sweden)

G. V. Levina

2006-01-01

Full Text Available A numerical approach is substantiated for searching for the large-scale alpha-like instability in thermoconvective turbulence. The main idea of the search strategy is the application of a forcing function which can have a physical interpretation. The forcing simulates the influence of small-scale helical turbulence generated in a rotating fluid with internal heat sources and is applied to naturally induced fully developed convective flows. The strategy is tested using the Rayleigh-Bénard convection in an extended horizontal layer of incompressible fluid heated from below. The most important finding is an enlargement of the typical horizontal scale of the forming helical convective structures accompanied by a cells merging, an essential increase in the kinetic energy of flows and intensification of heat transfer. The results of modeling allow explaining how the helical feedback can work providing the non-zero mean helicity generation and the mutual intensification of horizontal and vertical circulation, and demonstrate how the energy of the additional helical source can be effectively converted into the energy of intensive large-scale vortex flow.

Effect of plumes on measuring the large scale circulation in turbulent Rayleigh-Bénard convection

NARCIS (Netherlands)

Stevens, Richard Johannes Antonius Maria; Clercx, H.J.H.; Lohse, Detlef

2011-01-01

We studied the properties of the large-scale circulation (LSC) in turbulent Rayleigh-Bénard (RB) convection by using results from direct numerical simulations in which we placed a large number of numerical probes close to the sidewall. The LSC orientation is determined by either a cosine or a

Turbulent Superstructures in Rayleigh-Bénard convection at different Prandtl number

Science.gov (United States)

Schumacher, Jörg; Pandey, Ambrish; Ender, Martin; Westermann, Rüdiger; Scheel, Janet D.

2017-11-01

Large-scale patterns of the temperature and velocity field in horizontally extended cells can be considered as turbulent superstructures in Rayleigh-Bénard convection (RBC). These structures are obtained once the turbulent fluctuations are removed by a finite-time average. Their existence has been reported for example in Bailon-Cuba et al.. This large-scale order obeys a strong similarity with the well-studied patterns from the weakly nonlinear regime at lower Rayleigh number in RBC. In the present work we analyze the superstructures of RBC at different Prandtl number for Prandtl values between Pr = 0.005 for liquid sodium and 7 for water. The characteristic evolution time scales, the typical spatial extension of the rolls and the properties of the defects of the resulting superstructure patterns are analyzed. Data are obtained from well-resolved spectral element direct numerical simulations. The work is supported by the Priority Programme SPP 1881 of the Deutsche Forschungsgemeinschaft.

Direct numerical simulation and statistical analysis of turbulent convection in lead-bismuth

Energy Technology Data Exchange (ETDEWEB)

Otic, I.; Grotzbach, G. [Forschungszentrum Karlsruhe GmbH, Institut fuer Kern-und Energietechnik (Germany)

2003-07-01

Improved turbulent heat flux models are required to develop and analyze the reactor concept of an lead-bismuth cooled Accelerator-Driven-System. Because of specific properties of many liquid metals we have still no sensors for accurate measurements of the high frequency velocity fluctuations. So, the development of the turbulent heat transfer models which are required in our CFD (computational fluid dynamics) tools needs also data from direct numerical simulations of turbulent flows. We use new simulation results for the model problem of Rayleigh-Benard convection to show some peculiarities of the turbulent natural convection in lead-bismuth (Pr = 0.025). Simulations for this flow at sufficiently large turbulence levels became only recently feasible because this flow requires the resolution of very small velocity scales with the need for recording long-wave structures for the slow changes in the convective temperature field. The results are analyzed regarding the principle convection and heat transfer features. They are also used to perform statistical analysis to show that the currently available modeling is indeed not adequate for these fluids. Basing on the knowledge of the details of the statistical features of turbulence in this convection type and using the two-point correlation technique, a proposal for an improved statistical turbulence model is developed which is expected to account better for the peculiarities of the heat transfer in the turbulent convection in low Prandtl number fluids. (authors)

Ground Boundary Conditions for Thermal Convection Over Horizontal Surfaces at High Rayleigh Numbers

Science.gov (United States)

Hanjalić, K.; Hrebtov, M.

2016-07-01

We present "wall functions" for treating the ground boundary conditions in the computation of thermal convection over horizontal surfaces at high Rayleigh numbers using coarse numerical grids. The functions are formulated for an algebraic-flux model closed by transport equations for the turbulence kinetic energy, its dissipation rate and scalar variance, but could also be applied to other turbulence models. The three-equation algebraic-flux model, solved in a T-RANS mode ("Transient" Reynolds-averaged Navier-Stokes, based on triple decomposition), was shown earlier to reproduce well a number of generic buoyancy-driven flows over heated surfaces, albeit by integrating equations up to the wall. Here we show that by using a set of wall functions satisfactory results are found for the ensemble-averaged properties even on a very coarse computational grid. This is illustrated by the computations of the time evolution of a penetrative mixed layer and Rayleigh-Bénard (open-ended, 4:4:1 domain) convection, using 10 × 10 × 100 and 10 × 10 × 20 grids, compared also with finer grids (e.g. 60 × 60 × 100), as well as with one-dimensional treatment using 1 × 1 × 100 and 1 × 1 × 20 nodes. The approach is deemed functional for simulations of a convective boundary layer and mesoscale atmospheric flows, and pollutant transport over realistic complex hilly terrain with heat islands, urban and natural canopies, for diurnal cycles, or subjected to other time and space variations in ground conditions and stratification.

Thermal turbulent convection: thermal plumes and fluctuations; Convection thermique turbulente: panaches et fluctuations

Energy Technology Data Exchange (ETDEWEB)

Gibert, M

2007-10-15

In this study we investigate the phenomenon of thermal turbulent convection in new and unprecedented ways. The first system we studied experimentally is an infinite vertical channel, where a constant vertical mean gradient of temperature exists. Inside this channel the average mass flux is null. The results obtained from our measurements reveal that the flow is mainly inertial; indeed the dissipative coefficients (here the viscosity) play a role only to define a coherence length L. This length is the distance over which the thermal plumes can be considered as 'free falling' objects. The horizontal transport, of heat and momentum, is entirely due to fluctuations. The associated 'mixing length' is small compared to the channel width. In the other hand, the vertical heat transport is due to coherent structures: the heat plumes. Those objects were also investigated in a Lagrangian study of the flow in the bulk of a Rayleigh-Benard cell. The probe, which has the same density as the fluid used in this experiment, is a sphere of 2 cm in diameter with embarked thermometers and radio-emitter. The heat plumes transport it, which allows a statistical study of such objects. (author)

Arunn Narasimhan

Indian Academy of Sciences (India)

Volume 4 Issue 6 June 1999 pp 82-90 Classroom. Rayleigh-Benard Convection - Physics of a Widespread Phenomenon · Arunn Narasimhan · More Details Fulltext PDF. Volume 13 Issue 7 July 2008 pp 638-647 General Article. Why do Elephants have Big Ear Flaps? Arunn Narasimhan · More Details Fulltext PDF ...

Analysis of natural convection heat transfer with crust formation in the molten metal pool using CONV-2 and 3D computer codes

International Nuclear Information System (INIS)

Park, R. J.; Kang, K. H.; Kim, S. B.; Kim, H. D.; Choi, S. M.

1998-01-01

Analytical studies have been performed on natural convection heat transfer with crust formation in a molten metal pool to validate and evaluate experimental data using the CONV-2 and 3D computer codes. Two types of steady state tests, a low and high geometric aspect ratio case in the molten metal pool, were performed to investigate crust thickness as a function of boundary conditions. The CONV-2 and 3D computer codes were developed under the OECD/NEA RASPLAV project to simulate two- and three-dimensional natural convection heat transfer with crust formation, respectively. The Rayleigh-Benard flow patterns in the molten metal pool contribute to the temperature distribution, which affects non-uniform crust formation. The CONV-2D results on crust thickness are a little higher than the experimental data because of heat loss during the test. In comparison of the CONV-3D results with the CONV-2D results on crust thickness, the three-dimensional results are higher than the two-dimensional results, because of three dimensional natural convection flow and wall effect

The Effects of Radiation on the Linear Stability of a horizontal layer ...

African Journals Online (AJOL)

The effect of radiation on the onset of Rayleigh-Benard convection is studied in the case of a radiating Newtonian fluid in a fluid-saturated horizontal porous layer heated from below. The radiative heat transfer is treated using the differential approximation for optically thin limiting case. The linear stability theory is employed ...

Flux scaling: Ultimate regime

Indian Academy of Sciences (India)

First page Back Continue Last page Overview Graphics. Flux scaling: Ultimate regime. With the Nusselt number and the mixing length scales, we get the Nusselt number and Reynolds number (w'd/ν) scalings: and or. and. scaling expected to occur at extremely high Ra Rayleigh-Benard convection. Get the ultimate regime ...

Molten pool-lower head integrity. Heat transfer models including advanced numerical simulations (DNS)

Energy Technology Data Exchange (ETDEWEB)

Seiler, J.M.; Bonnet, J.M.; Bernaz, L. [CEA Grenoble (France)

2001-07-01

Extensive studies have been performed to investigate the heat transfer within a molten corium pool (homogeneous, stratified and with miscibility gap): Synthesis of heat transfer correlations in molten pool (homogeneous and stratified), Focusing effect in stratified metal layer, DNS analysis of Rayleigh Benard instabilities at the top boundary; interpretation of the different convection regimes and exponents affecting the Rayleigh number in the heat transfer correlations, Molten pool model for corium presenting a miscibility gap. Condition for de-stratification. (authors)

Molten pool-lower head integrity. Heat transfer models including advanced numerical simulations (DNS)

International Nuclear Information System (INIS)

Seiler, J.M.; Bonnet, J.M.; Bernaz, L.

2001-01-01

Extensive studies have been performed to investigate the heat transfer within a molten corium pool (homogeneous, stratified and with miscibility gap): Synthesis of heat transfer correlations in molten pool (homogeneous and stratified), Focusing effect in stratified metal layer, DNS analysis of Rayleigh Benard instabilities at the top boundary; interpretation of the different convection regimes and exponents affecting the Rayleigh number in the heat transfer correlations, Molten pool model for corium presenting a miscibility gap. Condition for de-stratification. (authors)

Dynamical and statistical phenomena of circulation and heat transfer in periodically forced rotating turbulent Rayleigh-Bénard convection

NARCIS (Netherlands)

Sterl, S.H.; Li, H.M.; Zhong, J.Q.

2016-01-01

In this paper, we present results from an experimental study into turbulent Rayleigh-Bénard convection forced externally by periodically modulated unidirectional rotation rates. We find that the azimuthal rotation velocity θ(t) and thermal amplitude δ(t) of the large-scale circulation (LSC) are

Supercritical Quasi-Conduction States in Stochastic Rayleigh-Benard Convection

Science.gov (United States)

2011-09-15

is 10 (see table 1). The sensitivity (in the sense of Sobol [39]) of the integrated Nusselt number with respect to the amplitude of the boundary...using a multi-element quadrature formula [32]. Following Sobol [39], we shall define global sensitivity indices as the ratio between the variance of...39] I. M. Sobol , Global sensitivity indices for nonlinear mathematical models and their monte carlo estimates, Math. Comput. Simul. 55 (2001) 271

An application of the unifying theory of thermal convection in vertical natural convection

Science.gov (United States)

Ng, Chong Shen; Ooi, Andrew; Lohse, Detlef; Chung, Daniel

2014-11-01

Using direct numerical simulations of vertical natural convection (VNC) at Rayleigh numbers 1 . 0 ×105 - 1 . 0 ×109 and Prandtl number 0 . 709 , we provide support for a generalised applicability of the Grossmann-Lohse (GL) theory, originally developed for horizontal natural (Rayleigh-Bénard) convection. In accordance with the theory, the boundary-layer thicknesses of the velocity and temperature fields in VNC obey laminar-like scaling, whereas away from the walls, the dissipation of the turbulent fluctuations obey the scaling for fully developed turbulence. In contrast to Rayleigh-Bénard convection, the direction of gravity in VNC is parallel to the mean flow. Thus, there no longer exists an exact relation linking the normalised global dissipations to the Nusselt, Rayleigh and Prandtl numbers. Nevertheless, we show that the unclosed term, namely the global-averaged buoyancy flux, also exhibits laminar and turbulent scaling, consistent with the GL theory. The findings suggest that, similar to Rayleigh-Bénard convection, a pure power-law relationship between the Nusselt, Rayleigh and Prandtl numbers is not the best description for VNC and existing empirical power-law relationships should be recalibrated to better reflect the underlying physics.

A new scaling law for temperature variance profile in the mixing zone of turbulent Rayleigh-Bénard convection

Science.gov (United States)

Wang, Yin; Xu, Wei; He, Xiao-Zhou; Yik, Hiu-Fai; Wang, Xiao-Ping; Schumacher, Jorg; Tong, Penger

2017-11-01

We report a combined experimental and numerical study of the scaling properties of the temperature variance profile η(z) along the central z axis of turbulent Rayleigh-Bénard convection in a thin disk cell and an upright cylinder of aspect ratio unity. In the mixing zone outside the thermal boundary layer region, the measured η(z) is found to scale with the cell height H in both cells and obey a power law, η(z) (z/H)ɛ, with the obtained values of ɛ being very close to -1. Based on the experimental and numerical findings, we derive a new equation for η(z) in the mixing zone, which has a power-law solution in good agreement with the experimental and numerical results. Our work thus provides a common framework for understanding the effect of boundary layer fluctuations on the scaling properties of the temperature variance profile in turbulent Rayleigh-Bénard convection. This work was supported in part by Hong Kong Research Grants Council.

Modeling of the thermal boundary layer in turbulent Rayleigh-Bénard convection

Science.gov (United States)

Emran, Mohammad; Shishkina, Olga

2016-11-01

We report modeling of the thermal boundary layer in turbulent Rayleigh-Bénard convection (RBC), which incorporates the effect of turbulent fluctuations. The study is based on the thermal boundary layer equation from Shishkina et al., and new Direct Numerical Simulations (DNS) of RBC in a cylindrical cell of the aspect ratio 1, for the Prandtl number variation of several orders of magnitude. Our modeled temperature profiles are found to agree with the DNS much better than those obtained with the classical Prandtl-Blasius or Falkner-Skan approaches. The work is supported by the Deutsche Forschungsgemeinschaft (DFG) under the Grant Sh405/4 - Heisenberg fellowship and SFB963, Project A06.

Thermal turbulent convection: thermal plumes and fluctuations

International Nuclear Information System (INIS)

Gibert, M.

2007-10-01

In this study we investigate the phenomenon of thermal turbulent convection in new and unprecedented ways. The first system we studied experimentally is an infinite vertical channel, where a constant vertical mean gradient of temperature exists. Inside this channel the average mass flux is null. The results obtained from our measurements reveal that the flow is mainly inertial; indeed the dissipative coefficients (here the viscosity) play a role only to define a coherence length L. This length is the distance over which the thermal plumes can be considered as 'free falling' objects. The horizontal transport, of heat and momentum, is entirely due to fluctuations. The associated 'mixing length' is small compared to the channel width. In the other hand, the vertical heat transport is due to coherent structures: the heat plumes. Those objects were also investigated in a Lagrangian study of the flow in the bulk of a Rayleigh-Benard cell. The probe, which has the same density as the fluid used in this experiment, is a sphere of 2 cm in diameter with embarked thermometers and radio-emitter. The heat plumes transport it, which allows a statistical study of such objects. (author)

Convection in an ideal gas at high Rayleigh numbers.

Science.gov (United States)

Tilgner, A

2011-08-01

Numerical simulations of convection in a layer filled with ideal gas are presented. The control parameters are chosen such that there is a significant variation of density of the gas in going from the bottom to the top of the layer. The relations between the Rayleigh, Peclet, and Nusselt numbers depend on the density stratification. It is proposed to use a data reduction which accounts for the variable density by introducing into the scaling laws an effective density. The relevant density is the geometric mean of the maximum and minimum densities in the layer. A good fit to the data is then obtained with power laws with the same exponent as for fluids in the Boussinesq limit. Two relations connect the top and bottom boundary layers: The kinetic energy densities computed from free fall velocities are equal at the top and bottom, and the products of free fall velocities and maximum horizontal velocities are equal for both boundaries.

Effect of velocity boundary conditions on the heat transfer and flow topology in two-dimensional Rayleigh-Bénard convection.

Science.gov (United States)

van der Poel, Erwin P; Ostilla-Mónico, Rodolfo; Verzicco, Roberto; Lohse, Detlef

2014-07-01

The effect of various velocity boundary condition is studied in two-dimensional Rayleigh-Bénard convection. Combinations of no-slip, stress-free, and periodic boundary conditions are used on both the sidewalls and the horizontal plates. For the studied Rayleigh numbers Ra between 10(8) and 10(11) the heat transport is lower for Γ=0.33 than for Γ=1 in case of no-slip sidewalls. This is, surprisingly, the opposite for stress-free sidewalls, where the heat transport increases for a lower aspect ratio. In wider cells the aspect-ratio dependence is observed to disappear for Ra ≥ 10(10). Two distinct flow types with very different dynamics can be seen, mostly dependent on the plate velocity boundary condition, namely roll-like flow and zonal flow, which have a substantial effect on the dynamics and heat transport in the system. The predominantly horizontal zonal flow suppresses heat flux and is observed for stress-free and asymmetric plates. Low aspect-ratio periodic sidewall simulations with a no-slip boundary condition on the plates also exhibit zonal flow. In all the other cases, the flow is roll like. In two-dimensional Rayleigh-Bénard convection, the velocity boundary conditions thus have large implications on both roll-like and zonal flow that have to be taken into consideration before the boundary conditions are imposed.

Heat transfer in cryogenic helium gas by turbulent Rayleigh-Bénard convection in a cylindrical cell of aspect ratio 1

Czech Academy of Sciences Publication Activity Database

Urban, Pavel; Hanzelka, Pavel; Musilová, Věra; Králík, Tomáš; La Mantia, M.; Srnka, Aleš; Skrbek, L.

2014-01-01

Roč. 16, č. 5 (2014), 053042: 1-40 ISSN 1367-2630 R&D Projects: GA ČR GPP203/12/P897 Institutional support: RVO:68081731 Keywords : Rayleigh-Bénard convection * heat transfer efficiency * cryogenic helium Subject RIV: BK - Fluid Dynamics Impact factor: 3.558, year: 2014

Transition to the Ultimate Regime in Two-Dimensional Rayleigh-Bénard Convection

Science.gov (United States)

Zhu, Xiaojue; Mathai, Varghese; Stevens, Richard J. A. M.; Verzicco, Roberto; Lohse, Detlef

2018-04-01

The possible transition to the so-called ultimate regime, wherein both the bulk and the boundary layers are turbulent, has been an outstanding issue in thermal convection, since the seminal work by Kraichnan [Phys. Fluids 5, 1374 (1962), 10.1063/1.1706533]. Yet, when this transition takes place and how the local flow induces it is not fully understood. Here, by performing two-dimensional simulations of Rayleigh-Bénard turbulence covering six decades in Rayleigh number Ra up to 1 014 for Prandtl number Pr =1 , for the first time in numerical simulations we find the transition to the ultimate regime, namely, at Ra*=1013 . We reveal how the emission of thermal plumes enhances the global heat transport, leading to a steeper increase of the Nusselt number than the classical Malkus scaling Nu ˜Ra1 /3 [Proc. R. Soc. A 225, 196 (1954), 10.1098/rspa.1954.0197]. Beyond the transition, the mean velocity profiles are logarithmic throughout, indicating turbulent boundary layers. In contrast, the temperature profiles are only locally logarithmic, namely, within the regions where plumes are emitted, and where the local Nusselt number has an effective scaling Nu ˜Ra0.38 , corresponding to the effective scaling in the ultimate regime.

GENETIC SOURCES AND TECTONOPHYSICAL REGULARITIES OF DIVISIBILITY OF THE LITHOSPHERE INTO BLOCKS OF VARIOUS RANKS AT DIFFERENT STAGES OF ITS FORMATION: TECTONOPHYSICAL ANALYSIS

Directory of Open Access Journals (Sweden)

Semen I. Sherman

2015-01-01

Full Text Available The paper presents the first tectonophysical reconstruction of initial divisibility of the protolithosphere as a result of convection in the cooling primitive mantle. Initial division of the protolithosphere into separate masses, i.e. prototypes of the blocks, and their size are predetermined by the emerging Rayleigh-Benard convection cells. In studies of geology and geodynamics, the Rayleigh-Benard convection cells were first referred to as a factor to explain the formation of initial continental cores. Considering the Rayleigh-Benard cells and their structural relics can help clarify initial divisibility of the protolithosphere and the origin of the major lithospheric plates, i.e. prototypes of continents. In our opinion, the initial mega-scale block structure of the protolithosphere and the emerging lithosphere were predetermined by the Rayleigh-Benard cells as they were preserved in the emerging lithosphere and their lower boundaries corresponded to the core-mantle boundary, i.e. one of the major discontinuities of the planet. Our theoretical estimations are in good agreement with the number and sizes of the Earth's theorized first supercontinents, Vaalbara and Ur. In our tectonophysical discussion of the formation of the lithospheric block structure, we analyze in detail the map of modern lithospheric plates [Bird, 2003] in combination with the materials from [Sherman et al., 2000]. In the hierarchy of the blocks comprising the contemporary lithosphere, which sizes are widely variable, two groups of blocks are clearly distinguished. The first group includes megablocks with the average geometric size above 6500 km. Their formation is related to convection in the Earth mantle at the present stage of the geodynamic evolution of the Earth, as well as at all the previous stages, including the earliest one, when the protolithosphere emerged. The second group includes medium-sized blocks with the average geometric size of less than 4500 km and

Lattice Boltzmann analysis of effect of heating location and Rayleigh number on natural convection in partially heated open ended cavity

Energy Technology Data Exchange (ETDEWEB)

Gangawane, Krunal Madhukar; Bharti, Ram Prakash; Kumar, Surendra [Indian Institute of Technology Roorkee, Uttarakhand (India)

2015-08-15

Natural convection characteristics of a partially heated open ended square cavity have been investigated numerically by using an in-house computational flow solver based on the passive scalar thermal lattice Boltzmann method (PS-TLBM) with D2Q9 (two-dimensional and nine-velocity link) lattice model. The partial part of left wall of the cavity is heated isothermally at either of the three different (bottom, middle and top) locations for the fixed heating length as half of characteristic length (H/2) while the right wall is open to the ambient conditions. The other parts of the cavity are thermally isolated. In particular, the influences of partial heating locations and Rayleigh number (103≤ Ra≤106) in the laminar zone on the local and global natural convection characteristics (such as streamline, vorticity and isotherm contours; centerline variations of velocity and temperature; and local and average Nusselt numbers) have been presented and discussed for the fixed value of the Prandtl number (Pr=0.71). The streamline patterns show qualitatively similar nature for all the three heating cases and Rayleigh numbers, except the change in the recirculation zone which is found to be largest for middle heating case. Isotherm patterns are shifted towards a partially heated wall on increasing Rayleigh number and/or shifting of heating location from bottom to top. Both the local and average Nusselt numbers, as anticipated, shown proportional increase with Rayleigh number. The cavity with middle heating location shown higher heat transfer rate than that for the top and bottom heating cases. Finally, the functional dependence of the average Nusselt number on flow governing parameters is also presented as a closure relationship for the best possible utilization in engineering practices and design.

The effect of centrifugal buoyancy on the heat transport in rotating Rayleigh-Bénard convection

Science.gov (United States)

Horn, Susanne; Aurnou, Jonathan

2017-11-01

In a rapidly rotating and differentially heated fluid, the centrifugal acceleration can play a similar role to that of gravity in generating convective motion. However, in the paradigm system of rotating Rayleigh-Bénard convection, centrifugal buoyancy is typically not considered in theoretical studies and, thus, usually undesired in laboratory experiments, despite being unavoidable. How centrifugal buoyancy affects the turbulent flow, including the heat transport, is still largely unknown, in particular, when it can be considered negligible. We study this problem by means of direct numerical simulations. Unlike in experiments, we are able to systematically vary the Froude number Fr (ratio of centrifugal to gravitational acceleration) and the Rossby number Ro (dimensionless rotation rate) independently, and even set each to zero exactly. We show that the centrifugal acceleration simultaneously leads to contending phenomena, e.g. reflected by an increase and a decrease of the center temperature, or a suppression and an enhancement of the heat transfer efficiency. Which one prevails as net effect strongly depends on the combination of Fr and Ro. Furthermore, we discuss implications for experiments of rapidly rotating convection. SH acknowledges funding by the Deutsche Forschungsgemeinschaft (DFG) under Grant HO 5890/1-1, JA by the NSF Geophysics Program.

Periodic Boundary Motion in Thermal Turbulence

International Nuclear Information System (INIS)

Zhang, Jun; Libchaber, Albert

2000-01-01

A free-floating plate is introduced in a Benard convection cell with an open surface. It partially covers the cell and distorts the local heat flux, inducing a coherent flow that in turn moves the plate. Remarkably, the plate can be driven to a periodic motion even under the action of a turbulent fluid. The period of the oscillation depends on the coverage ratio, and on the Rayleigh number of the convective system. The plate oscillatory behavior observed in this experiment may be related to a geological model, in which continents drift in a quasiperiodic fashion. (c) 2000 The American Physical Society

Rough horizontal plates: heat transfer and hysteresis

Energy Technology Data Exchange (ETDEWEB)

Tisserand, J-C; Gasteuil, Y; Pabiou, H; Castaing, B; Chilla, F [Universite de Lyon, ENS Lyon, CNRS, 46 Allee d' ltalie, 69364 Lyon Cedex 7 (France); Creyssels, M [LMFA, CNRS, Ecole Centrale Lyon, 69134 Ecully Cedex (France); Gibert, M, E-mail: mathieu.creyssels@ec-lyon.fr [Also at MPI-DS (LFPN) Gottingen (Germany)

2011-12-22

To investigate the influence of a rough-wall boundary layer on turbulent heat transport, an experiment of high-Rayleigh convection in water is carried out in a Rayleigh-Benard cell with a rough lower plate and a smooth upper plate. A transition in the heat transport is observed when the thermal boundary layer thickness becomes comparable to or smaller than the roughness height. Besides, at larger Rayleigh numbers than the threshold value, heat transport is found to be increased up to 60%. This enhancement cannot be explained simply by an increase in the contact area of the rough surface since the contact area is increased only by a factor of 40%. Finally, a simple model is proposed to explain the enhanced heat transport.

A priori study of subgrid-scale features in turbulent Rayleigh-Bénard convection

Science.gov (United States)

Dabbagh, F.; Trias, F. X.; Gorobets, A.; Oliva, A.

2017-10-01

At the crossroad between flow topology analysis and turbulence modeling, a priori studies are a reliable tool to understand the underlying physics of the subgrid-scale (SGS) motions in turbulent flows. In this paper, properties of the SGS features in the framework of a large-eddy simulation are studied for a turbulent Rayleigh-Bénard convection (RBC). To do so, data from direct numerical simulation (DNS) of a turbulent air-filled RBC in a rectangular cavity of aspect ratio unity and π spanwise open-ended distance are used at two Rayleigh numbers R a ∈{1 08,1 010 } [Dabbagh et al., "On the evolution of flow topology in turbulent Rayleigh-Bénard convection," Phys. Fluids 28, 115105 (2016)]. First, DNS at Ra = 108 is used to assess the performance of eddy-viscosity models such as QR, Wall-Adapting Local Eddy-viscosity (WALE), and the recent S3PQR-models proposed by Trias et al. ["Building proper invariants for eddy-viscosity subgrid-scale models," Phys. Fluids 27, 065103 (2015)]. The outcomes imply that the eddy-viscosity modeling smoothes the coarse-grained viscous straining and retrieves fairly well the effect of the kinetic unfiltered scales in order to reproduce the coherent large scales. However, these models fail to approach the exact evolution of the SGS heat flux and are incapable to reproduce well the further dominant rotational enstrophy pertaining to the buoyant production. Afterwards, the key ingredients of eddy-viscosity, νt, and eddy-diffusivity, κt, are calculated a priori and revealed positive prevalent values to maintain a turbulent wind essentially driven by the mean buoyant force at the sidewalls. The topological analysis suggests that the effective turbulent diffusion paradigm and the hypothesis of a constant turbulent Prandtl number are only applicable in the large-scale strain-dominated areas in the bulk. It is shown that the bulk-dominated rotational structures of vortex-stretching (and its synchronous viscous dissipative structures) hold

Extend of magnetic field interference in the natural convection of diamagnetic nanofluid

Science.gov (United States)

Roszko, Aleksandra; Fornalik-Wajs, Elzbieta

2017-10-01

Main objective of the paper was to experimentally investigate the thermo-magnetic convection of diamagnetic fluids in the Rayleigh-Benard configuration. For better understanding of the magnetic field influence on the phenomena occurring in cubical enclosure the following parameters were studied: absence or presence of nanoparticles (single and two-phase fluids), thermal conditions (temperature difference range of 5-25 K) and magnetic field strength (magnetic induction range of 0-10 T). A multi-stage approach was undertaken to achieve the aim. The multi-stage approach means that the forces system, flow structure and heat transfer were considered. Without understanding the reasons (forces) and the fluid behaviour it would be impossible to analyse the exchanged heat rates through the Nusselt number distribution. The forces were determined at the starting moment, so the inertia force was not considered. The flow structure was identified due to the FFT analysis and it proved that magnetic field application changed the diamagnetic fluid behaviour, either single or two-phase. Going further, the heat transfer analysis revealed dependence of the Nusselt number on the flow structure and at the same time on the magnetic field. It can be said that imposed magnetic field changed the energy transfer within the system. In the paper, it was shown that each of presented steps were linked together and that only a comprehensive approach could lead to better understanding of magnetic field interference in the convection phenomenon.

Effect of Darcy, fluid Rayleigh and heat generation parameters on natural convection in a porous square enclosure: A Brinkman-extended Darcy model

International Nuclear Information System (INIS)

Das, S.; Sahoo, R.K.

1999-01-01

Analysis of flow and convective heat transfer in volumetrically heated porous layer has become a separate topic for research in the last twenty five years in view of its importance in various engineering applications, such as heat removal from nuclear fuel debris, heat transfer associated with storage of nuclear waste, exothermic reaction in packed-bed reactors, heat recovery from geothermal systems and particularly in the field of large storage systems of agricultural products. Here, a pressure-velocity solution for natural convection for fluid saturated heat generating porous medium in a square enclosure is analyzed by finite element method. The numerical solutions obtained for wide range of fluid Rayleigh number, Ra f , Darcy number, Da, and heat generating number, Q d . The justification for taking these non-dimensional parameters independently is to establish the effect of individual parameters on flow patterns. It has been observed that peak temperature occurs at the top central part and weaker velocity prevails near the vertical walls of the enclosure due to the heat generation parameter alone. On comparison, the modified Rayleigh number used by the earlier investigators, can not explain explicitly the effect of heat generation parameter on natural convection within an enclosure having differentially heated vertical walls. At higher Darcy number, the peak temperature and peak velocity are comparatively more, resulting in better enhancement of heat transfer rate

Experimental determination of heat transfer in a Poiseuille-Rayleigh-Bénard flow

Science.gov (United States)

Taher, R.; Abid, C.

2018-05-01

This paper deals with an experimental study of heat transfer in a Poiseuille-Rayleigh-Bénard flow. This situation corresponds to a mixed convection phenomenon in a horizontal rectangular channel uniformly heated from below. Flow visualisation and temperature measurements were achieved in order to describe the flow regimes and heat transfer behaviour. The classical measurement techniques such employing thermocouples give local measurement on one hand and on other hand they often disturb the flow. As the flow is three-dimensional, these techniques are not efficient. In order to not disturb the flow, a non-intrusive method is used for thermal measurement. The Planar laser Induced Fluorescence (PLIF) was implemented to determine thermal fields in the fluid. Experiments conducted for various Reynolds and Rayleigh numbers allow to determine the heat transfer and thus to propose correlation for Nusselt number for a mixed convection flow in Poiseuille-Rayleigh-Bénard configuration. First a description of the use of this technique in water flow is presented and then the obtained results for various Reynolds and Rayleigh numbers allow to propose a correlation for the Nusselt number for such configuration of mixed convection. The comparison between the obtained heat transfer and the pure forced convection one confirms the well-known result that the convective heat transfer is greatly enhanced in mixed convection. Indeed, secondary flow induced by buoyant forces contributes to the refreshment of thermal boundary layers and so acts like mixers, which significantly enhances heat transfer.

Effect of Rayleigh accelerations applied to an initially moving fluid. [in circular cylinders under low gravity associated with space flight

Science.gov (United States)

Dressler, R. F.; Robertson, S. J.; Spradley, L. W.

1982-01-01

The General Interpolant Method computer code was used to analyze two-dimensional unsteady thermal convection in circular cylinders under variable low-g conditions associated with space flight. When an acceleration vector was applied parallel to the thermal gradient, in the case of a fluid at rest, no convection resulted for the stable direction, and an instability led to Rayleigh convection for the opposite direction. However, when the acceleration had a component orthogonal to the gradient, convection resulted at any Rayleigh number. The effect on convection of both types of acceleration, applied concurrently or sequentially, was investigated, including the case when the resultant vector varied in direction with time. An analysis of experimental results shows that for space flight conditions, the Rayleigh accelerations induce significant, but not dominating, changes in the established convection even when the Rayleigh number is less than critical.

Instabilities in fluid layers and in reaction-diffusion systems: Steady states, time-periodic solutions, non-periodic attractors, and related convective and otherwise non-linear phenomena

International Nuclear Information System (INIS)

Garcia Velarde, M.

1977-01-01

Thermoconvective instabilities in horizontal fluid layers are discussed with emphasis on the Rayleigh-Benard model problem. Steady solutions and time-dependent phenomena (relaxation oscillations and transition to turbulence) are studied within the nonlinear Boussinesq-Oberbeck approximation. Homogeneous steady solutions, limit cycles, and inhomogeneous (ordered) spatial structures are also studied in simple reaction-diffusion systems. Lastly, the non-periodic attractor that appears at large Rayleigh numbers in the truncated Boussinesq-Oberbeck model of Lorenz, is constructed, and a discussion of turbulent behavior is given. (author) [es

Kinetic thermal structure in turbulent Rayleigh-Bénard convection

Science.gov (United States)

Chen, Jun; Yin, Ze-Xia; She, Zhen-Su; Bao, Yun

2017-11-01

Plumes are believed to be the most important heat carrier in turbulent Rayleigh-Bénard convection (RBC). However, a physically sound and clear definition of plume is still absent. We report here the investigation of a definition of plume called kinetic thermal structure (KTS), based on the analysis of vertical velocity gradient (Λ = ∂w / ∂z), using direct numerical simulation (DNS) data of the three-dimensional RBC in a rectangular cell for Pr = 0.7 and Ra = 1 ×108 5 ×109 . It is shown that the conditional average of temperature on Λ exhibits such a behavior that when Λ is larger than a threshold, the volume carries a constant temperature of fluid, hence defines an unambiguous thermal structure, KTS. The DNS show that the KTS behaves in a sheet-like shape near the conducting plate, and becomes slender and smaller with increasing Ra . The heat flux carried by KTS displays a scaling law, with an exponent larger than the global- Nu - Ra scaling, indicating stronger heat transport than the turbulent background. An advantage of the KTS is its connection to the balance equation allowing, for the first time, a prediction of the Ra -dependence of its vertical velocity and the characteristic Λ threshold, validated by DNS. Supported by NSFC (11172006, 11221062, 11452002), and by MOST (China) 973 project (2009CB724100).

Vertical natural convection: application of the unifying theory of thermal convection

NARCIS (Netherlands)

Ng, C.S.; Ooi, A.; Lohse, Detlef; Chung, D.

2015-01-01

Results from direct numerical simulations of vertical natural convection at Rayleigh numbers 1.0×10 5 –1.0×10 9 and Prandtl number 0.709 support a generalised applicability of the Grossmann–Lohse (GL) theory, which was originally developed for horizontal natural (Rayleigh–Bénard) convection. In

Nonlinear traveling waves in rotating Rayleigh-Bacute enard convection: Stability boundaries and phase diffusion

International Nuclear Information System (INIS)

Liu, Y.; Ecke, R.E.

1999-01-01

We present experimental measurements of a sidewall traveling wave in rotating Rayleigh-Bacute enard convection. The fluid, water with Prandtl number about 6.3, was confined in a 1-cm-high cylindrical cell with radius-to-height ratio Γ=5. We used simultaneous optical-shadowgraph, heat-transport, and local temperature measurements to determine the stability and characteristics of the traveling-wave state for dimensionless rotation rates 60<Ω<420. The state is well described by the one-dimensional complex Ginzburg-Landau (CGL) equation for which the linear and nonlinear coefficients were determined for Ω=274. The Eckhaus-Benjamin-Feir-stability boundary was established and the phase-diffusion coefficient and nonlinear group velocity were determined in the stable regime. Higher-order corrections to the CGL equation were also investigated. copyright 1999 The American Physical Society

Nonlinear hydrodynamic stability and transition; Proceedings of the IUTAM Symposium, Nice, France, Sept. 3-7, 1990

Science.gov (United States)

Theoretical and experimental research on nonlinear hydrodynamic stability and transition is presented. Bifurcations, amplitude equations, pattern in experiments, and shear flows are considered. Particular attention is given to bifurcations of plane viscous fluid flow and transition to turbulence, chaotic traveling wave covection, chaotic behavior of parametrically excited surface waves in square geometry, amplitude analysis of the Swift-Hohenberg equation, traveling wave convection in finite containers, focus instability in axisymmetric Rayleigh-Benard convection, scaling and pattern formation in flowing sand, dynamical behavior of instabilities in spherical gap flows, and nonlinear short-wavelength Taylor vortices. Also discussed are stability of a flow past a two-dimensional grid, inertia wave breakdown in a precessing fluid, flow-induced instabilities in directional solidification, structure and dynamical properties of convection in binary fluid mixtures, and instability competition for convecting superfluid mixtures.

Nonlinear interaction of Rayleigh--Taylor and shear instabilities

International Nuclear Information System (INIS)

Finn, J.M.

1993-01-01

Results on the nonlinear behavior of the Rayleigh--Taylor instability and consequent development of shear flow by the shear instability [Phys. Fluids B 4, 488 (1992)] are presented. It is found that the shear flow is generated at sufficient amplitude to reduce greatly the convective transport. For high viscosity, the time-asymptotic state consists of an equilibrium with shear flow and vortex flow (with islands, or ''cat's eyes''), or a relaxation oscillation involving an interplay between the shear instability and the Rayleigh--Taylor instability in the presence of shear. For low viscosity, the dominant feature is a high-frequency nonlinear standing wave consisting of convective vortices localized near the top and bottom boundaries. The localization of these vortices is due to the smaller shear near the boundary regions. The convective transport is largest around these convective vortices near the boundary and there is a region of good confinement near the center. The possible relevance of this behavior to the H mode and edge-localized modes (ELM's) in the tokamak edge region is discussed

Predicting chaotic time series

International Nuclear Information System (INIS)

Farmer, J.D.; Sidorowich, J.J.

1987-01-01

We present a forecasting technique for chaotic data. After embedding a time series in a state space using delay coordinates, we ''learn'' the induced nonlinear mapping using local approximation. This allows us to make short-term predictions of the future behavior of a time series, using information based only on past values. We present an error estimate for this technique, and demonstrate its effectiveness by applying it to several examples, including data from the Mackey-Glass delay differential equation, Rayleigh-Benard convection, and Taylor-Couette flow

Vortex statistics in turbulent rotating convection

NARCIS (Netherlands)

Kunnen, R.P.J.; Clercx, H.J.H.; Geurts, B.J.

2010-01-01

The vortices emerging in rotating turbulent Rayleigh-Bénard convection in water at Rayleigh number Ra=6.0×108 are investigated using stereoscopic particle image velocimetry and by direct numerical simulation. The so-called Q criterion is used to detect the vortices from velocity fields. This

Stabilization of the Rayleigh - Taylor instability with convection in an ablatively accelerated laser plasma

International Nuclear Information System (INIS)

Bud'ko, A.B.; Liberman, M.A.

1992-01-01

In the framework of WKB approximation the problem is studied of stabilizing the Rayleigh - Taylor instability with unhomogeneous convective flow, developing in the ablation zone during the ablative acceleration of the laser target plasma. The eigenvalue (instability growth rates) problem is reduced to solving an algebraic equation with the coefficients depending on the unperturbed profile structure of hydrodynamic variables. For the important case of the incompressible plasma subsonic flow, the instability growth rates is shown to vanish at k=k 0 =max(2(g|∇ ln p|) 1/2 /ν). The consistency condition of the model consists in the smallness of the local Froude number in the region of instability development. However, as seen from the comparison with the numerical calculations, the model is well appicable also for the case of the sufficiently abrupt density gradient provided the Froude number is of order of unity

The Role of Viscosity Contrast on the Plume Structure and Dynamics in High Rayleigh Number Convection

Science.gov (United States)

Kr, Sreenivas; Prakash, Vivek N.; Arakeri, Jaywant H.

2010-11-01

We study the plume structure in high Rayleigh number convection in the limit of large Prandtl numbers. This regime is relevant in Mantle convection, where the plume dynamics is not well understood due to complex rheology and chemical composition. We use analogue laboratory experiments to mimic mantle convection. Our focus in this paper is to understand the role of viscosity ratio, U, between the plume fluid and the ambient fluid on the structure and dynamics of the plumes. The PLIF technique has been used to visualize the structures of plumes rising from a planar source of compositional buoyancy at different regimes of U (1/300 to 2500). In the near-wall planform when U is one, a well-known dendritic line plume structure is observed. As U increases (U > 1; mantle hot spots), there is a morphological transition from line plumes to discrete spherical blobs, accompanied by an increase in the plume spacing and thickness. In vertical sections, as U increases (U > 1), the plume head shape changes from a mushroom-like structure to a "spherical-blob." When the U is decreased below one, (U<1; subduction regime), the formation of cellular patterns is favoured with sheet plumes. Both velocity and mixing efficiency are maximum when U is one, and decreases for extreme values of U. We quantify the morphological changes, dynamics and mixing variations of the plumes from experiments at different regimes.

Turbulent convection experiment at high Rayleigh number to support CAP1400 IVR strategy

Energy Technology Data Exchange (ETDEWEB)

Ma, Li, E-mail: mali@snptrd.com [State Nuclear Hua Qing(Beijing) Nuclear Power Technology R& D Centre Co., Ltd, Building A, State Nuclear Power Research Institute, Future Science & Technology Park, Changping Dist., Beijing 102209 (China); Li, Jing, E-mail: lijing@snptrd.com [State Nuclear Hua Qing(Beijing) Nuclear Power Technology R& D Centre Co., Ltd, Building A, State Nuclear Power Research Institute, Future Science & Technology Park, Changping Dist., Beijing 102209 (China); Ji, Shui, E-mail: jishui@snptrd.com [State Nuclear Hua Qing(Beijing) Nuclear Power Technology R& D Centre Co., Ltd, Building A, State Nuclear Power Research Institute, Future Science & Technology Park, Changping Dist., Beijing 102209 (China); Chang, Huajian, E-mail: changhuajian@snptrd.com [State Nuclear Hua Qing(Beijing) Nuclear Power Technology R& D Centre Co., Ltd, Building A, State Nuclear Power Research Institute, Future Science & Technology Park, Changping Dist., Beijing 102209 (China); Institute of Nuclear and New Energy Technology, Tsinghua University, Beijing 100084 (China)

2015-10-15

Highlights: • The facility reached high Ra number at 10{sup 12} of CAP1400 working condition. • The fitting formula Nu = 0.085 × Ra{sup 0.315} was established to calculate the heat flux in the metal layer at high Ra for the CAP1400. • The coupling method can accurately and safely predict the heat flow distribution of metal layer in high Ra number conditions. • The experiment results will predict the relationship between axial and radial heat transfer well. - Abstract: The characteristics of the heat transfer and the calculation of heat flux in metal layer are both the critical problems for in-vessel retention (IVR) strategy. Turbulent convection occurs in the metal layer when the Rayleigh number (Ra) becomes sufficient high. The Globe–Dropkin (G–D) correlation (Globe and Dropkin, 1959) and Chu–Churchill (C–C) correlation (Churchill and Chu, 1975) have been widely used to calculate the heat flux in the metal layer, where the valid range of the Ra is from 1.5 × 10{sup 5} to 6.8 × 10{sup 8} in G–D correlation and less than 10{sup 12} in C–C correlation. However, with the increase of reactor power, both the Rayleigh number and the rate of heat transfer below the bottom of metal layer of the molten pool will increase, and in this case the Rayleigh number even can reach 10{sup 11} for the China Advanced Passive Plant CAP1400. Accordingly, the G–D correlation is not suitable for the CAP1400. Therefore, our experiment purposes are to establish the appropriate correlation at high Ra for the CAP1400 and predict the axial and radial distribution of the heat transfer in the metal layer with the heat transfer behavior of metal layer experiment (HELM) facility. The experiments are divided into two parts. Each part concerns 39 runs and 47 experimental conditions. Its corresponding results are obtained at middle Prandtl number (Pr = 7 for water) and the Nusselt number is found to be proportional to Ra{sup 0.315} in the range 3.93 × 10{sup 8} < Ra < 3.57 �

Turbulent convection experiment at high Rayleigh number to support CAP1400 IVR strategy

International Nuclear Information System (INIS)

Ma, Li; Li, Jing; Ji, Shui; Chang, Huajian

2015-01-01

Highlights: • The facility reached high Ra number at 10 12 of CAP1400 working condition. • The fitting formula Nu = 0.085 × Ra 0.315 was established to calculate the heat flux in the metal layer at high Ra for the CAP1400. • The coupling method can accurately and safely predict the heat flow distribution of metal layer in high Ra number conditions. • The experiment results will predict the relationship between axial and radial heat transfer well. - Abstract: The characteristics of the heat transfer and the calculation of heat flux in metal layer are both the critical problems for in-vessel retention (IVR) strategy. Turbulent convection occurs in the metal layer when the Rayleigh number (Ra) becomes sufficient high. The Globe–Dropkin (G–D) correlation (Globe and Dropkin, 1959) and Chu–Churchill (C–C) correlation (Churchill and Chu, 1975) have been widely used to calculate the heat flux in the metal layer, where the valid range of the Ra is from 1.5 × 10 5 to 6.8 × 10 8 in G–D correlation and less than 10 12 in C–C correlation. However, with the increase of reactor power, both the Rayleigh number and the rate of heat transfer below the bottom of metal layer of the molten pool will increase, and in this case the Rayleigh number even can reach 10 11 for the China Advanced Passive Plant CAP1400. Accordingly, the G–D correlation is not suitable for the CAP1400. Therefore, our experiment purposes are to establish the appropriate correlation at high Ra for the CAP1400 and predict the axial and radial distribution of the heat transfer in the metal layer with the heat transfer behavior of metal layer experiment (HELM) facility. The experiments are divided into two parts. Each part concerns 39 runs and 47 experimental conditions. Its corresponding results are obtained at middle Prandtl number (Pr = 7 for water) and the Nusselt number is found to be proportional to Ra 0.315 in the range 3.93 × 10 8 < Ra < 3.57 × 10 12 . Furthermore, the experiment

Solutal convection induced by dissolution. Influence on erosion dynamics and interface shaping.

Science.gov (United States)

Berhanu, Michael; Philippi, Julien; Cohen, Caroline; Derr, Julien; Courrech du Pont, Sylvain

2017-04-01

Rock fractures invaded by a water flow, are often subjected to dissolution, which let grow and evolve the initial fracture network, by evacuating the eroded minerals under a solute form. In the case of fast kinetic of dissolution, local erosion rate is set by the advection of the solute. The erosion velocity decreases indeed with the solute concentration at the interface and vanishes when this concentration reaches the saturation value. Even in absence of an imposed or external flow, advection can drive the dissolution, when buoyancy effects due to gravity induce a solutal convection flow, which controls the erosive dynamics and modifies the shape of the dissolving interface. Here, we investigate using model experiments with fast dissolving materials and numerical simulations in simplified situations, solutal convection induced by dissolution. Results are interpreted regarding a linear stability analysis of the corresponding solutal Rayleigh-Benard instability. A dissolving surface is suspended above a water height, initially at rest. In a first step, solute flux is transported through a growing diffusion layer. Then after an onset time, once the layer exceeds critical width, convection flow starts under the form of falling plumes. A dynamic equilibrium results in average from births and deaths of intermittent plumes, setting the size of the solute concentration boundary layer at the interface and thus the erosion velocity. Solutal convection can also induce a pattern on the dissolving interface. We show experimentally with suspended and inclined blocks of salt and sugar, that in a linear stage, the first wavelength of the dissolution pattern corresponds to the wavelength of the convection instability. Then pattern evolves to more complex shapes due to non-linear interactions between the flow and the eroded interface. More generally, we inquire what are the conditions to observe a such solutal convection instability in geological situations and if the properties of

State and parameter estimation of spatiotemporally chaotic systems illustrated by an application to Rayleigh-Bénard convection.

Science.gov (United States)

Cornick, Matthew; Hunt, Brian; Ott, Edward; Kurtuldu, Huseyin; Schatz, Michael F

2009-03-01

Data assimilation refers to the process of estimating a system's state from a time series of measurements (which may be noisy or incomplete) in conjunction with a model for the system's time evolution. Here we demonstrate the applicability of a recently developed data assimilation method, the local ensemble transform Kalman filter, to nonlinear, high-dimensional, spatiotemporally chaotic flows in Rayleigh-Bénard convection experiments. Using this technique we are able to extract the full temperature and velocity fields from a time series of shadowgraph measurements. In addition, we describe extensions of the algorithm for estimating model parameters. Our results suggest the potential usefulness of our data assimilation technique to a broad class of experimental situations exhibiting spatiotemporal chaos.

Comparison of scale analysis and numerical simulation for saturated zone convective mixing processes

International Nuclear Information System (INIS)

Oldenburg, C.M.

1998-01-01

Scale analysis can be used to predict a variety of quantities arising from natural systems where processes are described by partial differential equations. For example, scale analysis can be applied to estimate the effectiveness of convective missing on the dilution of contaminants in groundwater. Scale analysis involves substituting simple quotients for partial derivatives and identifying and equating the dominant terms in an order-of-magnitude sense. For free convection due to sidewall heating of saturated porous media, scale analysis shows that vertical convective velocity in the thermal boundary layer region is proportional to the Rayleigh number, horizontal convective velocity is proportional to the square root of the Rayleigh number, and thermal boundary layer thickness is proportional to the inverse square root of the Rayleigh number. These scale analysis estimates are corroborated by numerical simulations of an idealized system. A scale analysis estimate of mixing time for a tracer mixing by hydrodynamic dispersion in a convection cell also agrees well with numerical simulation for two different Rayleigh numbers. Scale analysis for the heating-from-below scenario produces estimates of maximum velocity one-half as large as the sidewall case. At small values of the Rayleigh number, this estimate is confirmed by numerical simulation. For larger Rayleigh numbers, simulation results suggest maximum velocities are similar to the sidewall heating scenario. In general, agreement between scale analysis estimates and numerical simulation results serves to validate the method of scale analysis. Application is to radioactive repositories

Stabilization of the Rayleigh-Taylor instability by convection in an ablatively accelerated laser plasma

International Nuclear Information System (INIS)

Bul'ko, A.B.; Liberman, M.A.

1992-01-01

The authors use the WKB-approximation to treat the problem of the stabilization by an inhomogeneous convective current of the Rayleigh-Taylor instability developing in the ablation zone when the plasma of laser targets is accelerated by ablation. The problem of the eigenvalues - the instability growth rates - is reduced to the solution of an algebraic equation with coefficients which depend on the structure of the unperturbed profiles of the hydrodynamic variables. They show for the practically important case of subsonic flow of an incompressible plasma that the instability growth rate vanishes for k = k o = max[2(g|∇lnρ|) 1/2 /v]. The condition for the self-consistency of the model is that the local Froude number be small in the region where the instability develops; however, comparison with numerical calculations shows that the model is also applicable in the case of rather steep density gradients when the Froude number is of order unity. 32 refs., 2 figs

Double-diffusive convection in a Darcy porous medium saturated with a couple-stress fluid

International Nuclear Information System (INIS)

Malashetty, M S; Kollur, Premila; Pal, Dulal

2010-01-01

The onset of double-diffusive convection in a couple-stress fluid-saturated horizontal porous layer is studied using linear and weak nonlinear stability analyses. The modified Darcy equation that includes the time derivative term and the inertia term is used to model the momentum equation. The expressions for stationary, oscillatory and finite-amplitude Rayleigh number are obtained as a function of the governing parameters. The effect of couple-stress parameter, solute Rayleigh number, Vadasz number and diffusivity ratio on stationary, oscillatory and finite-amplitude convection is shown graphically. It is found that the couple-stress parameter and the solute Rayleigh number have a stabilizing effect on stationary, oscillatory and finite-amplitude convection. The diffusivity ratio has a destabilizing effect in the case of stationary and finite-amplitude modes, with a dual effect in the case of oscillatory convection. The Vadasz number advances the onset of oscillatory convection. The heat and mass transfer decreases with an increase in the values of couple-stress parameter and diffusivity ratio, while both increase with an increase in the value of the solute Rayleigh number.

Influence of the Ringwoodite-Perovskite transition on mantle convection in spherical geometry as a function of Clapeyron slope and Rayleigh number

Directory of Open Access Journals (Sweden)

M. Wolstencroft

2011-12-01

Full Text Available We investigate the influence on mantle convection of the negative Clapeyron slope ringwoodite to perovskite and ferro-periclase mantle phase transition, which is correlated with the seismic discontinuity at 660 km depth. In particular, we focus on understanding the influence of the magnitude of the Clapeyron slope (as measured by the Phase Buoyancy parameter, P and the vigour of convection (as measured by the Rayleigh number, Ra on mantle convection. We have undertaken 76 simulations of isoviscous mantle convection in spherical geometry, varying Ra and P. Three domains of behaviour were found: layered convection for high Ra and more negative P, whole mantle convection for low Ra and less negative P, and transitional behaviour in an intervening domain. The boundary between the layered and transitional domain was fit by a curve P = α Ra^β where α = −1.05, and β = −0.1, and the fit for the boundary between the transitional and whole mantle convection domain was α = −4.8, and β = −0.25. These two curves converge at Ra ≈ 2.5 × 10⁴ (well below Earth mantle vigour and P ≈ −0.38. Extrapolating to high Ra, which is likely earlier in Earth history, this work suggests a large transitional domain. It is therefore likely that convection in the Archean would have been influenced by this phase change, with Earth being at least in the transitional domain, if not the layered domain.

Heat transport in bubbling turbulent convection.

Science.gov (United States)

Lakkaraju, Rajaram; Stevens, Richard J A M; Oresta, Paolo; Verzicco, Roberto; Lohse, Detlef; Prosperetti, Andrea

2013-06-04

Boiling is an extremely effective way to promote heat transfer from a hot surface to a liquid due to numerous mechanisms, many of which are not understood in quantitative detail. An important component of the overall process is that the buoyancy of the bubble compounds with that of the liquid to give rise to a much-enhanced natural convection. In this article, we focus specifically on this enhancement and present a numerical study of the resulting two-phase Rayleigh-Bénard convection process in a cylindrical cell with a diameter equal to its height. We make no attempt to model other aspects of the boiling process such as bubble nucleation and detachment. The cell base and top are held at temperatures above and below the boiling point of the liquid, respectively. By keeping this difference constant, we study the effect of the liquid superheat in a Rayleigh number range that, in the absence of boiling, would be between 2 × 10(6) and 5 × 10(9). We find a considerable enhancement of the heat transfer and study its dependence on the number of bubbles, the degree of superheat of the hot cell bottom, and the Rayleigh number. The increased buoyancy provided by the bubbles leads to more energetic hot plumes detaching from the cell bottom, and the strength of the circulation in the cell is significantly increased. Our results are in general agreement with recent experiments on boiling Rayleigh-Bénard convection.

Plume dynamics in quasi-2D turbulent convection

International Nuclear Information System (INIS)

Bizon, C.; Werne, J.; Predtechensky, A.A.; Julien, K.; McCormick, W.D.; Swift, J.B.; Swinney, H.L.

1997-01-01

We have studied turbulent convection in a vertical thin (Hele-Shaw) cell at very high Rayleigh numbers (up to 7x10 4 times the value for convective onset) through experiment, simulation, and analysis. Experimentally, convection is driven by an imposed concentration gradient in an isothermal cell. Model equations treat the fields in two dimensions, with the reduced dimension exerting its influence through a linear wall friction. Linear stability analysis of these equations demonstrates that as the thickness of the cell tends to zero, the critical Rayleigh number and wave number for convective onset do not depend on the velocity conditions at the top and bottom boundaries (i.e., no-slip or stress-free). At finite cell thickness δ, however, solutions with different boundary conditions behave differently. We simulate the model equations numerically for both types of boundary conditions. Time sequences of the full concentration fields from experiment and simulation display a large number of solutal plumes that are born in thin concentration boundary layers, merge to form vertical channels, and sometimes split at their tips via a Rayleigh-Taylor instability. Power spectra of the concentration field reveal scaling regions with slopes that depend on the Rayleigh number. We examine the scaling of nondimensional heat flux (the Nusselt number, Nu) and rms vertical velocity (the Pacute eclet number, Pe) with the Rayleigh number (Ra * ) for the simulations. Both no-slip and stress-free solutions exhibit the scaling NuRa * ∼Pe 2 that we develop from simple arguments involving dynamics in the interior, away from cell boundaries. In addition, for stress-free solutions a second relation, Nu∼√(nPe), is dictated by stagnation-point flows occurring at the horizontal boundaries; n is the number of plumes per unit length. (Abstract Truncated)

Direct numerical simulation of turbulent Rayleigh-Bénard convection in a vertical thin disk

Science.gov (United States)

Xu, Wei; Wang, Yin; He, Xiao-Zhou; Yik, Hiu-Fai; Wang, Xiao-Ping; Schumacher, Jorg; Tong, Penger

2017-11-01

We report a direct numerical simulation (DNS) of turbulent Rayleigh-Bénard convection in a thin vertical disk with a high-order spectral element method code NEK5000. An unstructured mesh is used to adapt the turbulent flow in the thin disk and to ensure that the mesh sizes satisfy the refined Groetzbach criterion and a new criterion for thin boundary layers proposed by Shishkina et al. The DNS results for the mean and variance temperature profiles in the thermal boundary layer region are found to be in good agreement with the predictions of the new boundary layer models proposed by Shishkina et al. and Wang et al.. Furthermore, we numerically calculate the five budget terms in the boundary layer equation, which are difficult to measure in experiment. The DNS results agree well with the theoretical predictions by Wang et al. Our numerical work thus provides a strong support for the development of a common framework for understanding the effect of boundary layer fluctuations. This work was supported in part by Hong Kong Research Grants Council.

An infinite-dimensional model of free convection

Energy Technology Data Exchange (ETDEWEB)

Iudovich, V.I. (Rostovskii Gosudarstvennyi Universitet, Rostov-on-Don (USSR))

1990-12-01

An infinite-dimensional model is derived from the equations of free convection in the Boussinesq-Oberbeck approximation. The velocity field is approximated by a single mode, while the heat-conduction equation is conserved fully. It is shown that, for all supercritical Rayleigh numbers, there exist exactly two secondary convective regimes. The case of ideal convection with zero viscosity and thermal conductivity is examined. The averaging method is used to study convection regimes at high Reynolds numbers. 10 refs.

Temperature oscillation and the sloshing motion of the large-scale circulation in turbulent Rayleigh-Bénard convection

Science.gov (United States)

Xi, Heng-Dong; Chen, Xin; Xia, Ke-Qing

2017-11-01

We report an experimental study of the temperature oscillation and the sloshing motion of the large-scale circulation (LSC) in turbulent Rayleigh-Bénard convection in water. Temperature measurements were made in aspect ratio one cylindrical cell by probes put in fluid and embedded in the sidewall simultaneously, and located at the 1/4, 1/2 and 3/4 heights of the convection cell. The results show that the temperature measured in fluid contains information of both the LSC and the signature of the hot and cold plumes, while the temperature measured in sidewall only contains information of the LSC. It is found that the sloshing motion of the LSC can be measured by both the temperatures in fluid and in sidewall. We also studies the effect of cell tilting on the temperature oscillation and sloshing motion of the LSC. It is found that both the amplitude and the frequency of the temperature oscillation (and the sloshing motion) increase when the tilt angle increases, while the off-center distance of the sloshing motion of the LSC remains unchanged. This work is supported by the NSFC of China (Grant Nos. 11472094 and U1613227), the RGC of Hong Kong SAR (Grant No. 403712) and the 111 project of China (Grant No. B17037).

Natural convection in nano-fluids: Are the thermophoresis and Brownian motion effects significant in nano-fluid heat transfer enhancement?

International Nuclear Information System (INIS)

Haddad, Zoubida; Abu-Nada, Eiyad; Oztop, Hakan F.; Mataoui, Amina

2012-01-01

Natural convection heat transfer and fluid flow of CuO-Water nano-fluids is studied using the Rayleigh-Benard problem. A two component non-homogenous equilibrium model is used for the nano-fluid that incorporates the effects of Brownian motion and thermophoresis. Variable thermal conductivity and variable viscosity are taken into account in this work. Finite volume method is used to solve governing equations. Results are presented by streamlines, isotherms, nano-particle distribution, local and mean Nusselt numbers and nano-particle profiles at top and bottom side. Comparison of two cases as absence of Brownian and thermophoresis effects and presence of Brownian and thermophoresis effects showed that higher heat transfer is formed with the presence of Brownian and thermophoresis effect. In general, by considering the role of thermophoresis and Brownian motion, an enhancement in heat transfer is observed at any volume fraction of nano-particles. However, the enhancement is more pronounced at low volume fraction of nano-particles and the heat transfer decreases by increasing nano-particle volume fraction. On the other hand, by neglecting the role of thermophoresis and Brownian motion, deterioration in heat transfer is observed and this deterioration elevates by increasing the volume fraction of nano-particles. (authors)

Transitional boundary layer in low-Prandtl-number convection at high Rayleigh number

Science.gov (United States)

Schumacher, Joerg; Bandaru, Vinodh; Pandey, Ambrish; Scheel, Janet

2016-11-01

The boundary layer structure of the velocity and temperature fields in turbulent Rayleigh-Bénard flows in closed cylindrical cells of unit aspect ratio is revisited from a transitional and turbulent viscous boundary layer perspective. When the Rayleigh number is large enough the boundary layer dynamics at the bottom and top plates can be separated into an impact region of downwelling plumes, an ejection region of upwelling plumes and an interior region (away from side walls) that is dominated by a shear flow of varying orientation. This interior plate region is compared here to classical wall-bounded shear flows. The working fluid is liquid mercury or liquid gallium at a Prandtl number of Pr = 0 . 021 for a range of Rayleigh numbers of 3 ×105 Deutsche Forschungsgemeinschaft.

Natural convection inside an irregular porous cavity

International Nuclear Information System (INIS)

Beltran, Jorge I. LLagostera; Trevisan, Osvair Vidal

1990-01-01

Natural convection flow induced by heating from below in a irregular porous cavity is investigated numerically. The influence of the modified Rayleigh number and geometric ratios on heat transfer and fluid flow is studied. Global and local Nusselt for Rayleigh numbers covering the range 0 - 1600 and for several geometric ratios. The fluid flow and the temperature field are illustrated by contour maps. (author)

Convective flows of colloidal suspension in an inclined closed cell

Energy Technology Data Exchange (ETDEWEB)

Smorodin, Boris; Ishutov, Sergey [Department of Physics of Phase Transitions, Perm State University, Perm (Russian Federation); Cherepanov, Ivan, E-mail: bsmorodin@yandex.ru [Department of Radio Electronics and Information Security, Perm State University, Perm (Russian Federation)

2016-12-15

The nonlinear spatiotemporal evolution of convective flows is numerically investigated in the case of colloidal suspension filling an inclined closed cell heated from below. The bifurcation diagram (the dependency of the Nusselt number on the Rayleigh number) is obtained. The characteristics of the wave and steady patterns are investigated depending on heat intensity. The travelling wave changing travel direction and the non-regular oscillatory flow are found to be stable solutions within a certain interval of the Rayleigh number. Temporal Fourier decomposition is used together with other diagnostic tools to analyse the complex bifurcation and spatiotemporal properties caused by the interplay of the gravity-induced gradient of concentration and convective mixing of the fluid. It is shown that a more complex flow structure exists at a lower heating intensity (Rayleigh number). (paper)

Vertical Slot Convection: A linear study

International Nuclear Information System (INIS)

McAllister, A.; Steinolfson, R.; Tajima, T.

1992-11-01

The linear stability properties of fluid convection in a vertical slot were studied. We use a Fourier-Chebychev decomposition was used to set up the linear eigenvalue problems for the Vertical Slot Convection and Benard problems. The eigenvalues, neutral stability curves, and critical point values of the Grashof number, G, and the wavenumber were determined. Plots of the real and imaginary parts of the eigenvalues as functions of G and α are given for a wide range of the Prandtl number, Pr, and special note is made of the complex mode that becomes linearly unstable above Pr ∼ 12.5. A discussion comparing different special cases facilitates the physical understanding of the VSC equations, especially the interaction of the shear-flow and buoyancy induced physics. Making use of the real and imaginary eigenvalues and the phase properties of the eigenmodes, the eigenmodes were characterized. One finds that the mode structure becomes progressively simpler with increasing Pr, with the greatest complexity in the mid ranges where the terms in the heat equation are of roughly the same size

Logarithmic spatial variations and universal f-1 power spectra of temperature fluctuations in turbulent Rayleigh-Bénard convection.

Science.gov (United States)

He, Xiaozhou; van Gils, Dennis P M; Bodenschatz, Eberhard; Ahlers, Guenter

2014-05-02

We report measurements of the temperature variance σ(2)(z,r) and frequency power spectrum P(f,z,r) (z is the distance from the sample bottom and r the radial coordinate) in turbulent Rayleigh-Bénard convection (RBC) for Rayleigh numbers Ra = 1.6 × 10(13) and 1.1 × 10(15) and for a Prandtl number Pr ≃ 0.8 for a sample with a height L = 224 cm and aspect ratio D/L=0.50 (D is the diameter). For z/L ≲ 0.1 σ(2)(z,r) was consistent with a logarithmic dependence on z, and there was a universal (independent of Ra, r, and z) normalized spectrum which, for 0.02 ≲ fτ(0) ≲ 0.2, had the form P(fτ(0)) = P(0)(fτ(0))(-1) with P(0) = 0.208 ± 0.008 a universal constant. Here τ(0) = sqrt[2R] where R is the radius of curvature of the temperature autocorrelation function C(τ) at τ = 0. For z/L ≃ 0.5 the measurements yielded P(fτ(0))∼(fτ(0))(-α) with α in the range from 3/2 to 5/3. All the results are similar to those for velocity fluctuations in shear flows at sufficiently large Reynolds numbers, suggesting the possibility of an analogy between the flows that is yet to be determined in detail.

Basal melting driven by turbulent thermal convection

Science.gov (United States)

Rabbanipour Esfahani, Babak; Hirata, Silvia C.; Berti, Stefano; Calzavarini, Enrico

2018-05-01

Melting and, conversely, solidification processes in the presence of convection are key to many geophysical problems. An essential question related to these phenomena concerns the estimation of the (time-evolving) melting rate, which is tightly connected to the turbulent convective dynamics in the bulk of the melt fluid and the heat transfer at the liquid-solid interface. In this work, we consider a convective-melting model, constructed as a generalization of the Rayleigh-Bénard system, accounting for the basal melting of a solid. As the change of phase proceeds, a fluid layer grows at the heated bottom of the system and eventually reaches a turbulent convection state. By means of extensive lattice-Boltzmann numerical simulations employing an enthalpy formulation of the governing equations, we explore the model dynamics in two- and three-dimensional configurations. The focus of the analysis is on the scaling of global quantities like the heat flux and the kinetic energy with the Rayleigh number, as well as on the interface morphology and the effects of space dimensionality. Independently of dimensionality, we find that the convective-melting system behavior shares strong resemblances with that of the Rayleigh-Bénard one, and that the heat flux is only weakly enhanced with respect to that case. Such similarities are understood, at least to some extent, considering the resulting slow motion of the melting front (with respect to the turbulent fluid velocity fluctuations) and its generally little roughness (compared to the height of the fluid layer). Varying the Stefan number, accounting for the thermodynamical properties of the material, also seems to have only a mild effect, which implies the possibility of extrapolating results in numerically delicate low-Stefan setups from more convenient high-Stefan ones. Finally, we discuss the implications of our findings for the geophysically relevant problem of modeling Arctic ice melt ponds.

Convective heat transfer around vertical jet fires: An experimental study

Energy Technology Data Exchange (ETDEWEB)

Kozanoglu, Bulent, E-mail: bulentu.kozanoglu@udlap.mx [Universidad de las Americas, Puebla (Mexico); Zarate, Luis [Universidad Popular Autonoma del Estado de Puebla (Mexico); Gomez-Mares, Mercedes [Universita di Bologna (Italy); Casal, Joaquim [Universitat Politecnica de Catalunya (Spain)

2011-12-15

Highlights: Black-Right-Pointing-Pointer Experiments were carried out to analyze convection around a vertical jet fire. Black-Right-Pointing-Pointer Convection heat transfer is enhanced increasing the flame length. Black-Right-Pointing-Pointer Nusselt number grows with higher values of Rayleigh and Reynolds numbers. Black-Right-Pointing-Pointer In subsonic flames, Nusselt number increases with Froude number. Black-Right-Pointing-Pointer Convection and radiation are equally important in causing a domino effect. - Abstract: The convection heat transfer phenomenon in vertical jet fires was experimentally analyzed. In these experiments, turbulent propane flames were generated in subsonic as well as sonic regimes. The experimental data demonstrated that the rate of convection heat transfer increases by increasing the length of the flame. Assuming the solid flame model, the convection heat transfer coefficient was calculated. Two equations in terms of adimensional numbers were developed. It was found out that the Nusselt number attains greater values for higher values of the Rayleigh and Reynolds numbers. On the other hand, the Froude number was analyzed only for the subsonic flames where the Nusselt number grows by this number and the diameter of the orifice.

Natural convection heat transfer of water in a horizontal circular gap

Institute of Scientific and Technical Information of China (English)

SU Guanghui; Kenichiro Sugiyama; WU Yingwei

2007-01-01

An experimental study on the natural convection heat transfer on a horizontal downward facing heated surface in a water gap was carried out under atmospheric pressure conditions. A total of 700 experimental data points were correlated using Rayleigh versus Nusselt number in various forms, based on different independent variables. The effects of different characteristic lengths and film temperatures were discussed. The results show that the buoyancy force acts as a resistance force for natural convecti on beat transfer ona downward facing horizontal heated surface in a confined space. For the estimation of the natural convection heat transfer under the present conditions, empirical correlations in which Nusselt number is expressed as a function of the Rayleigh number, or both Rayleigh and Prandtl numbers, may be used. When it is accurately predicted, the Nusselt number is expressed as a function of the Rayleigh and Prandtl numbers, as well as the gap width-to-heated surface diameter ratio; and uses the temperature difference between the heated surface and the ambient fluid in the definition of Rayleigh number. The characteristic length is the gap size and the film temperature is the average fluid temperature.

Natural convection between two concentric spheres

International Nuclear Information System (INIS)

Blondel-Roux, Marie

1983-01-01

After an overview of researches on natural convection in a confined or semi-confined environment, this research thesis reports the use of the Caltagirone and Mojtabi numerical model and the study of its validity for different values of the Rayleigh and Prandtl numbers. Results obtained with this model are compared with experimental ones. Thermal transfer curves are presented and discussed, as well as the different temperature fields numerically obtained, flow function fields, velocities in the fluid layer, and temperature profiles with respect to the Rayleigh number [fr

Natural convection heat transfer from a horizontal cylinder in liquid sodium. Pt. 2. Generalized correlation for laminar natural convection heat transfer

International Nuclear Information System (INIS)

Hata, K.; Takeuchi, Y.

1999-01-01

For pt.I see ibid., vol.193, p.105-18, 1999. Rigorous numerical solution of natural convection heat transfer, from a horizontal cylinder with uniform surface heat flux or with uniform surface temperature, to liquid sodium was derived by solving the fundamental equations for laminar natural convection heat transfer without the boundary layer approximation. It was made clear that the local and average Nusselt numbers experimentally obtained and reported in part 1 of this paper were described well by the numerical solutions for uniform surface heat fluxes, but that those for uniform surface temperatures could not describe the angular distribution of the local Nusselt numbers and about 10% underpredicted the average Nusselt numbers. Generalized correlation for natural convection heat transfer from a horizontal cylinder with a uniform surface heat flux in liquid metals was presented based on the rigorous theoretical values for a wide range of Rayleigh numbers. It was confirmed that the correlation can describe the authors' and other workers' experimental data on horizontal cylinders in various kinds of liquid metals for a wide range of Rayleigh numbers. Another correlation for a horizontal cylinder with a uniform surface temperature in liquid metals, which may be applicable for special cases such as natural convection heat transfer in a sodium-to-sodium heat exchanger etc. was also presented based on the rigorous theoretical values for a wide range of Rayleigh numbers. These correlations can also describe the rigorous numerical solutions for non-metallic liquids and gases for the Prandtl numbers up to 10. (orig.)

Concentration field in traveling-wave and stationary convection in fluid mixtures

International Nuclear Information System (INIS)

Eaton, K.D.; Ohlsen, D.R.; Yamamoto, S.Y.; Surko, C.M.; Barten, W.; Luecke, M.; Kamps, M.; Kolodner, P.

1991-01-01

By comparison of measurements of shadowgraph images of convection in ethanol-water mixtures with the results of recent numerical calculations, we study the role of the concentration field in traveling-wave and stationary convection. The results confirm the existence of a large concentration contrast between adjacent traveling-wave convection rolls. This concentration modulation, which decreases as the Rayleigh number is increased and the transition to stationary convection is approached, is fundamental to the translation of the pattern

Natural convection heat transfer within horizontal spent nuclear fuel assemblies

International Nuclear Information System (INIS)

Canaan, R.E.

1995-12-01

Natural convection heat transfer is experimentally investigated in an enclosed horizontal rod bundle, which characterizes a spent nuclear fuel assembly during dry storage and/or transport conditions. The basic test section consists of a square array of sixty-four stainless steel tubular heaters enclosed within a water-cooled rectangular copper heat exchanger. The heaters are supplied with a uniform power generation per unit length while the surrounding enclosure is maintained at a uniform temperature. The test section resides within a vacuum/pressure chamber in order to subject the assembly to a range of pressure statepoints and various backfill gases. The objective of this experimental study is to obtain convection correlations which can be used in order to easily incorporate convective effects into analytical models of horizontal spent fuel systems, and also to investigate the physical nature of natural convection in enclosed horizontal rod bundles in general. The resulting data consist of: (1) measured temperatures within the assembly as a function of power, pressure, and backfill gas; (2) the relative radiative contribution for the range of observed temperatures; (3) correlations of convective Nusselt number and Rayleigh number for the rod bundle as a whole; and (4) correlations of convective Nusselt number as a function of Rayleigh number for individual rods within the array

Heat Transfer and Flows of Thermal Convection in a Fluid-Saturated Rotating Porous Medium

Directory of Open Access Journals (Sweden)

Jianhong Kang

2015-01-01

Full Text Available Thermal convection at the steady state for high Rayleigh number in a rotating porous half space is investigated. Taking into account the effect of rotation, Darcy equation is extended to incorporate the Coriolis force term in a rotating reference frame. The velocity and temperature fields of thermal convection are obtained by using the homotopy analysis method. The influences of Taylor number and Rayleigh number on the Nusselt number, velocity profile, and temperature distribution are discussed in detail. It is found that the Nusselt number decreases rapidly with the increase of Taylor number but tends to have an asymptotic value. Besides, the rotation can give rise to downward flow in contrast with the upward thermal convection.

Experimental investigation of natural convection induced by internal heat generation

International Nuclear Information System (INIS)

Tasaka, Y; Kudoh, Y; Takeda, Y; Yanagisawa, T

2005-01-01

Dilatation of a convection cell with respect to its Rayleigh number, one of the problems in internally heated convection, was quantitatively investigated by analyzing temperature field in a cell. The temperature field visualized by a thermo-chromic liquid crystal (TLC) expresses the cell dilatation. A calibration system was developed to convert the visualized photographs of the temperature field to the temperature field. A calibration curve correlating color information extracted from the photograph and temperature was determined from the approximately linear temperature distribution in the horizontal fluid layer using the hue method. Photos taken at various internal Rayleigh numbers were converted to the temperature field by the obtained curve. Extracting individual cells from a temperature field achieves a quantitative expression of the cell dilatation as the variation of the wavenumber of the cell with Rayleigh number increases. The temperature profile in a cell shows that high temperature areas appear at the apexes of the cell, largely different from the profile obtained by linear theory

Application of fast Fourier transform in thermo-magnetic convection analysis

International Nuclear Information System (INIS)

Pyrda, L

2014-01-01

Application of Fast Fourier Transform in thermo-magnetic convection is reported. Cubical enclosure filled with paramagnetic fluid heated from below and placed in the strong magnetic field gradients was investigated. The main aim of study was connected with identification of flow types, especially transition to turbulence. For this purpose the Fast Fourier Transform (FFT) analysis was applied. It was followed by the heat transfer characteristic for various values of magnetic induction gradient. The analysis was done at two Rayleigh numbers 7.89·10 5 and 1.86·10 6 with thermo-magnetic Rayleigh numbers up to 1.8·10 8 and 4.5·10 8 respectively. The presented results clearly indicate flow types and also demonstrate augmented heat transfer in dependence on magnetic induction gradient. Detailed analysis of flow transition to turbulent state was compared with transition line for natural convection reported in literature. The transition to turbulence in the case of thermo-magnetic convection of paramagnetic fluid was in very good agreement with transition in the case of natural convection.

Finite bandwidth, nonlinear convective flow in a mushy layer

Energy Technology Data Exchange (ETDEWEB)

Riahi, D N, E-mail: daniel.riahi@utrgv.edu [School of Mathematical and Statistical Sciences, University of Texas Rio Grande Valley, One West University Boulevard, Brownsville, TX 78520 (United States)

2017-04-15

Finite amplitude convection with a continuous finite bandwidth of modes in a horizontal mushy layer during the solidification of binary alloys is investigated. We analyze the nonlinear convection for values of the Rayleigh number close to its critical value by using multiple scales and perturbation techniques. Applying a combined temporal and spatial evolution approach, we determine a set of three coupled differential equations for the amplitude functions of the convective modes. A large number of new subcritical or supercritical stable solutions to these equations in the form of steady rolls and hexagons with different horizontal length scales are detected. We find, in particular, that depending on the parameter values and on the magnitude and direction of the wave number vectors for the amplitude functions, hexagons with down-flow or up-flow at the cells’ centers or rolls can be stable. Rolls or hexagons with longer horizontal wave length can be stable at higher amplitudes, and there are cases where hexagons are unstable for any value of the Rayleigh number, while rolls are stable only for the values of the Rayleigh number beyond some value. We also detected new stable and irregular flow patterns with two different horizontal scales in the form of superposition of either two sets of hexagons or two sets of inclined rolls. (paper)

Simulation of regimes of convection and plume dynamics by the thermal Lattice Boltzmann Method

Science.gov (United States)

Mora, Peter; Yuen, David A.

2018-02-01

We present 2D simulations using the Lattice Boltzmann Method (LBM) of a fluid in a rectangular box being heated from below, and cooled from above. We observe plumes, hot narrow upwellings from the base, and down-going cold chutes from the top. We have varied both the Rayleigh numbers and the Prandtl numbers respectively from Ra = 1000 to Ra =1010 , and Pr = 1 through Pr = 5 ×104 , leading to Rayleigh-Bénard convection cells at low Rayleigh numbers through to vigorous convection and unstable plumes with pronounced vortices and eddies at high Rayleigh numbers. We conduct simulations with high Prandtl numbers up to Pr = 50, 000 to simulate in the inertial regime. We find for cases when Pr ⩾ 100 that we obtain a series of narrow plumes of upwelling fluid with mushroom heads and chutes of downwelling fluid. We also present simulations at a Prandtl number of 0.7 for Rayleigh numbers varying from Ra =104 through Ra =107.5 . We demonstrate that the Nusselt number follows power law scaling of form Nu ∼Raγ where γ = 0.279 ± 0.002 , which is consistent with published results of γ = 0.281 in the literature. These results show that the LBM is capable of reproducing results obtained with classical macroscopic methods such as spectral methods, and demonstrate the great potential of the LBM for studying thermal convection and plume dynamics relevant to geodynamics.

Planform structure and heat transfer in turbulent free convection over horizontal surfaces

Science.gov (United States)

Theerthan, S. Ananda; Arakeri, Jaywant H.

2000-04-01

This paper deals with turbulent free convection in a horizontal fluid layer above a heated surface. Experiments have been carried out on a heated surface to obtain and analyze the planform structure and the heat transfer under different conditions. Water is the working fluid and the range of flux Rayleigh numbers (Ra) covered is 3×107-2×1010. The different conditions correspond to Rayleigh-Bénard convection, convection with either the top water surface open to atmosphere or covered with an insulating plate, and with an imposed external flow on the heated boundary. Without the external flow the planform is one of randomly oriented line plumes. At large Rayleigh number Ra and small aspect ratio (AR), these line plumes seem to align along the diagonal, presumably due to a large scale flow. The side views show inclined dyelines, again indicating a large scale flow. When the external flow is imposed, the line plumes clearly align in the direction of external flow. The nondimensional average plume spacing, Raλ1/3, varies between 40 and 90. The heat transfer rate, for all the experiments conducted, represented as RaδT-1/3, where δT is the conduction layer thickness, varies only between 0.1-0.2, showing that in turbulent convection the heat transfer rates are similar under the different conditions.

Two-dimensional turbulent convection

Science.gov (United States)

Mazzino, Andrea

2017-11-01

We present an overview of the most relevant, and sometimes contrasting, theoretical approaches to Rayleigh-Taylor and mean-gradient-forced Rayleigh-Bénard two-dimensional turbulence together with numerical and experimental evidences for their support. The main aim of this overview is to emphasize that, despite the different character of these two systems, especially in relation to their steadiness/unsteadiness, turbulent fluctuations are well described by the same scaling relationships originated from the Bolgiano balance. The latter states that inertial terms and buoyancy terms balance at small scales giving rise to an inverse kinetic energy cascade. The main difference with respect to the inverse energy cascade in hydrodynamic turbulence [R. H. Kraichnan, "Inertial ranges in two-dimensional turbulence," Phys. Fluids 10, 1417 (1967)] is that the rate of cascade of kinetic energy here is not constant along the inertial range of scales. Thanks to the absence of physical boundaries, the two systems here investigated turned out to be a natural physical realization of the Kraichnan scaling regime hitherto associated with the elusive "ultimate state of thermal convection" [R. H. Kraichnan, "Turbulent thermal convection at arbitrary Prandtl number," Phys. Fluids 5, 1374-1389 (1962)].

Control strategy on the double-diffusive convection in a nanofluid layer with internal heat generation

Science.gov (United States)

Mokhtar, N. F. M.; Khalid, I. K.; Siri, Z.; Ibrahim, Z. B.; Gani, S. S. A.

2017-10-01

The influences of feedback control and internal heat source on the onset of Rayleigh-Bénard convection in a horizontal nanofluid layer is studied analytically due to Soret and Dufour parameters. The confining boundaries of the nanofluid layer (bottom boundary-top boundary) are assumed to be free-free, rigid-free, and rigid-rigid, with a source of heat from below. Linear stability theory is applied, and the eigenvalue solution is obtained numerically using the Galerkin technique. Focusing on the stationary convection, it is shown that there is a positive thermal resistance in the presence of feedback control on the onset of double-diffusive convection, while there is a positive thermal efficiency in the existence of internal heat generation. The possibilities of suppress or augment of the Rayleigh-Bénard convection in a nanofluid layer are also discussed in detail.

Ice-water convection in an inclined rectangular cavity filled with a porous medium

Energy Technology Data Exchange (ETDEWEB)

Zhang, X. (Dept. of Mechanical Engineering, Ecole Polytechnique de Montreal (Canada)); Kahawita, R. (Dept. of Civil Engineering, Ecole Polytechnique de Montreal (Canada))

1994-10-01

This paper reports on the results of a numerical study on the equilibrium state of the convection of water in the presence of ice in an inclined rectangular cavity filled with a porous medium. One side of the cavity is maintained at a temperature higher than the fusion temperature while the opposite side is cooled to a temperature lower than the fusion temperature. The two remaining sides are insulated. Results are analysed in terms of the density inversion parameter, the tilt angle, and the cooling temperature. It appears that the phenomenon of density inversion plays an important role in the equilibrium of an ice-water system when the heating temperature is below 20 . In a vertical cavity, the density inversion causes the formation of two counter-rotating vortices leading to a water volume which is wider at the bottom than at the top. When the cavity is inclined, there exist two branches of solutions which exhibit the bottom heating and the side heating characteristics, respectively (the Benard and side heating branches). Due to the inversion of density, the solution on the Benard branch may fail to converge to a steady state at small tilt angles and exhibits an oscillating behavior. On the side heating branch, a maximum heat transfer rate is obtained at a tilt angle of about 70 but the water volume was found to depend very weakly on the inclination of the cavity. Under the effect of subcooling, the interplay between conduction in the solid phase and convection in the liquid leads to an equilibrium ice-water interface which is most distorted at some intermediate cooling temperature. (orig.)

Vigorous convection as the explanation for Pluto's polygonal terrain.

Science.gov (United States)

Trowbridge, A J; Melosh, H J; Steckloff, J K; Freed, A M

2016-06-02

Pluto's surface is surprisingly young and geologically active. One of its youngest terrains is the near-equatorial region informally named Sputnik Planum, which is a topographic basin filled by nitrogen (N2) ice mixed with minor amounts of CH4 and CO ices. Nearly the entire surface of the region is divided into irregular polygons about 20-30 kilometres in diameter, whose centres rise tens of metres above their sides. The edges of this region exhibit bulk flow features without polygons. Both thermal contraction and convection have been proposed to explain this terrain, but polygons formed from thermal contraction (analogous to ice-wedges or mud-crack networks) of N2 are inconsistent with the observations on Pluto of non-brittle deformation within the N2-ice sheet. Here we report a parameterized convection model to compute the Rayleigh number of the N2 ice and show that it is vigorously convecting, making Rayleigh-Bénard convection the most likely explanation for these polygons. The diameter of Sputnik Planum's polygons and the dimensions of the 'floating mountains' (the hills of of water ice along the edges of the polygons) suggest that its N2 ice is about ten kilometres thick. The estimated convection velocity of 1.5 centimetres a year indicates a surface age of only around a million years.

Predictions of laminar natural convection in heated cavities

International Nuclear Information System (INIS)

Winters, K.H.

1982-06-01

Several examples of laminar, natural convection in heated cavities are discussed with illustrative calculations. These include convection in a square cavity at high Rayleigh number; in a narrow cavity at moderate aspect ratio; in a rectangular cavity heated from below; in a trapezoidal cavity, and in a rectangular cavity containing a conducting obstruction. The steady equations for the velocity, pressure and temperature are solved in the Boussinesq approximation, using a standard Galerkin formulation of the finite-element method. (author)

Oscillatory convection in low aspect ratio Czochralski melts

Science.gov (United States)

Anselmo, A.; Prasad, V.; Koziol, J.; Gupta, K. P.

1993-11-01

Modeling of the crucible in bulk crystal growth simulations as a right circular cylinder may be adequate for high aspect ratio melts but this may be unrealistic when the melt height is low. Low melt height is a unique feature of a solid feed continuous Czochralski growth process for silicon single crystals currently under investigation. At low melt heights, the crucible bottom curvature has a dampening effect on the buoyancy-induced oscillations, a source of inhomogeneities in the grown crystal. The numerical results demonstrate how the mode of convection changes from vertical wall-dominated recirculating flows to Benard convection as the aspect ratio is lowered. This phenomenon is strongly dependent on the boundary condition at the free surface of the melt, which has been generally considered to be either adiabatic or radiatively cooled. A comparison of the flow oscillations in crucibles with and without curved bottoms at aspect ratios in the range of 0.25 to 0.50, and at realistic Grashof numbers (10 7 < Gr < 10 8) illustrate that changing the shape of the crucible may be an effective means of suppressing oscillations and controlling the melt flow.

Natural convection in horizontal fluid layers

International Nuclear Information System (INIS)

Suo-Antilla, A.J.

1977-02-01

The experimental work includes developing and using a thermal convection cell to obtain measurements of the heat flux and turbulent core temperature of a horizontal layer of fluid heated internally and subject to both stabilizing and destabilizing temperature differences. The ranges of Rayleigh numbers tested were 10 7 equal to or less than R/sub I/ equal to or less than 10 13 and -10 10 equal to or less than R/sub E/ equal to or less than 10 10 . Power integral methods were found to be adequate for interpolating and extrapolating the data. The theoretical work consists of the derivation, solution and use of the mean field equations for study of thermally driven convection in horizontal layers of infinite extent. The equations were derived by a separation of variables technique where the horizontal directions were described by periodic structures and the vertical being some function of z. The derivation resulted in a coupled set of momentum and energy equations. The equations were simplified by using the infinite Prandtl number limit and neglecting direct intermodal interaction. Solutions to these equations are used to predict the existence of multi-wavenumber flows at all supercritical Rayleigh numbers. Subsequent inspection of existing experimental photographs of convecting fluids confirms their existence. The onset of time dependence is found to coincide with the onset of the second convective mode. Each mode is found to consist of two wavenumbers and typically the velocity and temperature fields of the right modal branch are found to be out of phase

Correlation development of natural convection heat transfer in consideration of aspect ratio change and coolant boiling

International Nuclear Information System (INIS)

Park, L. J.; Cho, Y. L.; Kang, K. H.; Kim, S. B.; Kim, H. D.; Cho, J. S.; Jung, C. H.

1999-01-01

A new correlation on natural convection heat transfer with crust formation in the molten metal pool has been developed in consideration of coolant boiling effect and of aspect ratio change by an increase in crust thickness. Two test results of the convection cooling case, natural and forced convection cooling cases, and of the boiling case were used in the present study. The experimental results have shown that the Nusselt number of the case with boiling condition in the molten metal pool is greater than that of the case with non-boiling condition at the same Rayleigh number. Even though the Rayleigh number rapidly decreases due to an increase of the crust thickness, the Nusselt number does not rapidly decrease because of the aspect ratio effect. From the experimental results, the new correlation between the Nusselt number and Rayleigh number in the molten metal pool with the crust formation has been developed as Nu 0.051(Ra) 1/3 (AR) . 0 .2441 (Φ) 0.025 using Globe and Dropkin correlation

Chaotic Darcy-Brinkman convection in a fluid saturated porous layer subjected to gravity modulation

Directory of Open Access Journals (Sweden)

Moli Zhao

2018-06-01

Full Text Available On the basis of Darcy-Brinkman model, the chaotic convection in a couple stress fluid saturated porous media under gravity modulation is investigated using the nonlinear stability analyses. The transition from steady convection to chaos is analysed with the effect of Darcy-Brinkman couple stress parameter and the gravity modulation. The results show that the chaotic behavior is connected with the critical value of Rayleigh number which is dependent upon the oscillation frequency and the Darcy-Brinkman couple stress parameter. If the oscillation frequency Ω is not zero, the Rayleigh number value R of the chaotic behavior increases with the increase of the Darcy-Brinkman couple stress parameter. The Darcy-Brinkman couple stress parameter and the gravity modulation decrease the rate of heat transfer. Keywords: Darcy-Brinkman model, Gravity modulation, Nonlinear stability, Chaotic convection

Evaporative and Convective Instabilities for the Evaporation of a Binary Mixture in a Bilayer System

Science.gov (United States)

Guo, Weidong; Narayanan, Ranga

2006-11-01

Evaporative convection in binary mixtures arises in a variety of industrial processes, such as drying of paint and coating technology. There have been theories devoted to this problem either by assuming a passive vapor layer or by isolating the vapor fluid dynamics. Previous work on evaporative and convective instabilities in a single component bilayer system suggests that active vapor layers play a major role in determining the instability of the interface. We have investigated the evaporation convection in binary mixtures taking into account the fluid dynamics of both phases. The liquid mixture and its vapor are assumed to be confined between two horizontal plates with a base state of zero evaporation but with linear vertical temperature profile. When the vertical temperature gradient reaches a critical value, the evaporative instability, Rayleigh and Marangoni convection set in. The effects of vapor and liquid depth, various wave numbers and initial composition of the mixture on the evaporative and convective instability are determined. The physics of the instability are explained and detailed comparison is made between the Rayleigh, Marangoni and evaporative convection in pure component and those in binary mixtures.

Breakdown of the large-scale circulation in $\\Gamma = 1/2$ rotating Rayleigh-Bénard flow

NARCIS (Netherlands)

Stevens, Richard Johannes Antonius Maria; Clercx, H.J.H.; Lohse, Detlef

2012-01-01

Experiments and simulations of rotating Rayleigh-Bénard convection in cylindrical samples have revealed an increase in heat transport with increasing rotation rate. This heat transport enhancement is intimately related to a transition in the turbulent flow structure from a regime dominated by a

Breakdown of large-scale circulation in turbulent rotating convection

NARCIS (Netherlands)

Kunnen, R.P.J.; Clercx, H.J.H.; Geurts, Bernardus J.

2008-01-01

Turbulent rotating convection in a cylinder is investigated both numerically and experimentally at Rayleigh number Ra = $10^9$ and Prandtl number $\\sigma$ = 6.4. In this Letter we discuss two topics: the breakdown under rotation of the domain-filling large-scale circulation (LSC) typical for

Behaviors and transitions along the path to magnetostrophic convection

Science.gov (United States)

Grannan, A. M.; Vogt, T.; Horn, S.; Hawkins, E. K.; Aggarwal, A.; Aurnou, J. M.

2017-12-01

The generation of magnetic fields in planetary and stellar interiors are believed to be controlled primarily by turbulent convection constrained by Coriolis and Lorentz forces in their electrically conducting fluid layers. Yet relatively few laboratory experiments are capable of investigating the different regimes of turbulent magnetohydrodynamic convection. In this work, we perform one laboratory experiment in a cylinder at a fixed heat flux using the liquid metal gallium in order to investigate, sequentially: Rayleigh-Bènard convection without any imposed constraints, magnetoconvection with a Lorentz constraint imposed by vertical magnetic field, rotating convection with a Coriolis constraint imposed by rotation, and finally the magnetostrophic convective regime where both Coriolis and Lorentz are imposed and equal. Using an array of internal and external temperature probes, we show that each regime along the path to magnetostrophic convection is unique. The behaviors and transitions in the dominant modes of convection as well as their fundamental frequencies and wavenumbers are investigated.

Scaling of Convection and Plate Tectonics in Super-Earths

Science.gov (United States)

Valencia, D. C.; O'Connell, R. J.; Sasselov, D. D.

2006-12-01

The discovery of three Super-Earths around different stars, possible only in the last year, prompts us to study the characteristics of our planet within a general context. The Earth, being the most massive terrestrial object in the solar system is the only planet that exhibits plate tectonics. We think this might not be a coincidence and explore the role that mass plays in determining the mode of convection. We use the scaling of convective vigor with Rayleigh number commonly used in parameterized convection. We study how the parameters controlling convection: Rayleigh number (Ra), boundary layer thickness (δ), internal temperature (T_i) and convective velocities (u) scale with mass. This is possible from the scaling of heat flux, mantle density, size and gravity with mass which we reported in Valencia, et. al 2006. The extrapolation to massive rocky planets is done from our knowledge of the Earth. Even though uncertainties arise from extrapolation and assumptions are needed we consider this simple scaling to be a first adequate step. As the mass of a planet increases, Ra increases, yielding a decrease in δ and an increase in u, while T_i increases very slightly. This is true for an isoviscous case and is more accentuated in a temperature dependent viscosity scenario. In a planet with vigorous convection (high u), a thin lithosphere (low δ) is easier to subduct and hence, initiate plate tectonics. The lithosphere also has to be dense enough (cold and thick) to have the bouyancy necessary for subduction. We calculate that a convective cycle for an isoviscous planet is τ ~ M^{-0.3} considering whole mantle convection. Meaning that if these planets have continents, the timescale for continental rearrangement is shorter (about half the Earth's for a 5 earth-mass planet). Additionally, we explore the negative feedback cycle between convection and temperature dependent viscosity and estimate a timescale for this effect.

Steady, three-dimensional, internally heated convection

International Nuclear Information System (INIS)

Schubert, G.; Glatzmaier, G.A.; Travis, B.

1993-01-01

Numerical calculations have been carried out of steady, symmetric, three-dimensional modes of convection in internally heated, infinite Prandtl number, Boussinesq fluids at a Rayleigh number of 1.4x10 4 in a spherical shell with inner/outer radius of 0.55 and in a 3x3x1 rectangular box. Multiple patterns of convection occur in both geometries. In the Cartesian geometry the patterns are dominated by cylindrical cold downflows and a broad hot upwelling. In the spherical geometry the patterns consist of cylindrical cold downwellings centered either at the vertices of a tetrahedron or the centers of the faces of a cube. The cold downflow cylinders are immersed in a background of upwelling within which there are cylindrical hot concentrations (plumes) and hot halos around the downflows. The forced hot upflow return plumes of internally heated spherical convection are fundamentally different from the buoyancy-driven plumes of heated from below convection

Cryogenic helium gas convection research

International Nuclear Information System (INIS)

Donnelly, R.J.

1994-10-01

This is a report prepared by a group interested in doing research in thermal convection using the large scale refrigeration facilities available at the SSC Laboratories (SSCL). The group preparing this report consists of Michael McAshan at SSCL, Robert Behringer at Duke University, Katepalli Sreenivasan at Yale University, Xiao-Zhong Wu at Northern Illinois University and Russell Donnelly at the University of Oregon, who served as Editor for this report. This study reports the research and development opportunities in such a project, the technical requirements and feasibility of its construction and operation, and the costs associated with the needed facilities and support activities. The facility will be a unique national resource for studies of high-Reynolds-number and high-Rayleigh-number and high Rayleigh number turbulence phenomena, and is one of the six items determined as suitable for potential funding through a screening of Expressions of Interest. The proposed facility is possible only because of the advanced cryogenic technology available at the SSCL. Typical scientific issues to be addressed in the facility will be discussed. It devolved during our study, that while the main experiment is still considered to be the thermal convection experiment discussed in our original Expression of Interest, there are now a very substantial set of other, important and fundamental experiments which can be done with the large cryostat proposed for the convection experiment. We believe the facility could provide several decades of front-line research in turbulence, and shall describe why this is so

Convective mass transfer around a dissolving bubble

Science.gov (United States)

Duplat, Jerome; Grandemange, Mathieu; Poulain, Cedric

2017-11-01

Heat or mass transfer around an evaporating drop or condensing vapor bubble is a complex issue due to the interplay between the substrate properties, diffusion- and convection-driven mass transfer, and Marangoni effects, to mention but a few. In order to disentangle these mechanisms, we focus here mainly on the convective mass transfer contribution in an isothermal mass transfer problem. For this, we study the case of a millimetric carbon dioxide bubble which is suspended under a substrate and dissolved into pure liquid water. The high solubility of CO2 in water makes the liquid denser and promotes a buoyant-driven flow at a high (solutal) Rayleigh number (Ra˜104 ). The alteration of p H allows the concentration field in the liquid to be imaged by laser fluorescence enabling us to measure both the global mass flux (bubble volume, contact angle) and local mass flux around the bubble along time. After a short period of mass diffusion, where the boundary layer thickens like the square root of time, convection starts and the CO2 is carried by a plume falling at constant velocity. The boundary layer thickness then reaches a plateau which depends on the bubble cross section. Meanwhile the plume velocity scales like (dV /d t )1 /2 with V being the volume of the bubble. As for the rate of volume loss, we recover a constant mass flux in the diffusion-driven regime followed by a decrease in the volume V like V2 /3 after convection has started. We present a model which agrees well with the bubble dynamics and discuss our results in the context of droplet evaporation, as well as high Rayleigh convection.

Onset of Vibrational Convection in a Binary Fluid Saturated Non-Darcy Porous Layer Heated from Above

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Saravanan S.

2012-07-01

Full Text Available A linear stability analysis is used to investigate the influence of mechanical vibration on the onset of thermosolutal convection in a horizontal porous layer heated and salted from above. Vibrations are considered with arbitrary amplitude and frequency. The Brinkman extended Darcy model is used to describe the flow and the Oberbeck-Boussinesq approximation is employed. Continued fraction method and Floquet theory are used to determine the convective instability threshold. It is found that the solutal Rayleigh number has the stabilizing effect. The existence of a closed disconnected loop of synchronous mode is predicted in the marginal curve for moderate values of solutal Rayleigh number and vibration amplitude.

Convection Cells in the Atmospheric Boundary Layer

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Fodor, Katherine; Mellado, Juan-Pedro

2017-04-01

In dry, shear-free convective boundary layers (CBLs), the turbulent flow of air is known to organise itself on large scales into coherent, cellular patterns, or superstructures, consisting of fast, narrow updraughts and slow, wide downdraughts which together form circulations. Superstructures act as transport mechanisms from the surface to the top of the boundary layer and vice-versa, as opposed to small-scale turbulence, which only modifies conditions locally. This suggests that a thorough investigation into superstructure properties may help us better understand transport across the atmospheric boundary layer as a whole. Whilst their existence has been noted, detailed studies into superstructures in the CBL have been scarce. By applying methods which are known to successfully isolate similar large-scale patterns in turbulent Rayleigh-Bénard convection, we can assess the efficacy of those detection techniques in the CBL. In addition, through non-dimensional analysis, we can systematically compare superstructures in various convective regimes. We use direct numerical simulation of four different cases for intercomparison: Rayleigh-Bénard convection (steady), Rayleigh-Bénard convection with an adiabatic top lid (quasi-steady), a stably-stratified CBL (quasi-steady) and a neutrally-stratified CBL (unsteady). The first two are non-penetrative and the latter two penetrative. We find that although superstructures clearly emerge from the time-mean flow in the non-penetrative cases, they become obscured by temporal averaging in the CBL. This is because a rigid lid acts to direct the flow into counter-rotating circulation cells whose axis of rotation remains stationary, whereas a boundary layer that grows in time and is able to entrain fluid from above causes the circulations to not only grow in vertical extent, but also to move horizontally and merge with neighbouring circulations. Spatial filtering is a useful comparative technique as it can be performed on boundary

Numerical Studies on Natural Convection Heat Losses from Open Cubical Cavities

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M. Prakash

2013-01-01

Full Text Available The natural convection heat losses occurring from cubical open cavities are analysed in this paper. Open cubical cavities of sides 0.1 m, 0.2 m, 0.25 m, 0.5 m, and 1 m with constant temperature back wall boundary conditions and opening ratio of 1 are studied. The Fluent CFD software is used to analyse the three-dimensional (3D cavity models. The studies are carried out for cavities with back wall temperatures between 35°C and 100°C. The effect of cavity inclination on the convective loss is analysed for angles of 0° (cavity facing sideways, 30°, 45°, 60°, and 90° (cavity facing vertically downwards. The Rayleigh numbers involved in this study range between 4.5 × 105 and 1.5 × 109. The natural convection loss is found to increase with an increase in back wall temperature. The natural convection loss is observed to decrease with an increase in cavity inclination; the highest convective loss being at 0° and the lowest at 90° inclination. This is observed for all cavities analysed here. Nusselt number correlations involving the effect of Rayleigh number and the cavity inclination angle have been developed from the current studies. These correlations can be used for engineering applications such as electronic cooling, low- and medium-temperature solar thermal systems, passive architecture, and also refrigeration systems.

EFFECTS OF STELLAR FLUX ON TIDALLY LOCKED TERRESTRIAL PLANETS: DEGREE-1 MANTLE CONVECTION AND LOCAL MAGMA PONDS

International Nuclear Information System (INIS)

Gelman, S. E.; Elkins-Tanton, L. T.; Seager, S.

2011-01-01

We model the geodynamical evolution of super-Earth exoplanets in synchronous rotation about their star. While neglecting the effects of a potential atmosphere, we explore the parameter spaces of both the Rayleigh number and intensity of incoming stellar flux, and identify two main stages of mantle convection evolution. The first is a transient stage in which a lithospheric temperature and thickness dichotomy emerges between the substellar and the antistellar hemispheres, while the style of mantle convection is dictated by the Rayleigh number. The second stage is the development of degree-1 mantle convection. Depending on mantle properties, the timescale of onset of this second stage of mantle evolution varies from order 1 to 100 billion years of simulated planetary evolution. Planets with higher Rayleigh numbers (due to, for instance, larger planetary radii than the Earth) and planets whose incoming stellar flux is high (likely for most detectable exoplanets) will develop degree-1 mantle convection most quickly, on the order of 1 billion years, which is within the age of many planetary systems. Surface temperatures range from 220 K to 830 K, implying the possibility of liquid water in some regions near the surface. These results are discussed in the context of stable molten magma ponds on hotter planets, and the habitability of super-Earths which may lie outside the Habitable Zone.

Transition to turbulence

International Nuclear Information System (INIS)

Pomeau, Y.

1981-07-01

In this work it is reviewed a few known types of transition to turbulence, as the cascade of period doubling and the intermittent transition. This happens in dynamical systems with a few degrees of freedom, as modelled by the iteration of non linear maps. Then it is presented specific transitions for systems with many degrees of freedom. It is condidered first the occurence of a low frequency broadband noise in large cells at the onset of Rayleigh-Benard convection; then the transition by intermittent bursts in parallel flows. In this last case, one is concerned with localized and finite amplitude perturbations. Simple geometric arguments show that these fluctuations, when they are isolated and with a well definite relative speed, exist for a single value of the Reynolds number only [fr

Delay in convection in nocturnal boundary layer due to aerosol-induced cooling

Science.gov (United States)

Singh, Dhiraj Kumar; Ponnulakshmi, V. K.; Subramanian, G.; Sreenivas, K. R.

2012-11-01

Heat transfer processes in the nocturnal boundary layer (NBL) influence the surface energy budget, and play an important role in many micro-meteorological processes including the formation of inversion layers, radiation fog, and in the control of air-quality near the ground. Under calm clear-sky conditions, radiation dominates over other transport processes, and as a result, the air layers just above ground cool the fastest after sunset. This leads to an anomalous post-sunset temperature profile characterized by a minimum a few decimeters above ground (Lifted temperature minimum). We have designed a laboratory experimental setup to simulate LTM, involving an enclosed layer of ambient air, and wherein the boundary condition for radiation is decoupled from those for conduction and convection. The results from experiments involving both ambient and filtered air indicate that the high cooling rates observed are due to the presence of aerosols. Calculated Rayleigh number of LTM-type profiles is of the order 105-107 in the field and of order 103-105 in the laboratory. In the LTM region, there is convective motion when the Rayleigh number is greater than 104 rather than the critical Rayleigh number (Rac = 1709). The diameter of convection rolls is a function of height of minimum of LTM-type profiles. The results obtained should help in the parameterization of transport process in the nocturnal boundary layer, and highlight the need to accounting the effects of aerosols and ground emissivity in climate models.

Study of heat transfer at the upper boundary of a fluid bath with voluminal power dissipation

International Nuclear Information System (INIS)

Bernaz, L.

1998-01-01

In order to examine the possibilities of external cooling of reactor vessels in the case of core meltdown accident in PWR reactors, it is necessary to determine the distribution of heat fluxes at the boundaries of the hemispherical bath. This distribution is controlled by the natural convection movements inside the bath. The first part of the document introduces the problem. The second part is a bibliographic analysis of previous works performed on natural convection inside a liquid bath with an internal heat source. The modeling of heat transfer at the upper boundary is assimilated to the Rayleigh-Benard turbulent convection. An analytical model of weak turbulence regime is developed in part 3. Different laws about the relationship between thermal plume characteristics and the parameters of the system are defined. Part 4 presents the experimental devices and scale models (MARABEC and BALI) used for the validation of the theoretical model and for the obtention of a database of reactor parameters. The laser induced fluorescence visualisation technique is used for the parametric study of between plumes spacing. The fifth part is devoted to the presentation and interpretation of results. (J.S.)

Natural convection of Al2O3-water nanofluid in a wavy enclosure

Science.gov (United States)

Leonard, Mitchell; Mozumder, Aloke K.; Mahmud, Shohel; Das, Prodip K.

2017-06-01

Natural convection heat transfer and fluid flow inside enclosures filled with fluids, such as air, water or oil, have been extensively analysed for thermal enhancement and optimisation due to their applications in many engineering problems, including solar collectors, electronic cooling, lubrication technologies, food processing and nuclear reactors. In comparison, little effort has been given to the problem of natural convection inside enclosures filled with nanofluids, while the addition of nanoparticles into a fluid base to alter thermal properties can be a feasible solution for many heat transfer problems. In this study, the problem of natural convection heat transfer and fluid flow inside a wavy enclosure filled with Al2O3-water nanofluid is investigated numerically using ANSYS-FLUENT. The effects of surface waviness and aspect ratio of the wavy enclosure on the heat transfer and fluid flow are analysed for various concentrations of Al2O3 nanoparticles in water. Flow fields and temperature fields are investigated and heat transfer rate is examined for different values of Rayleigh number. Results show that heat transfer within the enclosure can be enhanced by increasing surface waviness, aspect ratio or nanoparticles volume fraction. Changes in surface waviness have little effect on the heat transfer rate at low Rayleigh numbers, but when Ra ≥ 105 heat transfer increases with the increase of surface waviness from zero to higher values. Increasing the aspect ratio causes an increase in heat transfer rate, as the Rayleigh number increases the effect of changing aspect ratio is more apparent with the greatest heat transfer enhancement seen at higher Rayleigh numbers. Nanoparticles volume fraction has a little effect on the average Nusselt number at lower Rayleigh numbers when Ra ≥ 105 average Nusselt number increases with the increase of volume fraction. These findings provide insight into the heat transfer effects of using Al2O3-water nanofluid as a heat

Natural convection in wavy enclosures with volumetric heat sources

International Nuclear Information System (INIS)

Oztop, H.F.; Varol, Y.; Abu-Nada, E.; Chamkha, A.

2011-01-01

In this paper, the effects of volumetric heat sources on natural convection heat transfer and flow structures in a wavy-walled enclosure are studied numerically. The governing differential equations are solved by an accurate finite-volume method. The vertical walls of enclosure are assumed to be heated differentially whereas the two wavy walls (top and bottom) are kept adiabatic. The effective governing parameters for this problem are the internal and external Rayleigh numbers and the amplitude of wavy walls. It is found that both the function of wavy wall and the ratio of internal Rayleigh number (Ra I ) to external Rayleigh number (Ra E ) affect the heat transfer and fluid flow significantly. The heat transfer is predicted to be a decreasing function of waviness of the top and bottom walls in case of (IRa/ERa)>1 and (IRa/ERa)<1. (authors)

The structure of sidewall boundary layers in conned rotating Rayleigh-Bénard convection

NARCIS (Netherlands)

Kunnen, R.P.J.; Clercx, H.J.H.; van Heijst, G.J.F.

2013-01-01

Turbulent rotating convection is usually studied in a cylindrical geometry, as this is its most convenient experimental realization. In our previous work (Kunnen et al., J. Fluid Mech., vol. 688, 2011, pp. 422–442) we studied turbulent rotating convection in a cylinder with the emphasis on the

A numerical method for investigating crystal settling in convecting magma chambers

Science.gov (United States)

Verhoeven, J.; Schmalzl, J.

2009-12-01

Magma chambers can be considered as thermochemically driven convection systems. We present a new numerical method that describes the movement of crystallized minerals in terms of active spherical particles in a convecting magma that is represented by an infinite Prandtl number fluid. The main part focuses on the results we obtained. A finite volume thermochemical convection model for two and three dimensions and a discrete element method, which is used to model granular material, are combined. The new model is validated with floating experiments using particles of different densities and an investigation of single and multiparticle settling velocities. The resulting velocities are compared with theoretical predictions by Stokes's law and a hindered settling function for the multiparticle system. Two fundamental convection regimes are identified in the parameter space that is spanned by the Rayleigh number and the chemical Rayleigh number, which is a measure for the density of the particles. We define the T regime that is dominated by thermal convection. Here the thermal driving force is strong enough to keep all particles in suspension. As the particles get denser, they start settling to the ground, which results in a C regime. The C regime is characterized by the existence of a sediment layer with particle-rich material and a suspension layer with few particles. It is shown that the presence of particles can reduce the vigor of thermal convection. In the frame of a parameter study we discuss the change between the regimes that is systematically investigated. We show that the so-called TC transition fits a power law. Furthermore, we investigate the settling behavior of the particles in vigorous thermal convection, which can be linked to crystal settling in magma chambers. We develop an analytical settling law that describes the number of settled particles against time and show that the results fit the observations from numerical and laboratory experiments.

Constraints on the properties of Pluto's nitrogen-ice rich layer from convection simulations

Science.gov (United States)

Wong, T.; McKinnon, W. B.; Schenk, P.

2016-12-01

Pluto's Sputnik Planum basin (informally named) displays regular cellular patterns strongly suggesting that solid-state convection is occurring in a several-kilometers-deep nitrogen-ice rich layer (McKinnon et al., Convection in a volatile nitrogen-ice-rich layer drives Pluto's geological vigour, Nature 534, 82-85, 2016). We investigate the behavior of thermal convection in 2-D that covers a range of parameters applicable to the nitrogen ice layer to constrain its properties such that these long-wavelength surface features can be explained. We perform a suite of numerical simulations of convection with basal heating and temperature-dependent viscosity in either exponential form or Arrhenius form. For a plausible range of Rayleigh numbers and viscosity contrasts for solid nitrogen, convection can occur in all possible regimes: sluggish lid, transitional, or stagnant lid, or the layer could be purely conducting. We suggest the range of depth and temperature difference across the layer for convection to occur. We observe that the plume dynamics can be widely different in terms of the aspect ratio of convecting cells, or the width and spacing of plumes, and also in the lateral movement of plumes. These differences depend on the regime of convection determined by the Rayleigh number and the actual viscosity contrast across the layer, but is not sensitive to whether the viscosity is in Arrhenius or exponential form. The variations in plume dynamics result in different types of dynamic topography, which can be compared with the observed horizontal and vertical scales of the cells in Sputnik Planum. Based on these simulations we suggest several different possibilities for the formation and evolution of Sputnik Planum, which may be a consequence of the time-dependent behavior of thermal convection.

NUMERICAL ANALYSIS OF NATURAL CONVECTION IN A PRISMATIC ENCLOSURE

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Walid AICH

2011-01-01

Full Text Available Natural convection heat transfer and fluid flow have been examined numerically using the control-volume finite-element method in an isosceles prismatic cavity, submitted to a uniform heat flux from below when inclined sides are maintained isothermal and vertical walls are assumed to be perfect thermal insulators, without symmetry assumptions for the flow structure. The aim of the study is to examine a pitchfork bifurcation occurrence. Governing parameters on heat transfer and flow fields are the Rayleigh number and the aspect ratio of the enclosure. It has been found that the heated wall is not isothermal and the flow structure is sensitive to the aspect ratio. It is also found that heat transfer increases with increasing of Rayleigh number and decreases with increasing aspect ratio. The effects of aspect ratio become significant especially for higher values of Rayleigh number. Eventually the obtained results show that a pitchfork bifurcation occurs at a critical Rayleigh number, above which the symmetric solutions becomes unstable and asymmetric solutions are instead obtained.

Natural Convection Heat Transfer in Concentric Horizontal Annuli Containing a Saturated Porous Medi

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Ahmed F. Alfahaid, R.Y. Sakr

2012-10-01

Full Text Available Natural convection in horizontal annular porous media has become a subject receiving increasing attention due to its practical importance in the problem of insulators, such as ducting system in high temperature gas-cooled reactors, heating systems, thermal energy storage systems, under ground cable systems, etc. This paper presents a numerical study for steady state thermal convection in a fully saturated porous media bounded by two horizontal concentric cylinders, the cylinders are impermeable to fluid motion and maintained at different, uniform temperatures.  The solution scheme is based on two-dimensional model, which is governed by Darcy-Oberbeck-Boussinesq equations. The finite element method using Galerkin technique is developed and employed to solve the present problem. A numerical simulation is carried out to examine the parametric effects of Rayleigh number and radius ratio on the role played by natural convection heat transfer in the porous annuli. The numerical results obtained from the present model were compared with the available published results and good agreement is observed. The average Nusselt number at the heating surface of the inner cylinder is correlated to Rayleigh number and radius ratio.Keywords: Natural convection, numerical investigation, saturated porous media, finite element method, concentric horizontal annuli.

Entropy generation in natural convection in a symmetrically and uniformly heated vertical channel

Energy Technology Data Exchange (ETDEWEB)

Andreozzi, Assunta [Dipartimento di Energetica, Termofluidodinamica applicata e Condizionamenti ambientali, Universita degli Studi di Napoli Federico II, Piazzale Tecchio 80, 80125 Napoli (Italy); Auletta, Antonio [CIRA - Centro Italiano Ricerche Aerospaziali, Via Maiorise 1, 81043 Capua (CE) (Italy); Manca, Oronzio [Dipartimento di Ingegneria Aerospaziale e Meccanica, Seconda Universita degli Studi di Napoli, Real Casa dell' Annunziata, Via Roma 29, 81031 Aversa (CE) (Italy)

2006-08-15

In this study numerical predictions of local and global entropy generation rates in natural convection in air in a vertical channel symmetrically heated at uniform heat flux are reported. Results of entropy generation analysis are obtained by solving the entropy generation equation based on the velocity and temperature data. The analyzed regime is two-dimensional, laminar and steady state. The numerical procedure expands an existing computer code on natural convection in vertical channels. Results in terms of fields and profiles of local entropy generation, for various Rayleigh number, Ra, and aspect ratio values, L/b, are given. The distributions of local values show different behaviours for the different Ra values. A correlation between global entropy generation rates, Rayleigh number and aspect ratio is proposed in the ranges 10{sup 3}=

F(α) curves: Experimental results

International Nuclear Information System (INIS)

Glazier, J.A.; Gunaratne, G.; Libchaber, A.

1988-01-01

We study the transition to chaos at the golden and silver means for forced Rayleigh-Benard (RB) convection in mercury. We present f(α) curves below, at, and above the transition, and provide comparisons to the curves calculated for the one-dimensional circle map. We find good agreement at both the golden and silver means. This confirms our earlier observation that for low amplitude forcing, forced RB convection is well described by the one-dimensional circle map and indicates that the f(α) curve is a good measure of the approach to criticality. For selected subcritical experimental data sets we calculate the degree of subcriticality. We also present both experimental and calculated results for f(α) in the presence of a third frequency. Again we obtain agreement: The presence of random noise or a third frequency narrows the right-hand (negative q) side of the f(α) curve. Subcriticality results in symmetrically narrowed curves. We can also distinguish these cases by examining the power spectra and Poincare sections of the time series

Quantifying near-wall coherent structures in turbulent convection

Science.gov (United States)

Gunasegarane, G. S.; A Puthenveettil, Baburaj; K Agrawal, Yogesh; Schmeling, Daniel; Bosbach, Johannes; Arakeri, Jaywant; IIT Madras-DLR-IISc Collaboration

2011-11-01

We present planforms of line plumes formed on horizontal surfaces in turbulent convection, along with the length of near- wall line plumes measured from these planforms, in a six decade range of Rayleigh numbers (105 < Ra <1011) and at three Prandtl numbers (Pr = 0 . 7 , 6 , 602). Using geometric constraints on the relations for the mean plume spacings, we obtain expressions for the total length of these near-wall plumes in turbulent convection. The plume length per unit area (Lp / A), made dimensionless by the near-wall length scale in turbulent convection (Zw) remains a constant for a given fluid. The Nusselt number is shown to be directly proportional to Lp H / A for a given fluid layer of height H. Increase in Pr has a weak influence in decreasing Lp / A . These expressions match the measurements, thereby showing that the assumption of laminar natural convection boundary layers in turbulent convection is consistent with the observed total length of line plumes. We then show that similar relationships are obtained based on the assumption that the line plumes are the outcome of the instability of laminar natural convection boundary layers on the horizontal surfaces.

Numerical study of natural melt convection in cylindrical cavity with hot walls and cold bottom sink

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Ahmanache Abdennacer

2013-01-01

Full Text Available Numerical study of natural convection heat transfer and fluid flow in cylindrical cavity with hot walls and cold sink is conducted. Calculations are performed in terms of the cavity aspect ratio, the heat exchanger length and the thermo physical properties expressed via the Prandtl number and the Rayleigh number. Results are presented in the form of isotherms, streamlines, average Nusselt number and average bulk temperature for a range of Rayleigh number up to 106. It is observed that Rayleigh number and heat exchanger length influences fluid flow and heat transfer, whereas the cavity aspect ratio has no significant effects.

Effect of crust increase on natural convection heat transfer in the molten metal pool

International Nuclear Information System (INIS)

Park, Rae Joon; Kim, Sang Baik; Kim, Hee Dong; Choi, Sang Min

1999-01-01

An experimental study has been performed on natural convection heat transfer with a rapid crust formation in the molten metal pool of a low Prandtl number fluid. Two types of steady state tests, a low and high geometric aspect ratio cases in the molten metal pool, were performed. The crust thickness by solidification was measured as a function of boundary surface temperatures. The experimental results on the relationship between the Nusselt number and Rayleigh number in the molten metal pool with a crust formation were compared with existing correlations. The experimental study has shown that the bottom surface temperature of the molten metal layer, in all experiments, is the major influential parameter in the crust formation, due to the natural convection flow. The Nusselt number of the case without a crust formation in the molten metal pool is greater than that of the case with the crust formation at the same Rayleigh number. The present experimental results on the relationship between the Nusselt number and Rayleigh number in the molten metal pool match well with Globe and Dropkin's correlation. From the experimental results, a new correlation between the Nusselt number and Rayleigh number in the molten metal pool with the crust formation was developed as Nu=0.0923 (Ra) 0.0923 (2 X 10 4 7 ). (author)

Turbulent convection in liquid metal with and without rotation.

Science.gov (United States)

King, Eric M; Aurnou, Jonathan M

2013-04-23

The magnetic fields of Earth and other planets are generated by turbulent, rotating convection in liquid metal. Liquid metals are peculiar in that they diffuse heat more readily than momentum, quantified by their small Prandtl numbers, Pr rotating Rayleigh-Bénard convection experiments in the liquid metal gallium (Pr = 0.025) over a range of nondimensional buoyancy forcing (Ra) and rotation periods (E). Our primary diagnostic is the efficiency of convective heat transfer (Nu). In general, we find that the convective behavior of liquid metal differs substantially from that of moderate Pr fluids, such as water. In particular, a transition between rotationally constrained and weakly rotating turbulent states is identified, and this transition differs substantially from that observed in moderate Pr fluids. This difference, we hypothesize, may explain the different classes of magnetic fields observed on the Gas and Ice Giant planets, whose dynamo regions consist of Pr 1 fluids, respectively.

Transitions in rapidly rotating convection dynamos

Science.gov (United States)

Tilgner, A.

2013-12-01

It is commonly assumed that buoyancy in the fluid core powers the geodynamo. We study here the minimal model of a convection driven dynamo, which is a horizontal plane layer in a gravity field, filled with electrically conducting fluid, heated from below and cooled from above, and rotating about a vertical axis. Such a plane layer may be viewed as a local approximation to the geophysically more relevant spherical geometry. The numerical simulations have been run on graphics processing units with at least 960 cores. If the convection is driven stronger and stronger at fixed rotation rate, the flow behaves at some point as if it was not rotating. This transition shows in the scaling of the heat transport which can be used to distinguish slow from rapid rotation. One expects dynamos to behave differently in these two flow regimes. But even within the convection flows which are rapidly rotating according to this criterion, it will be shown that different types of dynamos exist. In one state, the magnetic field strength obeys a scaling indicative of a magnetostrophic balance, in which the Lorentz force is in equilibrium with the Coriolis force. The flow in this case is helical. A different state exists at higher magnetic Reynolds numbers, in which the magnetic energy obeys a different scaling law and the helicity of the flow is much reduced. As one increases the Rayleigh number, all other parameters kept constant, one may find both types of dynamos separated by an interval of Rayleigh numbers in which there are no dynamos at all. The effect of these transitions on energy dissipation and mean field generation have also been studied.

Unsteady three-dimensional behavior of natural convection in horizontal annulus

International Nuclear Information System (INIS)

Ohya, Toshizo; Miki, Yasutomi; Morita, Kouji; Fukuda, Kenji; Hasegawa, Shu

1988-01-01

An numerical analysis has been performed on unsteady three-dimensional natural convection in a concentric horizontal annulus filled with air. The explicit leap-frog scheme is used for integrating three-dimensional time-dependent equations and the fast Fourier transform (FFT) for solving the Poisson equations for pressure. An oscillatory flow is found to occur at high Rayleigh numbers, which agree qualitatively with the experimental observation made by Bishop et al. An experiment is also conducted to measure temperature fluctuations; a comparison between periods of fluctuations obtained numerically and experimentally shows a good agreement. Numerical calculations yield various statistical parameters of turbulence at higher Rayleigh numbers, which wait experimental verificaions, however. (author)

Turbulent Convection Insights from Small-Scale Thermal Forcing with Zero Net Heat Flux at a Horizontal Boundary.

Science.gov (United States)

Griffiths, Ross W; Gayen, Bishakhdatta

2015-11-13

A large-scale circulation, a turbulent boundary layer, and a turbulent plume are noted features of convection at large Rayleigh numbers under differential heating on a single horizontal boundary. These might be attributed to the forcing, which in all studies has been limited to a unidirectional gradient over the domain scale. We instead apply forcing on a length scale smaller than the domain, and with variation in both horizontal directions. Direct numerical simulations show turbulence throughout the domain, a regime transition to a dominant domain-scale circulation, and a region of logarithmic velocity in the boundary layer, despite zero net heat flux. The results show significant similarities to Rayleigh-Bénard convection, demonstrate the significance of plume merging, support the hypothesis that the key driver of convection is the production of available potential energy without necessarily supplying total potential energy, and imply that contributions to domain-scale circulation in the oceans need not be solely from the large-scale gradients of forcing.

Simulations of thermal Rayleigh-Marangoni convection in a three-layer liquid-metal-battery model

Science.gov (United States)

Köllner, Thomas; Boeck, Thomas; Schumacher, Jörg

2017-11-01

Operating a liquid-metal battery produces Ohmic losses in the electrolyte layer that separates both metal electrodes. As a consequence, temperature gradients establish which potentially cause thermal convection since density and interfacial tension depend on the local temperature. In our numerical investigations, we considered three plane, immiscible layers governed by the Navier-Stokes-Boussinesq equations held at a constant temperature of 500°C at the bottom and top. A homogeneous current is applied that leads to a preferential heating of the mid electrolyte layer. We chose a typical material combination of Li separated by LiCl-KCl (a molten salt) from Pb-Bi for which we analyzed the linear stability of pure thermal conduction and performed three-dimensional direct-numerical simulations by a pseudospectral method probing different: electrolyte layer heights, overall heights, and current densities. Four instability mechanisms are identified, which are partly coupled to each other: buoyant convection in the upper electrode, buoyant convection in the molten salt layer, and Marangoni convection at both interfaces between molten salt and electrode. The global turbulent heat transfer follows scaling predictions for internally heated buoyant convection. Financial support by the Deutsche Forschungsgemeinschaft under Grant No. KO 5515/1-1 is gratefully acknowledged.

Modeling Diffusion and Buoyancy-Driven Convection with Application to Geological CO2 Storage

KAUST Repository

Allen, Rebecca

2015-04-01

ABSTRACT Modeling Diffusion and Buoyancy-Driven Convection with Application to Geological CO2 Storage Rebecca Allen Geological CO2 storage is an engineering feat that has been undertaken around the world for more than two decades, thus accurate modeling of flow and transport behavior is of practical importance. Diffusive and convective transport are relevant processes for buoyancy-driven convection of CO2 into underlying fluid, a scenario that has received the attention of numerous modeling studies. While most studies focus on Darcy-scale modeling of this scenario, relatively little work exists at the pore-scale. In this work, properties evaluated at the pore-scale are used to investigate the transport behavior modeled at the Darcy-scale. We compute permeability and two different forms of tortuosity, namely hydraulic and diffusive. By generating various pore ge- ometries, we find hydraulic and diffusive tortuosity can be quantitatively different in the same pore geometry by up to a factor of ten. As such, we emphasize that these tortuosities should not be used interchangeably. We find pore geometries that are characterized by anisotropic permeability can also exhibit anisotropic diffusive tortuosity. This finding has important implications for buoyancy-driven convection modeling; when representing the geological formation with an anisotropic permeabil- ity, it is more realistic to also account for an anisotropic diffusivity. By implementing a non-dimensional model that includes both a vertically and horizontally orientated 5 Rayleigh number, we interpret our findings according to the combined effect of the anisotropy from permeability and diffusive tortuosity. In particular, we observe the Rayleigh ratio may either dampen or enhance the diffusing front, and our simulation data is used to express the time of convective onset as a function of the Rayleigh ratio. Also, we implement a lattice Boltzmann model for thermal convective flows, which we treat as an analog for

Convection in a colloidal suspension in a closed horizontal cell

International Nuclear Information System (INIS)

Smorodin, B. L.; Cherepanov, I. N.

2015-01-01

The experimentally detected [1] oscillatory regimes of convection in a colloidal suspension of nanoparticles with a large anomalous thermal diffusivity in a closed horizontal cell heated from below have been simulated numerically. The concentration inhomogeneity near the vertical cavity boundaries arising from the interaction of thermal-diffusion separation and convective mixing has been proven to serve as a source of oscillatory regimes (traveling waves). The dependence of the Rayleigh number at the boundary of existence of the traveling-wave regime on the aspect ratio of the closed cavity has been established. The spatial characteristics of the emerging traveling waves have been determined

Asymptotic solution of natural convection problem in a square cavity heated from below

NARCIS (Netherlands)

Grundmann, M; Mojtabi, A; vantHof, B

Studies a two-dimensional natural convection in a porous, square cavity using a regular asymptotic development in powers of the Rayleigh number. Carries the approximation through to the 34th order. Analyses convergence of the resulting series for the Nusselt number in both monocellular and

Simulation of natural convection in an inclined polar cavity using a finite-difference lattice Boltzmann method

Energy Technology Data Exchange (ETDEWEB)

Yang, Fan; Yang, Haicheng; Guo, Xueyan; Ren Dai [University of Shanghai for Science and Technology, Shanghai (China); Yan, Yonghua [Shanghai Key Laboratory of Multiphase Flow and Heat Transfer in Power Engineering, Shanghai (China); Liu, Chaoqun [University of Texas at Arlington, Arlington (United States)

2017-06-15

Natural convection heat transfer in an inclined polar cavity was studied using a Finite-difference lattice Boltzmann method (FDLBM) based on a double-population approach for body-fitted coordinates. A D2G9 model coupled with the simplest TD2Q4 lattice model was applied to determine the velocity field and temperature field. For both velocity and temperature fields, the discrete spatial derivatives were obtained by combining the upwind scheme with the central scheme, and the discrete temporal term is obtained using a fourth-order Runge-Kutta scheme. Studies were carried out for different Rayleigh numbers and different inclination angles. The results in terms of streamlines, isotherms, and Nusselt numbers explain the heat transfer mechanism of natural convection in an inclined polar cavity due to the change of Rayleigh number and inclination angle.

Some considerations about the symmetry and evolution of chaotic Rayleigh-Bénard convection: The flywheel mechanism and the ``wind'' of turbulence

Science.gov (United States)

Lappa, Marcello

2011-09-01

Rayleigh-Bénard convection in finite-size enclosures exhibits really intricate features when turbulent states are reached and thermal plumes play a crucial role in a number of them. This complex mechanism may be regarded as a "machine" containing many different working parts: boundary layers, mixing zones, jets, and a relatively free and isothermal central region. These parts are generally regarded as the constitutive "ingredients" whose interplay leads to the emergence of a macroscopic pattern with well-defined properties. Like the Lorenz model (but with the due differences) such a complex structure has a prevailing two-dimensional nature and can be oriented clockwise or anticlockwise (both configurations are equally likely to occur and the flow can exhibit occasional and irregular "reversals" from one to the other without a change in magnitude). It is usually referred to in the literature as "wind of turbulence" or "flywheel". The present article provides insights into the possible origin of such dynamics and related patterning behavior (supported by "ad hoc" novel numerical simulations carried out for Pr=15 and O(10)⩽Ra⩽O(10)) together with a short exposition of existing theories, also illustrating open points and future directions of research.

Non-Oberbeck-Boussinesq effects in strongly turbulent Rayleigh-Bénard convection

NARCIS (Netherlands)

Ahlers, Günter; Brown, Eric; Fontenele Araujo Junior, F.; Funfschilling, Denis; Grossmann, Siegfried; Lohse, Detlef

2006-01-01

Non-Oberbeck–Boussinesq (NOB) effects on the Nusselt number $Nu$ and Reynolds number $\\hbox{\\it Re}$ in strongly turbulent Rayleigh–Bénard (RB) convection in liquids were investigated both experimentally and theoretically. In the experiments the heat current, the temperature difference, and the

Turbulence statistics and energy budget in rotating Rayleigh-Bénard convection

NARCIS (Netherlands)

Kunnen, R.P.J.; Geurts, Bernardus J.; Clercx, H.J.H.

The strongly-modified turbulence statistics of Rayleigh–Bénard convection subject to various rotation rates is addressed by numerical investigations. The flow is simulated in a domain with periodic boundary conditions in the horizontal directions, and confined vertically by parallel no-slip

Estimation of the effect of thermal convection and casing on the temperature regime of boreholes: a review

International Nuclear Information System (INIS)

Eppelbaum, L V; Kutasov, I M

2011-01-01

In a vertical borehole, free heat convection arises when the temperature gradient equals or exceeds the so-called critical gradient. The critical temperature gradient is expressed through the critical Rayleigh number and depends on two parameters: (a) the ratio of formation (casings) to fluid (gas) conductivities (λ f /λ) and (b) the convective parameter of the fluid. Both these parameters depend on the temperature (depth). An empirical equation for the critical Rayleigh number as a function of the ratio λ f /λ is suggested. For the 0–100 °C range, empirical equations for convective parameters of water and air are proposed. The analysis of the published results of field investigations in deep boreholes and modelling shows that the temperature disturbances caused by thermal convection do not exceed 0.01–0.05 °C. Thus, in deep wells the temperature deviations due to thermal convection are usually within the accuracy of the temperature surveys. However, due to convection cells the geothermal gradient cannot be determined with sufficient accuracy for short well sections. In shallow boreholes the effect of thermal convection is more essential (up to 3–5 °C). To reduce the effect of convection on the temperature regime in shallow observational wells, it is necessary to reduce the diameter of the wellbores and use well fillers (fluids and gases) with low values of the convective parameters. The field observations and numerical calculations indicate that the distorting effect due to casing pipes is small and its influence is localized to the ends of the pipes, and this effect is independent of time. (topical review)

Numerical simulation of magnetic convection ferrofluid flow in a permanent magnet-inserted cavity

Science.gov (United States)

Ashouri, Majid; Behshad Shafii, Mohammad

2017-11-01

The magnetic convection heat transfer in an obstructed two-dimensional square cavity is investigated numerically. The walls of the cavity are heated with different constant temperatures at two sides, and isolated at two other sides. The cavity is filled with a high Prandtl number ferrofluid. The convective force is induced by a magnetic field gradient of a thermally insulated square permanent magnet located at the center of the cavity. The results are presented in the forms of streamlines, isotherms, and Nusselt number for various values of magnetic Rayleigh numbers and permanent magnet size. Two major circulations are generated in the cavity, clockwise flow in the upper half and counterclockwise in the lower half. In addition, strong circulations are observed around the edges of the permanent magnet surface. The strength of the circulations increase monotonically with the magnetic Rayleigh number. The circulations also increase with the permanent magnet size, but eventually, are suppressed for larger sizes. It is found that there is an optimum size for the permanent magnet due to the contrary effects of the increase in magnetic force and the increase in flow resistance by increasing the size. By increasing the magnetic Rayleigh number or isothermal walls temperature ratio, the heat transfer rate increases.

Approximation and stability of three-dimensional natural convection flows in a porous medium

International Nuclear Information System (INIS)

Janotto, Marie-Laurence

1991-01-01

The equations of the three-dimensional natural convection in a porous medium within a differentially heated horizontal walls cavity are solved by a pseudo-spectral method. First we will present the evolution of the two main modes according to two models of convection. A few asymptotic properties connected to the small and large eddies are set up and numerically validated. A new approximate inertial manifold is then proposed. The numerical scheme used is an exponential fitting algorithm the convergence of which is proved. We will present the physical mechanism at the origin of the un-stationary three-dimensional convection at high Rayleigh numbers. (author) [fr

Numerical Study of Mixed Convection of Nanofluid in a Concentric Annulus with Rotating Inner Cylinder

Directory of Open Access Journals (Sweden)

G. A. Sheikhzadeh

2013-01-01

Full Text Available In this work, the steady and laminar mixed convection of nanofluid in horizontal concentric annulus withrotating inner cylinder is investigated numerically. The inner and outer cylinders are kept at constanttemperature Ti and To respectively, where Ti>To. The annular space is filled with Alumina-water nanofluid.The governing equations with the corresponded boundary conditions in the polar coordinate are discretizedusing the finite volume method where pressure-velocity coupling is done by the SIMPLER algorithm.Numerical results have been obtained for Rayleigh number ranging from 102 to 105, Reynolds number from 1 to 300 and nanoparticles volume fraction from 0.01 to 0.06. The effects of the Reynolds and Rayleigh numbers, average diameter of nanoparticles and the volume fraction of the nanoparticles on the fluid flow and heat transfer inside the annuli are investigated. According to the results, the average Nusselt number decreases with increasing the Reynolds number. However, the average Nusselt number increases by increasing the Rayleigh number. Moreover, the maximum average Nusselt number occurs for an optimal nanoparticle volume fraction except situations that heat conduction predominates over the heat convection. In these conditions the average Nusselt number is close to unity.

Effect of Buoyancy on Forced Convection Heat Transfer in Vertical Channels - a Literature Survey

Energy Technology Data Exchange (ETDEWEB)

Bhattacharyya, A

1965-03-15

This report contains a short resume of the available information from various sources on the effect of free convection flow on forced convection heat transfer in vertical channels. Both theoretical and experimental investigations are included. Nearly all of the theoretical investigations are concerned with laminar flow with or without internal heat generation. More consistent data are available for upward flow than for downward flow. Curves are presented to determine whether free convection or forced convection mode of heat transfer is predominant for a particular Reynolds number and Rayleigh number. At Re{sub b} > 10{sup 5} free convection effects are negligible. Downward flow through a heated channel at low Reynolds number is unstable. Under similar conditions the overall heat transfer coefficient for downward flow tends to be higher than that for upward flow.

The nonlinear interaction of convection modes in a box of a saturated porous medium

Science.gov (United States)

Florio, Brendan J.; Bassom, Andrew P.; Fowkes, Neville; Judd, Kevin; Stemler, Thomas

2015-05-01

A plethora of convection modes may occur within a confined box of porous medium when the associated dimensionless Rayleigh number R is above some critical value dependent on the geometry. In many cases the crucial Rayleigh number Rc for onset is different for each mode, and in practice the mode with the lowest associated Rc is likely to be the dominant one. For particular sizes of box, however, it is possible for multiple modes (typically three) to share a common Rc. For box shapes close to these special geometries the modes interact and compete nonlinearly near the onset of convection. Here this mechanism is explored and it is shown that generically the dynamics of the competition takes on one of two possible structures. A specific example of each is described, while the general properties of the system enables us to compare our results with some previous calculations for particular box dimensions.

Nonlinear Multiplicative Schwarz Preconditioning in Natural Convection Cavity Flow

KAUST Repository

Liu, Lulu

2017-03-17

A natural convection cavity flow problem is solved using nonlinear multiplicative Schwarz preconditioners, as a Gauss-Seidel-like variant of additive Schwarz preconditioned inexact Newton (ASPIN). The nonlinear preconditioning extends the domain of convergence of Newton’s method to high Rayleigh numbers. Convergence performance varies widely with respect to different groupings of the fields of this multicomponent problem, and with respect to different orderings of the groupings.

Nonlinear Multiplicative Schwarz Preconditioning in Natural Convection Cavity Flow

KAUST Repository

Liu, Lulu; Zhang, Wei; Keyes, David E.

2017-01-01

A natural convection cavity flow problem is solved using nonlinear multiplicative Schwarz preconditioners, as a Gauss-Seidel-like variant of additive Schwarz preconditioned inexact Newton (ASPIN). The nonlinear preconditioning extends the domain of convergence of Newton’s method to high Rayleigh numbers. Convergence performance varies widely with respect to different groupings of the fields of this multicomponent problem, and with respect to different orderings of the groupings.

Heat transfer measurements of internally heated liquids in cylindrical convection cells

International Nuclear Information System (INIS)

Fieg, G.

1978-10-01

In hypothetical reactor accidents, the thermohydraulic behaviour of core melts heated by the after-heat must be analyzed. For this purpose model experiments have been performed to study the stationary, natural convective heat transfer of internally heated fluids in cylindrical convertion cells investigating also the influence of geometry (aspect ratio) as well as of difference thermal wall conditions on to the heat transport characteristics. Axial temperature profiles, local heat flux densities at the vertical walls and their dependence, on the external Rayleigh number ar in detail reported, besides the Nusselt vs Rayleigh correlations for the aspect ratios HID=1 and 0,25. The results of these experiments are compared, as for ar possible, with existing thermohydraulic codes and simpler model asoumptions like the zone-model of Baker et. al. and after experimental verification, be used to study realistic PAHR situations. Velocity measurements by means of Laser-Doppler-Method yield information about the flow characteristics near the vertical walls and within the central part of the convecting fluid. (GL) [de

Adiabatic partition effect on natural convection heat transfer inside a square cavity: experimental and numerical studies

Science.gov (United States)

Mahmoudinezhad, S.; Rezania, A.; Yousefi, T.; Shadloo, M. S.; Rosendahl, L. A.

2018-02-01

A steady state and two-dimensional laminar free convection heat transfer in a partitioned cavity with horizontal adiabatic and isothermal side walls is investigated using both experimental and numerical approaches. The experiments and numerical simulations are carried out using a Mach-Zehnder interferometer and a finite volume code, respectively. A horizontal and adiabatic partition, with angle of θ is adjusted such that it separates the cavity into two identical parts. Effects of this angel as well as Rayleigh number on the heat transfer from the side-heated walls are investigated in this study. The results are performed for the various Rayleigh numbers over the cavity side length, and partition angles ranging from 1.5 × 105 to 4.5 × 105, and 0° to 90°, respectively. The experimental verification of natural convective flow physics has been done by using FLUENT software. For a given adiabatic partition angle, the results show that the average Nusselt number and consequently the heat transfer enhance as the Rayleigh number increases. However, for a given Rayleigh number the maximum and the minimum heat transfer occurs at θ = 45°and θ = 90°, respectively. Two responsible mechanisms for this behavior, namely blockage ratio and partition orientation, are identified. These effects are explained by numerical velocity vectors and experimental temperatures contours. Based on the experimental data, a new correlation that fairly represents the average Nusselt number of the heated walls as functions of Rayleigh number and the angel of θ for the aforementioned ranges of data is proposed.

Method of generalized coordinates and an application to Rayleigh-Taylor instability

International Nuclear Information System (INIS)

Dienes, J.K.

1978-01-01

The method of generalized coordinates is extended to the analysis of continuous bodies for which the degrees of freedom are independent velocity distributions in the spatial coordinates. The corresponding Lagrange equations contain generalized convective terms as well as the usual generalized forces and masses. Since the existence of a potential is not assumed, the equations of motion can be applied to media with arbitrary (possible dissipative) constitutive laws. Material deformation is characterized by the rate of strain, which is taken as the symmetric part of the velocity gradient, making the approach valid for arbitrarily large deformations. As an example, infinitesimal Rayleigh-Taylor instability is considered by analytic methods. Then, large amplitude Rayleigh-Taylor instability is represented with a single-degree-of-freedom analysis that shows the development (by numerical integration) of the known spike-and-bubble configuration of the unstable interface. The infinitesimal stability of a plastically deforming solid and the growth of the instability to large amplitudes are also considered

Investigation of a natural convection in a small slot using a finite difference method

International Nuclear Information System (INIS)

Schira, P.; Guenther, C.; Mueller, U.

1984-07-01

Experimental results by Koster who studied natural convection processes in slender Hele-Shaw cells are simulated with an existing two-dimensional natural convection code. This investigation yields the following results: The basic model of the calculations, which assumes a constant temperature across the gap (smallest extent of the Hele-Shaw cell) and thus without heat exchange with the Plexiglas windows, leads to an underestimation of the experimentally obtained critical Rayleigh numbers (onset of convection, onset of oscillatory convection) by one order of magnitude and an overestimation of the nondimensional period compared to experimental findings. Another version of the code, which permits heat exchange with the windows reveals an overestimation of the critical Rayleigh numbers and smaller dimensionless periods than the experiments. By these two different approaches a twoside bounding the Koster's experiments are achieved. As the modified version overestimates the real heat transfer from and to the windows it may be concluded that using a suitably adapted heat transfer coefficient for the thermal coupling of the fluid and the windows numerical simulation would also reproduce quantitatively the results of Koster. The reason for the break down of the steady flow solution and the onset of transient flow was studied numerically by examining a model proposed by Howard. At this time no really satisfying answer to this question is available. (orig./GL) [de

Adiabatic partition effect on natural convection heat transfer inside a square cavity

DEFF Research Database (Denmark)

Mahmoudi Nezhad, Sajjad; Rezaniakolaei, Alireza; yousefi, Tooraj

2018-01-01

A steady state and two-dimensional laminar free convection heat transfer in a partitioned cavity with horizontal adiabatic and isothermal side walls is investigated using both experimental and numerical approaches. The experiments and numerical simulations are carried out using a Mach......-Zehnder interferometer and a finite volume code, respectively. A horizontal and adiabatic partition, with angle of θ is adjusted such that it separates the cavity into two identical parts. Effects of this angel as well as Rayleigh number on the heat transfer from the side-heated walls are investigated in this study...... partition angle, the results show that the average Nusselt number and consequently the heat transfer enhance as the Rayleigh number increases. However, for a given Rayleigh number the maximum and the minimum heat transfer occurs at θ = 45°and θ = 90°, respectively. Two responsible mechanisms...

Numerical simulation of turbulent buoyant flows in horizontal channels

International Nuclear Information System (INIS)

Seiter, C.

1995-09-01

A numerical method is presented, to calculate the three-dimensional, time-dependent large scale structure of turbulent buoyant flows. The subject of the study is the Rayleigh-Benard-convection with air (Pr=0.71, Ra=2.5 10 6 , 10 7 ) and sodium (Pr=0.006, Ra=8.4 10 4 , 2.5 10 5 , 10 6 , 10 7 ) and a fluid layer with water and an internal heat source (Pr=7.0, Ra I =1.5 10 10 ) at moderate and high Rayleigh-numbers. The goal of the work is both, the analysis of structures of instantaneous as well as the statistical analysis of spatially and/or time averaged data, to give a contribution to the investigation of the characteristics of turbulent natural convection mainly in fluids with small Prandtl-numbers. The large eddy simulation of natural convection requires the development of appropriate momentum and heat subgrid scale models and the formulation of new boundary conditions. The used energy-length-models in the computer code TURBIT are extended methodically by modification of the characteristic length scales of the sub scale turbulence. The reduction or the increase of the sub scale turbulence correlations, caused by the influence of solid boundaries or the stratification, is considered. In the same way the new boundary conditions for the diffusive terms of the conservation equations are seen to be necessary, when the thermal or in the case of liquid metals the more critical hydrodynamic boundary layer is resolved insufficiently or not at all. The extended and new methods, models and boundary conditions, which enabled the realization of the planned simulations, are presented. (orig.)

Evidence for Gravity Wave Seeding of Convective Ionosphere Storms Initiated by Deep Troposphere Convection

Science.gov (United States)

Kelley, M. C.; Pfaff, R. F., Jr.; Dao, E. V.; Holzworth, R. H., II

2014-12-01

With the increase in solar activity, the Communications/Outage Forecast System satellite (C/NOFS) now goes below the F peak. As such, we now can study the development of Convective Ionospheric Storms (CIS) and, most importantly, large-scale seeding of the low growth-rate Rayleigh-Taylor (R-T) instability. Two mechanisms have been suggested for such seeding: the Collisional Kelvin-Helmholtz Instability (CKHI) and internal atmospheric gravity waves. A number of observations have shown that the spectrum of fully developed topside structures peaks at 600 km and extends to over 1000 km. These structures are exceedingly difficult to explain by CKHI. Here we show that sinusoidal plasma oscillations on the bottomside during daytime develop classical R-T structures on the nightside with the background 600 km structure still apparent. In two case studies, thunderstorm activity was observed east of the sinusoidal features in the two hours preceding the C/NOFS passes. Thus, we argue that convective tropospheric storms are a likely source of these sinusoidal features.

Oscillatory Convection in Rotating Liquid Metals

Science.gov (United States)

Bertin, Vincent; Grannan, Alex; Aurnou, Jonathan

2016-11-01

We have performed laboratory experiments in a aspect ratio Γ = 2 cylinder using liquid gallium (Pr = 0 . 023) as the working fluid. The Ekman number varies from E = 4 ×10-5 to 4 ×10-6 and the Rayleigh number varies from Ra = 3 ×105 to 2 ×107 . Using heat transfer and temperature measurements within the fluid, we characterize the different styles of low Pr rotating convective flow. The convection threshold is first overcome in the form of a container scale inertial oscillatory mode. At stronger forcing, wall-localized modes develop, coexisting with the inertial oscillatory modes in the bulk. When the strength of the buoyancy increases further, the bulk flow becomes turbulent while the wall modes remain. Our results imply that rotating convective flows in liquid metals do not develop in the form of quasi-steady columns, as in Pr = 1 planetary and stellar dynamo models, but in the form of oscillatory motions. Therefore, convection driven dynamo action in low Pr fluids can differ substantively than that occurring in typical Pr = 1 numerical models. Our results also suggest that low wavenumber, wall modes may be dynamically and observationally important in liquid metal dynamo systems. We thank the NSF Geophysics Program for support of this project.

On a Five-Dimensional Chaotic System Arising from Double-Diffusive Convection in a Fluid Layer

Directory of Open Access Journals (Sweden)

R. Idris

2013-01-01

Full Text Available A chaotic system arising from double-diffusive convection in a fluid layer is investigated in this paper based on the theory of dynamical systems. A five-dimensional model of chaotic system is obtained using the Galerkin truncated approximation. The results showed that the transition from steady convection to chaos via a Hopf bifurcation produced a limit cycle which may be associated with a homoclinic explosion at a slightly subcritical value of the Rayleigh number.

Heat and momentum transport scalings in vertical convection

Science.gov (United States)

Shishkina, Olga

2016-11-01

For vertical convection, where a fluid is confined between two differently heated isothermal vertical walls, we investigate the heat and momentum transport, which are measured, respectively, by the Nusselt number Nu and the Reynolds number Re . For laminar vertical convection we derive analytically the dependence of Re and Nu on the Rayleigh number Ra and the Prandtl number Pr from our boundary layer equations and find two different scaling regimes: Nu Pr 1 / 4 Ra 1 / 4 , Re Pr - 1 / 2 Ra 1 / 2 for Pr > 1 . Direct numerical simulations for Ra from 105 to 1010 and Pr from 0.01 to 30 are in excellent ageement with our theoretical findings and show that the transition between the regimes takes place for Pr around 0.1. We summarize the results from and present new theoretical and numerical results for transitional and turbulent vertical convection. The work is supported by the Deutsche Forschungsgemeinschaft (DFG) under the Grant Sh 405/4 - Heisenberg fellowship.

Nonlinear thermal convection in a layer of nanofluid under G-jitter and internal heating effects

Directory of Open Access Journals (Sweden)

Bhadauria B. S.

2014-01-01

Full Text Available This paper deals with a mathematical model of controlling heat transfer in nanofluids. The time-periodic vertical vibrations of the system are considered to effect an external control of heat transport along with internal heating effects. A weakly non-linear stability analysis is based on the five-mode Lorenz model using which the Nusselt number is obtained as a function of the thermal Rayleigh number, nano-particle concentration based Rayleigh number, Prandtl number, Lewis number, modified diffusivity ratio, amplitude and frequency of modulation. It is shown that modulation can be effectively used to control convection and thereby heat transport. Further, it is found that the effect of internal Rayleigh number is to enhance the heat and nano-particles transport.

Natural convection in asymmetric triangular enclosures heated from below

Science.gov (United States)

Kamiyo, O. M.; Angeli, D.; Barozzi, G. S.; Collins, M. W.

2014-11-01

Triangular enclosures are typical configurations of attic spaces found in residential as well as industrial pitched-roof buildings. Natural convection in triangular rooftops has received considerable attention over the years, mainly on right-angled and isosceles enclosures. In this paper, a finite volume CFD package is employed to study the laminar air flow and temperature distribution in asymmetric rooftop-shaped triangular enclosures when heated isothermally from the base wall, for aspect ratios (AR) 0.2 <= AR <= 1.0, and Rayleigh number (Ra) values 8 × 105 <= Ra <= 5 × 107. The effects of Rayleigh number and pitch angle on the flow structure and temperature distributions within the enclosure are analysed. Results indicate that, at low pitch angle, the heat transfer between the cold inclined and the hot base walls is very high, resulting in a multi-cellular flow structure. As the pitch angle increases, however, the number of cells reduces, and the total heat transfer rate progressively reduces, even if the Rayleigh number, being based on the enclosure height, rapidly increases. Physical reasons for the above effect are inspected.

Numerical study of three-dimensional natural convection and entropy generation in a cubical cavity with partially active vertical walls

Directory of Open Access Journals (Sweden)

Abdullah A.A.A Al-Rashed

2017-09-01

Full Text Available Natural convection and entropy generation due to the heat transfer and fluid friction irreversibilities in a three-dimensional cubical cavity with partially heated and cooled vertical walls has been investigated numerically using the finite volume method. Four different arrangements of partially active vertical sidewalls of the cubical cavity are considered. Numerical calculations are carried out for Rayleigh numbers from (103 ≤ Ra ≤ 106, various locations of the partial heating and cooling vertical sidewalls, while the Prandtl number of air is considered constant as Pr=0.7 and the irreversibility coefficient is taken as (φ=10−4. The results explain that the total entropy generation rate increases when the Rayleigh number increases. While, the Bejan number decreases as the Rayleigh number increases. Also, it is found that the arrangements of heating and cooling regions have a significant effect on the fluid flow and heat transfer characteristics of natural convection and entropy generation in a cubical cavity. The Middle-Middle arrangement produces higher values of average Nusselt numbers.

Transient natural convection in an internally heated fluid layer. Topical report, June 1975--June 1976

International Nuclear Information System (INIS)

Kulacki, F.A.; Emara, A.A.

1976-06-01

An experimental study of the transient response of a horizontal fluid layer subjected to a step change in internal energy generation has been conducted to determine the time scales for the development and decay of natural convection driven solely by the internal heat release. The layer is bounded from above by a rigid, constant temperature surface and from below by a rigid, insulated surface. Two types of unsteady convection processes are considered. In the first, the layer is brought to a motionless, isothermal state, and internal energy generation is suddenly started. In the second, steady natural convection is the initial state, and internal energy generation is suddenly stopped. For both cases, the time required for the development of the final steady state is determined by measuring the temperature response of the fluid with a small thermocouple probe. The time required for the development of the maximum temperature difference in the layer with internal generation and the time required for the complete decay of the maximum temperature difference of steady convection at a given Rayleigh number when internal energy generation is suddenly stopped are correlated with the Rayleigh number in equations which will find general application in PAHR problems in nuclear power reactors and particularly in the analysis of the small-time thermal response of in-vessel and ex-vessel molten core retention devices

Heat Transfer Correlations for Free Convection from Suspended Microheaters

Directory of Open Access Journals (Sweden)

David GOSSELIN

2016-08-01

Full Text Available Portability and autonomy for biomedical diagnostic devices are two rising requirements. It is recognized that low-energy heating of such portable devices is of utmost importance for molecular recognition. This work focuses on screen-printed microheaters based on on Joule effect, which constitute an interesting solution for low-energy heating. An experimental study of the natural convection phenomena occurring with such microheaters is conducted. When they are suspended in the air, and because of the thinness of the supporting film, it is shown that the contributions of both the upward and downward faces have to be taken into account. A total Nusselt number and a total convective heat transfer coefficient have been used to describe the natural convection around these microheaters. In addition a relation between the Nusselt number and the Rayleigh number is derived, leading to an accurate prediction of the heating temperature (MRE< 2 %.

Mixing in heterogeneous internally-heated convection

Science.gov (United States)

Limare, A.; Kaminski, E. C.; Jaupart, C. P.; Farnetani, C. G.; Fourel, L.; Froment, M.

2017-12-01

Past laboratory experiments of thermo chemical convection have dealt with systems involving fluids with different intrinsic densities and viscosities in a Rayleigh-Bénard setup. Although these experiments have greatly improved our understanding of the Earth's mantle dynamics, they neglect a fundamental component of planetary convection: internal heat sources. We have developed a microwave-based method in order to study convection and mixing in systems involving two layers of fluid with different densities, viscosities, and internal heat production rates. Our innovative laboratory experiments are appropriate for the early Earth, when the lowermost mantle was likely enriched in incompatible and heat producing elements and when the heat flux from the core probably accounted for a small fraction of the mantle heat budget. They are also relevant to the present-day mantle if one considers that radioactive decay and secular cooling contribute both to internal heating. Our goal is to quantify how two fluid layers mix, which is still very difficult to resolve accurately in 3-D numerical calculations. Viscosities and microwave absorptions are tuned to achieve high values of the Rayleigh-Roberts and Prandtl numbers relevant for planetary convection. We start from a stably stratified system where the lower layer has higher internal heat production and density than the upper layer. Due to mixing, the amount of enriched material gradually decreases to zero over a finite time called the lifetime. Based on more than 30 experiments, we have derived a scaling law that relates the lifetime of an enriched reservoir to the layer thickness ratio, a, to the density and viscosity contrasts between the two layers, and to their two different internal heating rates in the form of an enrichment factor beta=1+2*a*H1/H, where H1 is the heating rate of the lower fluid and H is the average heating rate. We find that the lifetime of the lower enriched reservoir varies as beta**(-7/3) in the low

Analysis of recovery efficiency in high-temperature aquifer thermal energy storage: a Rayleigh-based method

Science.gov (United States)

Schout, Gilian; Drijver, Benno; Gutierrez-Neri, Mariene; Schotting, Ruud

2014-01-01

High-temperature aquifer thermal energy storage (HT-ATES) is an important technique for energy conservation. A controlling factor for the economic feasibility of HT-ATES is the recovery efficiency. Due to the effects of density-driven flow (free convection), HT-ATES systems applied in permeable aquifers typically have lower recovery efficiencies than conventional (low-temperature) ATES systems. For a reliable estimation of the recovery efficiency it is, therefore, important to take the effect of density-driven flow into account. A numerical evaluation of the prime factors influencing the recovery efficiency of HT-ATES systems is presented. Sensitivity runs evaluating the effects of aquifer properties, as well as operational variables, were performed to deduce the most important factors that control the recovery efficiency. A correlation was found between the dimensionless Rayleigh number (a measure of the relative strength of free convection) and the calculated recovery efficiencies. Based on a modified Rayleigh number, two simple analytical solutions are proposed to calculate the recovery efficiency, each one covering a different range of aquifer thicknesses. The analytical solutions accurately reproduce all numerically modeled scenarios with an average error of less than 3 %. The proposed method can be of practical use when considering or designing an HT-ATES system.

Convective instabilities in SN 1987A

Science.gov (United States)

Benz, Willy; Thielemann, Friedrich-Karl

1990-01-01

Following Bandiera (1984), it is shown that the relevant criterion to determine the stability of a blast wave, propagating through the layers of a massive star in a supernova explosion, is the Schwarzschild (or Ledoux) criterion rather than the Rayleigh-Taylor criterion. Both criteria coincide only in the incompressible limit. Results of a linear stability analysis are presented for a one-dimensional (spherical) explosion in a realistic model for the progenitor of SN 1987A. When applying the Schwarzschild criterion, unstable regions get extended considerably. Convection is found to develop behind the shock, with a characteristic growth rate corresponding to a time scale much smaller than the shock traversal time. This ensures that efficient mixing will take place. Since the entire ejected mass is found to be convectively unstable, Ni can be transported outward, even into the hydrogen envelope, while hydrogen can be mixed deep into the helium core.

Dynamical and statistical phenomena of circulation and heat transfer in periodically forced rotating turbulent Rayleigh-Bénard convection

Science.gov (United States)

Sterl, Sebastian; Li, Hui-Min; Zhong, Jin-Qiang

2016-12-01

In this paper, we present results from an experimental study into turbulent Rayleigh-Bénard convection forced externally by periodically modulated unidirectional rotation rates. We find that the azimuthal rotation velocity θ ˙(t ) and thermal amplitude δ (t ) of the large-scale circulation (LSC) are modulated by the forcing, exhibiting a variety of dynamics including increasing phase delays and a resonant peak in the amplitude of θ ˙(t ) . We also focus on the influence of modulated rotation rates on the frequency of occurrence η of stochastic cessation or reorientation events, and on the interplay between such events and the periodically modulated response of θ ˙(t ) . Here we identify a mechanism by which η can be amplified by the modulated response, and these normally stochastic events can occur with high regularity. We provide a modeling framework that explains the observed amplitude and phase responses, and we extend this approach to make predictions for the occurrence of cessation events and the probability distributions of θ ˙(t ) and δ (t ) during different phases of a modulation cycle, based on an adiabatic approach that treats each phase separately. Last, we show that such periodic forcing has consequences beyond influencing LSC dynamics, by investigating how it can modify the heat transport even under conditions where the Ekman pumping effect is predominant and strong enhancement of heat transport occurs. We identify phase and amplitude responses of the heat transport, and we show how increased modulations influence the average Nusselt number.

Combined Lorentz force and ultrasound Doppler velocimetry in a vertical convection liquid metal flow

Science.gov (United States)

Zürner, Till; Vogt, Tobias; Resagk, Christian; Eckert, Sven; Schumacher, Jörg

2017-11-01

We report experimental studies on turbulent vertical convection flow in the liquid metal alloy gallium-indium-tin. Flow measurements were conducted by a combined use of local Lorentz force velocimetry (LLFV) and ultrasound Doppler velocimetry (UDV). It is known that the forced convection flow in a duct generates a force on the LLFV magnet system, that grows proportional to the flow velocity. We show that for the slower flow of natural convection LLFV retains this linear dependence in the range of micronewtons. Furthermore experimental results on the scaling of heat and momentum transport with the thermal driving are presented. The results cover a range of Rayleigh numbers 3 ×105 Deutsche Forschungsgemeinschaft under Grant No. GRK 1567.

Study of natural convection characteristics in a narrow annular gap in (Part 1)

International Nuclear Information System (INIS)

Narahara, Nobuyuki; Uotani, Masaki; Kinoshita, Izumi

1986-01-01

To clarify the characteristics of natural convection in a narrow annular gap at the roof-slab penetrations in pool-type LMFBR, preliminary and visualization experiments were carried out. The results are summarized as follows. (1) In the preliminary experiment having the upper and bottom closed annular space nondimensional circumferential temperature difference increases with gap width decreasing, and decreses with Rayleigh number increasing at the range of rayleigh number 10 10 to 10 11 . (2) In the visualization experiment, which consists the upper and bottom closed annular space type apparatus and the upper-closed bottom-open type apparatus, flow pattern and its effect at temperature distribution are clarified. (author)

Effect of Carreau-Yasuda rheological parameters on subcritical Lapwood convection in horizontal porous cavity saturated by shear-thinning fluid

Science.gov (United States)

Khechiba, Khaled; Mamou, Mahmoud; Hachemi, Madjid; Delenda, Nassim; Rebhi, Redha

2017-06-01

The present study is focused on Lapwood convection in isotropic porous media saturated with non-Newtonian shear thinning fluid. The non-Newtonian rheological behavior of the fluid is modeled using the general viscosity model of Carreau-Yasuda. The convection configuration consists of a shallow porous cavity with a finite aspect ratio and subject to a vertical constant heat flux, whereas the vertical walls are maintained impermeable and adiabatic. An approximate analytical solution is developed on the basis of the parallel flow assumption, and numerical solutions are obtained by solving the full governing equations. The Darcy model with the Boussinesq approximation and energy transport equations are solved numerically using a finite difference method. The results are obtained in terms of the Nusselt number and the flow fields as functions of the governing parameters. A good agreement is obtained between the analytical approximation and the numerical solution of the full governing equations. The effects of the rheological parameters of the Carreau-Yasuda fluid and Rayleigh number on the onset of subcritical convection thresholds are demonstrated. Regardless of the aspect ratio of the enclosure and thermal boundary condition type, the subcritical convective flows are seen to occur below the onset of stationary convection. Correlations are proposed to estimate the subcritical Rayleigh number for the onset of finite amplitude convection as a function of the fluid rheological parameters. Linear stability of the convective motion, predicted by the parallel flow approximation, is studied, and the onset of Hopf bifurcation, from steady convective flow to oscillatory behavior, is found to depend strongly on the rheological parameters. In general, Hopf bifurcation is triggered earlier as the fluid becomes more and more shear-thinning.

Role of Rayleigh numbers on characteristics of double diffusive salt fingers

Science.gov (United States)

Rehman, F.; Singh, O. P.

2018-05-01

Double diffusion convection, driven by two constituents of the fluid with different molecular diffusivity, is widely applied in oceanography and large number of other fields like astrophysics, geology, chemistry and metallurgy. In case of ocean, heat (T) and salinity (S) are the two components with varying diffusivity, where heat diffuses hundred times faster than salt. Component (T) stabilizes the system whereas components (S) destabilizes the system with overall density remains stable and forms the rising and sinking fingers known as salt fingers. Recent observations suggest that salt finger characteristics such as growth rates, wavenumber, and fluxes are strongly depending on the Rayleigh numbers as major driving force. In this paper, we corroborate this observation with the help of experiments, numerical simulations and linear theory. An eigenvalue expression for growth rate is derived from the linearized governing equations with explicit dependence on Rayleigh numbers, density stability ratio, Prandtl number and diffusivity ratio. Expressions for fastest growing fingers are also derived as a function various non-dimensional parameter. The predicted results corroborate well with the data reported from the field measurements, experiments and numerical simulations.

Non-Oberbeck-Boussinesq effects in turbulent thermal convection in ethane close to the critical point

NARCIS (Netherlands)

Ahlers, Günter; Calzavarini, E.; Fontenele Araujo Junior, F.; Funfschilling, Denis; Grossmann, Siegfried; Lohse, Detlef; Sugiyama, K.

2008-01-01

As shown in earlier work [Ahlers et al., J. Fluid Mech. 569, 409 (2006)], non-Oberbeck-Boussinesq (NOB) corrections to the center temperature in turbulent Rayleigh-Bénard convection in water and also in glycerol are governed by the temperature dependences of the kinematic viscosity and the thermal

Rotating turbulent Rayleigh-Bénard convection subject to harmonically forced flow reversals

NARCIS (Netherlands)

Geurts, B.J.; Kunnen, R.P.J.

2014-01-01

The characteristics of turbulent flow in a cylindrical Rayleigh–B´enard convection cell which can be modified considerably in case rotation is included in the dynamics. By incorporating the additional effects of an Euler force, i.e., effects induced by nonconstant rotation rates, a remarkably strong

The potential for convection and implications for geothermal energy in the Perth Basin, Western Australia

Science.gov (United States)

Sheldon, Heather A.; Florio, Brendan; Trefry, Michael G.; Reid, Lynn B.; Ricard, Ludovic P.; Ghori, K. Ameed R.

2012-11-01

Convection of groundwater in aquifers can create areas of anomalously high temperature at shallow depths which could be exploited for geothermal energy. Temperature measurements in the Perth Basin (Western Australia) reveal thermal patterns that are consistent with convection in the Yarragadee Aquifer. This observation is supported by Rayleigh number calculations, which show that convection is possible within the range of aquifer thickness, geothermal gradient, salinity gradient and permeability encountered in the Yarragadee Aquifer, assuming that the aquifer can be treated as a homogeneous anisotropic layer. Numerical simulations of convection in a simplified model of the Yarragadee Aquifer show that: (1) the spacing of convective upwellings can be predicted from aquifer thickness and permeability anisotropy; (2) convective upwellings may be circular or elongate in plan view; (3) convective upwellings create significant temperature enhancements relative to the conductive profile; (4) convective flow rates are similar to regional groundwater flow rates; and (5) convection homogenises salinity within the aquifer. Further work is required to constrain the average horizontal and vertical permeability of the Yarragadee Aquifer, to assess the validity of treating the aquifer as a homogeneous anisotropic layer, and to determine the impact of realistic aquifer geometry and advection on convection.

Experimental Study on Natural Convection Heat Transfer From two Parallel Horizontal Cylinders in Horizontal Cylindrical Enclosure

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Ahmed T. Ahmed

2013-05-01

Full Text Available  An experimental study on natural convection heat transfer from two parallel horizontal cylinders in horizontal cylindrical enclosure was carried out under condition of constant surfaces temperature for two cylinders and cylindrical enclosure. The study included the effect of Rayleigh number, rotation angle that represent the confined angle between the passing horizontal plane in cylindrical enclosure center and passing line in two cylinders centers, and the spaces between two cylinders on their heat loss ability.39An experimental set-up was used for this purpose which consist watercontainer, test section which is formed of plastic cylinder that represent the cylindrical enclosure, and two heating elements which are formed of two copper cylinders with (19 mm in diameters heated internally by electrical sources that represents transfer and heat loss elements through this set-up.      The experiments were done at the range of Rayleigh number between ( , cylinders rotation angle at ( , and spacing ratio at ( .     The study showed that the ability of heat loss from two cylinders is a function of Rayleigh number, cylinders rotation angle, and the spaces between them. This ability is increased by increasing of Rayleigh number and it was showed that this ability reaches maximum value at the first cylinder ( and minimum value at the second cylinder ( at spacing ratio (S/D=3 and rotation angle ( for the first and ( for the second cylinder respectively.      The effective variables on natural convection heat transfer from the above two cylinders are related by two correlating equations, each one explains dimensionless relation of heat transfer from each cylinder that represented by Nusselt number against Rayleigh number, rotation angle, and the spacing ratio between two cylinders. 

Natural convection in asymmetric triangular enclosures heated from below

International Nuclear Information System (INIS)

Kamiyo, O M; Angeli, D; Enzo Ferrari, Universita di Modena e Reggio Emilia, via Vignolese 905, I-41125 Modena (Italy))" data-affiliation=" (DIEF – Dipartimento di Ingegneria Enzo Ferrari, Universita di Modena e Reggio Emilia, via Vignolese 905, I-41125 Modena (Italy))" >Barozzi, G S; Collins, M W

2014-01-01

Triangular enclosures are typical configurations of attic spaces found in residential as well as industrial pitched-roof buildings. Natural convection in triangular rooftops has received considerable attention over the years, mainly on right-angled and isosceles enclosures. In this paper, a finite volume CFD package is employed to study the laminar air flow and temperature distribution in asymmetric rooftop-shaped triangular enclosures when heated isothermally from the base wall, for aspect ratios (AR) 0.2 ≤ AR ≤ 1.0, and Rayleigh number (Ra) values 8 × 10 5 ≤ Ra ≤ 5 × 10 7 . The effects of Rayleigh number and pitch angle on the flow structure and temperature distributions within the enclosure are analysed. Results indicate that, at low pitch angle, the heat transfer between the cold inclined and the hot base walls is very high, resulting in a multi-cellular flow structure. As the pitch angle increases, however, the number of cells reduces, and the total heat transfer rate progressively reduces, even if the Rayleigh number, being based on the enclosure height, rapidly increases. Physical reasons for the above effect are inspected

Modeling the natural convective flow of micropolar nanofluids

KAUST Repository

Bourantas, Georgios

2014-01-01

A micropolar model for nanofluidic suspensions is proposed in order to investigate theoretically the natural convection of nanofluids. The microrotation of the nanoparticles seems to play a significant role into flow regime and in that manner it possibly can interpret the controversial experimental data and theoretical numerical results over the natural convection of nanofluids. Natural convection of a nanofluid in a square cavity is studied and computations are performed for Rayleigh number values up to 106, for a range of solid volume fractions (0 ≤ φ ≤ 0.2) and, different types of nanoparticles (Cu, Ag, Al2O3 and TiO 2). The theoretical results show that the microrotation of the nanoparticles in suspension in general decreases overall heat transfer from the heated wall and should not therefore be neglected when computing heat and fluid flow of micropolar fluids, as nanofluids. The validity of the proposed model is depicted by comparing the numerical results obtained with available experimental and theoretical data. © 2013 Elsevier Ltd. All rights reserved.

Natural convection heat transfer in a rectangular pool with volumetric heat sources

International Nuclear Information System (INIS)

Lee, Seung Dong; Lee, Kang Hee; Suh, Kune Y.

2003-01-01

Natural convection plays an important role in determining the thermal load from debris accumulated in the reactor vessel lower head during a severe accident. The heat transfer within the molten core material can be characterized by buoyancy-induced flows resulting from internal heating due to decay of fission products. The thermo-fluid dynamic characteristics of the molten pool depend strongly on the thermal boundary conditions. The spatial and temporal variation of heat flux on the pool wall boundaries and the pool superheat are mainly characterized by the natural convection flow inside the molten pool. In general, natural convection involving internal heat generation is delineated in terms of the modified Rayleigh number, Ra', which quantifies the internal heat source and hence the strength of buoyancy. The test section is of rectangular cavity whose length, width, and height are 500 mm, 80 mm, and 250 mm, respectively. A total of twenty-four T-type thermocouples were installed in the test loop to measure temperature distribution. Four T-type thermocouples were utilized to measure temperatures on the boundary. A direct heating method was adopted in this test to simulate the uniform heat generation. The experiments covered a range of Rayleigh number, Ra, between 4.87x10 7 and 2.32x10 14 and Prandtl number, Pr, between 0.7 and 3.98. Tests were conducted with water and air as simulant. The upper and lower boundary conditions were maintained at a uniform temperature of 10degC. (author)

MHD Natural Convection and Entropy Generation of Variable Properties Nanofluid in a Triangular Enclosure

Directory of Open Access Journals (Sweden)

A. Aghaei

2015-01-01

Full Text Available Natural convection heat transfer has many applications in different fields of industry; such as cooling industries, electronic transformer devices and ventilation equipment; due to simple process, economic advantage, low noise and renewed retrieval. Recently, heat transfer of nanofluids have been considered because of higher thermal conductivity coefficient compared with those of ordinary fluids. In this study; natural convection and entropy generation in a triangular enclosure filled by Al2O3 –water nanofluid affected by magnetic field considering Brownian motion is investigated numerically. Two inclined walls are maintained at constant cold temperature (Tc while the bottom wall is kept at constant high temperature (Th with (Th>Tc. In order to investigate natural convection, a computer program (FORTRAN language based on finite volume method and SIMPLER algorithm has been used. Analyses is performed for volume fraction of nanoparticles 0, 0.02, 0.04, Hartmann number 0, 50,100, Rayleigh numbers 103,104,105 and angle of inclined walls 450. In investigated angles and Rayleigh numbers; average Nusselt number is increased by enhancement of volume fraction of nanoparticles in a fixed Hartmann number. It is also observed that total entropy generation variations by increasing volume fraction of nanoparticles is similar to that of Nusselt number. By the results; effect of friction is always insignificant on generated entropy. It is observed that natural convection of nanofluid is decreased by enhancement of Hartmann number and its behavior is close to thermal conduction. It is also concluded that average Nusselt number and total generated entropy are decreased.

The onset of double diffusive convection in a viscoelastic fluid-saturated porous layer with non-equilibrium model.

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Zhixin Yang

Full Text Available The onset of double diffusive convection in a viscoelastic fluid-saturated porous layer is studied when the fluid and solid phase are not in local thermal equilibrium. The modified Darcy model is used for the momentum equation and a two-field model is used for energy equation each representing the fluid and solid phases separately. The effect of thermal non-equilibrium on the onset of double diffusive convection is discussed. The critical Rayleigh number and the corresponding wave number for the exchange of stability and over-stability are obtained, and the onset criterion for stationary and oscillatory convection is derived analytically and discussed numerically.

Effective thermal conductivity of a heat generating rod bundle dissipating heat by natural convection and radiation

International Nuclear Information System (INIS)

Senve, Vinay; Narasimham, G.S.V.L.

2011-01-01

Highlights: → Transport processes in isothermal hexagonal sheath with 19 heat generating rods is studied. → Correlation is given to predict the maximum temperature considering all transport processes. → Effective thermal conductivity of rod bundle can be obtained using max temperature. → Data on the critical Rayleigh numbers for p/d ratios of 1.1-2.0 is presented. → Radiative heat transfer contributes to heat dissipation of 38-65% of total heat. - Abstract: A numerical study of conjugate natural convection and surface radiation in a horizontal hexagonal sheath housing 19 solid heat generating rods with cladding and argon as the fill gas, is performed. The natural convection in the sheath is driven by the volumetric heat generation in the solid rods. The problem is solved using the FLUENT CFD code. A correlation is obtained to predict the maximum temperature in the rod bundle for different pitch-to-diameter ratios and heat generating rates. The effective thermal conductivity is related to the heat generation rate, maximum temperature and the sheath temperature. Results are presented for the dimensionless maximum temperature, Rayleigh number and the contribution of radiation with changing emissivity, total wattage and the pitch-to-diameter ratio. In the simulation of a larger system that contains a rod bundle, the effective thermal conductivity facilitates simplified modelling of the rod bundle by treating it as a solid of effective thermal conductivity. The parametric studies revealed that the contribution of radiation can be 38-65% of the total heat generation, for the parameter ranges chosen. Data for critical Rayleigh number above which natural convection comes into effect is also presented.

Direct numerical simulation and modeling of turbulent natural convection in a vertical differentially heated slot; Simulation numerique directe et modelisation de la convection naturelle turbulente dans un canal differentiellement chauffe

Energy Technology Data Exchange (ETDEWEB)

Boudjemadi, R.

1996-03-01

The main objectives of this thesis are the direct numerical simulation of natural convection in a vertical differentially heated slot and the improvements of second-order turbulence modelling. A three-dimensional direct numerical simulation code has been developed in order to gain a better understanding of turbulence properties in natural convection flows. This code has been validated in several physical configurations: non-stratified natural convection flows (conduction solution), stratified natural convection flows (double boundary layer solution), transitional and turbulent Poiseuille flows. For the conduction solution, the turbulent regime was reached at a Rayleigh number of 1*10{sup 5} and 5.4*10{sup 5}. A detailed analysis of these results has revealed the principal qualities of the available models but has also pointed our their shortcomings. This data base has been used in order to improve the triple correlations transport models and to select the turbulent time scales suitable for such flows. (author). 122 refs., figs., tabs., 4 appends.

Free-convective flow of fluid in a thin porous contour and geothermal anomalies

Energy Technology Data Exchange (ETDEWEB)

Magomedbekov Kh.G.; Ramazanov, M.M.; Vagabov, M.V.

1996-01-24

The problem of free convection in a thin porous contour, placed in uniform impermeable massif is considered. The approximate analitical solution of conjugate problem is obtained. The critical Rayleigh number is determined, by exceeding of which the steady fluid circulation in an annulus is established. The computations of abnormal heat flow near surface are carried out, stipulated by thermoconvection in a contour.

Combined natural convection and radiation in a volumetrically heated fluid layer

International Nuclear Information System (INIS)

Chawla, T.C.; Chan, S.H.; Cheung, F.B.; Cho, D.H.

1980-01-01

The effect of radiation in combination with turbulent natural convection on the rates of heat transfer in volumetrically heated fluid layers characterized by high temperatures has been considered in this study. It is demonstrated that even at high Rayleigh numbers the radiation mode is as effective as the turbulent natural convection mode in removing the heat from the upper surface of the molten pools with adiabatic lower boundary. As a result of this improved heat transfer, it is shown that considerably thicker molten pools with internal heat generation can be supported without boiling inception. The total Nusselt number at a moderate but fixed value of conduction-radiation parameter, can be represented as a function of Rayleigh number in a simple power-law form. As a consequence of this relationship it is shown that maximum nonboiling pool thicknesses vary approximately inversely as the 0.9% power of internal heat generation rate. A comparison between exact analysis using the integral formulation of radiation flux and Rosseland approximation shows that the latter approximation bears out very adequately for optically thick pools with conduction-radiation parameters greater than or equal to 0.4 inspite of the fact that individual components of Nusselt number due to radiation and convection, respectively, are grossly in error. These errors in component heat fluxes are compensating due to the total heat balance constraint. However, the comparison between Rosseland approximation and exact formulation gets poorer as the value of conduction-radiation parameters decreases. This increase in error is principally incurred due to the error in estimating wall temperature differences

Combined natural convection and radiation in a volumetrically heated fluid layer

International Nuclear Information System (INIS)

Chawla, T.C.; Chan, S.H.; Cheung, F.B.; Cho, D.H.

1980-01-01

The effect of radiation in combining with turbulent natural convection on the rates of heat transfer in volumetrically heated fluid layers characterized by high temperatures has been considered in this study. It is demonstrated that even at high Rayleigh numbers the radiation mode is as effective as the turbulent natural convection mode in removing the heat from the upper surface of molten pools with adiabatic lower boundary. As a result of this improved heat transfer, it is shown that considerably thicker molten pools with internal heat generation can be supported without boiling inception. The total Nusselt number at a moderate but fixed value of conduction-radiation parameter, can be represented as a function of Rayleigh number in a simple power-law form. As a consequence of this relationship it is shown that maximum nonboiling pool thicknesses vary approximately inversely as the 0.9 power of internal heat generation rate. A comparison between exact analysis using the integral formulation of radiation flux and Rosseland approximateion shows that the latter approximation bears out very adequately for optically thick pools with conduction-radiation parameter > or approx. =0.4 inspite of the fact that individual components of Nusselt number due to radiation and convection, respectively, are grossly in error. These errors in component heat fluxes are compensating due to the total heat balance constraint. However, the comparison between Rosseland approximation and exact formulation gets poorer as the value of conduction-radiation parameter decreases. This increase in error is principally incurred due to the error in estimating wall temperature differences

Periodic mixed convection in horizontal porous layer heated from below by isoflux heater

International Nuclear Information System (INIS)

Saeid, Nawaf H.; Pop, I.

2006-01-01

Numerical study for transient mixed convection in a two-dimensional horizontal porous layer heated from below by a constant heat flux source is carried out in the present paper. The transient thermal field, flow field and average Nusselt number are presented for a wide range of the Peclet number, Pe, for the particular case of Rayleigh number Ra=10x2 and the ratio of heater length to the porous layer thickness A=1, 3 and 5. It is found that for A=3 and A=5 with small values of the Peclet number, the free convection mode is dominated, while for large values, of the Peclet number, the forced convection mode is dominated. However, for moderate values the oscillatory mixed convection is observed and a periodic variation of the average Nusselt number is obtained. When the heater length is equal to the porous layer thickness (A=1) the steady-state results are obtained for the range of Pe=0.01-10. (author)

Thermal convection of liquid sodium in inclined cylinders

Science.gov (United States)

Khalilov, Ruslan; Kolesnichenko, Ilya; Pavlinov, Alexander; Mamykin, Andrey; Shestakov, Alexander; Frick, Peter

2018-04-01

The effect of inclination on the low Prandtl number turbulent convection in a cylinder of unit aspect ratio was studied experimentally. The working fluid was sodium (Prandtl number Pr =0.0094 ), the measurements were performed for a fixed Rayleigh number Ra =(1.47 ±0.03 ) ×107 , and the inclination angle varied from β =0∘ (the Rayleigh-Bénard convection, the temperature gradient is vertical) up to β =90∘ (the applied temperature gradient is horizontal) with a step Δ β =10∘ . The effective axial heat flux characterized by the Nusselt number is minimal at β =0∘ and demonstrates a smooth growth with the increase of the cylinder inclination, reaching a maximum at angle β ≈70∘ and decreasing with a further increase of β . The maximal value of the normalized Nusselt number Nu (β )/Nu (0 ) was 1.21. In general, the dependence of Nu (β ) in a cylinder with unit aspect ratio is similar to what was observed in sodium convection in inclined long cylinders but is much weaker. The structure of the flow undergoes a significant transformation with inclination. Under moderate inclination (β ≲30∘ ), the fluctuations are strong and are provided by regular oscillations of large-scale circulation (LSC) and by turbulence. Under large inclination (β >60∘ ), the LSC is regular and the turbulence is weak, while in transient regimes (30∘border of transient and large inclinations. We find the first evidence of strong LSC fluctuations in low Prandtl number convective flow under moderate inclination. The rms azimuthal fluctuations of LSC, about 27∘ at β =0∘ , decrease almost linearly up to β =30∘ , where they are about 9∘. The angular fluctuations in the vicinity of the end faces are much stronger (about 37∘ at β =0∘ ) and weakly decrease up to β =20∘ . The strong anticorrelation of the fluctuations in two halves of the cylinder indicates the torsional character of LSC fluctuations. At β =30∘ , the intensity of the oscillations at the

Thermal convection around a heat source embedded in a box containing a saturated porous medium

Energy Technology Data Exchange (ETDEWEB)

Himasekhar, K.; Bau, H.H. (Univ. of Pennsylvania, Philadelphia (USA))

1988-08-01

A study of the thermal convection around a uniform flux cylinder embedded in a box containing a saturated porous medium is carried out experimentally and theoretically. The experimental work includes heat transfer and temperature field measurements. It is observed that for low Rayleigh numbers, the flow is two dimensional and time independent. Once a critical Rayleigh number is exceeded, the flow undergoes a Hopf bifurcation and becomes three dimensional and time dependent. The theoretical study involves the numerical solution of the two-dimensional Darcy-Oberbeck-Boussinesq equations. The complicated geometry is conveniently handled by mapping the physical domain onto a rectangle via the use of boundary-fitted coordinates. The numerical code can easily be extended to handle diverse geometric configurations. For low Rayleigh numbers, the theoretical results agree favorably with the experimental observations. However, the appearance of three-dimensional flow phenomena limits the range of utility of the numerical code.

Regimes of Axisymmetric Flow and Scaling Laws in a Rotating Annulus with Local Convective Forcing

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Susie Wright

2017-07-01

Full Text Available We present a numerical study of axisymmetric flow in a rotating annulus in which local thermal forcing, via a heated annular ring on the outside of the base and a cooled circular disk in the centre of the top surface, drives convection. This new configuration is a variant of the classical thermally-driven annulus, where uniform heating and cooling are applied through the outer and inner sidewalls respectively. The annulus provides an analogue to a planetary circulation and the new configuration, with its more relaxed vertical thermal boundary conditions, is expected to better emulate vigorous convection in the tropics and polar regions as well as baroclinic instability in the mid-latitude baroclinic zone. Using the Met Office/Oxford Rotating Annulus Laboratory (MORALS code, we have investigated a series of equilibrated, two dimensional axisymmetric flows across a large region of parameter space. These are characterized in terms of their velocity and temperature fields. When rotation is applied several distinct flow regimes may be identified for different rotation rates and strengths of differential heating. These regimes are defined as a function of the ratio of the horizontal Ekman layer thickness to the non-rotating thermal boundary layer thickness and are found to be similar to those identified in previous annulus experiments. Convection without rotation is also considered and the scaling of the heat transport with Rayleigh number is calculated. This is then compared with existing work on the classical annulus as well as horizontal and Rayleigh-Bénard convection. As with previous studies on both rotating and non-rotating convection the system’s behaviour is found to be aspect ratio dependent. This dependence is seen in the scaling of the non-rotating Nusselt number and in transitions between regimes in the rotating case although further investigation is required to fully explain these observations.

Turbulent mixed convection in asymmetrically heated vertical channel

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Mokni Ameni

2012-01-01

Full Text Available In this paper an investigation of mixed convection from vertical heated channel is undertaken. The aim is to explore the heat transfer obtained by adding a forced flow, issued from a flat nozzle located in the entry section of a channel, to the up-going fluid along its walls. Forced and free convection are combined studied in order to increase the cooling requirements. The study deals with both symmetrically and asymmetrically heated channel. The Reynolds number based on the nozzle width and the jet velocity is assumed to be 3 103 and 2.104; whereas, the Rayleigh number based on the channel length and the wall temperature difference varies from 2.57 1010 to 5.15 1012. The heating asymmetry effect on the flow development including the mean velocity and temperature the local Nusselt number, the mass flow rate and heat transfer are examined.

Influence of the angle between the wind and the isothermal surfaces on the boundary layer structures in turbulent thermal convection.

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Shishkina, Olga; Wagner, Sebastian; Horn, Susanne

2014-03-01

We derive the asymptotes for the ratio of the thermal to viscous boundary layer thicknesses for infinite and infinitesimal Prandtl numbers Pr as functions of the angle β between the large-scale circulation and an isothermal heated or cooled surface for the case of turbulent thermal convection with laminar-like boundary layers. For this purpose, we apply the Falkner-Skan ansatz, which is a generalization of the Prandtl-Blasius one to a nonhorizontal free-stream flow above the viscous boundary layer. Based on our direct numerical simulations (DNS) of turbulent Rayleigh-Bénard convection for Pr=0.1, 1, and 10 and moderate Rayleigh numbers up to 108 we evaluate the value of β that is found to be around 0.7π for all investigated cases. Our theoretical predictions for the boundary layer thicknesses for this β and the considered Pr are in good agreement with the DNS results.

Prediction of refrigerant absorption and onset of natural convection in lubricant oil

Energy Technology Data Exchange (ETDEWEB)

Barbosa, Jader R.; Marcelino Neto, Moises A. [Department of Mechanical Engineering, Federal University of Santa Catarina, Florianopolis, SC 88040900 (Brazil); Thoma, Stefan M. [Department of Mechanical and Process Engineering, Swiss Federal Institute of Technology, Sonneggstrasse 3, 8092 Zurich (Switzerland)

2008-11-15

Refrigerant absorption and mixing in lubricant oil are important in the design of refrigeration compressors and refrigeration systems. Experimental work is reported on absorption of R-134a vapour through the top interface of an initially stagnant layer of pure lubricant oil. Since the liquid refrigerant is heavier than the oil, mixing is enhanced due to natural mass convection. In the present paper, the behaviour of the liquid temperature during absorption is described based on measurements carried out in a test rig consisting of a transparent 70 mm ID, 150 mm long, vertical glass tube through which absorption can be directly observed. Transient liquid temperatures were measured at three different heights in the test section (two in the vapour, one in the liquid). The experimental work is complemented by a theoretical analysis of the critical time for the onset of mass transfer induced Rayleigh instability. The model is based on a critical mass transfer Rayleigh number criterion widely reported in the literature and takes into account the variation of physical properties in the liquid layer. The critical time for the onset of natural mass convection increases with decreasing system pressure as a result of a lower equilibrium concentration at the vapour-liquid interface. (author)

Experimental transient natural convection heat transfer from a vertical cylindrical tank

International Nuclear Information System (INIS)

Fernandez-Seara, Jose; Uhia, Francisco J.; Alberto Dopazo, J.

2011-01-01

In this paper heat transfer experimental data is presented and compared to general correlations proposed in the literature for transient laminar free convection from a vertical cylindrical tank. The experimental data has been obtained from heating and cooling experiments carried out with a cylindrical full-scale hot water storage tank working under real operating conditions. The experimental device and the data acquisition system are described. The calculation procedures established to obtain the experimental values of the heat transfer coefficients, as well as the data reduction process, are detailed. The local convection and radiation heat transfer coefficients are obtained from different heating power conditions for local Rayleigh numbers within the range of 1x10 5 -3x10 8 . The great quantity of available experimental data allows a detailed analysis with a reliable empirical base. The experimental local convection heat transfer coefficients are correlated and compared to correlations proposed in open literature for engineering calculations. - Highlights: → Experimental data of transient local convection heat transfer coefficients from a cylindrical tank for heating and cooling processes is obtained. → The transient behaviour of the convection coefficients is dependent on temperature difference evolutions between the surface and the air. → The Nu.Ra -1/4 ratio decreases proportionally in (T s -T ∞ ) -0.9 . → A new correlation based on the semi-infinite region theory for laminar transient free convection is proposed.

Counterintuitive Constraints on Chaos Formation Set by Heat Flux through Europa's Ocean

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Goodman, J. C.

2013-12-01

Models for the formation of disruptive chaos features on the icy surface of Europa fall into two broad categories: either chaos is formed when basal heating causes localized melting and thinning of the ice shell, or basal heating drives diapiric convection within the ice shell. We argue that in both of these cases, heating of the ice shell from below does not lead to chaos formation at the location of heating. If chaos is formed when a localized oceanic heat source, such as a hydrothermal plume, "melts through" the ice crust, we must consider what happens to the melted liquid. If Europa's ocean is salty, the melt will form a buoyant pool inside the melted cavity, leading to a stable interface between cold fresh meltwater and warm salty seawater. This stable interface acts like an ablative heat shield, protecting the ice from further damage. Some heat can be transferred across the stable layer by double diffusion, but this transfer is very inefficient. We calculate that local ocean heating cannot be balanced by local flux through the stable layer: instead, the warm ocean water must spread laterally until it is delivering heat to the ice base on a regional or global scale (a heating zone hundreds or thousands of km across, for conservative parameters.) If chaos is formed by diapiric solid-state convection within the ice shell, many investigators have assumed that diapirism and chaos should be most prevalent where the basal heat flux is strongest. We argue that this is not the case. In Rayleigh-Benard convection, increasing the heat flux will make convection more vigorous --- if and only if the convecting layer thickness does not change. We argue that increased basal heat flux will thin the ice shell, reducing its Rayleigh number and making convection less likely, not more. This insight allows us to reverse the logic of recent discussions of the relationship between ocean circulation and chaos (for instance, Soderlund et al, 2013 LPSC). We argue that global oceanic

Subcritical thermal convection of liquid metals in a rapidly rotating sphere

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Cardin, P.; Schaeffer, N.; Guervilly, C.; Kaplan, E.

2017-12-01

Planetary cores consist of liquid metals (low Prandtl number Pr) that convect as the core cools. Here we study nonlinear convection in a rotating (low Ekman number Ek) planetary core using a fully 3D direct (down to Ek=10-7) and a quasi geostrophic (down to Ek=10-10) numerical simulations. Near the critical thermal forcing (Rayleigh number Ra), convection onsets as thermal Rossby waves, but as Ra increases, this state is superceded by one dominated by advection. At moderate rotation, these states (here called the weak branch and strong branch, respectively) are continuously connected. As the planetary core rotates faster, the continuous transition is replaced by hysteresis cycles and subcriticality until the weak branch disappears entirely and the strong branch onsets in a turbulent state at Ekforcing decreases well below the linear onset of convection (Ra 0.4Racrit in this study for Ek=10-10 and Pr=0.01). We highlight the importance of the Reynolds stress, which is required for convection to persist below the linear onset. We further note the presence of a strong zonal flow that is nonetheless unimportant to the convective subcritical state. Our study suggests that, in the asymptotic regime of rapid rotation relevant for planetary interiors, thermal convection of liquid metals in a sphere onsets and shuts down through a subcritical bifurcation. This scenario may be relevant to explain the lunar and martian dynamo extinctions.

The Rayleigh-Taylor instability in inertial fusion, astrophysical plasma and flames

International Nuclear Information System (INIS)

Bychkov, V; Modestov, M; Akkerman, V; Eriksson, L-E

2007-01-01

Previous results are reviewed and new results are presented on the Rayleigh-Taylor instability in inertial confined fusion, flames and supernovae including gravitational and thermonuclear explosion mechanisms. The instability couples micro-scale plasma effects to large-scale hydrodynamic phenomena. In inertial fusion the instability reduces target compression. In supernovae the instability produces large-scale convection, which determines the fate of the star. The instability is often accompanied by mass flux through the unstable interface, which may have either a stabilizing or a destabilizing influence. Destabilization happens due to the Darrieus-Landau instability of a deflagration front. Still, it is unclear whether the instabilities lead to well-organized large-scale structures (bubbles) or to relatively isotropic turbulence (mixing layer)

MHD natural convection of hybrid nanofluid in an open wavy cavity

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Ashorynejad, Hamid Reza; Shahriari, Alireza

2018-06-01

In this paper, natural convection heat transfer of Al2O3-Cu/water hybrid nanofluid within open wavy cavity and subjected to a uniform magnetic field is examined by adopting the lattice Boltzmann method scheme. The left wavy wall is heated sinusoidal, while the right wall is open and maintained to the ambient conditions. The top and the bottom horizontal walls are smooth and insulated against heat and mass. The influence of solid volume fraction of nanoparticles (φ = 0, 0.02, 0.04), Rayleigh number (Ra = 103, 104, 105), Hartmann number (Ha = 0, 30, 60, 90) and phase deviation (Φ = 0, π/4, π/2, 3π/4) are investigated on flow and heat transfer fields. The results proved that the Nusselt number decreases with the increase of the Hartmann number, but it increases by the increment of Rayleigh number and nanoparticle volume fraction. The magnetic field rises or falls the effect produced by the presence of nanoparticles with respect to Rayleigh number. At Ra = 103, the effect of the raising phase deviation on heat transfer is erratic while it has a positive role in the improvement of nanoparticles effect at Ra = 105.

Moment-based boundary conditions for lattice Boltzmann simulations of natural convection in cavities

KAUST Repository

Allen, Rebecca

2016-06-29

We study a multiple relaxation time lattice Boltzmann model for natural convection with moment-based boundary conditions. The unknown primary variables of the algorithm at a boundary are found by imposing conditions directly upon hydrodynamic moments, which are then translated into conditions for the discrete velocity distribution functions. The method is formulated so that it is consistent with the second order implementation of the discrete velocity Boltzmann equations for fluid flow and temperature. Natural convection in square cavities is studied for Rayleigh numbers ranging from 103 to 108. An excellent agreement with benchmark data is observed and the flow fields are shown to converge with second order accuracy. Copyright © 2016 Inderscience Enterprises Ltd.

Lattice Boltzmann simulation of natural convection heat transfer in an open enclosure filled with Cu–water nanofluid in a presence of magnetic field

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Hussein, Ahmed Kadhim, E-mail: ahmedkadhim7474@gmail.com [Department of Mechanical Engineering, College of Engineering, Babylon University, Babylon City (Iraq); Ashorynejad, Hamid Reza; Shikholeslami, Mohsen [Faculty of Mechanical Engineering, Babol University of Technology, Babol, Mazandaran, Islamic Republic of Iran (Iran, Islamic Republic of); Sivasankaran, S. [Institute of Mathematical Sciences, University of Malaya, Kuala Lumpur 50603 (Malaysia)

2014-03-15

Highlights: • Convection very strong when Ra is high and Ha = 0. • Isotherms smooth when Ra is low and Ha is high. • Maximum stream function increases by adding nano-particle. • Flow circulation decreases when magnetic orientation angle increases. • Nusselt number ratio increases when Ra increases. - Abstract: In this paper magneto hydrodynamic (MHD) natural convection flow of Cu–water nanofluid in an open enclosure is investigated numerically using lattice Boltzmann method (LBM) scheme. The effective thermal conductivity and viscosity of nanofluid are calculated by the Maxwell–Garnetts (MG) and Brinkman models, respectively. In addition, the MDF model was used for simulating the effect of uniform magnetic field. The influence of pertinent parameters such as Hartmann number, nanoparticle volume fraction, Rayleigh number and the inclination of magnetic field on the flow and heat transfer characteristics have been examined. The results indicate that the absolute values of stream function decline significantly by increasing Hartmann numbers while these values rise by increasing Rayleigh numbers. Moreover, the results show that the solid volume fraction has a significant influence on stream function and heat transfer, depending on the value of Hartmann and Rayleigh numbers.

Heating-insensitive scale increase caused by convective precipitation

Science.gov (United States)

Haerter, Jan; Moseley, Christopher; Berg, Peter

2017-04-01

The origin of intense convective extremes and their unusual temperature dependence has recently challenged traditional thermodynamic arguments, based on the Clausius-Clapeyron relation. In a sequence of studies (Lenderink and v. Mejgaard, Nat Geosc, 2008; Berg, Haerter, Moseley, Nat Geosc, 2013; and Moseley, Hohenegger, Berg, Haerter, Nat Geosc, 2016) the argument of convective-type precipitation overcoming the 7%/K increase in extremes by dynamical, rather than thermodynamic, processes has been promoted. How can the role of dynamical processes be approached for precipitating convective cloud? One-phase, non-precipitating Rayleigh-Bénard convection is a classical problem in complex systems science. When a fluid between two horizontal plates is sufficiently heated from below, convective rolls spontaneously form. In shallow, non-precipitating atmospheric convection, rolls are also known to form under specific conditions, with horizontal scales roughly proportional to the boundary layer height. Here we explore within idealized large-eddy simulations, how the scale of convection is modified, when precipitation sets in and intensifies in the course of diurnal solar heating. Before onset of precipitation, Bénard cells with relatively constant diameter form, roughly on the scale of the atmospheric boundary layer. We find that the onset of precipitation then signals an approximately linear (in time) increase in horizontal scale. This scale increase progresses at a speed which is rather insensitive to changes in surface temperature or changes in the rate at which boundary conditions change, hinting at spatial characteristics, rather than temperature, as a possible control on spatial scales of convection. When exploring the depth of spatial correlations, we find that precipitation onset causes a sudden disruption of order and a subsequent complete disintegration of organization —until precipitation eventually ceases. Returning to the initial question of convective

Numerical investigation of Rayleigh–Bénard convection in a cylinder of unit aspect ratio

Energy Technology Data Exchange (ETDEWEB)

Wang, Bo-Fu; Jiang, Jin [School of Power and Mechanical Engineering, Wuhan University, Wuhan 430072 (China); Zhou, Lin [Institute of Structural Mechanics, Chinese Academy of Engineering Physics, Mianyang, 621900 (China); Sun, De-Jun, E-mail: jinjiang@whu.edu.cn [Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027 (China)

2016-02-15

Thermal convection in a vertical cylindrical cavity with a heated bottom, cooled top and insulated sidewall is investigated numerically. The radius to height ratio (Γ = height/radius) is fixed to unity and the Prandtl number is varied from 0.04 to 1. Rayleigh numbers up to 16 000 are considered in this study. Ten different kinds of flow regime have been identified, including both steady and unsteady patterns. The transition from steady to oscillatory flow occurs at a much lower Rayleigh number for small Prandtl number flow than for large Prandtl number flow. A bifurcation analysis shows the coexistence of two flow patterns in a certain parameter regime. The effect of flow structure on heat transfer is studied for a Prandtl number of unity. (paper)

Natural convection in porous media with heat generation

International Nuclear Information System (INIS)

Hardee, H.C. Jr.; Nilson, R.H.

1976-12-01

Heat transfer characteristics of a fluid saturated porous media are investigated for the case of uniform internal heat generation with cooling from above. Analytical models of conduction and single phase cellular convection show good agreement with previous Rayleigh number correlations and with experimental data obtained by Joule heating of salt water in a sand bed. An approximate dryout criterion is also derived for two phase boiling heat transfer in a fixed bed which is neither channeled nor fluidized. Correlation of dryout data using this criterion is encouraging, especially considering the analytical rather than correlational basis of the criterion

Direct numerical simulation and modeling of turbulent natural convection in a vertical differentially heated slot

International Nuclear Information System (INIS)

Boudjemadi, R.

1996-03-01

The main objectives of this thesis are the direct numerical simulation of natural convection in a vertical differentially heated slot and the improvements of second-order turbulence modelling. A three-dimensional direct numerical simulation code has been developed in order to gain a better understanding of turbulence properties in natural convection flows. This code has been validated in several physical configurations: non-stratified natural convection flows (conduction solution), stratified natural convection flows (double boundary layer solution), transitional and turbulent Poiseuille flows. For the conduction solution, the turbulent regime was reached at a Rayleigh number of 1*10 5 and 5.4*10 5 . A detailed analysis of these results has revealed the principal qualities of the available models but has also pointed our their shortcomings. This data base has been used in order to improve the triple correlations transport models and to select the turbulent time scales suitable for such flows. (author). 122 refs., figs., tabs., 4 appends

A Single Mode Study of a Quasi-Geostrophic Convection-Driven Dynamo Model

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Plumley, M.; Calkins, M. A.; Julien, K. A.; Tobias, S.

2017-12-01

Planetary magnetic fields are thought to be the product of hydromagnetic dynamo action. For Earth, this process occurs within the convecting, turbulent and rapidly rotating outer core, where the dynamics are characterized by low Rossby, low magnetic Prandtl and high Rayleigh numbers. Progress in studying dynamos has been limited by current computing capabilities and the difficulties in replicating the extreme values that define this setting. Asymptotic models that embrace these extreme parameter values and enforce the dominant balance of geostrophy provide an option for the study of convective flows with actual relevance to geophysics. The quasi-geostrophic dynamo model (QGDM) is a multiscale, fully-nonlinear Cartesian dynamo model that is valid in the asymptotic limit of low Rossby number. We investigate the QGDM using a simplified class of solutions that consist of a single horizontal wavenumber which enforces a horizontal structure on the solutions. This single mode study is used to explore multiscale time stepping techniques and analyze the influence of the magnetic field on convection.

Large plasma pressure perturbations and radial convective transport in a tokamak

International Nuclear Information System (INIS)

Krasheninnikov, Sergei; Yu, Guanghui; Ryutov, Dmitri

2004-01-01

Strongly localized plasma structures with large pressure inhomogeneities (such as plasma blobs in the scrape-off-layer (SOL)/shadow regions, pellet clouds, Edge localized Modes (ELMs)) observed in the tokamaks, stellarators and linear plasma devices. Experimental studies of these phenomena reveal striking similarities including more convective rather than diffusive radial plasma transport. We suggest that rather simple models can describe many essentials of blobs, ELMs, and pellet clouds dynamics. The main ingredient of these models is the effective plasma gravity caused by magnetic curvature, centrifugal or friction forces effects. As a result, the equations governing plasma transport in such localized structures appear to be rather similar to that used to describe nonlinear evolution of thermal convection in the Boussinesq approximation (directly related to the Rayleigh-Taylor (RT) instability). (author)

Natural convection with evaporation in a vertical cylindrical cavity under the effect of temperature-dependent surface tension

Science.gov (United States)

Kozhevnikov, Danil A.; Sheremet, Mikhail A.

2018-01-01

The effect of surface tension on laminar natural convection in a vertical cylindrical cavity filled with a weak evaporating liquid has been analyzed numerically. The cylindrical enclosure is insulated at the bottom, heated by a constant heat flux from the side, and cooled by a non-uniform evaporative heat flux from the top free surface having temperature-dependent surface tension. Governing equations with corresponding boundary conditions formulated in dimensionless stream function, vorticity, and temperature have been solved by finite difference method of the second-order accuracy. The influence of Rayleigh number, Marangoni number, and aspect ratio on the liquid flow and heat transfer has been studied. Obtained results have revealed that the heat transfer rate at free surface decreases with Marangoni number and increases with Rayleigh number, while the average temperature inside the cavity has an opposite behavior; namely, it growths with Marangoni number and reduces with Rayleigh number.

On the relationship between finger width, velocity, and fluxes in thermohaline convection

Science.gov (United States)

Sreenivas, K. R.; Singh, O. P.; Srinivasan, J.

2009-02-01

Double-diffusive finger convection occurs in many natural processes. The theories for double-diffusive phenomena that exist at present consider systems with linear stratification in temperature and salinity. The double-diffusive systems with step change in salinity and temperature are, however, not amenable to simple stability analysis. Hence factors that control the width of the finger, velocity, and fluxes in systems that have step change in temperature and salinity have not been understood so far. In this paper we provide new physical insight regarding factors that influence finger convection in two-layer double-diffusive system through two-dimensional numerical simulations. Simulations have been carried out for density stability ratios (Rρ) from 1.5 to 10. For each density stability ratio, the thermal Rayleigh number (RaT) has been systematically varied from 7×103 to 7×108. Results from these simulations show how finger width, velocity, and flux ratios in finger convection are interrelated and the influence of governing parameters such as density stability ratio and the thermal Rayleigh number. The width of the incipient fingers at the time of onset of instability has been shown to vary as RaT-1/3. Velocity in the finger varies as RaT1/3/Rρ. Results from simulation agree with the scale analysis presented in the paper. Our results demonstrate that wide fingers have lower velocities and flux ratios compared to those in narrow fingers. This result contradicts present notions about the relation between finger width and flux ratio. A counterflow heat-exchanger analogy is used in understanding the dependence of flux ratio on finger width and velocity.

Natural convection in enclosures containing lead-bismuth and lead

International Nuclear Information System (INIS)

Dzodzo, M.; Cuckovic-Dzodzo, D.

2001-01-01

The design of liquid metal reactors such as Encapsulated Nuclear Heat Source (ENHS) which are based predominantly on the flow generated by natural convection effects demands knowledge of velocity and temperature fields, distribution of the local Nusselt numbers and values of the average Nusselt numbers for small coolant velocity regimes. Laminar natural convection in rectangular enclosures with different aspect ratios, containing lead-bismuth and lead is studied numerically in this paper. The numerical model takes into account variable properties of the liquid metals. The developed correlation for average Nusselt numbers is presented. It is concluded that average Nusselt numbers are lower than in 'normal' fluids (air, water and glycerol) for the same values of Rayleigh numbers. However, the heat flux, which can be achieved, is greater due to the high thermal conductivity of liquid metals. Some specific features of the flow fields generated by natural convection in liquid metals are presented. Their consequences on the design of heat exchangers for liquid metals are discussed. An application of the obtained results to the design of a new type of steam generator, which integrates the intermediate heat exchanger and secondary pool functions of the ENHS reactor, is presented. (authors)

Mantle dynamics in Mars and Venus: Influence of an immobile lithosphere on three-dimensional mantle convection

International Nuclear Information System (INIS)

Schubert, G.; Bercovici; Glatzmaier, G.A.

1990-01-01

Numerical calculations of fully three-dimensional convection in constant viscosity, compressible spherical shells are interpreted in terms of possible convective motions in the mantles of Venus and Mars. The shells are heated both internally and from below to account for radiogenic heating, secular cooling, and heat flow from the core. The lower boundary of each of the shells is isothermal and shear stress free, as appropriate to the interface between a mantle and a liquid outer core. The upper boundary of each of the shells is rigid and isothermal, as appropriate to the base of a thick immobile lithosphere. Calculations with shear stress-free upper boundaries are also carried out to assess the role of the rigid surface condition. The ratio of the inner radius of each shell to its outer radius is in accordance with possible core sizes in both Venus and Mars. A calculation is also carried out for a Mars model with a small core to simulate mantle convection during early core formation. Different relative proportions of internal and bottom heating are investigated, ranging from nearly complete heating from within to almost all heating from below. The Rayleigh numbers of all the cases are approximately 100 times the critical Rayleigh numbers for the onset of convection. Cylindrical plumes are the prominent form of upwelling in the models independent of the surface boundary condition so long as sufficient heat derives from the core. Thus major volcanic centers on Mars, such as Tharsis and Elysium, and the coronae and some equatorial highlands on Venus may be the surface expressions of cylindrical mantle plumes

Effect of volumetric radiation on natural convection in a cavity with a horizontal fin using the lattice Boltzmann method

Science.gov (United States)

Tighchi, Hashem Ahmadi; Sobhani, Masoud; Esfahani, Javad Abolfazli

2018-01-01

The lattice Boltzmann method (LBM) is presented for the effects of volumetric radiation on laminar natural convection in a square cavity with a horizontal fin on the hot wall containing an absorbing, emitting and scattering medium. Accordingly, the flow, energy and radiative equations are solved by separate distribution functions in the LBM. A parametric study is performed: the effects of Rayleigh number and radiative parameters, such as extinction coefficient and scattering albedo on the flow and temperature fields are investigated. It is found that the isotherms become dense near the cold wall, due to highly participating properties and Rayleigh number. Also, the Nusselt number ratio (NNR) on the clod wall is examined for values of fin length and height. The maximum NNR is found at the longest fin length and near top wall for a given Rayleigh number.

Active Control of Thermal Convection in a Rectangular Loop by Changing its Spatial Orientation

Science.gov (United States)

Bratsun, Dmitry A.; Krasnyakov, Ivan V.; Zyuzgin, Alexey V.

2018-02-01

The problem of the automatic control of the fluid flow in a rectangular convective loop heated from below is studied theoretically and experimentally. The control is performed by using a feedback subsystem which changes the convection regimes by introducing small discrete changes in the spatial orientation of the loop with respect to gravity. We focus on effects that arise when the feedback controller operates with an unavoidable time delay, which is cause by the thermal inertia of the medium. The mathematical model of the phenomenon is developed. The dynamic regimes of the convection in the thermosyphon loop under control are studied. It is shown that the proposed control method can successfully stabilize not only a no-motion state of the fluid, but also time-dependent modes of convection including the irregular fluid flow at high values of the Rayleigh number. It is shown that the excessive gain of the proportional feedback can result in oscillations in the loop orientation exciting the unsteady convection modes. The comparison of the experimental data obtained for dielectric oil and dodecane with theory is given, and their good agreement is demonstrated.

The Numerical Study on the Influence of Prandtl Number and Height of the Enclosure

International Nuclear Information System (INIS)

Moon, Je-Young; Chung, Bum-Jin

2016-01-01

This study investigated numerically the internal flow depending on Prandtl number of fluid and height of enclosure. The two-dimensional numerical simulations were performed for several heights of enclosure in the range between 0.01 m and 0.074 m. It corresponds to the aspect ratio (H/L) ranged from 0.07 to 0.5. Prandtl number was 0.2, 0.7 and 7. Rayleigh number based on the height of enclosure ranged between 8.49x10 3 and 1.20x10 8 . The numerical calculations were carried out using FLUENT 6.3. In order to confirm the influence of Prandtl number and height of side walls on the internal flow and heat transfer of the horizontal enclosure, the numerical study is carried out using the FLUENT 6.3. The numerical results for the condition of top cooling only agree well with Rayleigh-Benard natural convection. When the top and side walls were cooled, the internal flow of enclosure is more complex. The thickness of thermal and velocity boundary layer varies with Prandtl number. For Pr>1 the behavior of cells is unstable and irregular owing to the entrained plume, whereas the internal flow for Pr<1 is stable and regular. Also, the number of cells increases depending on decrease of height. As a result, the heat exchange increases

Hydrodynamic theory of convective transport across a dynamically stabilized diffuse boundary layer

International Nuclear Information System (INIS)

Gerhauser, H.

1983-09-01

The diffuse boundary layer between miscible liquids is subject to Rayleigh-Taylor instabilities if the heavy fluid is supported by the light one. The resulting rapid interchange of the liquids can be suppressed by enforcing vertical oscillations on the whole system. This dynamic stabilization is incomplete and produces some peculiar novel transport phenomena such as decay off the density profile into several steps, periodic peeling of density sheets of the boundary layer and the appearance of steady vortex flow. The theory presented in this paper identifies the basic mechanism as formation of convective cells leading to enhanced diffusion, and explains previous experimental results with water and ZnJ 2 -solutions. A nonlinear treatment of the stationary convective flow problem gives the saturation amplitude of the ground mode and provides an upper bound for the maximum convective transport. The hydrodynamic model can be used for visualizing similar transport processes in the plasma of toroidal confinement devices such as sawtooth oscillations in soft disruptions of tokamak discharges and anomalous diffusion by excitation of convective cells. The latter process is investigated here in some detail, leading to the result that the maximum possible transport is of the order of Bohm diffusion. (orig.)

Instabilities of convection patterns in a shear-thinning fluid between plates of finite conductivity

Science.gov (United States)

Varé, Thomas; Nouar, Chérif; Métivier, Christel

2017-10-01

Rayleigh-Bénard convection in a horizontal layer of a non-Newtonian fluid between slabs of arbitrary thickness and finite thermal conductivity is considered. The first part of the paper deals with the primary bifurcation and the relative stability of convective patterns at threshold. Weakly nonlinear analysis combined with Stuart-Landau equation is used. The competition between squares and rolls, as a function of the shear-thinning degree of the fluid, the slabs' thickness, and the ratio of the thermal conductivity of the slabs to that of the fluid is investigated. Computations of heat transfer coefficients are in agreement with the maximum heat transfer principle. The second part of the paper concerns the stability of the convective patterns toward spatial perturbations and the determination of the band width of the stable wave number in the neighborhood of the critical Rayleigh number. The approach used is based on the Ginzburg-Landau equations. The study of rolls stability shows that: (i) for low shear-thinning effects, the band of stable wave numbers is bounded by zigzag instability and cross-roll instability. Furthermore, the marginal cross-roll stability boundary enlarges with increasing shear-thinning properties; (ii) for high shear-thinning effects, Eckhaus instability becomes more dangerous than cross-roll instability. For square patterns, the wave number selection is always restricted by zigzag instability and by "rectangular Eckhaus" instability. In addition, the width of the stable wave number decreases with increasing shear-thinning effects. Numerical simulations of the planform evolution are also presented to illustrate the different instabilities considered in the paper.

An investigation of implicit turbulence modeling for laminar-turbulent transition in natural convection

Science.gov (United States)

Li, Chunggang; Tsubokura, Makoto; Wang, Weihsiang

2017-11-01

The automatic dissipation adjustment (ADA) model based on truncated Navier-Stokes equations is utilized to investigate the feasibility of using implicit large eddy simulation (ILES) with ADA model on the transition in natural convection. Due to the high Rayleigh number coming from the larger temperature difference (300K), Roe scheme modified for low Mach numbers coordinating ADA model is used to resolve the complicated flow field. Based on the qualitative agreement of the comparisons with DNS and experimental results and the capability of numerically predicating a -3 decay law for the temporal power spectrum of the temperature fluctuation, this study thus validates the feasibility of ILES with ADA model on turbulent natural convection. With the advantages of ease of implementation because no explicit modeling terms are needed and nearly free of tuning parameters, ADA model offers to become a promising tool for turbulent thermal convection. Part of the results is obtained using the K computer at the RIKEN Advanced Institute for Computational Science (Proposal number hp160232).

Aspect ratio effects of an adiabatic rectangular obstacle on natural convection and entropy generation of a nanofluid in an enclosure

International Nuclear Information System (INIS)

Sheikhzadeh, G. A.; Nikfar, M.

2013-01-01

In the present study, aspect ratio (AR) effects of a centered adiabatic rectangular obstacle numerically investigated on natural convection and entropy generation in a differentially heated enclosure filled with either water or nanofluid (Cu-water). The governing equations are solved numerically with finite volume method using the SIMPLER algorithm. The study has been done for Rayleigh numbers between 10"3 and 10"6 , the aspect ratio of 1/3, 1/2, 1, 2 and 3 and for base fluid as well as nanofluid. It is found that, using the nanofluid leads to increase the flow strength, average Nusselt number and entropy generation and decrease the Bejan number especially at high Rayleigh numbers. At low Rayleigh numbers entropy generation is very low. By increasing Rayleigh number, entropy generation and Bejan number increases. It is observed that the viscose entropy generation is more considerable than the thermal entropy generation and has dominant role in total entropy generation. The maximum entropy generation occurs at AR = 1/3 and 3 and the minimum entropy generation occurs at AR = 1 and 1/2. It is observed that the effect of AR on Nusselt number, entropy generation and Bejan number depends on Rayleigh number.

An Experimental Study on the Heat Focusing of the Metallic layer in a Severe Accident

Energy Technology Data Exchange (ETDEWEB)

Moon, Je-Young; Chung, Bum-Jin [Kyung Hee Univ., Yongin (Korea, Republic of)

2014-10-15

By flooding the reactor cavity that surrounds the vessel, significant energy can be removed from relocated corium materials through the vessel wall. The aim of this study is to investigate the heat focusing depending on the aspect ratios and heat transfer characteristic of upper boundary for applications related to severe accident phenomena. Experiments were carried out for Rayleigh numbers and aspect ratio in the range of 8.49x10{sup 7}-5.49x10{sup 9}, 0.128-0.512 respectively. Also, the conditions of the top wall and the side wall are considered: (a) top plate cooling, side wall adiabatic, (b) top plate adiabatic, side wall cooling, (c) both walls cooling. In order to achieve high Rayleigh numbers, the heat transfer experiments were replaced by mass transfer experiments based on heat and mass transfer analogy concept. A sulfuric acid-copper sulfate (H{sub 2}SO{sub 4}-CuSO{sub 4}) electroplating system was adopted as the mass transfer system.An experimental study was performed to investigate the focusing effect appeared in the metallic layer in a severe accident condition. Mass transfer experiments, based on the analogy concept, carried out in order to achieve high Rayleigh number. The height of the side wall was varied for three different cooling conditions: top only, side only, and both top and side. The experimental results agreed well with the Rayleigh-Benard convection correlations of Dropkin and Somerscales and Globe and Dropkin. The test results for the three configurations (only top cooling, only side wall cooling and both walls cooling) presented that the heat transfer on side wall cooling condition without top cooling is biggest. Also, the heat transfer was enhanced by decreasing the aspect ratio (H/R)

Instabilities in fluid layers and in reaction-diffusion systems: Steady states, time-periodic solutions, non-periodic attractors, and related convective and otherwise non-linear phenomena

Energy Technology Data Exchange (ETDEWEB)

Garcia Velarde, M

1977-07-01

Thermo convective instabilities in horizontal fluid layers are discussed with emphasis on the Rayleigh-Bernard model problem. Steady solutions and time-dependent phenomena (relaxation oscillations and transition to turbulence) are studied within the nonlinear Boussinesq-Oberbeck approximation. Homogeneous steady solutions, limit cycles, and inhomogeneous (ordered) spatial structures are also studied in simple reaction-diffusion systems. Lastly, the non-periodic attractor that appears at large Rayleigh numbers in the truncated Boussinesq-Oberbeck model of Lorenz, is constructed, and a discussion of turbulent behavior is given. (Author) 105 refs.

Instabilities in fluid layers and in reaction-diffusion systems: Steady states, time-periodic solutions, non-periodic attractors, and related convective and otherwise non-linear phenomena

International Nuclear Information System (INIS)

Garcia Velarde, M.

1977-01-01

Thermo convective instabilities in horizontal fluid layers are discussed with emphasis on the Rayleigh-Bernard model problem. Steady solutions and time-dependent phenomena (relaxation oscillations and transition to turbulence) are studied within the nonlinear Boussinesq-Oberbeck approximation. Homogeneous steady solutions, limit cycles, and inhomogeneous (ordered) spatial structures are also studied in simple reaction-diffusion systems. Lastly, the non-periodic attractor that appears at large Rayleigh numbers in the truncated Boussinesq-Oberbeck model of Lorenz, is constructed, and a discussion of turbulent behavior is given. (Author) 105 refs

Three-dimensional unsteady natural convection and entropy generation in an inclined cubical trapezoidal cavity with

Directory of Open Access Journals (Sweden)

Ahmed Kadhim Hussein

2016-06-01

Full Text Available Numerical computation of unsteady laminar three-dimensional natural convection and entropy generation in an inclined cubical trapezoidal air-filled cavity is performed for the first time in this work. The vertical right and left sidewalls of the cavity are maintained at constant cold temperatures. The lower wall is subjected to a constant hot temperature, while the upper one is considered insulated. Computations are performed for Rayleigh numbers varied as 103 ⩽ Ra ⩽ 105, while the trapezoidal cavity inclination angle is varied as 0° ⩽ Φ ⩽ 180°. Prandtl number is considered constant at Pr = 0.71. Second law of thermodynamics is applied to obtain thermodynamic losses inside the cavity due to both heat transfer and fluid friction irreversibilities. The variation of local and average Nusselt numbers is presented and discussed, while, streamlines, isotherms and entropy contours are presented in both two and three-dimensional pattern. The results show that when the Rayleigh number increases, the flow patterns are changed especially in three-dimensional results and the flow circulation increases. Also, the inclination angle effect on the total entropy generation becomes insignificant when the Rayleigh number is low. Moreover, when the Rayleigh number increases the average Nusselt number increases.

Natural convection in square enclosure induced by inner circular cylinder with time-periodic pulsating temperature

KAUST Repository

Huang, Zhu

2015-03-01

The periodic unsteady natural convection flow and heat transfer in a square enclosure containing a concentric circular cylinder is numerically studied. The temperature of the inner circular cylinder fluctuates periodically with time at higher averaged value while the temperature of the enclosure keeps lower constant, and the natural convection is driven by the temperature difference. The two-dimensional natural convection is simulated with high accuracy temporal spectral method and local radial basis functions method. The Rayleigh number is studied in the range 103 ≤ Ra ≤ 106, the temperature pulsating period ranges from 0.01 to 100 and the temperature pulsating amplitudes are a = 0.5, 1.0 and 1.5. Numerical results reveal that the fluid flow and heat transfer is strongly dependent on the pulsating temperature of inner cylinder. Comparing with the steady state natural convection, the heat transfer is enhanced generally for the time-periodic unsteady natural convection, and the local maximum heat transfer rate is observed for Ra = 105 and 106. Moreover, the phenomenon of backward heat transfer is discussed quantitatively. Also, the influence of pulsating temperature on the unsteady fluid flow and heat transfer are discussed and analyzed.

Numerical resolution of the Navier-Stokes equations for a low Mach number by a spectral method

International Nuclear Information System (INIS)

Frohlich, Jochen

1990-01-01

The low Mach number approximation of the Navier-Stokes equations, also called isobar, is an approximation which is less restrictive than the one due to Boussinesq. It permits strong density variations while neglecting acoustic phenomena. We present a numerical method to solve these equations in the unsteady, two dimensional case with one direction of periodicity. The discretization uses a semi-implicit finite difference scheme in time and a Fourier-Chebycheff pseudo-spectral method in space. The solution of the equations of motion is based on an iterative algorithm of Uzawa type. In the Boussinesq limit we obtain a direct method. A first application is concerned with natural convection in the Rayleigh-Benard setting. We compare the results of the low Mach number equations with the ones in the Boussinesq case and consider the influence of variable fluid properties. A linear stability analysis based on a Chebychev-Tau method completes the study. The second application that we treat is a case of isobaric combustion in an open domain. We communicate results for the hydrodynamic Darrieus-Landau instability of a plane laminar flame front. [fr

Combined Natural Convection and Radiation Heat Transfer of Various Absorbing-Emitting-Scattering Media in a Square Cavity

Directory of Open Access Journals (Sweden)

Xianglong Liu

2014-01-01

Full Text Available A numerical model is developed to simulate combined natural convection and radiation heat transfer of various anisotropic absorbing-emitting-scattering media in a 2D square cavity based on the discrete ordinate (DO method and Boussinesq assumption. The effects of Rayleigh number, optical thickness, scattering ratio, scattering phase function, and aspect ratio of square cavity on the behaviors of heat transfer are studied. The results show that the heat transfer of absorbing-emitting-scattering media is the combined results of radiation and natural convection, which depends on the physical properties and the aspect ratio of the cavity. When the natural convection becomes significant, the convection heat transfer is enhanced, and the distributions of NuR and Nuc along the walls are obviously distorted. As the optical thickness increases, NuR along the hot wall decreases. As the scattering ratio decreases, the NuR along the walls decreases. At the higher aspect ratio, the more intensive thermal radiation and natural convection are formed, which increase the radiation and convection heat fluxes. This paper provides the theoretical research for the optimal thermal design and practical operation of the high temperature industrial equipments.

Rayleigh-Taylor mixing in supernova experiments

International Nuclear Information System (INIS)

Swisher, N. C.; Abarzhi, S. I.; Kuranz, C. C.; Arnett, D.; Hurricane, O.; Remington, B. A.; Robey, H. F.

2015-01-01

We report a scrupulous analysis of data in supernova experiments that are conducted at high power laser facilities in order to study core-collapse supernova SN1987A. Parameters of the experimental system are properly scaled to investigate the interaction of a blast-wave with helium-hydrogen interface, and the induced Rayleigh-Taylor instability and Rayleigh-Taylor mixing of the denser and lighter fluids with time-dependent acceleration. We analyze all available experimental images of the Rayleigh-Taylor flow in supernova experiments and measure delicate features of the interfacial dynamics. A new scaling is identified for calibration of experimental data to enable their accurate analysis and comparisons. By properly accounting for the imprint of the experimental conditions, the data set size and statistics are substantially increased. New theoretical solutions are reported to describe asymptotic dynamics of Rayleigh-Taylor flow with time-dependent acceleration by applying theoretical analysis that considers symmetries and momentum transport. Good qualitative and quantitative agreement is achieved of the experimental data with the theory and simulations. Our study indicates that in supernova experiments Rayleigh-Taylor flow is in the mixing regime, the interface amplitude contributes substantially to the characteristic length scale for energy dissipation; Rayleigh-Taylor mixing keeps order

Geodynamo and mantle convection simulations on the Earth Simulator using the Yin-Yang grid

International Nuclear Information System (INIS)

Kageyama, Akira; Yoshida, Masaki

2005-01-01

We have developed finite difference codes based on the Yin-Yang grid for the geodynamo simulation and the mantle convection simulation. The Yin-Yang grid is a kind of spherical overset grid that is composed of two identical component grids. The intrinsic simplicity of the mesh configuration of the Yin-Yang grid enables us to develop highly optimized simulation codes on massively parallel supercomputers. The Yin-Yang geodynamo code has achieved 15.2 Tflops with 4096 processors on the Earth Simulator. This represents 46% of the theoretical peak performance. The Yin-Yang mantle code has enabled us to carry out mantle convection simulations in realistic regimes with a Rayleigh number of 10 7 including strongly temperature dependent viscosity with spatial contrast up to 10 6

Crystalline heterogeneities and instabilities in thermally convecting magma chamber

Science.gov (United States)

Culha, C.; Suckale, J.; Qin, Z.

2016-12-01

A volcanic vent can supply different densities of crystals over an eruption time period. This has been seen in Hawai'i's Kilauea Iki 1959 eruption; however it is not common for all Kilauea or basaltic eruptions. We ask the question: Under what conditions can homogenous magma chamber cultivate crystalline heterogeneities? In some laboratory experiments and numerical simulations, a horizontal variation is observed. The region where crystals reside is identified as a retention zone: convection velocity balances settling velocity. Simulations and experiments that observe retention zones assume crystals do not alter the convection in the fluid. However, a comparison of experiments and simulations of convecting magma with crystals suggest that large crystal volume densities and crystal sizes alter fluid flow considerably. We introduce a computational method that fully resolves the crystalline phase. To simulate basaltic magma chambers in thermal convection, we built a numerical solver of the Navier-Stoke's equation, continuity equation, and energy equation. The modeled magma is assumed to be a viscous, incompressible fluid with a liquid and solid phase. Crystals are spherical, rigid bodies. We create Rayleigh-Taylor instability through a cool top layer and hot bottom layer and update magma density while keeping crystal temperature and size constant. Our method provides a detailed picture of magma chambers, which we compare to other models and experiments to identify when and how crystals alter magma chamber convection. Alterations include stratification, differential settling and instabilities. These characteristics are dependent on viscosity, convection vigor, crystal volume density and crystal characteristics. We reveal that a volumetric crystal density variation may occur over an eruption time period, if right conditions are met to form stratifications and instabilities in magma chambers. These conditions are realistic for Kilauea Iki's 1959 eruption.

The Oscillatory Nature of Rotating Convection in Liquid Metal

Science.gov (United States)

Aurnou, J. M.; Bertin, V. L.; Grannan, A. M.

2016-12-01

Earth's magnetic field is assumed to be generated by fluid motions in its liquid metal core. In this fluid, the heat diffuses significantly more than momentum and thus, the ratio of these two diffusivities, the Prandtl number Pr=ν/Κ, is well below unity. The convective flow dynamics of liquid metal is very different from Pr ≈ 1 fluids like water and those used in current dynamo simulations. In order to characterize rapidly rotating thermal convection in low Pr number fluids, we have performed laboratory experiments in a cylinder using liquid gallium (Pr ≈ 0.023) as the working fluid. The Ekman number, which characterizes the effect of rotation, varies from E = 4 10-5 to 4 10-6 and the dimensionless buoyancy forcing (Rayleigh number, Ra) varies from Ra =3 105 to 2 107. Using heat transfer measurements (Nusselt number, Nu) as well as temperature measurements within the fluid, we characterize the different styles of low Pr rotating convective flow. The convection threshold is first overcome in the form of a container scale inertial oscillatory mode. At stronger forcing, wall-localized modes are identified for the first time in liquid metal laboratory experiments. These wall modes coexist with the bulk inertial oscillatory modes. When the strengh of the buoyancy increases, the bulk flow becomes turbulent while the wall modes remain. Our results imply that rotating convective flows in liquid metals do not develop in the form of quasi-steady columns, as in Pr ≈ 1 dynamo models, but in the form of oscillatory motions. Therefore, the flows that drive thermally-driven dynamo action in low Pr geophysical and astrophysical fluids can differ substantively than those occuring in current-day Pr ≈ 1 numerical models. In addition, our results suggest that relatively low wavenumber, wall-attached modes may be dynamically important in rapidly-rotating convection in liquid metals.

Study of natural convection heat transfer characteristics. (1) Influence of ventilation duct height

International Nuclear Information System (INIS)

Wakamatsu, Mitsuo; Iwaki, Chikako; Ikeda, Tatsumi; Morooka, Shinichi; Ikeda, Hiroshi; Nakada, Kotaro; Masaki, Yoshikazu

2008-01-01

Natural cooling system has been investigated in waste storage. It is important to evaluate the flow by natural draft enough to removal the decay heat from the waste. In this study, we carried out the fundamental experiment of ventilation duct height effect for natural convection on vertical cylindrical heater in atmospheric air. The scale of test facility is about 4m height with single heater. The heating value is varied in the range of 33-110W, where Rayleigh number is over 10 10 . Natural convection flow rate were calculated by measured velocity with thermo anemometer in the inlet duct. The temperature of the cylindrical heater wall and fluid were measured with thermocouples. It was found that the heat transfer coefficient difference between long duct and short duct is small in this experiment. (author)

Importance sampling the Rayleigh phase function

DEFF Research Database (Denmark)

Frisvad, Jeppe Revall

2011-01-01

Rayleigh scattering is used frequently in Monte Carlo simulation of multiple scattering. The Rayleigh phase function is quite simple, and one might expect that it should be simple to importance sample it efficiently. However, there seems to be no one good way of sampling it in the literature....... This paper provides the details of several different techniques for importance sampling the Rayleigh phase function, and it includes a comparison of their performance as well as hints toward efficient implementation....

Natural convection of nanofluid in a wavy cavity in the presence of magnetic field on variable heat surface temperature

Energy Technology Data Exchange (ETDEWEB)

Javaherdeh, Korosh; Moslemi, Mehdi; Shahbazi, Mona [University of Guilan, Rasht (Iran, Islamic Republic of)

2017-04-15

A numerical analysis has been performed to investigate the laminar natural convection heat characteristics in a wavy cavity filled with CuO/water nanofluid. One of the sinusoidal walls (BC) is at the volatile high temperature and the opposite wavy surface is at a stable low temperature and the two other walls are considered flat and insulated while the uniform magnetic field is considered. Performing the analysis, the governing equations are given in terms of the stream function-vorticity formulation. In order to solve the nondimensionalized equations, discretizing with second-order accurate central difference method is performed then the successive under relaxation method with appropriate boundary conditions is considered. To validate the numerical model, various comparisons with previously published studies have been conducted and the results are in a good agreement. The main objective is to survey the effects of the Rayleigh number, Hartmann number, and nanoparticles volume fraction on the fluid flow and heat transfer characteristics. The results are illustrated in contours of stream function, constant temperature, and Nusselt number. The results show that the presence of the magnetic field the local Nusselt number decreases at the hot wall. Moreover, the enhancement in the heat transfer performance increases with an increasing nanoparticle concentration. However, for all values of Rayleigh number, the presence of nanoparticles leads to significant enhancement in heat transfer and the increase of Rayleigh number causes the heat transfer mechanism to change from conduction to convection.

Natural convection heat transfer in the molten metal pool

International Nuclear Information System (INIS)

Park, R.J.; Kim, S.B.; Kim, H.D.; Choi, S.M.

1997-01-01

Analytical studies using the FLOW-3D computer program have been performed on natural convection heat transfer of a high density molten metal pool, in order to evaluate the coolability of the corium pool. The FLOW-3D results on the temperature distribution and the heat transfer rate in the molten metal pool region have been compared and evaluated with the experimental data. The FLOW-3D results have shown that the developed natural convection flow contributes to the solidified crust formation of the high density molten metal pool. The present FLOW-3D results, on the relationship between the Nusselt number and the Rayleigh number in the molten metal pool region, are more similar to the calculated results of Globe and Dropkin's correlation than any others. The natural convection heat transfer in the low aspect ratio case is more substantial than that in the high aspect ratio case. The FLOW-3D results, on the temperature profile and on the heat transfer rate in the molten metal pool region, are very similar to the experimental data. The heat transfer rate of the internal heat generation case is higher than that of the bottom heating case at the same heat supply condition. (author)

An experimental investigation of laminar free convection from a vertical flat plate at general boundary condition

International Nuclear Information System (INIS)

Aharon, J.; Lahav, C.; Kalman, H.; Shai, I.

1996-01-01

The present work deals with natural convection on a vertical flat plate, where one side of the plate is exposed to an environment of constant temperature - T a , with which heat is exchanged at an effective heat transfer coefficient, Glen. The other side of the plate is exposed to a fluid at a different temperature -T ∞ . The temperature gradient induces a natural convection in the fluid. The present investigation treats the heat transfer problem in the laminar cone in air (P r =1). An experimental apparatus has been constructed to confirm the heat transfer features predicted analytically in previous work. The local experimental Nusselt number was correlated with the modified Rayleigh number, for the laminar range. (authors)

Experimental and numerical investigation on natural convection heat transfer in nanofluids

International Nuclear Information System (INIS)

Kulkarni, P.P.; Nayak, A.K.; Vijayan, P.K.

2014-01-01

Currently, a lot of research is being carried out on the potential application of nanofluids as a coolant in nuclear reactors owing to their enhanced heat transfer characteristics as compared to base fluid. In this regards, an experimental study has been undertaken concerning natural convection heat transfer of nanofluids over a cylindrical heater with a constant wall heat flux condition. The heat flux was varied from 0-50000 W/m 2 and Rayleigh number range is 30000 to 1.65 X 10 5 . Results show that there was a reduction in natural convection heat transfer coefficient of nanofluids as compared to water. Experimental results were compared with existing models for similar geometry. However, the available correlation was found to be unable to predict experimental data. A new empirical model was developed based on the experimental data including the effect of nanoparticles concentration which predicts the experimental data satisfactorily. (author)

Aspect ratio effects of an adiabatic rectangular obstacle on natural convection and entropy generation of a nanofluid in an enclosure

Energy Technology Data Exchange (ETDEWEB)

Sheikhzadeh, G. A.; Nikfar, M. [University of Kashan, Kashan (Iran, Islamic Republic of)

2013-11-15

In the present study, aspect ratio (AR) effects of a centered adiabatic rectangular obstacle numerically investigated on natural convection and entropy generation in a differentially heated enclosure filled with either water or nanofluid (Cu-water). The governing equations are solved numerically with finite volume method using the SIMPLER algorithm. The study has been done for Rayleigh numbers between 10{sup 3} and 10{sup 6} , the aspect ratio of 1/3, 1/2, 1, 2 and 3 and for base fluid as well as nanofluid. It is found that, using the nanofluid leads to increase the flow strength, average Nusselt number and entropy generation and decrease the Bejan number especially at high Rayleigh numbers. At low Rayleigh numbers entropy generation is very low. By increasing Rayleigh number, entropy generation and Bejan number increases. It is observed that the viscose entropy generation is more considerable than the thermal entropy generation and has dominant role in total entropy generation. The maximum entropy generation occurs at AR = 1/3 and 3 and the minimum entropy generation occurs at AR = 1 and 1/2. It is observed that the effect of AR on Nusselt number, entropy generation and Bejan number depends on Rayleigh number.

Natural convection in square cavity filled with ferrofluid saturated porous medium in the presence of uniform magnetic field

Energy Technology Data Exchange (ETDEWEB)

Javed, Tariq [Department of Mathematics and Statistics, FBAS, International Islamic University, Islamabad 44000 (Pakistan); Mehmood, Z., E-mail: rajaziafat@yahoo.com [Department of Mathematics and Statistics, FBAS, International Islamic University, Islamabad 44000 (Pakistan); Abbas, Z. [Department of Mathematics, The Islamia University, Bahawalpur (Pakistan)

2017-02-01

This article contains numerical results for free convection through square enclosure enclosing ferrofluid saturated porous medium when uniform magnetic field is applied upon the flow along x-axis. Heat is provided through bottom wall and a square blockage placed near left or right bottom corner of enclosure as a heat source. Left and right vertical boundaries of the cavity are considered insulated while upper wall is taken cold. The problem is modelled in terms of system of nonlinear partial differential equations. Finite element method has been adopted to compute numerical simulations of mathematical problem for wide range of pertinent flow parameters including Rayleigh number, Hartman number, Darcy number and Prandtl number. Analysis of results reveals that the strength of streamline circulation is an increasing function of Darcy and Prandtl number where convection heat transfer is dominant for large values of these parameters whereas increase in Hartman number has opposite effects on isotherms and streamline circulations. Thermal conductivity and hence local heat transfer rate of fluid gets increased when ferroparticles are introduced in the fluid. Average Nusselt number increases with increase in Darcy and Rayleigh numbers while it is decreases when Hartman number is increased.

Natural convection in square cavity filled with ferrofluid saturated porous medium in the presence of uniform magnetic field

International Nuclear Information System (INIS)

Javed, Tariq; Mehmood, Z.; Abbas, Z.

2017-01-01

This article contains numerical results for free convection through square enclosure enclosing ferrofluid saturated porous medium when uniform magnetic field is applied upon the flow along x-axis. Heat is provided through bottom wall and a square blockage placed near left or right bottom corner of enclosure as a heat source. Left and right vertical boundaries of the cavity are considered insulated while upper wall is taken cold. The problem is modelled in terms of system of nonlinear partial differential equations. Finite element method has been adopted to compute numerical simulations of mathematical problem for wide range of pertinent flow parameters including Rayleigh number, Hartman number, Darcy number and Prandtl number. Analysis of results reveals that the strength of streamline circulation is an increasing function of Darcy and Prandtl number where convection heat transfer is dominant for large values of these parameters whereas increase in Hartman number has opposite effects on isotherms and streamline circulations. Thermal conductivity and hence local heat transfer rate of fluid gets increased when ferroparticles are introduced in the fluid. Average Nusselt number increases with increase in Darcy and Rayleigh numbers while it is decreases when Hartman number is increased.

Non-Boussinesq Dissolution-Driven Convection in Porous Media

Science.gov (United States)

Amooie, M. A.; Soltanian, M. R.; Moortgat, J.

2017-12-01

Geological carbon dioxide (CO2) sequestration in deep saline aquifers has been increasingly recognized as a feasible technology to stabilize the atmospheric carbon concentrations and subsequently mitigate the global warming. Solubility trapping is one of the most effective storage mechanisms, which is associated initially with diffusion-driven slow dissolution of gaseous CO2 into the aqueous phase, followed by density-driven convective mixing of CO2 throughout the aquifer. The convection includes both diffusion and fast advective transport of the dissolved CO2. We study the fluid dynamics of CO2 convection in the underlying single aqueous-phase region. Two modeling approaches are employed to define the system: (i) a constant-concentration condition for CO2 in aqueous phase at the top boundary, and (ii) a sufficiently low, constant injection-rate for CO2 from top boundary. The latter allows for thermodynamically consistent evolution of the CO2 composition and the aqueous phase density against the rate at which the dissolved CO2 convects. Here we accurately model the full nonlinear phase behavior of brine-CO2 mixture in a confined domain altered by dissolution and compressibility, while relaxing the common Boussinesq approximation. We discover new flow regimes and present quantitative scaling relations for global characters of spreading, mixing, and dissolution flux in two- and three-dimensional media for the both model types. We then revisit the universal Sherwood-Rayleigh scaling that is under debate for porous media convective flows. Our findings confirm the sublinear scaling for the constant-concentration case, while reconciling the classical linear scaling for the constant-injection model problem. The results provide a detailed perspective into how the available modeling strategies affect the prediction ability for the total amount of CO2 dissolved in the long term within saline aquifers of different permeabilities.

Visualization of Natural Convection Heat Transfer on a Single Sphere using the Electroplating System

Energy Technology Data Exchange (ETDEWEB)

Lee, Dong Young; Chung, Bum Jin [Kyunghee University, Yongin (Korea, Republic of)

2016-05-15

The natural convective flows on outer sphere rise along surface. At top of sphere, the flows are lifted-up plume shape. For laminar flows, the local heat transfer shows maximum at the bottom of sphere and a monotonic decreases as flows approached to the top. The laminar natural convection heat transfer on a single sphere has been studied experimentally and numerically by several researchers. However, relatively less study has been performed for turbulent flows as it requires large facilities to achieve high Rayleigh numbers. The flows, which occur transition, is hard to experiment because of unstable. This study tried measurement of heat transfer and visualization external natural convection on a single sphere. The basic idea is that the plating patterns of copper on the sphere in mass transfer system will reveal the amount of heat transfer according to angular distance from the bottom. This study simulated natural convection on a single sphere and performed a mass transfer experiment using heat and mass transfer analogy concept. For visualization experiment, streak form plating pattern was observed. In this case, it seems that turbulence sets on the top of sphere and increases local heat transfer.

The Weight Loss Effect of Heated Inner Cylinder by Free Convection in Horizontal Cylindrical Enclosure

Science.gov (United States)

Sboev, I. O.; Kondrashov, A. N.; Rybkin, K. A.; Burkova, L. N.; Goncharov, M. M.

2018-03-01

The work presents results of numerical simulations of natural convection in cavity formed by the surfaces of two horizontal coaxial cylinders. The temperature of the outer cylinder is constant. The area between the cylinders is filled with an ideal incompressible fluid. The inner cylinder is set as the heater. The solution of the equations of thermal convection in a two-dimensional approximation performed by the software package ANSYS Fluent with finite volume method. The study compares the results of numerical simulation with several well-known theoretical and experimental results. The nature of interaction of the inner cylinder with a convection current created in the gap was observed. It was shown that the flux appeared around a heated cylinder affects the weight of the heat source and causes an additional lift force from the surrounding fluid. The various Rayleigh numbers (from 1.0 ṡ 103 to 1.5 ṡ 106) and fluid with different Prandtl number (from 0.5 to 1.0 ṡ 105) are considered.

Modules for Experiments in Stellar Astrophysics (MESA): Convective Boundaries, Element Diffusion, and Massive Star Explosions

Science.gov (United States)

Paxton, Bill; Schwab, Josiah; Bauer, Evan B.; Bildsten, Lars; Blinnikov, Sergei; Duffell, Paul; Farmer, R.; Goldberg, Jared A.; Marchant, Pablo; Sorokina, Elena; Thoul, Anne; Townsend, Richard H. D.; Timmes, F. X.

2018-02-01

We update the capabilities of the software instrument Modules for Experiments in Stellar Astrophysics (MESA) and enhance its ease of use and availability. Our new approach to locating convective boundaries is consistent with the physics of convection, and yields reliable values of the convective-core mass during both hydrogen- and helium-burning phases. Stars with Meffects of Rayleigh-Taylor instabilities that, in combination with the coupling to a public version of the STELLA radiation transfer instrument, creates new avenues for exploring Type II supernova properties. These capabilities are exhibited with exploratory models of pair-instability supernovae, pulsational pair-instability supernovae, and the formation of stellar-mass black holes. The applicability of MESA is now widened by the capability to import multidimensional hydrodynamic models into MESA. We close by introducing software modules for handling floating point exceptions and stellar model optimization, as well as four new software tools - MESA-Web, MESA-Docker, pyMESA, and mesastar.org - to enhance MESA's education and research impact.

Recent results in Rayleigh scattering

International Nuclear Information System (INIS)

Kahane, S.; Shahal, O.; Moreh, R.; Ben-Gurion Univ. of the Negev, Beer-Sheva

1997-01-01

New measurements of Rayleigh scattering, employing neutron capture γ rays are presented. Experimental conditions are achieved such that the Rayleigh contribution is dominant and much larger than other competing coherent process. A detailed comparison with the modified relativistic form factor approximation (MRFF) is made. It is found that MRFF overestimates the true cross sections by 3-4%. (author)

Short Rayleigh Length Free Electron Lasers

CERN Document Server

Crooker, P P; Armstead, R L; Blau, J

2004-01-01

Conventional free electron laser (FEL) oscillators minimize the optical mode volume around the electron beam in the undulator by making the resonator Rayleigh length about one third of the undulator length. This maximizes gain and beam-mode coupling. In compact configurations of high-power infrared FELs or moderate power UV FELs, the resulting optical intensity can damage the resonator mirrors. To increase the spot size and thereby reduce the optical intensity at the mirrors below the damage threshold, a shorter Rayleigh length can be used, but the FEL interaction is significantly altered. A new FEL interaction is described and analyzed with a Rayleigh length that is only one tenth the undulator length, or less. The effect of mirror vibration and positioning are more critical in the short Rayleigh length design, but we find that they are still within normal design tolerances.

Large-scale thermal convection of viscous fluids in a faulted system: 3D test case for numerical codes

Science.gov (United States)

Magri, Fabien; Cacace, Mauro; Fischer, Thomas; Kolditz, Olaf; Wang, Wenqing; Watanabe, Norihiro

2017-04-01

In contrast to simple homogeneous 1D and 2D systems, no appropriate analytical solutions exist to test onset of thermal convection against numerical models of complex 3D systems that account for variable fluid density and viscosity as well as permeability heterogeneity (e.g. presence of faults). Owing to the importance of thermal convection for the transport of energy and minerals, the development of a benchmark test for density/viscosity driven flow is crucial to ensure that the applied numerical models accurately simulate the physical processes at hands. The presented study proposes a 3D test case for the simulation of thermal convection in a faulted system that accounts for temperature dependent fluid density and viscosity. The linear stability analysis recently developed by Malkovsky and Magri (2016) is used to estimate the critical Rayleigh number above which thermal convection of viscous fluids is triggered. The numerical simulations are carried out using the finite element technique. OpenGeoSys (Kolditz et al., 2012) and Moose (Gaston et al., 2009) results are compared to those obtained using the commercial software FEFLOW (Diersch, 2014) to test the ability of widely applied codes in matching both the critical Rayleigh number and the dynamical features of convective processes. The methodology and Rayleigh expressions given in this study can be applied to any numerical model that deals with 3D geothermal processes in faulted basins as by example the Tiberas Basin (Magri et al., 2016). References Kolditz, O., Bauer, S., Bilke, L., Böttcher, N., Delfs, J. O., Fischer, T., U. J. Görke, T. Kalbacher, G. Kosakowski, McDermott, C. I., Park, C. H., Radu, F., Rink, K., Shao, H., Shao, H.B., Sun, F., Sun, Y., Sun, A., Singh, K., Taron, J., Walther, M., Wang,W., Watanabe, N., Wu, Y., Xie, M., Xu, W., Zehner, B., 2012. OpenGeoSys: an open-source initiative for numerical simulation of thermo-hydro-mechanical/chemical (THM/C) processes in porous media. Environmental

Enhanced Natural Convection in a Metal Layer Cooled by Boiling Water

International Nuclear Information System (INIS)

Cho, Jae-Seon; Suh, Kune Y.; Chung, Chang-Hyun; Park, Rae-Joon; Kim, Sang-Baik

2004-01-01

An experimental study is performed to investigate the natural convection heat transfer characteristics and the solidification of the molten metal pool concurrently with forced convective boiling of the overlying coolant to simulate a severe accident in a nuclear power plant. The relationship between the Nusselt number (Nu) and the Rayleigh number (Ra) in the molten metal pool region is determined and compared with the correlations in the literature and experimental data with subcooled water. Given the same Ra condition, the present experimental results for Nu of the liquid metal pool with coolant boiling are found to be higher than those predicted by the existing correlations or measured from the experiment with subcooled boiling. To quantify the observed effect of the external cooling on the natural convection heat transfer rate from the molten pool, it is proposed to include an additional dimensionless group characterizing the temperature gradients in the molten pool and in the external coolant region. Starting from the Globe and Dropkin correlation, engineering correlations are developed for the enhancement of heat transfer in the molten metal pool when cooled by an overlying coolant. The new correlations for predicting natural convection heat transfer are applicable to low-Prandtl-number (Pr) materials that are heated from below and solidified by the external coolant above. Results from this study may be used to modify the current model in severe accident analysis codes

Heat transfer augmentation of magnetohydrodynamics natural convection in L-shaped cavities utilizing nanofluids

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Sourtiji Ehsan

2012-01-01

Full Text Available A numerical study of natural convection heat transfer through an alumina-water nanofluid inside L-shaped cavities in the presence of an external magnetic field is performed. The study has been carried out for a wide range of important parame­ters such as Rayleigh number, Hartmann number, aspect ratio of the cavity and solid volume fraction of the nanofluid. The influence of the nanoparticle, buoyancy force and the magnetic field on the flow and temperature fields have been plotted and discussed. The results show that after a critical Rayleigh number depending on the aspect ratio, the heat transfer in the cavity rises abruptly due to some significant changes in flow field. It is also found that the heat transfer enhances in the presence of the nanoparticles and increases with solid volume fraction of the nanofluid. In addition, the performance of the nanofluid utilization is more effective at high Ray­leigh numbers. The influence of the magnetic field has been also studied and de­duced that it has a remarkable effect on the heat transfer and flow field in the cavity that as the Hartmann number increases the overall Nusselt number is significantly decreased specially at high Rayleigh numbers.

Numerical analysis of natural convection in a double-layer immiscible system

International Nuclear Information System (INIS)

Gubaidullin, A.A.; Sehgal, B.R.

2001-01-01

In the present paper numerical analysis has been applied to study the natural convection heat transfer in a system composed of two immiscible fluids with uniform internal heat generation in the lower layer or in both layers enclosed in a rectangular or in a semi-circular vessel. The objective of the work is to perform a parametric study to assess the effect of physical properties on the heat transfer characteristics as well as to complement results obtained from experiments by means of CFD simulations for a range of lower Rayleigh number and combine the experimental data and the computational results. (author)

Dynamo Scaling Laws for Uranus and Neptune: The Role of Convective Shell Thickness on Dipolarity

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Stanley, Sabine; Yunsheng Tian, Bob

2017-10-01

Previous dynamo scaling law studies (Christensen and Aubert, 2006) have demonstrated that the morphology of a planet’s magnetic field is determined by the local Rossby number (Ro_l): a non-dimensional diagnostic variable that quantifies the ratio of inertial forces to Coriolis forces on the average length scale of the flow. Dynamos with Ro_l ~ 0.1 produce multipolar magnetic fields. Scaling studies have also determined the dependence of the local Rossby number on non-dimensional parameters governing the system - specifically the Ekman, Prandtl, magnetic Prandtl and flux-based Rayleigh numbers (Olson and Christensen, 2006). When these scaling laws are applied to the planets, it appears that Uranus and Neptune should have dipole-dominated fields, contrary to observations. However, those scaling laws were derived using the specific convective shell thickness of the Earth’s core. Here we investigate the role of convective shell thickness on dynamo scaling laws. We find that the local Rossby number depends exponentially on the convective shell thickness. Including this new dependence on convective shell thickness, we find that the dynamo scaling laws now predict that Uranus and Neptune reside deeply in the multipolar regime, thereby resolving the previous contradiction with observations.

Rayleigh wave effects in an elastic half-space.

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Aggarwal, H. R.

1972-01-01

Consideration of Rayleigh wave effects in a homogeneous isotropic linearly elastic half-space subject to an impulsive uniform disk pressure loading. An approximate formula is obtained for the Rayleigh wave effects. It is shown that the Rayleigh waves near the center of loading arise from the portion of the dilatational and shear waves moving toward the axis, after they originate at the edge of the load disk. A study is made of the vertical displacement due to Rayleigh waves at points on the axis near the surface of the elastic half-space.

Wavelength selection in traveling-wave convection in a fluid mixture

International Nuclear Information System (INIS)

Surko, C.M.; Eaton, K.D.; Baxter, G.W.; Iwata, K.

1993-01-01

The mechanisms by which a one-dimensional pattern of traveling waves changes wavelength (i.e. the Eckhaus instability) is studied in a binary fluid mixture. Propagating wavelength modulations develop when the Rayleigh number of the system is decreased below a wavelength-dependent threshold, commonly referred to as the Eckhaus boundary. These wavelength modulations increase in amplitude and narrow in spatial extent until they trigger the creation or annihilation of convection roll pairs and thereby change the average wavelength of the system. The authors find qualitatively different dynamics for wavelength-increasing events and wavelength-decreasing events; these differences are due to the strong wavelength dependence of the group velocity

Integral transform solution of natural convection in a square cavity with volumetric heat generation

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C. An

2013-12-01

Full Text Available The generalized integral transform technique (GITT is employed to obtain a hybrid numerical-analytical solution of natural convection in a cavity with volumetric heat generation. The hybrid nature of this approach allows for the establishment of benchmark results in the solution of non-linear partial differential equation systems, including the coupled set of heat and fluid flow equations that govern the steady natural convection problem under consideration. Through performing the GITT, the resulting transformed ODE system is then numerically solved by making use of the subroutine DBVPFD from the IMSL Library. Therefore, numerical results under user prescribed accuracy are obtained for different values of Rayleigh numbers, and the convergence behavior of the proposed eigenfunction expansions is illustrated. Critical comparisons against solutions produced by ANSYS CFX 12.0 are then conducted, which demonstrate excellent agreement. Several sets of reference results for natural convection with volumetric heat generation in a bi-dimensional square cavity are also provided for future verification of numerical results obtained by other researchers.

Nanofluid MHD natural convection through a porous complex shaped cavity considering thermal radiation

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Sheikholeslami, M.; Li, Zhixiong; Shamlooei, M.

2018-06-01

Control volume based finite element method (CVFEM) is applied to simulate H2O based nanofluid radiative and convective heat transfer inside a porous medium. Non-Darcy model is employed for porous media. Influences of Hartmann number, nanofluid volume fraction, radiation parameter, Darcy number, number of undulations and Rayleigh number on nanofluid behavior were demonstrated. Thermal conductivity of nanofluid is estimated by means of previous experimental correlation. Results show that Nusselt number enhances with augment of permeability of porous media. Effect of Hartmann number on rate of heat transfer is opposite of radiation parameter.

From Geodynamics to Simplicity

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Anderson, D. L.

2002-12-01

Mantle convection and plate tectonics are often thought as synonymous. Convection is sometimes treated as the driver or plate tectonics is viewed as simply a manifestation of mantle convection. Mantle plumes are regarded as supplying some of the elements missing in the plate tectonic and mantle convection paradigms, such as island chains, swells and large igneous provinces. An alternate view is motivated by Prigogine's concept of far-from-equilibrium self-organization ( SOFFE), not to be confused with Bak's self-organized criticality ( SOC) . In a SOFFE system the components interact, and the system is small compared to the outside world to which it is open. There must be multiple possible states and dissipation is important. Such a system is sensitive to small changes. Rayleigh-Benard convection in a container with isothermal walls is such a self-organizing system ; the driving bouyancy and the dissipation ( viscosity ) are in the fluid. In Marangoni convection the driving forces ( surface tension ) and dissipation are in the surface film and this organizes the surface and the underlying fluid. The mantle provides energy and matter to the interacting plate system but forces in the plates drive and dissipate the energy. Thus, plate tectonics may be a SOFFEE system that drives convection,as are systems cooled from above, in general. If so, plates will reorganize as boundary conditions change ; incipient plate boundaries will emerge as volcanic chains at tensile regions. Plates are defined as regions of lateral compression ( force chains ), rather than strength, and they are ephemeral. The plate system, rather than mantle viscosity, will modulate mantle cooling. The supercontinent cycle, with episodes of reorganization and massive magmatism, may be a manifestation of this far-from-equilibrium, driven from above, system. Geodynamics may be simpler than we think. Plate tectonics is certainly a more powerful concept once the concepts of rididity, elasticity, homogeneity

Two-parameter study of the quasiperiodic route to chaos in convecting 3He--superfluid-4He mixtures

International Nuclear Information System (INIS)

Mainieri, R.; Sullivan, T.S.; Ecke, R.E.

1989-01-01

We study the frequency lockings of two intrinsic hydrodynamic modes of a convecting 3 He-superfluid- 4 He mixture by independently varying the Rayleigh and Prandtl numbers. We establish points on the critical line in this parameter space using a transient technique to locate the spiral-node transition in the interior of three resonance horns. Universal scaling is demonstrated at winding numbers with golden mean tails by computing the f(α) singularity spectrum

Rayleigh scattering in few-mode optical fibers.

Science.gov (United States)

Wang, Zhen; Wu, Hao; Hu, Xiaolong; Zhao, Ningbo; Mo, Qi; Li, Guifang

2016-10-24

The extremely low loss of silica fibers has enabled the telecommunication revolution, but single-mode fiber-optic communication systems have been driven to their capacity limits. As a means to overcome this capacity crunch, space-division multiplexing (SDM) using few-mode fibers (FMF) has been proposed and demonstrated. In single-mode optical fibers, Rayleigh scattering serves as the dominant mechanism for optical loss. However, to date, the role of Rayleigh scattering in FMFs remains elusive. Here we establish and experimentally validate a general model for Rayleigh scattering in FMFs. Rayleigh backscattering not only sets the intrinsic loss limit for FMFs but also provides the theoretical foundation for few-mode optical time-domain reflectometry, which can be used to probe perturbation-induced mode-coupling dynamics in FMFs. We also show that forward inter-modal Rayleigh scattering ultimately sets a fundamental limit on inter-modal-crosstalk for FMFs. Therefore, this work not only has implications specifically for SDM systems but also broadly for few-mode fiber optics and its applications in amplifiers, lasers, and sensors in which inter-modal crosstalk imposes a fundamental performance limitation.

Bivariate Rayleigh Distribution and its Properties

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Ahmad Saeed Akhter

2007-01-01

Full Text Available Rayleigh (1880 observed that the sea waves follow no law because of the complexities of the sea, but it has been seen that the probability distributions of wave heights, wave length, wave induce pitch, wave and heave motions of the ships follow the Rayleigh distribution. At present, several different quantities are in use for describing the state of the sea; for example, the mean height of the waves, the root mean square height, the height of the “significant waves” (the mean height of the highest one-third of all the waves the maximum height over a given interval of the time, and so on. At present, the ship building industry knows less than any other construction industry about the service conditions under which it must operate. Only small efforts have been made to establish the stresses and motions and to incorporate the result of such studies in to design. This is due to the complexity of the problem caused by the extensive variability of the sea and the corresponding response of the ships. Although the problem appears feasible, yet it is possible to predict service conditions for ships in an orderly and relatively simple manner Rayleigh (1980 derived it from the amplitude of sound resulting from many independent sources. This distribution is also connected with one or two dimensions and is sometimes referred to as “random walk” frequency distribution. The Rayleigh distribution can be derived from the bivariate normal distribution when the variate are independent and random with equal variances. We try to construct bivariate Rayleigh distribution with marginal Rayleigh distribution function and discuss its fundamental properties.

Fully determined scaling laws for volumetrically heated convective systems, a tool for assessing habitability of exoplanets

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Vilella, Kenny; Kaminski, Edouard

2017-05-01

The long-term habitability of a planet rises from its ability to generate and maintain an atmosphere through partial melting and volcanism. This question has been mainly addressed in the framework of plate tectonics, which may be too specific to apply to the wide range of internal dynamics expected for exoplanets, and even to the thermal evolution of the early Earth. Here we propose a more general theoretical approach of convection to build a regime diagram giving the conditions for partial melting to occur, in planetary bodies, as a function of key parameters that can be estimated for exoplanets, their size and internal heating rate. To that aim, we introduce a refined view of the Thermal Boundary Layer (TBL) in a convective system heated from within, that focuses on the temperature and thickness of the TBL at the top of the hottest temperature profiles, along which partial melting shall first occur. This ;Hottest Thermal Boundary Layer; (HotTBL) is first characterized using fully theoretical scaling laws based on the dynamics of thermal boundary layers. These laws are the first ones proposed in the literature that do not rely on empirical determinations of dimensionless constants and that apply to both low Rayleigh and high Rayleigh convective regimes. We show that the scaling laws can be successfully applied to planetary bodies by comparing their predictions to full numerical simulations of the Moon. We then use the scaling laws to build a regime diagram for exoplanets. Combined with estimates of internal heating in exoplanets, the regime diagram predicts that in the habitable zone partial melting occurs in planets younger than the Earth.

Criterios para el inicio de la convección y la formación de estructuras coherentes sobre Camagüey, Cuba Criteria for the onset of convection and the formation of coherent structures over Camaguey, Cuba

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Nivian Quintana Rodríguez

2011-09-01

Full Text Available São apresentados os resultados de uma investigação sobre o processo de convecção de Rayleigh - Bénard partindo do cálculo dos números adimensionais de Rayleigh (Ra e de Richardson (Ri, com o objetivo de encontrar critérios que sejam representativos do disparo da convecção nas condições tropicais e insulares de Cuba. Os resultados são comparados com os obtidos empregando-se a técnica de ondeleta, e as observações de nebulosidade obtidas das imagens de satélites meteorológicos. Utilizaram-se as medições do mês de Junho do ano 2007 na torre de gradiente em Camagüey, e foram obtidos resultados como o número Ra crítico, (Ra = 1.32 x 10³. A velocidade vertical positiva foi empregada como condição necessária para o disparo da convecção. Encontrou-se que o Ra é um parâmetro indicador do tipo de convecção que deve formar-se, enquanto que o Ri é um indicador de sua intensidade.Results from an investigation on the physical process of Rayleigh-Bernard convection, based on the calculus of the dimensional Rayleigh (Ra and Richardson (Ri numbers, with the objective of finding criteria representative of the onset of convection in Cuba's tropical and insular conditions are shown. The obtained results are compared to those based on the Wavelets Technique and cloudiness derived from meteorological satellite images. Observations on June 2007 at Camagüey gradient Tower were used, and some results were derived, such as the critical (Ra = 1.32 x 10³. Positive value of the vertical velocity was set as the necessary condition for the onset of convection. It was found that Ra is an indicator of the convection type that should form, whereas Ri is an indicator of its intensity.

Conduction and convection heat transfer characteristics of water-based au nanofluids in a square cavity with differentially heated side walls subjected to constant temperatures

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Ternik Primož

2014-01-01

Full Text Available The present work deals with the natural convection in a square cavity filled with the water-based Au nanofluid. The cavity is heated on the vertical and cooled from the adjacent wall, while the other two horizontal walls are adiabatic. The governing differential equations have been solved by the standard finite volume method and the hydrodynamic and thermal fields were coupled together using the Boussinesq approximation. The main objective of this study is to investigate the influence of the nanoparticles’ volume fraction on the heat transfer characteristics of Au nanofluids at the given base fluid’s (i.e. water Rayleigh number. Accurate results are presented over a wide range of the base fluid Rayleigh number and the volume fraction of Au nanoparticles. It is shown that adding nanoparticles in a base fluid delays the onset of convection. Contrary to what is argued by many authors, we show by numerical simulations that the use of nanofluids can reduce the heat transfer rate instead of increasing it.

Open Channel Natural Convection Heat Transfer on a Vertical Finned Plate

International Nuclear Information System (INIS)

Park, Joo Hyun; Heo, Jeong Hwan; Chung, Bum Jin

2013-01-01

The natural convection heat transfer of vertical plate fin was investigated experimentally. Heat transfer systems were replaced by mass-transfer systems, based on the analogy concept. The experimental results lie within the predictions of the existing heat transfer correlations of plate-fin for the natural convections. An overlapped thermal boundary layers caused increasing heat transfer, and an overlapped momentum boundary layers caused decreasing heat transfer. As the fin height increases, heat transfer was enhanced due to increased inflow from the open side of the fin spacing. When fin spacing and fin height are large, heat transfer was unaffected by the fin spacing and fin height. Passive cooling by natural convection becomes more and more important for the nuclear systems as the station black out really happened at the Fukushima NPPs. In the RCCS (Reactor Cavity Cooling System) of a VHTR (Very High Temperature Reactor), natural convection cooling through duct system is adopted. In response to the stack failure event, extra cooling capacity adopting the fin array has to be investigated. The finned plate increases the surface area and the heat transfer increases. However, the plate of fin arrays may increase the pressure drop and the heat transfer decreases. Therefore, in order to enhance the passive cooling with fin arrays, the parameters for the fin arrays should be optimized. According to Welling and Wooldridge, a natural convection on vertical plate fin is function of Gr, Pr, L, t, S, and H. The present work investigated the natural convection heat transfer of a vertical finned plate with varying the fin height and the fin spacing. In order achieve high Rayleigh numbers, an electroplating system was employed and the mass transfer rates were measured using a copper sulfate electroplating system based on the analogy concept

Experimental study of the steady natural convection in a horizontal annulus with irregular boundaries

International Nuclear Information System (INIS)

Boyd, R.D.

1980-01-01

The natural convective heat transfer across an annulus with irregular boundaries was studied using a Mach-Zehnder interferometer. The annulus was formed by an inner hexagonal cylinder and an outer concentric circular cylinder. This configuration models, in two dimensions, a liquid metal fast breeder reactor spent fuel subassembly inside a shipping container. During the test, the annulus was filled with a single gas, either neon, air, argon, krypton, or xenon, at a pressure of about 0.5 MPa. From temperature measurements, both local and mean Nusselt numbers (Nu/sub Δ/) at the surface of the inner cylinder were evaluated, with the mean Rayleigh number (anti Ra/sub Δ/) varying from 4.54 x 10 4 to 0.915 x 10 6 (Δ is the local gas width). The data correlation for the mean Nusselt and Rayleigh numbers is given by anti Nu/sub Δ/ = 0.183 anti Ra/sub Δ/ 0 310

Convection due to an unstable density difference across a permeable membrane

Science.gov (United States)

Puthenveettil, Baburaj A.; Arakeri, Jaywant H.

We study natural convection driven by unstable concentration differences of sodium chloride (NaCl) across a horizontal permeable membrane at Rayleigh numbers (Ra) of 1010 to 1011 and Schmidt number (Sc)=600. A layer of brine lies over a layer of distilled water, separated by the membrane, in square-cross-section tanks. The membrane is permeable enough to allow a small flow across it at higher driving potentials. Based on the predominant mode of transport across the membrane, three regimes of convection, namely an advection regime, a diffusion regime and a combined regime, are identified. The near-membrane flow in all the regimes consists of sheet plumes formed from the unstable layers of fluid near the membrane. In the advection regime observed at higher concentration differences (Bb) show a common log-normal probability density function at all Ra. We propose a phenomenology which predicts /line{lambda}_b sqrt{Z_w Z_{V_i}}, where Zw and Z_{V_i} are, respectively, the near-wall length scales in Rayleighnard convection (RBC) and due to the advection velocity. In the combined regime, which occurs at intermediate values of C/2)4/3. At lower driving potentials, in the diffusion regime, the flux scaling is similar to that in turbulent RBC.

Rayleigh scattering and depolarization ratio in linear alkylbenzene

International Nuclear Information System (INIS)

Liu, Qian; Zhou, Xiang; Huang, Wenqian; Zhang, Yuning; Wu, Wenjie; Luo, Wentai; Yu, Miao; Zheng, Yangheng; Zhou, Li; Cao, Jun; Wang, Yifang

2015-01-01

It is planned to use linear alkylbenzene (LAB) as the organic solvent for the Jiangmen Underground Neutrino Observatory (JUNO) liquid scintillator detectors, due to its ultra-transparency. However, the current Rayleigh scattering length calculation for LAB disagrees with the experimental measurement. This paper reports for the first time that the Rayleigh scattering of LAB is anisotropic, with a depolarization ratio of 0.31±0.01(stat.)±0.01(sys.). We use an indirect method for Rayleigh scattering measurement with the Einstein–Smoluchowski–Cabannes formula, and the Rayleigh scattering length of LAB is determined to be 28.2±1.0 m at 430 nm

Mixed convection of nanofluids in a lid-driven rough cavity

Science.gov (United States)

Guo, Zhimeng; Wang, Jinyu; Mozumder, Aloke K.; Das, Prodip K.

2017-06-01

Mixed convection heat transfer and fluid flow of air, water or oil in enclosures have been studied extensively using experimental and numerical means for many years due to their ever-increasing applications in many engineering fields. In comparison, little effort has been given to the problem of mixed convection of nanofluids in spite of several applications in solar collectors, electronic cooling, lubrication technologies, food processing, and nuclear reactors. Mixed convection of nanofluids is a challenging problem due to the complex interactions among inertia, viscous, and buoyancy forces. In this study, mixed convection of nanofluids in a lid-driven square cavity with sinusoidal roughness elements at the bottom is studied numerically using the Navier-Stokes equations with the Boussinesq approximation. The numerical model is developed using commercial finite volume software ANSYS-FLUENT for Al2O3-water and CuO-water nanofluids inside a square cavity with various roughness elements. The effects of number and amplitude of roughness elements on the heat transfer and fluid flow are analysed for various volume concentrations of Al2O3 and CuO nanoparticles. The flow fields, temperature fields, and heat transfer rates are examined for different values of Rayleigh and Reynolds numbers. The outcome of this study provides some important insight into the heat transfer behaviour of Al2O3-water and CuO-water nanofluids inside a lid-driven rough cavity. This knowledge can be further used in developing novel geometries with enhanced and controlled heat transfer for solar collectors, electronic cooling, and food processing industries.

Numerical Approach of Coupling Vibration Magneto-convection In Nanofluid

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K Syham

2016-06-01

Full Text Available The objective of our work is to visualize numerically the effect of coupling vibratory excitation and magnetic field on cooling an electronic component or a solar cell (originality of our study in arid and semi-arid area. A square cavity of side H filled with Al2O3-water nanofluid where an electronic component is placed on the bottom horizontal wall is maintained at isothermal hot temperature Th. The top horizontal wall is maintained at a cold temperature Tc. The vertical walls are adiabatic. The equations describing the natural convection flow in the square cavity consist of mass conservation, momentum and energy. For the physical parameters of Al2O3-water nanofluid, we use the Brinkman and Wasp model. Transport equations are solved numerically by finite element method. The results are obtained for Rayleigh number Ra= 105, Hartmann numbers between 0 and 100 and vibratory excitation inclination angle between 0° and 90°. The external magnetic field inclination angle varies between 0° and 90° and the Rayleigh number ratio between 0 and 50.  Results are presented in the form of heat transfer flux ratio and maximum absolute value of stream function.

RAYLEIGH SCATTERING MODELS WITH CORRELATION INTEGRAL

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S. F. Kolomiets

2014-01-01

Full Text Available This article offers one of possible approaches to the use of the classical correlation concept in Rayleigh scattering models. Classical correlation in contrast to three types of correlations corresponding to stochastic point flows opens the door to the efficient explanation of the interaction between periodical structure of incident radiation and discreet stochastic structure of distributed scatters typical for Rayleigh problems.

Chromo-Rayleigh interactions of dark matter

International Nuclear Information System (INIS)

Bai, Yang; Osborne, James

2015-01-01

For a wide range of models, dark matter can interact with QCD gluons via chromo-Rayleigh interactions. We point out that the Large Hadron Collider (LHC), as a gluon machine, provides a superb probe of such interactions. In this paper, we introduce simplified models to UV-complete two effective dark matter chromo-Rayleigh interactions and identify the corresponding collider signatures, including four jets or a pair of di-jet resonances plus missing transverse energy. After performing collider studies for both the 8 TeV and 14 TeV LHC, we find that the LHC can be more sensitive to dark matter chromo-Rayleigh interactions than direct detection experiments and thus provides the best opportunity for future discovery of this class of models.

Numerical study on the effect of temperature oscillations on the crystallization front shape during Czochralski growth of gadolinium gallium garnet crystal

Science.gov (United States)

Faiez, Reza; Rezaei, Yazdan

2017-10-01

Time-dependent, finite volume method calculations of momentum and heat transfer were carried out to investigate the correlation between oscillatory convection and the crystallization front dynamics during the Czochralski (Cz) growth of an oxide material. The present modeling allows us to illustrate the modification of the interface shape during the time period of oscillation of the flow manifesting as the formation of a cold plume beneath the phase boundary. It was shown that the instability mechanism is associated with an irreversible dramatic change in the interface shape, which occurs at a critical Reynolds number significantly lower than that is predicted by the quasi-stationary global model analysis of the Cz growth system. The baroclinic term which appears in the vorticity equation in a rotating stratified fluid is used to describe the numerical results of the model. The properties of the thermal waves were studied in the monitoring points located nearby the interface. The waves are regular but not in fact vertically correlated as observed in the case of baroclinic waves. The Rayleigh-Benard dynamics is suggested to be the predominant mechanism even though the instability is primarily baroclinic.

On the interaction of Rayleigh surface waves with structures

International Nuclear Information System (INIS)

Simpson, I.C.

1976-12-01

A two-dimensional soil-structure interaction analysis is carried out for transient Rayleigh surface waves that are incident on a structure. The structure is modelled by a three-degree of freedom rigid basemat to which is attached a flexible superstructure, modelled by a single mass-spring system. The structural responses to a given Rayleigh wave train are compared with those that would have been obtained if the free-field acceleration-time history had been applied as a normally incident body wave. The results clearly exhibit the 'frequency filtering' effects of the rigid basemat on the incident Rayleigh waves. It is shown that, if seismic excitation of a structure is, in fact, due to Rayleigh surface waves, then an analysis assuming normally incident body waves can considerably over-estimate structural response, both at basemat level for horizontal and vertical oscillations of the superstructure. However, in the examples considered here, relatively large rocking effects were induced by the Rayleigh waves, thus giving maximum horizontal accelerations in the superstructure that were of comparable magnitude for Rayleigh and normally incident body waves. (author)

Nd:YAG Laser-Based Dual-Line Detection Rayleigh Scattering and Current Efforts on UV, Filtered Rayleigh Scattering

Science.gov (United States)

Otugen, M. Volkan; Popovic, Svetozar

1996-01-01

Ongoing research in Rayleigh scattering diagnostics for variable density low speed flow applications and for supersonic flow measurements are described. During the past several years, the focus has been on the development and use of a Nd:YAG-based Rayleigh scattering system with improved signal-to-noise characteristics and with applicability to complex, confined flows. This activity serves other research projects in the Aerodynamics Laboratory which require the non-contact, accurate, time-frozen measurement of gas density, pressure, and temperature (each separately), in a fairly wide dynamic range of each parameter. Recently, with the acquisition of a new seed-injected Nd:YAG laser, effort also has been directed to the development of a high-speed velocity probe based on a spectrally resolved Rayleigh scattering technique.

Direct numerical simulation of vacillation in convection induced by centrifugal buoyancy

Science.gov (United States)

Pitz, Diogo B.; Marxen, Olaf; Chew, John W.

2017-11-01

Flows induced by centrifugal buoyancy occur in industrial systems, such as in the compressor cavities of gas turbines, as well as in flows of geophysical interest. In this numerical study we use direct numerical simulation (DNS) to investigate the transition between the steady waves regime, which is characterized by great regularity, to the vacillation regime, which is critical to understand transition to the fully turbulent regime. From previous work it is known that the onset of convection occurs in the form of pairs of nearly-circular rolls which span the entire axial length of the cavity, with small deviations near the parallel, no-slip end walls. When non-linearity sets in triadic interactions occur and, depending on the value of the centrifugal Rayleigh number, the flow is dominated by either a single mode and its harmonics or by broadband effects if turbulence develops. In this study we increase the centrifugal Rayleigh number progressively and investigate mode interactions during the vacillation regime which eventually lead to chaotic motion. Diogo B. Pitz acknowledges the financial support from the Capes foundation through the Science without Borders program.

Numerical investigation on mixed convection flow in a trapezoidal cavity heated from below

International Nuclear Information System (INIS)

Tmartnhad, Ilham; El Alami, Mustapha; Najam, Mostafa; Oubarra, Abdelaziz

2008-01-01

A numerical study of mixed convection from a trapezoidal cavity is carried out. Two openings are adjusted on the plates of the cavity. The inlet opening is horizontal or vertical, while the outlet one is placed horizontally on the bottom wall. The Navier-Stokes equations are solved using a control volume method and the SIMPLEC algorithm is used for the treatment of pressure-velocity coupling. Special emphasis is given to detail the effect of the Reynolds number on the heat transfer generated by mixed convection. The results are given for the parameters of control as, Rayleigh number (Ra = 10 5 ), Prandtl number (Pr = 0.72), the inlet and outlet opening width are respectively (C 1 = 0.38 and C 2 = 0.25), the inclination of the tilted wall (θ = 22 deg. ) and Reynolds number (10 ≤ Re ≤ 1000). The results show that the flow structure and the heat transfer depends significantly on the inlet opening site. Two principal kinds of the problem solution are raised

Rayleigh scattering in an emitter-nanofiber-coupling system

Science.gov (United States)

Tang, Shui-Jing; Gao, Fei; Xu, Da; Li, Yan; Gong, Qihuang; Xiao, Yun-Feng

2017-04-01

Scattering is a general process in both fundamental and applied physics. In this paper, we investigate Rayleigh scattering of a solid-state-emitter coupled to a nanofiber, by S -matrix-like theory in k -space description. Under this model, both Rayleigh scattering and dipole interaction are studied between a two-level artificial atom embedded in a nanocrystal and fiber modes (guided and radiation modes). It is found that Rayleigh scattering plays a critical role in the transport properties and quantum statistics of photons. On the one hand, Rayleigh scattering produces the transparency in the optical transmitted field of the nanofiber, accompanied by the change of atomic phase, population, and frequency shift. On the other hand, the interference between two kinds of scattering fields by Rayleigh scattering and dipole transition modifies the photon statistics (second-order autocorrelation function) of output fields, showing a strong wavelength dependence. This study provides guidance for the solid-state emitter acting as a single-photon source and can be extended to explore the scattering effect in many-body physics.

Research of heat transfer of staggered horizontal bundles of finned tubes at free air convection

Science.gov (United States)

Novozhilova, A. V.; Maryna, Z. G.; Samorodov, A. V.; Lvov, E. A.

2017-11-01

The study of free-convective processes is important because of the cooling problem in many machines and systems, where other ways of cooling are impossible or impractical. Natural convective processes are common in the steam turbine air condensers of electric power plants located within the city limits, in dry cooling towers of circulating water systems, in condensers cooled by air and water, in radiators cooling oil of power electric transformers, in emergency cooling systems of nuclear reactors, in solar power, as well as in air-cooling of power semiconductor energy converters. All this makes actual the synthesis of the results of theoretical and experimental research of free convection for heat exchangers with finned tube bundles. The results of the study of free-convection heat transfer for two-, three- and four-row staggered horizontal bundles of industrial bimetallic finned tubes with finning factor of 16.8 and equilateral tubes arrangement are presented. Cross and diagonal steps in the bundles are the same: 58; 61; 64; 70; 76; 86; 100 mm, which corresponds to the relative steps: 1.042; 1.096; 1.152; 1.258; 1.366; 1.545; 1.797. These steps are standardized for air coolers. An equation for calculating the free-convection heat transfer, taking into account the influence of geometrical parameters in the range of Rayleigh number from 30,000 to 350,000 with an average deviation of ± 4.8%, has been obtained. The relationship presented in the article allows designing a wide range of air coolers for various applications, working in the free convection modes.

Initial investigations of microscale cellular convection in an equatorial marine atmospheric boundary layer revealed by lidar

Science.gov (United States)

Cooper, D. I.; Eichinger, W. E.; Ecke, R. E.; Kao, J. C. Y.; Reisner, J. M.; Tellier, L. L.

During the Combined Sensor Program (CSP) in March of 1996, the Los Alamos National Laboratory (LANL) fielded an advanced scanning Raman lidar. The lidar was part of a larger suite of micrometeorological sensors to quantify processes associated with the ocean-atmosphere interface, including intermittency and coherent atmospheric features in the “warm pool” of the Tropical Western Pacific (TWP) near Manus Island (2° S. lat, 147° E. long). Initial inspection of the data has revealed excellent information on the microscale vertical and horizontal spatial and temporal structure of the equatorial Marine Atmospheric Boundary Layer (MABL). The data from this experiment have added to the increasing body of measurements on surface layer convection and intermittency including, for the first time, the observation of microscale cellular convective structures such as hexagonal patterns associated with Rayleigh-Bénard cells.

Multiple zonal jets and convective heat transport barriers in a quasi-geostrophic model of planetary cores

Science.gov (United States)

Guervilly, C.; Cardin, P.

2017-10-01

We study rapidly rotating Boussinesq convection driven by internal heating in a full sphere. We use a numerical model based on the quasi-geostrophic approximation for the velocity field, whereas the temperature field is 3-D. This approximation allows us to perform simulations for Ekman numbers down to 10-8, Prandtl numbers relevant for liquid metals (˜10-1) and Reynolds numbers up to 3 × 104. Persistent zonal flows composed of multiple jets form as a result of the mixing of potential vorticity. For the largest Rayleigh numbers computed, the zonal velocity is larger than the convective velocity despite the presence of boundary friction. The convective structures and the zonal jets widen when the thermal forcing increases. Prograde and retrograde zonal jets are dynamically different: in the prograde jets (which correspond to weak potential vorticity gradients) the convection transports heat efficiently and the mean temperature tends to be homogenized; by contrast, in the cores of the retrograde jets (which correspond to steep gradients of potential vorticity) the dynamics is dominated by the propagation of Rossby waves, resulting in the formation of steep mean temperature gradients and the dominance of conduction in the heat transfer process. Consequently, in quasi-geostrophic systems, the width of the retrograde zonal jets controls the efficiency of the heat transfer.

Comparison of CFD Natural Convection and Conduction-only Models for Heat Transfer in the Yucca Mountain Project Drifts

International Nuclear Information System (INIS)

Hadgu, T.; Webb, S.; Itamura, M.

2004-01-01

Yucca Mountain, Nevada has been designated as the nation's high-level radioactive waste repository and the U.S. Department of Energy has been approved to apply to the U.S. Nuclear Regulatory Commission for a license to construct a repository. Heat transfer in the Yucca Mountain Project (YMP) drift enclosures is an important aspect of repository waste emplacement. Canisters containing radioactive waste are to be emplaced in tunnels drilled 500 m below the ground surface. After repository closure, decaying heat is transferred from waste packages to the host rock by a combination of thermal radiation, natural convection and conduction heat transfer mechanism?. Current YMP mountain-scale and drift-scale numerical models often use a simplified porous medium code to model fluid and heat flow in the drift openings. To account for natural convection heat transfer, the thermal conductivity of the air was increased in the porous medium model. The equivalent thermal conductivity, defined as the ratio of total heat flow to conductive heat flow, used in the porous media models was based on horizontal concentric cylinders. Such modeling does not effectively capture turbulent natural convection in the open spaces as discussed by Webb et al. (2003) yet the approach is still widely used on the YMP project. In order to mechanistically model natural convection conditions in YMP drifts, the computational fluid dynamics (CFD) code FLUENT (Fluent, Incorporated, 2001) has been used to model natural convection heat transfer in the YMP emplacement drifts. A two-dimensional (2D) model representative of YMP geometry (e.g., includes waste package, drip shield, invert and drift wall) has been developed and numerical simulations made (Francis et al., 2003). Using CFD simulation results for both natural convection and conduction-only heat transfer in a single phase, single component fluid, equivalent thermal conductivities have been calculated for different Rayleigh numbers. Correlation

Computational simulation of turbulent natural convection in a corium pool

International Nuclear Information System (INIS)

Vieira, Camila B.; Su, Jian; Niceno, Bojan

2013-01-01

After a severe accident in a nuclear power plant, the total thermal loading on the vessel of a nuclear reactor is controlled by the convective heat transfer. Taking that fact into account, this work aimed to analyze the turbulent natural convection inside a representative lower head cavity. By means of an open-source CFD code, OpenFOAM (Open Field Operation and Manipulation), numerical simulations were performed to investigate a volumetrically heated fluid (Pr = 7.0) at internal Rayleigh (Ra) numbers ranging from 10 8 to 10 15 . Bearing in mind that severe accident scenario and the physical-chemical effects are many and complex, the fluid analyzed was considered Newtonian, with constant physical properties, homogeneous and single phase. Even working with that simplifications, the modeling of turbulent natural convection has posed a considerable challenge for the Reynolds Averaged Navier-Stokes (RANS) equations based models, not only because of the complete unsteadiness of the flow and the strong turbulence effects in the near wall regions, but also because of the correct treatment of the turbulent heat fluxes (θu i ). So, this work outlined three approaches for treating the turbulent heat fluxes: the Simple Gradient Diffusion Hypothesis (SGDH), the Generalized Gradient Diffusion Hypothesis (GGDH) and the Algebraic Flux Model (AFM). Simulations performed at BALI test based geometry with a four equations model, k-ε-v 2 -f (commonly called as v 2 -f and V2-f), showed that despite of AFM and GGDH have provided reasonable agreement with experimental data for turbulent natural convection in a differentially heated cavity, they proved to be very unstable for buoyancy-driven flows with internal source in comparison to SGDH model. (author)

Parametric numerical investigaion of natural convection in a heat-generating fluid with phase transitions

Energy Technology Data Exchange (ETDEWEB)

Aksenova, A.E.; Chudanov, V.V.; Strizhov, V.F.; Vabishchevich, P.N. [Institute of Nuclear Safety Russian Academy Science, Moscow (Russian Federation)

1995-09-01

Unsteady natural convection of a heat-generating fluid with phase transitions in the enclosures of a square section with isothermal rigid walls is investigated numerically for a wide range of dimensionless parameters. The quasisteady state solutions of conjugate heat and mass transfer problem are compared with available experimental results. Correlation relations for heat flux distributions at the domain boundaries depending on Rayleigh and Ostrogradskii numbers are obtained. It is shown that generally heat transfer is governed both by natural circulation and crust formation phenomena. Results of this paper may be used for analysis of experiments with prototypic core materials.

Long-term unsteadiness and large-scale structures in Rayleigh-Bénard convection with and without electromagnetic forcing

NARCIS (Netherlands)

Verdoold, J.

2010-01-01

This dissertation focuses on turbulent thermal convection, which occurs in a wide range of (geo)physical situations, like in the atmosphere, the oceans, the interior of stars or planets, and engineering applications, like metal casting or crystal growth processes. In this work, a special type of

Onset of oscillatory binary fluid convection in three-dimensional cells

Energy Technology Data Exchange (ETDEWEB)

Alonso, Arantxa; Batiste, Oriol [Universitat Politecnica de Catalunya, Departament de Fisica Aplicada, Barcelona (Spain)

2004-11-01

The purpose of this work is to investigate the influence of the transverse walls on the onset of convection in a horizontal rectangular cavity of infinite length filled with a binary mixture when heated from below. For the first time we take into account the effect of the third dimension without making any approximation and considering realistic boundary conditions. In previous numerical works the width of the cell was either taken to be infinity (bulk mixtures) or different approximations usually valid in the narrow cell limit were assumed (i.e., Hele-Shaw and non-ideal Hele-Shaw approximations). The results we find show that the presence of the walls has a considerable effect on the onset of convection even for intermediate transverse aspect ratio cells. They also show that the approximations generally assumed fail to reproduce the correct behaviour of the critical parameters in an important range of aspect ratio values when the primary bifurcation is oscillatory. We have compared the critical values of the Rayleigh number and the frequency with those reported in the literature (Ohlsen et al. [1]) and we find a quantitative agreement within the experimental error. (orig.)

Numerical Investigation of the Effect of Magnetic Field on Natural Convection in a Curved-Shape Enclosure

Directory of Open Access Journals (Sweden)

M. Sheikholeslami

2013-01-01

Full Text Available This investigation reports the magnetic field effect on natural convection heat transfer in a curved-shape enclosure. The numerical investigation is carried out using the control volume-based-finite element method (CVFEM. The numerical investigations are performed for various values of Hartmann number and Rayleigh number. The obtained results are depicted in terms of streamlines and isotherms which show the significant effects of Hartmann number on the fluid flow and temperature distribution inside the enclosure. Also, it was found that the Nusselt number decreases with an increase in the Hartmann number.

Measurement of the Cupric Ion Concentration in the Simulation of the Focusing effect

Energy Technology Data Exchange (ETDEWEB)

Moon, Je-Young; Hong, Seung-Hyun; Chung, Bum-Jin [Kyung Hee University, Seoul (Korea, Republic of)

2015-10-15

The Rayleigh number and aspect ratio (H/R) ranged from 8.49x10{sup 7} to 5.43x10{sup 9} and 0.135 to 0.541 respectively. In order to simulate the different temperature conditions of top and side wall, an electrical resistance was attached to the top wall so that it is mimics hotter wall condition. The heat transfer experiments were replaced by mass transfer experiments based on the heat and mass transfer analogy concept. A sulfuric acid-copper sulfate (H{sub 2}SO{sub 4} - CuSO{sub 4}) electroplating system was adopted as the mass transfer system. The experimental study was performed to investigate the focusing effect according to the different temperature conditions and the height in metallic layer. This work devised a method to simulate the different cooling conditions of the top and side walls and adopted an electrical resistance to the top plate. The electrical resistance was varied for the height of side wall. The experimental results agreed well with the Rayleigh-Benard convection correlations of Dropkin and Somerscales and Globe and Dropkin. The heat transfer was enhanced by increasing the electrical resistance and decreasing the height of side wall. The focusing effect at the side wall was improved by the hotter top wall condition. In order to overcome the limitations of mass transfer, this work tried to measure the cupric ion concentration. The methods of concentration measurement are RGB, Brightness, ICP and PIV. The key of RGB, Brightness and PIV method is the clear images of the thermal boundary layer.

Turbulent natural convection between a perforated vertical cylinder and a surrounding array

International Nuclear Information System (INIS)

McEligot, D.M.; Stoots, C.M.; Christenson, W.A.; O'Brien, J.E.; Mecham, D.C.; Lussie, W.G.

1992-01-01

A number of situations can be hypothesized to occur in an advanced or special purpose nuclear reactor such that the core is filled with a gas but there is no forced flow to remove the thermal energy evolved. Experiments were conducted by resistively hearing a vertical circular cylinder of length-to-diameter ratio of about 160 centered inside a concentric perforated tube which was, in turn, surrounded by three larger diameter tubes cooled internally with water flow. The ratio of the test section temperature to the cooling tube temperature was varied up to 2.6; and the Rayleigh number, based on tube diameter and properties evaluated at the cooling tube temperature, ranged from 2.9 x 10 4 to 9.2 x 10 5 . Results indicate that the convective heat transfer parameters for the perforated tube are about fifteen per cent higher than for the smooth bare tube centered in the same position relative to the array. The Nusselt number for convective heat transfer across the annulus between the heated test section and the perforated tube corresponded to parallel laminar flow

Numerical analysis of steady and transient natural convection in an enclosed cavity

Science.gov (United States)

Mehedi, Tanveer Hassan; Tahzeeb, Rahat Bin; Islam, A. K. M. Sadrul

2017-06-01

The paper presents the numerical simulation of natural convection heat transfer of air inside an enclosed cavity which can be helpful to find out the critical width of insulation in air insulated walls seen in residential buildings and industrial furnaces. Natural convection between two walls having different temperatures have been simulated using ANSYS FLUENT 12.0 in both steady and transient conditions. To simulate different heat transfer and fluid flow conditions, Rayleigh number ranging from 103 to 105 has been maintained (i.e. Laminar flow.) In case of steady state analysis, the CFD predictions were in very good agreement with the reviewed literature. Transient simulation process has been performed by using User Defined Functions, where the temperature of the hot wall varies with time linearly. To obtain and compare the heat transfer properties, Nusselt number has been calculated at the hot wall at different conditions. The buoyancy driven flow characteristics have been investigated by observing the flow pattern in a graphical manner. The characteristics of the system at different temperature differences between the wall has been observed and documented.

Study of Rayleigh-Love coupling from Spatial Gradient Observation

Science.gov (United States)

Lin, C. J.; Hosseini, K.; Donner, S.; Vernon, F.; Wassermann, J. M.; Igel, H.

2017-12-01

We present a new method to study Rayleigh-Love coupling. Instead of using seismograms solely, where ground motion is recorded as function of time, we incorporate with rotation and strain, also called spatial gradient where ground is represented as function of distance. Seismic rotation and strain are intrinsic different observable wavefield so are helpful to indentify wave type and wave propagation. A Mw 7.5 earthquake on 29 March 2015 occurred in Kokopo, Papua New Guinea recorded by a dense seismic array at PFO, California are used to obtaint seismic spatial gradient. We firstly estimate time series of azimuthal direction and phase velocity of SH wave and Rayleigh wave by analyzing collocated seismograms and rotations. This result also compares with frequency wavenumber methods using a nearby ANZA seismic array. We find the direction of Rayleigh wave fits well with great-circle back azimuth during wave propagation, while the direction of Love wave deviates from that, especially when main energy of Rayleigh wave arrives. From the analysis of cross-correlation between areal strain and vertical rotation, it reveals that high coherence, either positive or negative, happens at the same time when Love wave deparate from great-circle path. We also find the observed azimuth of Love wave and polarized particle motion of Rayleigh wave fits well with the fast direction of Rayleigh wave, for the period of 50 secs. We conclude the cause of deviated azimuth of Love wave is due to Rayleigh-Love coupling, as surface wave propagates through the area with anisotropic structure.

Thermal convection in dielectric liquids in a cylindrical annulus

Science.gov (United States)

Mutabazi, Innocent; Kang, Changwoo; Meyer, Antoine; Meier, Martin; Egbers, Christoph

2017-11-01

Thermal convection is investigated in a dielectric liquid of thermal expansion coefficient α, kinematic viscosity ν, thermal diffusivity κ and electric permittivity ɛ in a cylindrical annulus of inner radius a and outer radius bwith a radial temperature gradient and a high-frequency electric tension. The coupling between the electric field and the gradient of the permittivity yields the dielectrophoretic force. The control parameters are η = a/b, Pr = ν / κ, the classic Rayleigh number Ra = αΔ T gd3 / νκ , and the electric Rayleigh number L = αΔ T ged3 / νκ The electric gravity ge is the gradient of the electric energy in the condenser. Linear stability analysis shows that for infinite annulus, depending on values of η, Ra and L, critical modes are either hydrodynamic or thermal modes, helical electric modes or columnar vortices. Experiments in an annulus of aspect ratio Γ = 19.6 during parabolic flight campaigns indicate the existence of columns. Columnar vortices result from the competition between Archimedean buoyancy and dielectrophoretic force. Direct numerical simulations in the annulus of Γ = 20 show that the columnar vortices occupy the central part of the annulus, while near the end-zones the flow is laminar and dominated by an azimuthal vorticity. This work was supported by CNRS (LIA ISTROF), CNES and DLR.

Natural convection heat transfer characteristics of the molten metal pool with solidification by boiling coolant

Energy Technology Data Exchange (ETDEWEB)

Cho, Jae Seon; Suh, Kune Yull; Chung, Chang Hyun [Seoul National University, Seoul (Korea, Republic of); Paark, Rae Joon; Kim, Sang Baik [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)

1998-12-31

This paper presents results of experimental studies on the heat transfer and solidification of the molten metal pool with overlying coolant with boiling. The metal pool is heated from the bottom surface and coolant is injected onto the molten metal pool. Ad a result, the crust, which is a solidified layer, may form at the top of the molten metal pool. Heat transfer is accomplished by a conjugate mechanism, which consists of the natural convection of the molten metal pool, the conduction in the crust layer and the convective boiling heat transfer in the coolant. This work examines the crust formation and the heat transfer rate on the molten metal pool with boiling coolant. The simulant molten pool material is tin (Sn) with the melting temperature of 232 deg C. Demineralized water is used as the working coolant. The crust layer thickness was ostensibly varied by the heated bottom surface temperature of the test section, but not much affected by the coolant injection rate. The correlation between the Nusselt number and the Rayleigh number in the molten metal pool region of this study is compared against the crust formation experiment without coolant boiling and the literature correlations. The present experimental results are higher than those from the experiment without coolant boiling, but show general agreement with the Eckert correlation, with some deviations in the high and low ends of the Rayleigh number. This discrepancy is currently attributed to concurrent rapid boiling of the coolant on top of the metal layer. 10 refs., 4 figs., 1 tab. (Author)

Natural convection heat transfer characteristics of the molten metal pool with solidification by boiling coolant

Energy Technology Data Exchange (ETDEWEB)

Cho, Jae Seon; Suh, Kune Yull; Chung, Chang Hyun [Seoul National University, Seoul (Korea, Republic of); Paark, Rae Joon; Kim, Sang Baik [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)

1997-12-31

This paper presents results of experimental studies on the heat transfer and solidification of the molten metal pool with overlying coolant with boiling. The metal pool is heated from the bottom surface and coolant is injected onto the molten metal pool. Ad a result, the crust, which is a solidified layer, may form at the top of the molten metal pool. Heat transfer is accomplished by a conjugate mechanism, which consists of the natural convection of the molten metal pool, the conduction in the crust layer and the convective boiling heat transfer in the coolant. This work examines the crust formation and the heat transfer rate on the molten metal pool with boiling coolant. The simulant molten pool material is tin (Sn) with the melting temperature of 232 deg C. Demineralized water is used as the working coolant. The crust layer thickness was ostensibly varied by the heated bottom surface temperature of the test section, but not much affected by the coolant injection rate. The correlation between the Nusselt number and the Rayleigh number in the molten metal pool region of this study is compared against the crust formation experiment without coolant boiling and the literature correlations. The present experimental results are higher than those from the experiment without coolant boiling, but show general agreement with the Eckert correlation, with some deviations in the high and low ends of the Rayleigh number. This discrepancy is currently attributed to concurrent rapid boiling of the coolant on top of the metal layer. 10 refs., 4 figs., 1 tab. (Author)

Effects of shock waves on Rayleigh-Taylor instability

International Nuclear Information System (INIS)

Zhang Yongtao; Shu Chiwang; Zhou Ye

2006-01-01

A numerical simulation of two-dimensional compressible Navier-Stokes equations using a high-order weighted essentially nonoscillatory finite difference shock capturing scheme is carried out in this paper, to study the effect of shock waves on the development of Rayleigh-Taylor instability. Shocks with different Mach numbers are introduced ahead or behind the Rayleigh-Taylor interface, and their effect on the transition to instability is demonstrated and compared. It is observed that shock waves can speed up the transition to instability for the Rayleigh-Taylor interface significantly. Stronger shocks are more effective in this speed-up process

Dynamical role of Ekman pumping in rapidly rotating convection

Science.gov (United States)

Stellmach, Stephan; Julien, Keith; Cheng, Jonathan; Aurnou, Jonathan

2015-04-01

The exact nature of the mechanical boundary conditions (i.e. no-slip versus stress-free) is usually considered to be of secondary importance in the rapidly rotating parameter regime characterizing planetary cores. While they have considerable influence for the Ekman numbers achievable in today's global simulations, for planetary values both the viscous Ekman layers and the associated secondary flows are generally expected to become negligibly small. In fact, usually the main purpose of using stress-free boundary conditions in numerical dynamo simulations is to suppress unrealistically large friction and pumping effects. In this study, we investigate the influence of the mechanical boundary conditions on core convection systematically. By restricting ourselves to the idealized case of rapidly rotating Rayleigh-Bénard convection, we are able to combine results from direct numerical simulations (DNS), laboratory experiments and asymptotic theory into a coherent picture. Contrary to the general expectation, we show that the dynamical effects of Ekman pumping increase with decreasing Ekman number over the investigated parameter range. While stress-free DNS results converge to the asymptotic predictions, both no-slip simulations and laboratory experiments consistently reveal increasingly large deviations from the existing asymptotic theory based on dynamically passive Ekman layers. The implications of these results for core dynamics are discussed briefly.

Effects of radial distribution of entropy diffusivity on critical modes of anelastic thermal convection in rotating spherical shells

Science.gov (United States)

Sasaki, Youhei; Takehiro, Shin-ichi; Ishiwatari, Masaki; Yamada, Michio

2018-03-01

Linear stability analysis of anelastic thermal convection in a rotating spherical shell with entropy diffusivities varying in the radial direction is performed. The structures of critical convection are obtained in the cases of four different radial distributions of entropy diffusivity; (1) κ is constant, (2) κT0 is constant, (3) κρ0 is constant, and (4) κρ0T0 is constant, where κ is the entropy diffusivity, T0 is the temperature of basic state, and ρ0 is the density of basic state, respectively. The ratio of inner and outer radii, the Prandtl number, the polytropic index, and the density ratio are 0.35, 1, 2, and 5, respectively. The value of the Ekman number is 10-3 or 10-5 . In the case of (1), where the setup is same as that of the anelastic dynamo benchmark (Jones et al., 2011), the structure of critical convection is concentrated near the outer boundary of the spherical shell around the equator. However, in the cases of (2), (3) and (4), the convection columns attach the inner boundary of the spherical shell. A rapidly rotating annulus model for anelastic systems is developed by assuming that convection structure is uniform in the axial direction taking into account the strong effect of Coriolis force. The annulus model well explains the characteristics of critical convection obtained numerically, such as critical azimuthal wavenumber, frequency, Rayleigh number, and the cylindrically radial location of convection columns. The radial distribution of entropy diffusivity, or more generally, diffusion properties in the entropy equation, is important for convection structure, because it determines the distribution of radial basic entropy gradient which is crucial for location of convection columns.

QUADRO: A SUPERVISED DIMENSION REDUCTION METHOD VIA RAYLEIGH QUOTIENT OPTIMIZATION.

Science.gov (United States)

Fan, Jianqing; Ke, Zheng Tracy; Liu, Han; Xia, Lucy

We propose a novel Rayleigh quotient based sparse quadratic dimension reduction method-named QUADRO (Quadratic Dimension Reduction via Rayleigh Optimization)-for analyzing high-dimensional data. Unlike in the linear setting where Rayleigh quotient optimization coincides with classification, these two problems are very different under nonlinear settings. In this paper, we clarify this difference and show that Rayleigh quotient optimization may be of independent scientific interests. One major challenge of Rayleigh quotient optimization is that the variance of quadratic statistics involves all fourth cross-moments of predictors, which are infeasible to compute for high-dimensional applications and may accumulate too many stochastic errors. This issue is resolved by considering a family of elliptical models. Moreover, for heavy-tail distributions, robust estimates of mean vectors and covariance matrices are employed to guarantee uniform convergence in estimating non-polynomially many parameters, even though only the fourth moments are assumed. Methodologically, QUADRO is based on elliptical models which allow us to formulate the Rayleigh quotient maximization as a convex optimization problem. Computationally, we propose an efficient linearized augmented Lagrangian method to solve the constrained optimization problem. Theoretically, we provide explicit rates of convergence in terms of Rayleigh quotient under both Gaussian and general elliptical models. Thorough numerical results on both synthetic and real datasets are also provided to back up our theoretical results.

Numerical Simulation of Natural Convection in a Vertically Installed Wet Thermal Insulator

Energy Technology Data Exchange (ETDEWEB)

Bae, Youngmin; Kim, Seong H.; Seo, Jae K.; Kim, Young I. [KAERI, Daejeon (Korea, Republic of)

2016-05-15

Natural convection in an enclosure with disconnected vertical partitions inside is thought of as major concerns in the design of thermal insulators. For example, in a system-integrated modular advanced reactor (SMART), vertical partitions are disposed inside the so-called wet thermal insulator with gaps at the top and bottom ends to compensate for thermal expansion . In such a case, buoyancy driven flow circulates throughout the enclosure, i.e., fluid rises up in the hot-side layers, passing through the gap at the top, moving downward in the vertical channels near the cold side, and returning to the hot-side layers via the gap at the bottom. Compared with the case of connected partitions, this often causes an undesirable increase in the circulation flow rate and heat transfer within the enclosure, thus deteriorating the thermal insulation performance. In this study, laminar natural convection in a tall rectangular enclosure with disconnected vertical partitions inside is investigated numerically. The effects of main governing parameters such as the modified Rayleigh number, enclosure height to width ratio, and number of fluid layers are scrutinized along with a discussion of the heat transfer regimes. This study investigates the laminar natural convection in a tall rectangular enclosure having isothermal side walls of different temperatures and insulated top and bottom walls with disconnected vertical partitions inside.

Numerical Simulation of Natural Convection in a Vertically Installed Wet Thermal Insulator

International Nuclear Information System (INIS)

Bae, Youngmin; Kim, Seong H.; Seo, Jae K.; Kim, Young I.

2016-01-01

Natural convection in an enclosure with disconnected vertical partitions inside is thought of as major concerns in the design of thermal insulators. For example, in a system-integrated modular advanced reactor (SMART), vertical partitions are disposed inside the so-called wet thermal insulator with gaps at the top and bottom ends to compensate for thermal expansion . In such a case, buoyancy driven flow circulates throughout the enclosure, i.e., fluid rises up in the hot-side layers, passing through the gap at the top, moving downward in the vertical channels near the cold side, and returning to the hot-side layers via the gap at the bottom. Compared with the case of connected partitions, this often causes an undesirable increase in the circulation flow rate and heat transfer within the enclosure, thus deteriorating the thermal insulation performance. In this study, laminar natural convection in a tall rectangular enclosure with disconnected vertical partitions inside is investigated numerically. The effects of main governing parameters such as the modified Rayleigh number, enclosure height to width ratio, and number of fluid layers are scrutinized along with a discussion of the heat transfer regimes. This study investigates the laminar natural convection in a tall rectangular enclosure having isothermal side walls of different temperatures and insulated top and bottom walls with disconnected vertical partitions inside

Rayleigh scattering from ions near threshold

International Nuclear Information System (INIS)

Roy, S.C.; Gupta, S.K.S.; Kissel, L.; Pratt, R.H.

1988-01-01

Theoretical studies of Rayleigh scattering of photons from neon atoms with different degrees of ionization, for energies both below and above the K-edges of the ions, are presented. Some unexpected structures both in Rayleigh scattering and in photoionization from neutral and weakly ionized atoms, very close to threshold, have been reported. It has recently been realized that some of the predicted structures may have a nonphysical origin and are due to the limitation of the independent-particle model and also to the use of a Coulombic Latter tail. Use of a K-shell vacancy potential - in which an electron is assumed to be removed from the K-shell - in calculating K-shell Rayleigh scattering amplitudes removes some of the structure effects near threshold. We present in this work a discussion of scattering angular distributions and total cross sections, obtained utilizing vacancy potentials, and compare these predictions with those previously obtained in other potential model. (author) [pt

Stabilization of the Rayleigh-Taylor instability by convection and thermal conduction in smooth density gradient: WKB analysis

International Nuclear Information System (INIS)

Bud'ko, A.B.; Liberman, M.A.; Bondarenko, E.A.

1992-01-01

Since development of the RT modes in the ablatively accelerated plasma of laser targets imposes crucial limitations on symmetry of spherical implosions and hence on energy cumulation, it has been the subject of intensive numerical and analytical analysis in the recent years, particularly in the context of inertial confinement fusion. Recent thin-foil ablative-acceleration experiments as well as the results of 2D numerical simulations demonstrated substantial reduction of the instability growth rates compared with the classical theory predictions up to the total stabilization in the short-wavelength limit. The numerical results indicated that the main stabilization mechanism is convection. To derive the scaling laws for the RT growth rates and cut-off wavenumbers in the wide range of flow parameters, analytical solutions attract special interest. The analytical approach based on the discontinuity model was developed to analyze the reduction of the RT growth rates by the plasma convective flow and the thermal conductivity effects. The following major problem arises in the discontinuity approximation, which leaves the solution undetermined: the number of the boundary conditions on the perturbed ablation surface is not sufficient to derive the dispersion equation. One needs additional boundary conditions not associated with the conservation laws on the discontinuity surface to close the system of linearized equations for small perturbations. The stabilization effect of highly structured hydrodynamic profiles was studied by Mikaelian and Munro for a stationary plasma. Nevertheless, no reasonable analytical model was constructed taking into account the combined convective, thermal conductivity and density gradient reduction of the RT growth rates. In this report we develop the analytical approach based on the WKB approximation to analyze the stabilization of the RT modes in plasma with smooth density and velocity gradients. (author) 9 refs., 1 fig

Natural convection heat transfer for a staggered array of heated, horizontal cylinders within a rectangular enclosure

Energy Technology Data Exchange (ETDEWEB)

Triplett, C.E.

1996-12-01

This thesis presents the results of an experimental investigation of natural convection heat transfer in a staggered array of heated cylinders, oriented horizontally within a rectangular enclosure. The main purpose of this research was to extend the knowledge of heat transfer within enclosed bundles of spent nuclear fuel rods sealed within a shipping or storage container. This research extends Canaan`s investigation of an aligned array of heated cylinders that thermally simulated a boiling water reactor (BWR) spent fuel assembly sealed within a shipping or storage cask. The results are presented in terms of piecewise Nusselt-Rayleigh number correlations of the form Nu = C(Ra){sup n}, where C and n are constants. Correlations are presented both for individual rods within the array and for the array as a whole. The correlations are based only on the convective component of the heat transfer. The radiative component was calculated with a finite-element code that used measured surface temperatures, rod array geometry, and measured surface emissivities as inputs. The correlation results are compared to Canaan`s aligned array results and to other studies of natural convection in horizontal tube arrays.

Natural convection heat transfer for a staggered array of heated, horizontal cylinders within a rectangular enclosure

International Nuclear Information System (INIS)

Triplett, C.E.

1996-12-01

This thesis presents the results of an experimental investigation of natural convection heat transfer in a staggered array of heated cylinders, oriented horizontally within a rectangular enclosure. The main purpose of this research was to extend the knowledge of heat transfer within enclosed bundles of spent nuclear fuel rods sealed within a shipping or storage container. This research extends Canaan's investigation of an aligned array of heated cylinders that thermally simulated a boiling water reactor (BWR) spent fuel assembly sealed within a shipping or storage cask. The results are presented in terms of piecewise Nusselt-Rayleigh number correlations of the form Nu = C(Ra) n , where C and n are constants. Correlations are presented both for individual rods within the array and for the array as a whole. The correlations are based only on the convective component of the heat transfer. The radiative component was calculated with a finite-element code that used measured surface temperatures, rod array geometry, and measured surface emissivities as inputs. The correlation results are compared to Canaan's aligned array results and to other studies of natural convection in horizontal tube arrays

Computational simulation of turbulent natural convection in a corium pool

Energy Technology Data Exchange (ETDEWEB)

Vieira, Camila B.; Su, Jian, E-mail: camila@lasme.coppe.ufrj.br, E-mail: sujian@lasme.coppe.ufrj.br [Coordenacao dos Cursos de Pos-Graduacao em Engenharia (COPPE/UFRJ), Rio de Janeiro, RJ (Brazil). Programa de Engenharia Nuclear; Niceno, Bojan, E-mail: bojan.niceno@psi.ch [Paul Scherrer Institut (PSI), Villigen (Switzerland). Nuclear Energy and Safety

2013-07-01

After a severe accident in a nuclear power plant, the total thermal loading on the vessel of a nuclear reactor is controlled by the convective heat transfer. Taking that fact into account, this work aimed to analyze the turbulent natural convection inside a representative lower head cavity. By means of an open-source CFD code, OpenFOAM (Open Field Operation and Manipulation), numerical simulations were performed to investigate a volumetrically heated fluid (Pr = 7.0) at internal Rayleigh (Ra) numbers ranging from 10{sup 8} to 10{sup 15}. Bearing in mind that severe accident scenario and the physical-chemical effects are many and complex, the fluid analyzed was considered Newtonian, with constant physical properties, homogeneous and single phase. Even working with that simplifications, the modeling of turbulent natural convection has posed a considerable challenge for the Reynolds Averaged Navier-Stokes (RANS) equations based models, not only because of the complete unsteadiness of the flow and the strong turbulence effects in the near wall regions, but also because of the correct treatment of the turbulent heat fluxes (θu{sub i}). So, this work outlined three approaches for treating the turbulent heat fluxes: the Simple Gradient Diffusion Hypothesis (SGDH), the Generalized Gradient Diffusion Hypothesis (GGDH) and the Algebraic Flux Model (AFM). Simulations performed at BALI test based geometry with a four equations model, k-ε-v{sup 2} -f (commonly called as v{sup 2}-f and V2-f), showed that despite of AFM and GGDH have provided reasonable agreement with experimental data for turbulent natural convection in a differentially heated cavity, they proved to be very unstable for buoyancy-driven flows with internal source in comparison to SGDH model. (author)

Mixed convection flow of nanofluid in a square enclosure with an intruded rectangular fin

International Nuclear Information System (INIS)

Cong, Ran; Zhou, Xuanyu; De Souza Machado, Bruno; Das, Prodip K.

2016-01-01

Mixed convection flow in enclosures has been a subject of interest for many years due to their ever increasing applications in solar collectors, electronic cooling, lubrication technologies, food processing, and nuclear reactors. In comparison, little effort has been given to the problem of mixed convection in enclosures filled with nanofluids, while the addition of nanoparticles in a fluid base to alter specific material properties is considered a feasible solution for many heat transfer problems. Mixed convection of nanofluids is a challenging problem as the addition of nanoparticles changes the fluid’s thermo-physical properties as well as due to the complex interactions among inertia, viscous, and buoyancy forces. In this study, a two-dimensional steady-state numerical model has been developed to investigate mixed convection flow of nanofluids in a square enclosure with an intruded rectangular fin and to optimize the fin geometry for maximizing the heat transfer using the Constructal design. The model has been developed using ANSYS-FLUENT for various fin geometries. Flow fields, temperature fields, and heat transfer rates are examined for different values of Rayleigh and Reynolds numbers for several geometries of the fin with the aim of maximizing the heat transfer from the fin to the surrounding flow. Outcome of this study provides important insight into the heat transfer behavior of nanofluids, which will help in developing novel geometries with enhanced and controlled heat transfer for solar collectors and electronic devices.

Mixed convection flow of nanofluid in a square enclosure with an intruded rectangular fin

Energy Technology Data Exchange (ETDEWEB)

Cong, Ran; Zhou, Xuanyu; De Souza Machado, Bruno; Das, Prodip K., E-mail: prodip.das@ncl.ac.uk [School of Mechanical and Systems Engineering Newcastle University Newcastle upon Tyne, NE1 7RU United Kingdom (United Kingdom)

2016-07-12

Mixed convection flow in enclosures has been a subject of interest for many years due to their ever increasing applications in solar collectors, electronic cooling, lubrication technologies, food processing, and nuclear reactors. In comparison, little effort has been given to the problem of mixed convection in enclosures filled with nanofluids, while the addition of nanoparticles in a fluid base to alter specific material properties is considered a feasible solution for many heat transfer problems. Mixed convection of nanofluids is a challenging problem as the addition of nanoparticles changes the fluid’s thermo-physical properties as well as due to the complex interactions among inertia, viscous, and buoyancy forces. In this study, a two-dimensional steady-state numerical model has been developed to investigate mixed convection flow of nanofluids in a square enclosure with an intruded rectangular fin and to optimize the fin geometry for maximizing the heat transfer using the Constructal design. The model has been developed using ANSYS-FLUENT for various fin geometries. Flow fields, temperature fields, and heat transfer rates are examined for different values of Rayleigh and Reynolds numbers for several geometries of the fin with the aim of maximizing the heat transfer from the fin to the surrounding flow. Outcome of this study provides important insight into the heat transfer behavior of nanofluids, which will help in developing novel geometries with enhanced and controlled heat transfer for solar collectors and electronic devices.

Mixed convection flow of nanofluid in a square enclosure with an intruded rectangular fin

Science.gov (United States)

Cong, Ran; Zhou, Xuanyu; De Souza Machado, Bruno; Das, Prodip K.

2016-07-01

Mixed convection flow in enclosures has been a subject of interest for many years due to their ever increasing applications in solar collectors, electronic cooling, lubrication technologies, food processing, and nuclear reactors. In comparison, little effort has been given to the problem of mixed convection in enclosures filled with nanofluids, while the addition of nanoparticles in a fluid base to alter specific material properties is considered a feasible solution for many heat transfer problems. Mixed convection of nanofluids is a challenging problem as the addition of nanoparticles changes the fluid's thermo-physical properties as well as due to the complex interactions among inertia, viscous, and buoyancy forces. In this study, a two-dimensional steady-state numerical model has been developed to investigate mixed convection flow of nanofluids in a square enclosure with an intruded rectangular fin and to optimize the fin geometry for maximizing the heat transfer using the Constructal design. The model has been developed using ANSYS-FLUENT for various fin geometries. Flow fields, temperature fields, and heat transfer rates are examined for different values of Rayleigh and Reynolds numbers for several geometries of the fin with the aim of maximizing the heat transfer from the fin to the surrounding flow. Outcome of this study provides important insight into the heat transfer behavior of nanofluids, which will help in developing novel geometries with enhanced and controlled heat transfer for solar collectors and electronic devices.

Numerical simulation of thermomagnetic convection of cold water near its density maximum in a square enclosure under a magnetic quadrupole field

Energy Technology Data Exchange (ETDEWEB)

Shi, Er; Sun, Xiaoqin; He, Yecong; Jiang, Changwei, E-mail: cw_jiang@163.com [School of Energy and Power Engineering, Changsha University of Science and Technology, Changsha 410114 (China)

2017-06-15

Natural convection of cold water near its density maximum in a square enclosure is studied numerically under the influence of a magnetic quadrupole field without gravity. A generalized model which includes a non-Boussinesq parabolic density–temperature relationship is established. The governing equations in primitive variables are discretized using the finite-volume method and solved using the SIMPLE algorithm. The effects of magnetic force number, Rayleigh number and density inversion parameter on flow and heat transfer characteristics are analyzed. The results show that the primary flow pattern depends mainly on the density inversion parameter. Multi-cellular flow structures are observed for certain ranges of density inversion parameter independent of the value of Rayleigh number and magnetic force number. The heat transfer changes non-monotonically under combined actions of the quadrupole magnetic field and density inversion. (paper)

MHD nanofluid free convection and entropy generation in porous enclosures with different conductivity ratios

Science.gov (United States)

Ghasemi, Kasra; Siavashi, Majid

2017-11-01

MHD natural convection of Cu-water nanofluid in a square porous enclosure is investigated using a parallel LBM code, considering temperature dependence of viscosity and viscous dissipation. Effects of nanofluid concentration (φ = 0 - 0.12), Rayleigh (Ra =103 -106), Hartmann (Ha = 0-20) and porous-fluid thermal conductivity ratio (K∗ = 1-70) on heat transfer and entropy generation are investigated. It is shown that K∗ is a very important parameter, and porous media with low K∗ numbers can confine convection effects, but by increasing K∗ both conduction and convection effects can substantially improve. Also, magnetic field always has negative impact on Nu, however this impact can be controlled by φ and K∗. A magnetic instability has also observed in Ra = 104, and Nu exhibits a sinusoidal variation with Ha. It is proved that, depending on K∗, Ra and Ha values, use of nanofluid with porous media to enhance heat transfer can be either beneficial or detrimental. Also, for given K∗, Ra and Ha numbers an optimal φ exists to improve heat transfer. Finally, entropy generation study performed and results state that in low and high Ra values the thermal and frictional entropy generation are respectively dominant, while for moderate Ra they have the same order of magnitude.

Simulating deep convection with a shallow convection scheme

Directory of Open Access Journals (Sweden)

C. Hohenegger

2011-10-01

Full Text Available Convective processes profoundly affect the global water and energy balance of our planet but remain a challenge for global climate modeling. Here we develop and investigate the suitability of a unified convection scheme, capable of handling both shallow and deep convection, to simulate cases of tropical oceanic convection, mid-latitude continental convection, and maritime shallow convection. To that aim, we employ large-eddy simulations (LES as a benchmark to test and refine a unified convection scheme implemented in the Single-column Community Atmosphere Model (SCAM. Our approach is motivated by previous cloud-resolving modeling studies, which have documented the gradual transition between shallow and deep convection and its possible importance for the simulated precipitation diurnal cycle.

Analysis of the LES reveals that differences between shallow and deep convection, regarding cloud-base properties as well as entrainment/detrainment rates, can be related to the evaporation of precipitation. Parameterizing such effects and accordingly modifying the University of Washington shallow convection scheme, it is found that the new unified scheme can represent both shallow and deep convection as well as tropical and mid-latitude continental convection. Compared to the default SCAM version, the new scheme especially improves relative humidity, cloud cover and mass flux profiles. The new unified scheme also removes the well-known too early onset and peak of convective precipitation over mid-latitude continental areas.

Simple lecture demonstrations of instability and self-organization

International Nuclear Information System (INIS)

Mayer, V V; Varaksina, E I; Saranin, V A

2014-01-01

A dielectric liquid layer with an electric field created inside it is proposed as a means for demonstrating the phenomenon of self-organization. The field is produced by the distributed charge transferred by a corona discharge from the tip to the liquid surface. The theory of the phenomenon is presented. An analogy with the Rayleigh – Taylor instability is drawn and a comparison with the Benard instability is given. The practicality of the method for both natural sciences and the humanities is discussed. (methodological notes)

CFD Calculation of Internal Natural Convection in the Annulus between Horizontal Concentric Cylinders

International Nuclear Information System (INIS)

Francis, N.D. Jr.; Itamura, M.T.; Webb, S.W.; James, D.L.

2002-01-01

The objective of this heat transfer and fluid flow study is to assess the ability of a computational fluid dynamics (CFD) code to reproduce the experimental results, numerical simulation results, and heat transfer correlation equations developed in the literature for natural convection heat transfer within the annulus of horizontal concentric cylinders. In the literature, a variety of heat transfer expressions have been developed to compute average equivalent thermal conductivities. However, the expressions have been primarily developed for very small inner and outer cylinder radii and gap-widths. In this comparative study, interest is primarily focused on large gap widths (on the order of half meter or greater) and large radius ratios. From the steady-state CFD analysis it is found that the concentric cylinder models for the larger geometries compare favorably to the results of the Kuehn and Goldstein correlations in the Rayleigh number range of about 10 5 to 10 8 (a range that encompasses the laminar to turbulent transition). For Rayleigh numbers greater than 10 8 , both numerical simulations and experimental data (from the literature) are consistent and result in slightly lower equivalent thermal conductivities than those obtained from the Kuehn and Goldstein correlations

Rayleigh scattering under light-atom coherent interaction

OpenAIRE

Takamizawa, Akifumi; Shimoda, Koichi

2012-01-01

Semi-classical calculation of an oscillating dipole induced in a two-level atom indicates that spherical radiation from the dipole under coherent interaction, i.e., Rayleigh scattering, has a power level comparable to that of spontaneous emission resulting from an incoherent process. Whereas spontaneous emission is nearly isotropic and has random polarization generally, Rayleigh scattering is strongly anisotropic and polarized in association with incident light. In the case where Rabi frequen...

High-frequency Rayleigh-wave method

Science.gov (United States)

Xia, J.; Miller, R.D.; Xu, Y.; Luo, Y.; Chen, C.; Liu, J.; Ivanov, J.; Zeng, C.

2009-01-01

High-frequency (???2 Hz) Rayleigh-wave data acquired with a multichannel recording system have been utilized to determine shear (S)-wave velocities in near-surface geophysics since the early 1980s. This overview article discusses the main research results of high-frequency surface-wave techniques achieved by research groups at the Kansas Geological Survey and China University of Geosciences in the last 15 years. The multichannel analysis of surface wave (MASW) method is a non-invasive acoustic approach to estimate near-surface S-wave velocity. The differences between MASW results and direct borehole measurements are approximately 15% or less and random. Studies show that simultaneous inversion with higher modes and the fundamental mode can increase model resolution and an investigation depth. The other important seismic property, quality factor (Q), can also be estimated with the MASW method by inverting attenuation coefficients of Rayleigh waves. An inverted model (S-wave velocity or Q) obtained using a damped least-squares method can be assessed by an optimal damping vector in a vicinity of the inverted model determined by an objective function, which is the trace of a weighted sum of model-resolution and model-covariance matrices. Current developments include modeling high-frequency Rayleigh-waves in near-surface media, which builds a foundation for shallow seismic or Rayleigh-wave inversion in the time-offset domain; imaging dispersive energy with high resolution in the frequency-velocity domain and possibly with data in an arbitrary acquisition geometry, which opens a door for 3D surface-wave techniques; and successfully separating surface-wave modes, which provides a valuable tool to perform S-wave velocity profiling with high-horizontal resolution. ?? China University of Geosciences (Wuhan) and Springer-Verlag GmbH 2009.

Turbulent thermal convection at high Rayleigh numbers for a Boussinesq fluid of constant Prandtl number

International Nuclear Information System (INIS)

Amati, G.; Koal, K.; Massaioli, F.; Sreenivasan, K.R.; Verzicco, R.

2006-12-01

The results from direct numerical simulations of turbulent Boussinesq convection are briefly presented. The flow is computed for a cylindrical cell of aspect ratio 1/2 in order to compare with the results from recent experiments. The results span eight decades of Ra from 2x10 6 to 2x10 14 and form the baseline data for a strictly Boussinesq fluid of constant Prandtl number (Pr=0.7). A conclusion is that the Nusselt number varies nearly as the 1/3 power of Ra for about four decades towards the upper end of the Ra range covered. (author)

Centrifugally Driven Rayleigh-Taylor Instability

Science.gov (United States)

Scase, Matthew; Hill, Richard

2017-11-01

The instability that develops at the interface between two fluids of differing density due to the rapid rotation of the system may be considered as a limit of high-rotation rate Rayleigh-Taylor instability. Previously the authors have considered the effect of rotation on a gravitationally dominated Rayleigh-Taylor instability and have shown that some growth modes of instability may be suppressed completely by the stabilizing effect of rotation (Phys. Rev. Fluids 2:024801, Sci. Rep. 5:11706). Here we consider the case of very high rotation rates and a negligible gravitational field. The initial condition is of a dense inner cylinder of fluid surrounded by a lighter layer of fluid. As the system is rotated about the generating axis of the cylinder, the dense inner fluid moves away from the axis and the familiar bubbles and spikes of Rayleigh-Taylor instability develop at the interface. The system may be thought of as a ``fluid-fluid centrifuge''. By developing a model based on an Orr-Sommerfeld equation, we consider the effects of viscosity, surface tension and interface diffusion on the growth rate and modes of instability. We show that under particular circumstances some modes may be stabilized. School of Mathematical Sciences.

Breakdown of the large-scale circulation in Γ=1/2 rotating Rayleigh-Bénard flow.

Science.gov (United States)

Stevens, Richard J A M; Clercx, Herman J H; Lohse, Detlef

2012-11-01

Experiments and simulations of rotating Rayleigh-Bénard convection in cylindrical samples have revealed an increase in heat transport with increasing rotation rate. This heat transport enhancement is intimately related to a transition in the turbulent flow structure from a regime dominated by a large-scale circulation (LSC), consisting of a single convection roll, at no or weak rotation to a regime dominated by vertically aligned vortices at strong rotation. For a sample with an aspect ratio Γ=D/L=1 (D is the sample diameter and L is its height) the transition between the two regimes is indicated by a strong decrease in the LSC strength. In contrast, for Γ=1/2, Weiss and Ahlers [J. Fluid Mech. 688, 461 (2011)] revealed the presence of a LSC-like sidewall temperature signature beyond the critical rotation rate. They suggested that this might be due to the formation of a two-vortex state, in which one vortex extends vertically from the bottom into the sample interior and brings up warm fluid while another vortex brings down cold fluid from the top; this flow field would yield a sidewall temperature signature similar to that of the LSC. Here we show by direct numerical simulations for Γ=1/2 and parameters that allow direct comparison with experiment that the spatial organization of the vertically aligned vortical structures in the convection cell do indeed yield (for the time average) a sinusoidal variation of the temperature near the sidewall, as found in the experiment. This is also the essential and nontrivial difference with the Γ=1 sample, where the vertically aligned vortices are distributed randomly.

Radiation effects on bifurcation and dual solutions in transient natural convection in a horizontal annulus

Energy Technology Data Exchange (ETDEWEB)

Luo, Kang; Yi, Hong-Liang, E-mail: yihongliang@hit.edu.cn; Tan, He-Ping, E-mail: tanheping@hit.edu.cn [School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001 (China)

2014-05-15

Transitions and bifurcations of transient natural convection in a horizontal annulus with radiatively participating medium are numerically investigated using the coupled lattice Boltzmann and direct collocation meshless (LB-DCM) method. As a hybrid approach based on a common multi-scale Boltzmann-type model, the LB-DCM scheme is easy to implement and has an excellent flexibility in dealing with the irregular geometries. Separate particle distribution functions in the LBM are used to calculate the density field, the velocity field and the thermal field. In the radiatively participating medium, the contribution of thermal radiation to natural convection must be taken into account, and it is considered as a radiative term in the energy equation that is solved by the meshless method with moving least-squares (MLS) approximation. The occurrence of various instabilities and bifurcative phenomena is analyzed for different Rayleigh number Ra and Prandtl number Pr with and without radiation. Then, bifurcation diagrams and dual solutions are presented for relevant radiative parameters, such as convection-radiation parameter Rc and optical thickness τ. Numerical results show that the presence of volumetric radiation changes the static temperature gradient of the fluid, and generally results in an increase in the flow critical value. Besides, the existence and development of dual solutions of transient convection in the presence of radiation are greatly affected by radiative parameters. Finally, the advantage of LB-DCM combination is discussed, and the potential benefits of applying the LB-DCM method to multi-field coupling problems are demonstrated.

Numerical study of natural convection in a horizontal cylinder filled with water-based alumina nanofluid.

Science.gov (United States)

Meng, Xiangyin; Li, Yan

2015-01-01

Natural heat convection of water-based alumina (Al2O3/water) nanofluids (with volume fraction 1% and 4%) in a horizontal cylinder is numerically investigated. The whole three-dimensional computational fluid dynamics (CFD) procedure is performed in a completely open-source way. Blender, enGrid, OpenFOAM and ParaView are employed for geometry creation, mesh generation, case simulation and post process, respectively. Original solver 'buoyantBoussinesqSimpleFoam' is selected for the present study, and a temperature-dependent solver 'buoyantBoussinesqSimpleTDFoam' is developed to ensure the simulation is more realistic. The two solvers are used for same cases and compared to corresponding experimental results. The flow regime in these cases is laminar (Reynolds number is 150) and the Rayleigh number range is 0.7 × 10(7) ~ 5 × 10(7). By comparison, the average natural Nusselt numbers of water and Al2O3/water nanofluids are found to increase with the Rayleigh number. At the same Rayleigh number, the Nusselt number is found to decrease with nanofluid volume fraction. The temperature-dependent solver is found better for water and 1% Al2O3/water nanofluid cases, while the original solver is better for 4% Al2O3/water nanofluid cases. Furthermore, due to strong three-dimensional flow features in the horizontal cylinder, three-dimensional CFD simulation is recommended instead of two-dimensional simplifications.

Steady convection in MHD Benard problem with Hall effects

Directory of Open Access Journals (Sweden)

Lidia Palese

2017-10-01

Full Text Available In this paper we apply some variants of the classical energy method to study the nonlinear Lyapunov stability of the thermodiffusive equilibrium for a viscous thermoelectroconducting fully ionized fluid in a horizontal layer heated from below. The classical L^2 norm, too weak to highlight some stabilizing or unstabilizing effects, can be used to dominate the nonlinear terms. A more fine Lyapunov function is obtained by reformulating the initial perturbation evolution problem, in terms of some independent scalar fields. In such a way, if the principle of exchange of stabilities holds, we obtain the coincidence of linear and nonlinear stability bounds.

Benard C. Rusche nomination. Hearing before the Committee on Energy and Natural Resources, US Senate, Ninety-Eighth Congress, Second Session, May 17, 1984

International Nuclear Information System (INIS)

Anon.

1984-01-01

A hearing on the nomination of Benard C. Rusche to the new position of Director of the Office of Civilian Radioactive Waste Management in DOE began with an introduction and endorsement by Senator Thurmond of South Carolina. Testimony by the nominee emphasized the need to move ahead on radioactive waste disposal and storage arrangements that will provide protection for the environment and the public. His key points included the need for a common framework and an integrated program that would include opportunities for public discussion of all affected parties. He expressed a commitment to responsible and accountable procedures and cooperation with other regulatory agencies

A linear analytical study of Soret-driven ferrothermohaline convection in an anisotropic porous medium

International Nuclear Information System (INIS)

Sekar, R.; Raju, K.; Vasanthakumari, R.

2013-01-01

The Soret-driven ferrothermoconvective instability of multi- component fluid in an anisotropic porous medium heated from below and salted from above has been analyzed using Brinkman model for various values of anisotropic parameter. The salinity effect is contained in magnetization and density of the ferrofluid and the system is assumed to have anisotropy in the vertical direction and isotropy in the horizontal direction. A small perturbation imparted on the basic state and a linear stability analysis is used for this model for which the normal mode technique is applied. The present analysis has been carried out through both stationary as well as oscillatory modes. The vertical anisotropy tends to destabilize the system. -- Highlights: ► We examine the effect of anisotropy and magnetization of convection in Soret effect. ► The system loses its stability for critical Rayleigh number for various parameters like R s and K 1 . ► The larger temperature difference is needed to guarantee the occurring of convection. ► The Soret effect plays a dominant role for the stability of the system

Numerical simulation of nonstationary dissipative structures in 3D double-diffusive convection at large Rayleigh numbers

Science.gov (United States)

Kozitskiy, Sergey

2018-05-01

Numerical simulation of nonstationary dissipative structures in 3D double-diffusive convection has been performed by using the previously derived system of complex Ginzburg-Landau type amplitude equations, valid in a neighborhood of Hopf bifurcation points. Simulation has shown that the state of spatiotemporal chaos develops in the system. It has the form of nonstationary structures that depend on the parameters of the system. The shape of structures does not depend on the initial conditions, and a limited number of spectral components participate in their formation.

Study of natural convection heat transfer characteristics. (2) Verification for numerical simulation

International Nuclear Information System (INIS)

Ikeda, Hiroshi; Nakada, Kotaro; Ikeda, Tatsumi; Wakamatsu, Mitsuo; Iwaki, Chikako; Morooka, Shinichi; Masaki, Yoshikazu

2008-01-01

In the natural cooling system for waste storage, it is important to evaluate the flow by natural draft enough to remove the decay heat from the waste. In this study, we carried out the fundamental study of natural convection on vertical cylindrical heater by experiment and numerical simulation. The dimension of test facility is about 4m heights with single heater. Heating power is varied in the range of 33-110W, where Rayleigh number is over 10 10 . We surveyed the velocity distribution around heater by some turbulent models, mesh sizes around heated wall and turbulent Prandtl numbers. Results of numerical simulation of the velocity distribution and averaged heat transfer coefficient agreed well with experimental data and references. (author)

Natural convection in a cubical cavity with a coaxial heated cylinder

Energy Technology Data Exchange (ETDEWEB)

Aithal, S. M.

2018-03-01

High-resolution three-dimensional simulations were conducted to investigate the velocity and temperature fields in a cold cubical cavity due to natural convection induced by a centrally placed hot cylinder. Unsteady, incompressible Navier-Stokes equations were solved by using a spectral- element method for Rayleigh numbers ranging from 103 to 109. The effect of spanwise thermal boundary conditions, aspect ratio (radius of the cylinder to the side of the cavity), and spanwise temperature distribution of the inner cylinder on the velocity and thermal fields were investigated for each Rayleigh number. Results from two-dimensional calculations were compared with three-dimensional simulations. The 3D results indicate a complex flow structure in the vicinity of the spanwise walls. The results also show that the imposed thermal wall boundary condition impacts the flow and temperature fields strongly near the spanwise walls. The variation of the local Nusselt number on the cylinder surface and enclosure walls at various spanwise locations was also investigated. The local Nusselt number on the cylinder surface and enclosure walls at the cavity mid-plane (Z = 0) is close to 2D simulations for 103 ≤ Ra ≤ 108. Simulations also show a variation in the local Nusselt number, on both the cylinder surface and the enclosure walls, in the spanwise direction, for all Rayleigh numbers studied in this work. The results also indicate that if the enclosure walls are insulated in the spanwise direction (as opposed to a constant temperature), the peak Nusselt number on the enclosure surface occurs near the spanwise walls and is about 20% higher than the peak Nusselt number at the cavity mid-plane. The temporal characteristics of 3D flows are also different from 2D results for Ra > 108. These results suggest that 3D simulations would be more appropriate for flows with Ra > 108.

Convective aggregation in realistic convective-scale simulations

OpenAIRE

Holloway, Christopher E.

2017-01-01

To investigate the real-world relevance of idealized-model convective self-aggregation, five 15-day cases of real organized convection in the tropics are simulated. These include multiple simulations of each case to test sensitivities of the convective organization and mean states to interactive radiation, interactive surface fluxes, and evaporation of rain. These simulations are compared to self-aggregation seen in the same model configured to run in idealized radiative-convective equilibriu...

Crust formation and its effect on the molten pool coolability

Energy Technology Data Exchange (ETDEWEB)

Park, R.J.; Lee, S.J.; Sim, S.K. [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)

1995-09-01

Experimental and analytical studies of the crust formation and its effect on the molten pool coolability have been performed to examine the crust formation process as a function of boundary temperatures as well as to investigate heat transfer characteristics between molten pool and overlying water in order to evaluate coolability of the molten pool. The experimental test results have shown that the surface temperature of the bottom plate is a dominant parameter in the crust formation process of the molten pool. It is also found that the crust thickness of the case with direct coolant injection into the molten pool is greater than that of the case with a heat exchanger. Increasing mass flow rate of direct coolant injection to the molten pool does not affect the temperature of molten pool after the crust has been formed in the molten pool because the crust behaves as a thermal barrier. The Nusselt number between the molten pool and the coolant of the case with no crust formation is greater than that of the case with crust formation. The results of FLOW-3D analyses have shown that the temperature distribution contributes to the crust formation process due to Rayleigh-Benard natural convection flow.

Experimental Characterization of Radiation Forcing due to Atmospheric Aerosols

Science.gov (United States)

Sreenivas, K. R.; Singh, D. K.; Ponnulakshmi, V. K.; Subramanian, G.

2011-11-01

Micro-meteorological processes in the nocturnal atmospheric boundary layer (NBL) including the formation of radiation-fog and the development of inversion layers are controlled by heat transfer and the vertical temperature distribution close to the ground. In a recent study, it has been shown that the temperature profile close to the ground in stably-stratified, NBL is controlled by the radiative forcing due to suspended aerosols. Estimating aerosol forcing is also important in geo-engineering applications to evaluate the use of aerosols to mitigate greenhouse effects. Modeling capability in the above scenarios is limited by our knowledge of this forcing. Here, the design of an experimental setup is presented which can be used for evaluating the IR-radiation forcing on aerosols under either Rayleigh-Benard condition or under conditions corresponding to the NBL. We present results indicating the effect of surface emissivities of the top and bottom boundaries and the aerosol concentration on the temperature profiles. In order to understand the observed enhancement of the convection-threshold, we have determined the conduction-radiation time constant of an aerosol laden air layer. Our results help to explain observed temperature profiles in the NBL, the apparent stability of such profiles and indicate the need to account for the effect of aerosols in climatic/weather models.

Convection and field-aligned currents, related to polar cap arcs, during strongly northward IMF (11 January 1983)

International Nuclear Information System (INIS)

Israelevich, P.L.; Podgorny, I.M.; Kuzmin, A.K.; Nikolaeva, N.S.; Dubinin, E.M.

1988-01-01

Electric and magnetic fields and auroral emissions have been measured by the Intercosmos-Bulgaria-1300 satellite on 10-11 January 1983. The measured distributions of the plasma drift velocity show that viscous convection is diminished in the evening sector under IMF B y y > 0. A number of sun-aligned polar cap arcs were observed at the beginning of the period of strongly northward IMF and after a few hours a θ-aurora appeared. The intensity of ionized oxygen emission increased significantly reaching up to several kilo-Rayleighs in the polar cap arc. A complicated pattern of convection and field-aligned currents existed in the nightside polar cap which differed from the four-cell model of convection and NBZ field-aligned current system. This pattern was observed during 12 h and could be interpreted as six large scale field-aligned current sheets and three convective vortices inside the polar cap. Sun-aligned polar cap arcs may be located in regions both of sunward and anti-sunward convection. Structures of smaller spatial scale-correspond to the boundaries of hot plasma regions related to polar cap arcs. Obviously these structures are due to S-shaped distributions of electric potential. Parallel electric fields in these S-structures provide electron acceleration up to 1 keV at the boundaries of polar cap arcs. The pairs of field-aligned currents correspond to those S-structures: a downward current at the external side of the boundary and an upward current at the internal side of it. (author)

Effects of heater location and heater size on the natural convection heat transfer in a square cavity using finite element method

Energy Technology Data Exchange (ETDEWEB)

Ngo, Ich Long; Byon, Chan [Yeungnam University, Gyeongsan (Korea, Republic of)

2015-07-15

Finite element method was used to investigate the effects of heater location and heater size on the natural convection heat transfer in a 2D square cavity heated partially or fully from below and cooled from above. Rayleigh number (5 X 10{sup 2} ≤ Ra ≤ 5X10{sup 5}), heater size (0.1 ≤ D/L ≤ 1.0), and heater location (0.1 ≤ x{sub h}/L ≤ 0.5) were considered. Numerical results indicated that the average Nusselt number (Nu{sub m}) increases as the heater size decreases. In addition, when x{sub h}/L is less than 0.4, Nu{sub m} increases as x{sub h}/L increases, and Num decreases again for a larger value of x{sub h}/L. However, this trend changes when Ra is less than 10{sup 4}, suggesting that Nu{sub m} attains its maximum value at the region close to the bottom surface center. This study aims to gain insight into the behaviors of natural convection in order to potentially improve internal natural convection heat transfer.

When is the Anelastic Approximation a Valid Model for Compressible Convection?

Science.gov (United States)

Alboussiere, T.; Curbelo, J.; Labrosse, S.; Ricard, Y. R.; Dubuffet, F.

2017-12-01

Compressible convection is ubiquitous in large natural systems such Planetary atmospheres, stellar and planetary interiors. Its modelling is notoriously more difficult than the case when the Boussinesq approximation applies. One reason for that difficulty has been put forward by Ogura and Phillips (1961): the compressible equations generate sound waves with very short time scales which need to be resolved. This is why they introduced an anelastic model, based on an expansion of the solution around an isentropic hydrostatic profile. How accurate is that anelastic model? What are the conditions for its validity? To answer these questions, we have developed a numerical model for the full set of compressible equations and compared its solutions with those of the corresponding anelastic model. We considered a simple rectangular 2D Rayleigh-Bénard configuration and decided to restrict the analysis to infinite Prandtl numbers. This choice is valid for convection in the mantles of rocky planets, but more importantly lead to a zero Mach number. So we got rid of the question of the interference of acoustic waves with convection. In that simplified context, we used the entropy balances (that of the full set of equations and that of the anelastic model) to investigate the differences between exact and anelastic solutions. We found that the validity of the anelastic model is dictated by two conditions: first, the superadiabatic temperature difference must be small compared with the adiabatic temperature difference (as expected) ɛ = Δ TSA / delta Ta << 1, and secondly that the product of ɛ with the Nusselt number must be small.

Solution for laminar natural convection flows in a square cavity with temperature dependent viscosity

Energy Technology Data Exchange (ETDEWEB)

Sanchez, J.G. [Parsons Brinckerhoff, New York, NY (United States)

1995-12-31

This paper presents an examination of numerical results for the buoyancy-driven convection heat transfer problem, in a two-dimensional enclosure under steady-state, laminar, incompressible, and temperature dependent viscosity fluid flow conditions. The vertical walls are exposed to different temperatures and the top and bottom are insulated. Rayleigh numbers of 10{sup 4}, 10{sup 5}, and 10{sup 6} are considered. Specific heat, thermal conductivity, and the thermal expansion coefficient are assumed constant. Density variation is included using the Oberbeck-Boussinesq approximation. The results are obtained using the SIMPLEC solution technique based on a power-law, finite-volume discretization scheme. The hydrodynamic and thermal fields are presented at various locations in the enclosures.

Rayleigh Waves in a Rotating Orthotropic Micropolar Elastic Solid Half-Space

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Baljeet Singh

2013-01-01

Full Text Available A problem on Rayleigh wave in a rotating half-space of an orthotropic micropolar material is considered. The governing equations are solved for surface wave solutions in the half space of the material. These solutions satisfy the boundary conditions at free surface of the half-space to obtain the frequency equation of the Rayleigh wave. For numerical purpose, the frequency equation is approximated. The nondimensional speed of Rayleigh wave is computed and shown graphically versus nondimensional frequency and rotation-frequency ratio for both orthotropic micropolar elastic and isotropic micropolar elastic cases. The numerical results show the effects of rotation, orthotropy, and nondimensional frequency on the nondimensional speed of the Rayleigh wave.

Onset of convection in a porous medium with sidewall heat transfer

International Nuclear Information System (INIS)

Kassoy, D.R.; Wang, M.; Weidman, P.D.

1985-01-01

A linear stability analysis is developed for convection in a vertically oriented finite slab of saturated porous material. The large vertical sidewall surfaces admit heat transfer while the small endwalls are insulated. A vertical temperature difference is imposed between the upper and lower horizontal surfaces. Results are obtained from an asymptotic evaluation of the exact stability criteria for a rectangular parallelpiped in the limit of small gap width element of → 0, where element of = narrow horizontal dimension/height. The critical Rayleigh number R/sub c/ = 0(element of/sup -2/) when the heat transfer boundary condition is applied directly to the sidewall. The convection mode consists of tightly packed three-dimensional cells with a wave number α = 0(element of/sup -1/2/). Only when the effective Biot number is sufficiently small, 0(element of/sup 2/), are the classical results approached; R/sub c/ → 4π/sup 2/, α/sub c/ = 0(1). If the slab is sandwiched between two impermeable conducting blocks with horizontal extent similar to the slab height, then the small scale modes disappear and R/sub c/ = 0(element of/sup -1/). However, sufficiently thin conducting blocks are compatible with R/sub c/ = 0(element of/sup -2/) and α = 0(element of/sup -1/2/

Application of the Proper Orthogonal Decomposition to Turbulent Czochralski Convective Flows

International Nuclear Information System (INIS)

Rahal, S; Cerisier, P; Azuma, H

2007-01-01

The aim of this work is to study the general aspects of the convective flow instabilities in a simulated Czochralski system. We considered the influence of the buoyancy and crystal rotation. Velocity fields, obtained by an ultrasonic technique, the corresponding 2D Fourier spectra and a correlation function, have been used. Steady, quasi-periodic and turbulent flows, are successively recognized, as the Reynolds number was increased, for a fixed Rayleigh number. The orthogonal decomposition method was applied and the numbers of modes, involved in the dynamics of turbulent flows, calculated. As far as we know, this method has been used for the first time to study the Czochralski convective flows. This method provides also information on the most important modes and allows simple theoretical models to be established. The large rotation rates of the crystal were found to stabilize the flow, and conversely the temperature gradients destabilize the flow. Indeed, the increase of the rotation effects reduces the number of involved modes and oscillations, and conversely, as expected, the increase of the buoyancy effects induces more modes to be involved in the dynamics. Thus, the flow oscillations can be reduced either by increasing the crystal rotation rate to the adequate value, as shown in this study or by imposing a magnetic field

Nanofluid heat transfer under mixed convection flow in a tube for solar thermal energy applications.

Science.gov (United States)

Sekhar, Y Raja; Sharma, K V; Kamal, Subhash

2016-05-01

The solar flat plate collector operating under different convective modes has low efficiency for energy conversion. The energy absorbed by the working fluid in the collector system and its heat transfer characteristics vary with solar insolation and mass flow rate. The performance of the system is improved by reducing the losses from the collector. Various passive methods have been devised to aid energy absorption by the working fluid. Also, working fluids are modified using nanoparticles to improve the thermal properties of the fluid. In the present work, simulation and experimental studies are undertaken for pipe flow at constant heat flux boundary condition in the mixed convection mode. The working fluid at low Reynolds number in the mixed laminar flow range is undertaken with water in thermosyphon mode for different inclination angles of the tube. Local and average coefficients are determined experimentally and compared with theoretical values for water-based Al2O3 nanofluids. The results show an enhancement in heat transfer in the experimental range with Rayleigh number at higher inclinations of the collector tube for water and nanofluids.

Preliminary study of Rayleigh-Taylor instability in wire-array Z-pinch

International Nuclear Information System (INIS)

He Kaihui; Feng Kaiming; Li Qiang; Gao Chunming

2000-01-01

It is important to research into the MHD Rayleigh-Taylor instability developed in Z-pinch implosion. A snowplough model of the single wire Z-pinch is presented. The perturbation amplitude of Rayleigh-Taylor instability in the wire-array Z-pinch is analyzed quantitatively. Sheared axial flow is put forward to mitigate and reduce the Rayleigh-Taylor instability. And other approaches used to mitigate MHD instability in such a super-fast process are explored

Attractors of the periodically forced Rayleigh system

Directory of Open Access Journals (Sweden)

Petre Bazavan

2011-07-01

Full Text Available The autonomous second order nonlinear ordinary differential equation(ODE introduced in 1883 by Lord Rayleigh, is the equation whichappears to be the closest to the ODE of the harmonic oscillator withdumping.In this paper we present a numerical study of the periodic andchaotic attractors in the dynamical system associated with the generalized Rayleigh equation. Transition between periodic and quasiperiodic motion is also studied. Numerical results describe the system dynamics changes (in particular bifurcations, when the forcing frequency is varied and thus, periodic, quasiperiodic or chaotic behaviour regions are predicted.

Evenly-spaced columns in the Bishop Tuff as relicts of hydrothermal convection

Science.gov (United States)

Randolph-Flagg, N. G.; Breen, S. J.; Hernandez, A.; Self, S.; Manga, M.

2015-12-01

A few square km of the Bishop Tuff in eastern California, USA have evenly spaced erosional columns. These columns are more resistant to erosion due to the precipitation of the low-temperature zeolite (120-200 ºC), mordenite, which is not found in the surrounding tuff. Similar features observed in the Bandelier Tuff were hypothesized to form when cold water from above infiltrated into the still-hot tuff interior. This water would become gravitationally unstable and produced convection with steam upwellings and liquid water downwellings. These downwellings became cemented with mordenite while the upwellings were too dry for chemical reactions. We use two methods to quantitatively assess this hypothesis. First, scaling that ignores the effects of latent heat and mineral precipitation suggests the Rayleigh number (Ra, a measure of convective vigor) for this system is ~103 well above the critical Ra of 4π2. Second, to account for the effect of multiphase flow and latent heat, we use two-dimensional numerical models in the finite difference code HYDROTHERM. We find that the geometry of flow is consistent with field observations and confirm that geometry is sensitive to permeability and topography. These tests suggest a few things about low-pressure hydrothermal systems. 1) The geometry of at least some convection appears to be broadly captured by linear stability theory that ignores reactive transport, heterogeneity of host rock, and the effects of latent heat. 2) Topographic flow sets the wavelength of convection meaning that these columns formed somewhere without topography—probably a lake. Finally, these observations imply a wet paleoclimate in the Eastern Sierra namely that, in the aftermath of the Long Valley eruption, either rain or snow was able to pool in the caldera before the tuff cooled on the order of a hundred years after the eruption.

Nonlinear saturation of the Rayleigh endash Taylor instability

International Nuclear Information System (INIS)

Das, A.; Mahajan, S.; Kaw, P.; Sen, A.; Benkadda, S.; Verga, A.

1997-01-01

A detailed numerical simulation of the nonlinear state of the Rayleigh endash Taylor instability has been carried out. There are three distinct phases of evolution where it is governed by the (i) linear effects, (ii) effects arising from the conventional nonlinear terms and (iii) subtle nonlinear effects arising through the coupling terms. During the third phase of evolution, there is a self-consistent generation of shear flow which saturates the Rayleigh endash Taylor instability even in situations (with periodic boundaries) where, in principle, an infinite amount of gravitational energy can be tapped. The Galerkin approximation is presented to provide an understanding of our numerical findings. Last, there is an attempt to provide a comprehensive understanding of the nonlinear state of the Rayleigh endash Taylor instability by comparing and contrasting this work with earlier studies. copyright 1997 American Institute of Physics

True polar wander on convecting planets

Science.gov (United States)

Rose, Ian Robert

Rotating planets are most stable when spinning around their maximum moment of inertia, and will tend to reorient themselves to achieve this configuration. Geological activity redistributes mass in the planet, making the moment of inertia a function of time. As the moment of inertia of the planet changes, the spin axis shifts with respect to a mantle reference frame in order to maintain rotational stability. This process is known as true polar wander (TPW). Of the processes that contribute to a planet's moment of inertia, convection in the mantle generates the largest and longest-period fluctuations, with corresponding shifts in the spin axis. True polar wander has been hypothesized to explain several physiographic features on planets and moons in our solar system. On Earth, TPW events have been invoked in some interpretations of paleomagnetic data. Large swings in the spin axis could have enormous ramifications for paleogeography, paleoclimate, and the history of life. Although the existence of TPW is well-verified, it is not known whether its rate and magnitude have been large enough for it to be an important process in Earth history. If true polar wander has been sluggish compared to plate tectonic speeds, then it would be difficult to detect and its consequences would be minor. I investigate rates of true polar wander on convecting planets using scaling, numerics, and inverse problems. I perform a scaling analysis of TPW on a convecting planet, identifying a minimal set of nondimensional parameters which describe the problem. The primary nondimensional numbers that control the rate of TPW are the ratio of centrifugal to gravitational forces m and the Rayleigh number Ra. The parameter m sets the size of a planet's rotational bulge, which determines the amount of work that needs to be done to move the spin axis. The Rayleigh number controls the size, distribution, and rate of change of moment of inertia anomalies, all of which affect the rate of TPW. I find that

Convective Propagation Characteristics Using a Simple Representation of Convective Organization

Science.gov (United States)

Neale, R. B.; Mapes, B. E.

2016-12-01

Observed equatorial wave propagation is intimately linked to convective organization and it's coupling to features of the larger-scale flow. In this talk we a use simple 4 level model to accommodate vertical modes of a mass flux convection scheme (shallow, mid-level and deep). Two paradigms of convection are used to represent convective processes. One that has only both random (unorganized) diagnosed fluctuations of convective properties and one with organized fluctuations of convective properties that are amplified by previously existing convection and has an explicit moistening impact on the local convecting environment We show a series of model simulations in single-column, 2D and 3D configurations, where the role of convective organization in wave propagation is shown to be fundamental. For the optimal choice of parameters linking organization to local atmospheric state, a broad array of convective wave propagation emerges. Interestingly the key characteristics of propagating modes are the low-level moistening followed by deep convection followed by mature 'large-scale' heating. This organization structure appears to hold firm across timescales from 5-day wave disturbances to MJO-like wave propagation.

Extended Rayleigh Damping Model

Directory of Open Access Journals (Sweden)

Naohiro Nakamura

2016-07-01

Full Text Available In dynamic analysis, frequency domain analysis can be used if the entire structure is linear. However, time history analysis is generally used if nonlinear elements are present. Rayleigh damping has been widely used in time history response analysis. Many articles have reported the problems associated with this damping and suggested remedies. A basic problem is that the frequency area across which the damping ratio is almost constant is too narrow. If the area could be expanded while incurring only a small increase in computational cost, this would provide an appropriate remedy for this problem. In this study, a novel damping model capable of expanding the constant frequency area by more than five times was proposed based on the study of a causal damping model. This model was constructed by adding two terms to the Rayleigh damping model and can be applied to the linear elements in the time history analysis of a nonlinear structure. The accuracy and efficiency of the model were confirmed using example analyses.

New phenomena in variable-density Rayleigh-Taylor turbulence

Energy Technology Data Exchange (ETDEWEB)

Livescu, D; Ristorcelli, J R; Petersen, M R; Gore, R A, E-mail: livescu@lanl.gov [Los Alamos National Laboratory, Los Alamos, NM 87545 (United States)

2010-12-15

This paper presents several issues related to mixing and turbulence structure in buoyancy-driven turbulence at low to moderate Atwood numbers, A, found from direct numerical simulations in two configurations: classical Rayleigh-Taylor instability and an idealized triply periodic Rayleigh-Taylor flow. Simulations at A up to 0.5 are used to examine the turbulence characteristics and contrast them with those obtained close to the Boussinesq approximation. The data sets used represent the largest simulations to date in each configuration. One of the more remarkable issues explored, first reported in (Livescu and Ristorcelli 2008 J. Fluid Mech. 605 145-80), is the marked difference in mixing between different density fluids as opposed to the mixing that occurs between fluids of commensurate densities, corresponding to the Boussinesq approximation. Thus, in the triply periodic configuration and the non-Boussinesq case, an initially symmetric density probability density function becomes skewed, showing that the mixing is asymmetric, with pure heavy fluid mixing more slowly than pure light fluid. A mechanism producing the mixing asymmetry is proposed and the consequences for the classical Rayleigh-Taylor configuration are discussed. In addition, it is shown that anomalous small-scale anisotropy found in the homogeneous configuration (Livescu and Ristorcelli 2008 J. Fluid Mech. 605 145-80) and Rayleigh-Taylor turbulence at A=0.5 (Livescu et al 2008 J. Turbul. 10 1-32) also occurs near the Boussinesq limit. Results pertaining to the moment closure modelling of Rayleigh-Taylor turbulence are also presented. Although the Rayleigh-Taylor mixing layer width reaches self-similar growth relatively fast, the lower-order terms in the self-similar expressions for turbulence moments have long-lasting effects and derived quantities, such as the turbulent Reynolds number, are slow to follow the self-similar predictions. Since eddy diffusivity in the popular gradient transport hypothesis

The Rayleigh-Taylor instability in the spherical pinch

International Nuclear Information System (INIS)

Chen, H.B.; Hilko, B.; Panarella, E.

1994-01-01

The spherical pinch (SP) concept is an outgrowth of the inertial confinement model (ICF). Unlike the ICF where instabilities, especially the Rayleigh-Taylor instability, have been studied extensively, the instability study of the spherical pinch has just begun. The Raleigh-Taylor instability is investigated for the first time in the SP in the present work. By using the simple condition for the Rayleigh-Taylor instability ∇p · ∇p < O (density and pressure gradients have opposite direction), we have qualitatively identified the regions for development of instabilities in the SP. It is found that the explosion phase (central discharge) is stable and instabilities take place in the imploding phase. However, the growth rate for the instability is not in exponential form, and the appearance of the Rayleigh-Taylor instability does not prevent the main shock wave from converging to the center of the sphere

Numerical Study of Natural Convection within a Wavy Enclosure Using Meshfree Approach: Effect of Corner Heating

Directory of Open Access Journals (Sweden)

Sonam Singh

2014-01-01

Full Text Available This paper presents a numerical study of natural convection within a wavy enclosure heated via corner heating. The considered enclosure is a square enclosure with left wavy side wall. The vertical wavy wall of the enclosure and both of the corner heaters are maintained at constant temperature, Tc and Th, respectively, with Th>Tc while the remaining horizontal, bottom, top and side walls are insulated. A penalty element-free Galerkin approach with reduced gauss integration scheme for penalty terms is used to solve momentum and energy equations over the complex domain with wide range of parameters, namely, Rayleigh number (Ra, Prandtl number (Pr, and range of heaters in the x- and y-direction. Numerical results are represented in terms of isotherms, streamlines, and Nusselt number. It is observed that the rate of heat transfer depends to a great extent on the Rayleigh number, Prandtl number, length of the corner heaters and the shape of the heat transfer surface. The consistent performance of the adopted numerical procedure is verified by comparison of the results obtained through the present meshless technique with those existing in the literature.

Rayleigh reciprocity relations: Applications

International Nuclear Information System (INIS)

Lin Ju; Li Xiao-Lei; Wang Ning

2016-01-01

Classical reciprocity relations have wide applications in acoustics, from field representation to generalized optical theorem. In this paper we introduce our recent results on the applications and generalization of classical Rayleigh reciprocity relation: higher derivative reciprocity relations as a generalization of the classical one and a theoretical proof on the Green’s function retrieval from volume noises. (special topic)

Mixed Convection Heat Transfer on the Outside of a Vertical Cylinder

Energy Technology Data Exchange (ETDEWEB)

Bhattacharyya, A

1965-10-15

An experimental study was made of turbulent heat transfer from a vertical cylinder placed in a square channel. The flow medium was water flowing upwards. Basic differential equations governing the mixed flow heat transfer phenomena in a vertical annulus are presented. A dimensional analysis is done to find the dimensionless variables affecting the relative magnitude of the effect of buoyancy on forced convection heat transfer. Dimensionless equations correlating the experimental data ana incorporating a buoyancy parameter of the form Gr/Re{sup 2} are presented. Reynolds number range covered is 690 to 129,500 and the Rayleigh num- ber range covered is 10{sup 9} to 4.2 x 10{sup 13} . Effect of different length parameters, like hydraulic diameter and distance of the measuring point from the inlet of the test section, on dimensionless equations are studied.

Experimental study on convective heat transfer of water flow in a heated tube under natural circulation

International Nuclear Information System (INIS)

Yang Ruichang; Liu Ruolei; Zhong Yong; Liu Tao

2006-01-01

This paper reports on an experimental study on transitional heat transfer of water flow in a heated vertical tube under natural circulation conditions. In the experiments the local and average heat transfer coefficients were obtained. The experimental data were compared with the predictions by a forced flow correlation available in the literature. The comparisons show that the Nusselt number value in the fully developed region is about 30% lower than the predictions by the forced flow correlation due to flow laminarization in the layer induced by co-current bulk natural circulation and free convection. By using the Rayleigh number Ra to represent the influence of free convection on heat transfer, the empirical correlations for the calculation of local and average heat transfer behavior in the tube at natural circulation have been developed. The empirical correlations are in good agreement with the experimental data. Based on the experimental results, the effect of the thermal entry-length behavior on heat transfer design in the tube under natural circulation was evaluated

Direct numerical simulation of free convection in a vertical channel: a tool for second moment closure modeling

International Nuclear Information System (INIS)

Maupu, V.; Laurence, D.; Boudjemadi, R.; Le Quere, P.

1996-03-01

Natural turbulent convection in a differentially heated infinite vertical slot is computed with a mixed finite differences/Fourier code. At a Rayleigh number of 10 5 , periodic perturbations from the laminar solution develop and transition to a fully turbulent flow occurs. From then on, a database of high order correlations is constituted and used for testing a second moment closure based on the LRR model and elliptic relaxation near wall effects. Counter gradient turbulent transport, found in the central part of the channel, requires an algebraic model for the triple correlations instead of the standard DH or HL, gradient diffusion models. (authors). 18 refs., 14 figs., 1 tab

Natural convection in Bingham plastic fluids from an isothermal spheroid: Effects of fluid yield stress, viscous dissipation and temperature-dependent viscosity

Science.gov (United States)

Gupta, Anoop Kumar; Gupta, Sanjay; Chhabra, Rajendra Prasad

2017-08-01

In this work, the buoyancy-induced convection from an isothermal spheroid is studied in a Bingham plastic fluid. Extensive results on the morphology of approximate yield surfaces, temperature profiles, and the local and average Nusselt numbers are reported to elucidate the effects of the pertinent dimensionless parameters: Rayleigh number, 102 ≤ Ra ≤ 106; Prandtl number, 20 ≤ Pr ≤ 100; Bingham number, 0 ≤ Bn ≤ 103, and aspect ratio, 0.2 ≤ e ≤ 5. Due to the fluid yield stress, fluid-like (yielded) and solid-like (unyielded) regions coexist in the flow domain depending upon the prevailing stress levels vis-a-vis the value of the fluid yield stress. The yielded parts progressively grow in size with the rising Rayleigh number while this tendency is countered by the increasing Bingham and Prandtl numbers. Due to these two competing effects, a limiting value of the Bingham number ( Bn max) is observed beyond which heat transfer occurs solely by conduction due to the solid-like behaviour of the fluid everywhere in the domain. Such limiting values bear a positive dependence on the Rayleigh number ( Ra) and aspect ratio ( e). In addition to this, oblate shapes ( e 1) impede it. Finally, simple predictive expressions for the maximum Bingham number and the average Nusselt number are developed which can be used to predict a priori the overall heat transfer coefficient in a new application. Also, a criterion is developed in terms of the composite parameter Bn• Gr-1/2 which predicts the onset of convection in such fluids. Similarly, another criterion is developed which delineates the conditions for the onset of settling due to buoyancy effects. The paper is concluded by presenting limited results to delineate the effects of viscous dissipation and the temperature-dependent viscosity on the Nusselt number. Both these effects are seen to be rather small in Bingham plastic fluids.

Rayleigh wave ellipticity across the Iberian Peninsula and Morocco

Science.gov (United States)

Gómez García, Clara; Villaseñor, Antonio

2015-04-01

Spectral amplitude ratios between horizontal and vertical components (H/V ratios) from seismic records are useful to evaluate site effects, predict ground motion and invert for S velocity in the top several hundred meters. These spectral ratios can be obtained from both ambient noise and earthquakes. H/V ratios from ambient noise depend on the content and predominant wave types: body waves, Rayleigh waves, a mixture of different waves, etc. The H/V ratio computed in this way is assumed to measure Rayleigh wave ellipticity since ambient vibrations are dominated by Rayleigh waves. H/V ratios from earthquakes are able to determine the local crustal structure at the vicinity of the recording station. These ratios obtained from earthquakes are based on surface wave ellipticity measurements. Although long period (>20 seconds) Rayleigh H/V ratio is not currently used because of large scatter has been reported and uncertainly about whether these measurements are compatible with traditional phase and group velocity measurements, we will investigate whether it is possible to obtain stable estimates after collecting statistics for many earthquakes. We will use teleseismic events from shallow earthquakes (depth ≤ 40 km) between 2007 January 1 and 2012 December 31 with M ≥ 6 and we will compute H/V ratios for more than 400 stations from several seismic networks across the Iberian Peninsula and Morocco for periods between 20 and 100 seconds. Also H/V ratios from cross-correlations of ambient noise in different components for each station pair will be computed. Shorter period H/V ratio measurements based on ambient noise cross-correlations are strongly sensitive to near-surface structure, rather than longer period earthquake Rayleigh waves. The combination of ellipticity measurements based on earthquakes and ambient noise will allow us to perform a joint inversion with Rayleigh wave phase velocity. Upper crustal structure is better constrained by the joint inversion compared

Turbulent natural convection in an enclosure formed by an array of vertical cylinders

International Nuclear Information System (INIS)

McEligot, D.M.; Stoots, C.M.; Christenson, W.A.; O'Brien, J.E.; Larson, T.K.; Mecham, D.C.; Lussie, W.G.

1992-04-01

A number of situations can be hypothesized to occur in an advanced or special purpose nuclear reactor such that the core is filled with a gas but there is no forced flow to remove the thermal energy evolved. Typically, the dimensions are so large that the magnitudes of the governing parameters indicate that the flow regime is probably turbulent. The generic situation considered in the present work is natural convection between heated, slender, vertical, circular cylinders and a surrounding array of cooler vertical cylinders in a triangular pattern. Experiments were conducted by resistively heating a vertical circular cylinder of length-to-diameter ratio of about 160 centered inside a concentric perforated tube which was, in turn, surrounded by three larger diameter tubes cooled internally with water flow. The medium was air. In order to deduce the contribution due to thermal radiation, thermal emissivities of the tubes were determined in-situ during the experiment and the emissivities of samples of the surfaces involved were measured separately. The ratio of the test section temperature to the cooling tube temperature was varied up to 2.6 by adjusting the electrical power. The Rayleigh number, based on tube diameter and properties evaluated at the cooling tube temperature, ranged from 2.9 x 10 4 to 9.2 x 10 5 . Results indicate that the convective heat transfer parameters for the perforated tube are about fifteen per cent higher than for the smooth bare tube centered in the same position relative to the array. The Nusselt number for convective heat transfer across the annulus-between the heated test section and the perforated tube corresponded to parallel laminar flow. Data with water films flowing down the outside surfaces of the cooling tubes demonstrated no significant change in the convective heat transfer parameters deduced

Rayleigh radiance computations for satellite remote sensing: accounting for the effect of sensor spectral response function.

Science.gov (United States)

Wang, Menghua

2016-05-30

To understand and assess the effect of the sensor spectral response function (SRF) on the accuracy of the top of the atmosphere (TOA) Rayleigh-scattering radiance computation, new TOA Rayleigh radiance lookup tables (LUTs) over global oceans and inland waters have been generated. The new Rayleigh LUTs include spectral coverage of 335-2555 nm, all possible solar-sensor geometries, and surface wind speeds of 0-30 m/s. Using the new Rayleigh LUTs, the sensor SRF effect on the accuracy of the TOA Rayleigh radiance computation has been evaluated for spectral bands of the Visible Infrared Imaging Radiometer Suite (VIIRS) on the Suomi National Polar-orbiting Partnership (SNPP) satellite and the Joint Polar Satellite System (JPSS)-1, showing some important uncertainties for VIIRS-SNPP particularly for large solar- and/or sensor-zenith angles as well as for large Rayleigh optical thicknesses (i.e., short wavelengths) and bands with broad spectral bandwidths. To accurately account for the sensor SRF effect, a new correction algorithm has been developed for VIIRS spectral bands, which improves the TOA Rayleigh radiance accuracy to ~0.01% even for the large solar-zenith angles of 70°-80°, compared with the error of ~0.7% without applying the correction for the VIIRS-SNPP 410 nm band. The same methodology that accounts for the sensor SRF effect on the Rayleigh radiance computation can be used for other satellite sensors. In addition, with the new Rayleigh LUTs, the effect of surface atmospheric pressure variation on the TOA Rayleigh radiance computation can be calculated precisely, and no specific atmospheric pressure correction algorithm is needed. There are some other important applications and advantages to using the new Rayleigh LUTs for satellite remote sensing, including an efficient and accurate TOA Rayleigh radiance computation for hyperspectral satellite remote sensing, detector-based TOA Rayleigh radiance computation, Rayleigh radiance calculations for high altitude

Evidence for thermal convection in the deep carbonate aquifer of the eastern sector of the Po Plain, Italy

Science.gov (United States)

Pasquale, V.; Chiozzi, P.; Verdoya, M.

2013-05-01

Temperatures recorded in wells as deep as 6 km drilled for hydrocarbon prospecting were used together with geological information to depict the thermal regime of the sedimentary sequence of the eastern sector of the Po Plain. After correction for drilling disturbance, temperature data were analyzed through an inversion technique based on a laterally constant thermal gradient model. The obtained thermal gradient is quite low within the deep carbonate unit (14 mK m- 1), while it is larger (53 mK m- 1) in the overlying impermeable formations. In the uppermost sedimentary layers, the thermal gradient is close to the regional average (21 mK m- 1). We argue that such a vertical change cannot be ascribed to thermal conductivity variation within the sedimentary sequence, but to deep groundwater flow. Since the hydrogeological characteristics (including litho-stratigraphic sequence and structural setting) hardly permit forced convection, we suggest that thermal convection might occur within the deep carbonate aquifer. The potential of this mechanism was evaluated by means of the Rayleigh number analysis. It turned out that permeability required for convection to occur must be larger than 3 10- 15 m2. The average over-heat ratio is 0.45. The lateral variation of hydrothermal regime was tested by using temperature data representing the aquifer thermal conditions. We found that thermal convection might be more developed and variable at the Ferrara High and its surroundings, where widespread fracturing may have increased permeability.

Identification of dominant flow structures in rapidly rotating convection of liquid metals using Dynamic Mode Decomposition

Science.gov (United States)

Horn, S.; Schmid, P. J.; Aurnou, J. M.

2016-12-01

The Earth's metal core acts as a dynamo whose efficiency in generating and maintaining the magnetic field is essentially determined by the rotation rate and the convective motions occurring in its outer liquid part. For the description of the primary physics in the outer core the idealized system of rotating Rayleigh-Bénard convection is often invoked, with the majority of studies considering only working fluids with Prandtl numbers of Pr ≳ 1. However, liquid metals are characterized by distinctly smaller Prandtl numbers which in turn result in an inherently different type of convection. Here, we will present results from direct numerical simulations of rapidly rotating convection in a fluid with Pr ≈ 0.025 in cylindrical containers and Ekman numbers as low as 5 × 10-6. In this system, the Coriolis force is the source of two types of inertial modes, the so-called wall modes, that also exist at moderate Prandtl numbers, and cylinder-filling oscillatory modes, that are a unique feature of small Prandtl number convection. The obtained flow fields were analyzed using the Dynamic Mode Decomposition (DMD). This technique allows to extract and identify the structures that govern the dynamics of the system as well as their corresponding frequencies. We have investigated both the regime where the flow is purely oscillatory and the regime where wall modes and oscillatory modes co-exist. In the purely oscillatory regime, high and low frequency oscillatory modes characterize the flow. When both types of modes are present, the DMD reveals that the wall-attached modes dominate the flow dynamics. They precess with a relatively low frequency in retrograde direction. Nonetheless, also in this case, high frequency oscillations have a significant contribution.

Numerical simulation of Rayleigh-Taylor turbulent mixing layers

International Nuclear Information System (INIS)

Poujade, O.; Lardjane, N.; Peybernes, M.; Boulet, M.

2009-01-01

Accelerations in actual Rayleigh-Taylor instabilities are often variable. This article focuses on a particular class of variable accelerations where g(t) ∝ t n . A reference database is built from high resolution hydrodynamic numerical simulations. The successful comparison with a simple OD analytical model and the statistical 2SFK (2-Structure, 2-Fluid, 2-Turbulence) turbulence model is provided. Moreover, we show the difference between the mechanism at play in the Rayleigh-Taylor turbulent mixing zone and Kolmogorov's in the self similar developed turbulent regime. (authors)

Rayleigh waves in elastic medium with double porosity

Directory of Open Access Journals (Sweden)

Rajneesh KUMAR

2018-03-01

Full Text Available The present paper deals with the propagation of Rayleigh waves in isotropic homogeneous elastic half-space with double porosity whose surface is subjected to stress-free boundary conditions. The compact secular equations for elastic solid half-space with voids are deduced as special cases from the present analysis. In order to illustrate the analytical developments, the secular equations have been solved numerically. The computer simulated results for copper materials in respect of Rayleigh wave velocity and attenuation coe¢ cient have been presented graphically.

DNS of buoyancy-driven flows and Lagrangian particle tracking in a square cavity at high Rayleigh numbers

International Nuclear Information System (INIS)

Puragliesi, R.; Dehbi, A.; Leriche, E.; Soldati, A.; Deville, M.O.

2011-01-01

Highlights: → 2D study of micro-size particle depletion driven by chaotic natural convective flows in square domains. → Description of velocity and temperature first and second moments with changing in the Rayleigh number. → Strong decoupling between the turbulent kinetic energy and the dissipation rate. → Particle recirculation sustained by the vertical hot boundary layer. → Deposition mostly induced by gravity, thermophoretic and lift forces are negligible. - Abstract: In this work we investigate numerically particle deposition in the buoyancy driven flow of the differentially heated cavity (DHC). We consider two values of the Rayleigh number (Ra = 10 9 , 10 10 ) and three values of the particle diameter (d p = 15, 25, 35 [μm]). We consider the cavity filled with air and particles with the same density of water ρ w = 1000 [kg/m 3 ] (aerosol). We use direct numerical simulations (DNS) for the continuous phase, and we solve transient Navier-Stokes and energy transport equations written in an Eulerian framework, under the Boussinesq approximation, for the viscous incompressible Newtonian fluid with constant Prandtl number (Pr = 0.71). First- and second-order statistics are presented for the continuous phase as well as important quantities like turbulent kinetic energy (TKE) and temperature variance with the associated production and dissipation fields. The TKE production shows different behaviour at the two Rayleigh numbers. The Lagrangian approach has been chosen for the dispersed phase description. The forces taken into account are drag, gravity, buoyancy, lift and thermophoresis. A first incursion in the sedimentation mechanisms is presented. Current results indicate that the largest contribution to particle deposition is caused by gravitational settling, but a strong recirculating zone, which liftoffs and segregates particles, contributes to decrease settling. Deposition takes place mostly at the bottom wall. The influence of lift and thermophoretic

DNS of buoyancy-driven flows and Lagrangian particle tracking in a square cavity at high Rayleigh numbers

Energy Technology Data Exchange (ETDEWEB)

Puragliesi, R., E-mail: riccardo.puragliesi@psi.ch [Nuclear Energy and Safety Research Department, Paul Scherrer Institut, CH-5232 Villigen PSI (Switzerland); Laboratoire d' Ingenierie Numerique, Ecole Polytechnique Federale de Lausanne, Station 9, CH-1015 Lausanne (Switzerland); Dehbi, A., E-mail: abdel.dehbi@psi.ch [Nuclear Energy and Safety Research Department, Paul Scherrer Institut, CH-5232 Villigen PSI (Switzerland); Leriche, E., E-mail: emmanuel.leriche@univ-st-etienne.fr [Universite de Lyon, F-42023 Saint-Etienne, LMFA-UJM St-Etienne, CNRS UMR 5509 Universite de St-Etienne, 23 rue Docteur Paul Michelon, F-42023 Saint-Etienne (France); Soldati, A., E-mail: soldati@uniud.it [Dipartimento di Energetica e Macchine, Universita di Udine, Via delle Scienze 208, IT-33100 Udine (Italy); Deville, M.O., E-mail: michel.deville@epfl.ch [Laboratoire d' Ingenierie Numerique, Ecole Polytechnique Federale de Lausanne, Station 9, CH-1015 Lausanne (Switzerland)

2011-10-15

Highlights: > 2D study of micro-size particle depletion driven by chaotic natural convective flows in square domains. > Description of velocity and temperature first and second moments with changing in the Rayleigh number. > Strong decoupling between the turbulent kinetic energy and the dissipation rate. > Particle recirculation sustained by the vertical hot boundary layer. > Deposition mostly induced by gravity, thermophoretic and lift forces are negligible. - Abstract: In this work we investigate numerically particle deposition in the buoyancy driven flow of the differentially heated cavity (DHC). We consider two values of the Rayleigh number (Ra = 10{sup 9}, 10{sup 10}) and three values of the particle diameter (d{sub p} = 15, 25, 35 [{mu}m]). We consider the cavity filled with air and particles with the same density of water {rho}{sub w} = 1000 [kg/m{sup 3}] (aerosol). We use direct numerical simulations (DNS) for the continuous phase, and we solve transient Navier-Stokes and energy transport equations written in an Eulerian framework, under the Boussinesq approximation, for the viscous incompressible Newtonian fluid with constant Prandtl number (Pr = 0.71). First- and second-order statistics are presented for the continuous phase as well as important quantities like turbulent kinetic energy (TKE) and temperature variance with the associated production and dissipation fields. The TKE production shows different behaviour at the two Rayleigh numbers. The Lagrangian approach has been chosen for the dispersed phase description. The forces taken into account are drag, gravity, buoyancy, lift and thermophoresis. A first incursion in the sedimentation mechanisms is presented. Current results indicate that the largest contribution to particle deposition is caused by gravitational settling, but a strong recirculating zone, which liftoffs and segregates particles, contributes to decrease settling. Deposition takes place mostly at the bottom wall. The influence of lift

Computational study of the Rayleigh light scattering properties of atmospheric pre-nucleation clusters

DEFF Research Database (Denmark)

Elm, Jonas; Norman, Patrick; Bilde, Merete

2014-01-01

The Rayleigh and hyper Rayleigh scattering properties of the binary (H 2SO4)(H2O)n and ternary (H 2SO4)(NH3)(H2O)n clusters are investigated using a quantum mechanical response theory approach. The molecular Rayleigh scattering intensities are expressed using the dipole polarizability α...... and hyperpolarizability β tensors. Using density functional theory, we elucidate the effect of cluster morphology on the scattering properties using a combinatorial sampling approach. We find that the Rayleigh scattering intensity depends quadratically on the number of water molecules in the cluster and that a single...... ammonia molecule is able to induce a high anisotropy, which further increases the scattering intensity. The hyper Rayleigh scattering activities are found to be extremely low. This study presents the first attempt to map the scattering of atmospheric molecular clusters using a bottom-up approach...

Rayleigh Pareto Distribution

Directory of Open Access Journals (Sweden)

Kareema ‎ Abed Al-Kadim

2017-12-01

Full Text Available In this paper Rayleigh Pareto distribution have  introduced denote by( R_PD. We stated some  useful functions. Therefor  we  give some of its properties like the entropy function, mean, mode, median , variance , the r-th moment about the mean, the rth moment about the origin, reliability, hazard functions, coefficients of variation, of sekeness and of kurtosis. Finally, we estimate the parameters  so the aim of this search  is to introduce a new distribution

Two regimes of flux scaling in axially homogeneous turbulent convection in vertical tube

Science.gov (United States)

Pawar, Shashikant S.; Arakeri, Jaywant H.

2016-08-01

From experiments of axially homogeneous turbulent convection in a vertical tube using heat (Prandtl number Pr≃6 ) and brine (Pr≃600 ) we show that at sufficiently high Rayleigh numbers (Rag), the Nusselt number Nug˜(RagPr)1/2, which corresponds to the so-called ultimate regime scaling. In heat experiments below certain Rag,however,there is transition to a new regime, Nug˜(RagPr)0.3. This transition also seems to exist in earlier reported data for Pr=1 and Pr≃600 , at different Rag. However, the transition occurs at a single Grashof number, Grgc≃1.6 ×105 , and unified flux scalings for Pr≥1 , Nug/Pr˜Grg0.3, and Nug/Pr˜Grg1/2 can be given for the two regimes.

Stability of an expanding cylindrical plasma envelope: Rayleigh--Taylor instability

International Nuclear Information System (INIS)

Han, S.J.

1982-01-01

The stability of a cylindrically symmetric plasma envelope driven outward by blast waves is considered. The plasma fluid is assumed to be a compressible, isentropic gas describable as an ideal gas ( p = arho/sup γ/, γ>1). The stability problem of such an envelope undergoing self-similar motion is solved by considering the initial-value problem. It is shown that in the early phase of an expansion, the envelope is unstable to Rayleigh--Taylor modes which develop at the inner surface. In the later phase of the expansion, the Rayleigh--Taylor modes are weakened due to the geometrical divergence effect. The implications of the time-dependent behavior of the Rayleigh--Taylor instability for plasma switches are discussed

Thermal convection as a possible mechanism for the origin of polygonal structures on Pluto's surface

Science.gov (United States)

Vilella, Kenny; Deschamps, Frédéric

2017-05-01

High-resolution pictures of Pluto's surface obtained by the New Horizons spacecraft revealed, among other surface features, a large nitrogen ice glacier informally named Sputnik Planitia. The surface of this glacier is separated into a network of polygonal cells with a wavelength of ˜20-40 km. This network is similar to the convective patterns obtained under certain conditions by laboratory experiments, suggesting that it is the surface expression of thermal convection. Here we investigate the surface planform obtained for different convective systems in 3-D Cartesian geometry with different modes of heating and rheologies. We find that bottom heated systems, as assumed by previous studies, do not produce surface planforms consistent with the observed pattern. Alternatively, for a certain range of Rayleigh-Roberts number, RaH, a volumetrically heated system produces a surface planform similar to this pattern. We then combine scaling laws with values of RaH within its possible range to establish relationships between the critical parameters of Sputnik Planitia. In particular, our calculations indicate that the glacier thickness and the surface heat flux are in the ranges 2-10 km and 0.1-10 mW m-2, respectively. However, a difficulty is to identify a proper source of internal heating. We propose that the long-term variations of surface temperature caused by variations in Pluto's orbit over millions of years produces secular cooling equivalent to internal heating. We find that this source of heating is sufficient to trigger thermal convection, but additional investigations are needed to determine under which conditions it can produce surface patterns similar to those of Sputnik Planitia.

Experimental study of natural convection heat transfer from an isothermal combined geometry (downward cone- cylinder)

Energy Technology Data Exchange (ETDEWEB)

Mokhtari, A. [Yazd Univ., Yazd (Iran, Islamic Republic of). Dept. of Mechanical Engineering; Goharkhah, M.; Ashjaee, M. [Tehran Univ., Tehran (Iran, Islamic Republic of). Dept. of Mechanical Engineering

2009-07-01

Laminar free convection heat transfer from an isothermal combined geometry which consists of a downward cone attached to a vertical cylinder was studied. In particular, a Mach-Zehnder interferometer was used to determine the change in local and average heat transfer coefficients on the surface of an isothermal combined geometry for different vertex angles. The effect of the vertex angle on heat transfer was also investigated by keeping the height of the cylinder and slant length of the cone constant for all objects. The experimental data showed that the local heat transfer coefficient on the conical part increased in the vicinity of the cylinder and cone intersection. The distance between the point of minimum heat transfer coefficient on the cone and vertex of the cone decreased as the vertex angle increased. The maximum average Nusselt number for a constant Rayleigh number was obtained for the geometry with the smallest vertex angle. For all objects, the average Nusselt number increased with an increase in the Rayleigh number. An experiment was carried out on a vertical isothermal cylinder of circular cross section in order to validate the experimental approach. An analytical solution was found to be in good agreement with experimental results. 31 refs., 9 figs.

Computational simulation of turbulent natural convection in a volumetrically heated square cavity

International Nuclear Information System (INIS)

Vieira, Camila Braga; Su, Jian; Niceno, Bojan

2012-01-01

This work aims to analyze the turbulent natural convection in a volumetrically heated fluid with similar characteristics of an oxide layer of a molten core in the lower head of the pressure vessel. The simulations were carried out in a square cavity with isothermal walls, for Rayleigh numbers (Ra) ranging from 10 9 to 10 11 . Different turbulence models based on Reynolds Averaged Navier-Stokes equations were studied, such as the standard k - ε, low-Reynolds-k - ε, and Shear Stress Transport (SST), using the open-source Computational Fluid Dynamics (CFD) code - Open FOAM (Open Field Operation and Manipulation). The results of the three turbulence models were compared versus the results of experimental correlations and other authors’ simulations, and the conclusion was that the most promising model proves to be the SST, due to its accuracy and robustness. (author)

Rayleigh- and Prandtl-number dependence of the large-scale flow-structure in weakly-rotating turbulent thermal convection

Science.gov (United States)

Weiss, Stephan; Wei, Ping; Ahlers, Guenter

2015-11-01

Turbulent thermal convection under rotation shows a remarkable variety of different flow states. The Nusselt number (Nu) at slow rotation rates (expressed as the dimensionless inverse Rossby number 1/Ro), for example, is not a monotonic function of 1/Ro. Different 1/Ro-ranges can be observed with different slopes ∂Nu / ∂ (1 / Ro) . Some of these ranges are connected by sharp transitions where ∂Nu / ∂ (1 / Ro) changes discontinuously. We investigate different regimes in cylindrical samples of aspect ratio Γ = 1 by measuring temperatures at the sidewall of the sample for various Prandtl numbers in the range 3 Deutsche Forschungsgemeinschaft.

Convective thermal fluxes in unsteady non-homogeneous flows generating complex three dimensional vorticity patterns

Science.gov (United States)

Tellez Alvarez, Jackson David; Redondo, Jose Manuel; Sanchez, Jesu Mary

2016-04-01

The improvements in experimental methods and high resolution image analysis are nowadays able to detect subtle changes in the structure of the turbulence over a wide range of temporal and spatial scales [1], we compare the scaling shown by different mixing fronts driven by buoyancy that form convective driven mixing. We use PIV and density front tracking in several experimental configurations akin to geophysical overturning [2, 3]. We parametrize the role of unstable stratification by means of the Rayleigh and Atwood numbers and compare the scaling and the multifractal structure functions of the different markers used to visualize the non-homogeneous. Both reactive and passive scalar tracers are used to investigate the mixing structure and the intermittency of the flow. Different initial conditions are compared and the mixing efficiency of the overall turbulent process is evaluated [4 - 6]. Diffusion is measured in the transition from a homogeneous linearly stratified fluid to a cellular or layered structure by means of Thermoelectric generated heating and cooling [2, 4]. Patterns arise by setting up a convective flow generated by a buoyant heat flux either in the base or in a side wall of the convective enclosure [1, 6]. The experiments described here investigate high Prandtl number mixing using brine or sugar solutions and fresh water in order to form a density interface and low Prandtl number mixing with only temperature gradients [7]. The set of dimensionless parameters define conditions of numeric and small scale laboratory modeling of environmental flows. Fields of velocity, density and their gradients were computed and visualized [8, 9]. When convective heating and cooling takes place the combination of internal waves and buoyant turbulence is much more complicated if the Rayleigh and Reynolds numbers are high in order to study entrainment and mixing. The experiments described here investigate high Prandtl number mixing using salt or sugar solutions and

Estimation of Rayleigh-wave spectral ratio from microtremors using a three-component single-station seismograph; Itten sanseibun bido kansoku ni motozuita Rayleigh ha shinpukuhi no suitei

Energy Technology Data Exchange (ETDEWEB)

Yamamoto, H; Mizutani, K; Saito, t [Iwate University, Iwate (Japan). Faculty of Engineering

1997-10-22

Discussions were given on the possibility of estimating Rayleigh-wave spectral ratio utilizing phase difference between horizontal movements and vertical movements by using a three-component single-station seismograph. The test has selected as an observation point a location in the city of Kushiro where a pulp and paper mill generating microtremors is the focal point, and the underground structure at that point has been estimated by using the vertical array observation method. The observation system has used three components of a velocity type seismograph having a natural period of one second, an amplifier and an analog data recorder. As a result of the discussions, the following matters were made clear: the spectral ratio with a phase difference of 90 degrees agrees with the frequency at a peak trough of the theoretical Rayleigh-wave spectral ratio; the values of the spectral ratio at the phase difference of 90 degrees and the values of the theoretical Rayleigh-wave spectral ratio correspond well excepting in frequency bands of the peak trough; and these results suggest that the Rayleigh-wave spectral ratio may be estimated by utilizing the phase difference between horizontal movements and vertical movements. Estimation of the underground structure by using the inverse analysis of this Rayleigh-wave spectral ratio is expected in the future. 6 refs., 5 figs., tab.

Natural convection heat transfer from a vertical circular tube sheet

International Nuclear Information System (INIS)

Dharne, S.P.; Gaitonde, U.N.

1996-01-01

Experiments were conducted to determine natural convection heat transfer coefficients (a) on a plain vertical circular plate, and (b) on a similar plate with a square array of non-conducting tubes fixed in it. The experiments were carried out using air as the heat transfer medium. The diameter of the brass plates used was 350 mm. The diameter of the bakelite tubes used was 19.2 mm. The range of Rayleigh numbers was from 1.06x10 8 to 1.66x10 8 . The results show that the heat transfer coefficients in case (a) are very close to those obtained using standard correlations for vertical flat plates, whereas for case (b) the heat transfer coefficients are at least 50 percent higher than those predicted by the Churchill-Chu correlation. It is hence concluded that the disturbance to boundary layer caused by the presence of tubes enhances the heat transfer coefficient significantly. (author). 4 refs., 3 figs

Rayleigh-Taylor instability and mixing in SN 1987A

International Nuclear Information System (INIS)

Ebisuzaki, T.; Shigeyama, T.; Nomoto, K.

1989-01-01

The stability of the supernova ejecta is compared with the Rayleigh-Taylor instability for a realistic model of SN 1987A. A linear analysis indicates that the layers around the composition interface between the hydrogen-rich and helium zones, and become Rayleigh-Taylor unstable between the helium and metal zones. In these layers, the pressure increases outward because of deceleration due to the reverse shock which forms when the blast shock hits the massive hydrogen-rich envelope. On the contrary, the density steeply decreases outward because of the preexisting nuclear burning shell. Then, these layers undergo the Raleigh-Taylor instability because of the opposite signs of the pressure and density gradients. The estimated growth rate is larger than the expansion rate of the supernova. The Rayleigh-Taylor instability near the composition interface is likely to induce mixing, which has been strongly suggested from observations of SN 1987A. 25 refs

Rayleigh-Taylor instability of cylindrical jets with radial motion

Energy Technology Data Exchange (ETDEWEB)

Chen, Xiang M. [GE Nuclear, Wilmington, NC (United States); Schrock, V.E.; Peterson, P.F. [Univ. of California, Berkeley, CA (United States)

1995-09-01

Rayleigh-Taylor instability of an interface between fluids with different densities subjected to accelleration normal to itself has interested researchers for almost a century. The classic analyses of a flat interface by Rayleigh and Taylor have shown that this type of instability depends on the direction of acceleration and the density differences of the two fluids. Plesset later analyzed the stability of a spherically symmetric flows (and a spherical interface) and concluded that the instability also depends on the velocity of the interface as well as the direction and magnitude of radial acceleration. The instability induced by radial motion in cylindrical systems seems to have been neglected by previous researchers. This paper analyzes the Rayleigh-Taylor type of the spherical case, the radial velocity also plays an important role. As an application, the example of a liquid jet surface in an Inertial Confinement Fusion (ICF) reactor design is analyzed.

A simple analytic approximation to the Rayleigh-Bénard stability threshold

NARCIS (Netherlands)

Prosperetti, Andrea

2011-01-01

The Rayleigh-Bénard linear stability problem is solved by means of a Fourier series expansion. It is found that truncating the series to just the first term gives an excellent explicit approximation to the marginal stability relation between the Rayleigh number and the wave number of the

A solution of the dispersion-convection equation of radial tracer transportation by the finite element variational method

International Nuclear Information System (INIS)

Hubert, J.

1979-01-01

The variational finite element method (of the Rayleigh-Ritz type) has been applied to solve the standard diffusion-convection equation of radial flow in a dispersive medium. It was shown that the imposing of the boundary condition ΔC/Δx = 0 (=null concentration gradient) introduced great errors in computation results. To remedy it this condition was imposed at the free end of the artifical domain. Its other end joined to the downstream boundary of the investigated domain. The results of calculations compared with the known analytical solutions of the parallel flow show their good accuracy. The method was used to discuss the applicability of the approximate analytical solutions of the radial flow. (author)

Dipping-interface mapping using mode-separated Rayleigh waves

Science.gov (United States)

Luo, Y.; Xia, J.; Xu, Y.; Zeng, C.; Miller, R.D.; Liu, Q.

2009-01-01

Multichannel analysis of surface waves (MASW) method is a non-invasive geophysical technique that uses the dispersive characteristic of Rayleigh waves to estimate a vertical shear (S)-wave velocity profile. A pseudo-2D S-wave velocity section is constructed by aligning 1D S-wave velocity profiles at the midpoint of each receiver spread that are contoured using a spatial interpolation scheme. The horizontal resolution of the section is therefore most influenced by the receiver spread length and the source interval. Based on the assumption that a dipping-layer model can be regarded as stepped flat layers, high-resolution linear Radon transform (LRT) has been proposed to image Rayleigh-wave dispersive energy and separate modes of Rayleigh waves from a multichannel record. With the mode-separation technique, therefore, a dispersion curve that possesses satisfactory accuracy can be calculated using a pair of consecutive traces within a mode-separated shot gather. In this study, using synthetic models containing a dipping layer with a slope of 5, 10, 15, 20, or 30 degrees and a real-world example, we assess the ability of using high-resolution LRT to image and separate fundamental-mode Rayleigh waves from raw surface-wave data and accuracy of dispersion curves generated by a pair of consecutive traces within a mode-separated shot gather. Results of synthetic and real-world examples demonstrate that a dipping interface with a slope smaller than 15 degrees can be successfully mapped by separated fundamental waves using high-resolution LRT. ?? Birkh??user Verlag, Basel 2009.

A Numerical Model for Prediction of Residual Stress Using Rayleigh Waves

International Nuclear Information System (INIS)

Yuan, Mao Dan; Kang, To; Kim, Hak Joon; Song, Sung Jin

2011-01-01

In this work, a numerical model is proposed for the relation between the magnitudes and the depth residual stress with the velocity of Rayleigh wave. Three cases, stress-free, uniform stress and layered stress, are investigated for the change tendency of the Rayleigh wave speed. Using the simulated signal with variation of residual stress magnitude and depth, investigation of the parameters for fitting residual stress and velocity change are performed. The speed change of Rayleigh wave shows a linear relation with the magnitude and an exponential relation with the depth of residual stress. The combination of these two effects could be used for the depth profile evaluation of the residual stress

Chemical Applications of Second Harmonic Rayleigh Scattering ...

Indian Academy of Sciences (India)

Chemical Applications of Second Harmonic Rayleigh Scattering Puspendu Kumar Das Department of Inorganic and Physical Chemistry Indian Institute of Science Bangalore 560012, India pkdas@ipc.iisc.ernet.in.

Numerical simulations of the effect of an isotropic heat field on the entropy generation due to natural convection in a square cavity

International Nuclear Information System (INIS)

El-Maghlany, Wael M.; Saqr, Khalid M.; Teamah, Mohamed A.

2014-01-01

Highlights: • Entropy generation in laminar natural convection in square cavity numerically studied. • The cavity subjected to an isotropic heat field with different intensities. • Study ranges 10 3 ⩽ Ra ⩽ 10 5 , 0 ⩽ ϕ ⩽ 10 and Pr = 0.7. • Entropy generation drastically affected by the superposition of an isotropic heat field. • CFD based empirical were derived for entropy generation as a function of Ra and φ. - Abstract: Entropy generation associated with laminar natural convection in an infinite square cavity, subjected to an isotropic heat field with different intensities; was numerically investigated for different values of Rayleigh number. The numerical work was carried out using, an in-house CFD code written in FORTRAN, which discretizes non-dimensional forms of the governing equations using the finite volume method and solves the resulting system of equations using Gauss-Seidal method utilizing a TDMA algorithm. Proper code validation was undertaken in order to establish the entropy generation calculations. It was found that the increase in the isotropic heat field intensity resulted in a corresponding exponential increase of the entropy augmentation number, and promoted high values of Bejan number within the flow. The entropy generation due to heat transfer was approximately one order of magnitude higher than the entropy generation due to fluid friction. The spatial uniformity of the Bejan number was more sensitive to the change in Rayleigh number than to the heat field intensity. The thermodynamic penalty of the isotropic heat field is shown by means of global integrals of the entropy source terms over the entire flow domain

Investigation of Focusing Effect according to the Cooling Condition and Height of the Metallic layer in a Severe Accident

Energy Technology Data Exchange (ETDEWEB)

Moon, Je-Young; Chung, Bum-Jin [Kyung Hee University, Yongin (Korea, Republic of)

2015-05-15

The Fukushima nuclear power plant accident has led to renewed research interests in severe accidents of nuclear power plants. In-Vessel Retention (IVR) of core melt is one of key severe accident management strategies adopted in nuclear power plant design. The metallic layer is heated from below by the radioactive decay heat generated at the oxide pool, and is cooled from above and side walls. During the IVR process, reactor vessel may be cooled externally (ERVC) and the heat fluxes to the side wall increase with larger temperature difference than above. This {sup F}ocusing effect{sup i}s varied by cooling condition of upper boundary and height of the metallic layer. A sulfuric acid–copper sulfate (H{sub 2}SO{sub 4} - CuSO{sub 4}) electroplating system was adopted as the mass transfer system. Numerical analysis using the commercial CFD program FLUENT 6.3 were carried out with the same material properties and cooling conditions to examine the variation of the cell. The experimental and numerical studies were performed to investigate the focusing effect according to cooling condition of upper boundary and the height in metallic layer. The height of the side wall was varied for three different cooling conditions: top only, side only, and both top and side. Mass transfer experiments, based on the analogy concept, were carried out in order to achieve high Rayleigh number. The experimental results agreed well with the Rayleigh-Benard convection correlations of Dropkin and Somerscales and Globe and Dropkin. The heat transfer on side wall cooling condition without top cooling is highest and was enhanced by decreasing the aspect ratio. The numerical results agreed well with the experimental results. Each cell pattern (cell size, cell direction, central location of cell) differed in the cooling condition. Therefore, it is difficult to predict the internal flow due to complexity of cell formation behavior.

Grain size measurements by ultrasonic Rayleigh surface waves

International Nuclear Information System (INIS)

Palanichamy, P.; Jayakumar, T.

1996-01-01

The use of Rayleigh surface waves to determine average grain size nondestructively in an austenitic stainless steel AISI type 316 stainless is discussed. Two commercial type 4MHz frequency surface wave transducers, one as transmitter and the other as receiver were employed for the measurement of surface wave amplitudes. Relative amplitudes of the Rayleigh surface waves were correlated with the metallographically obtained grain sizes. Results indicate that surface/sub-surface average grain sizes of AISI type 316 austenitic stainless steel can be estimated with a confidence level of more than 80% in the grain size range 30-170 μm. (author)

Rayleigh-Schrödinger series and Birkhoff decomposition

Science.gov (United States)

Novelli, Jean-Christophe; Paul, Thierry; Sauzin, David; Thibon, Jean-Yves

2018-01-01

We derive new expressions for the Rayleigh-Schrödinger series describing the perturbation of eigenvalues of quantum Hamiltonians. The method, somehow close to the so-called dimensional renormalization in quantum field theory, involves the Birkhoff decomposition of some Laurent series built up out of explicit fully non-resonant terms present in the usual expression of the Rayleigh-Schrödinger series. Our results provide new combinatorial formulae and a new way of deriving perturbation series in quantum mechanics. More generally we prove that such a decomposition provides solutions of general normal form problems in Lie algebras.

Depolarization Rayleigh scattering as a means of molecular concentration determination in plasmas

NARCIS (Netherlands)

Meulenbroeks, R.F.G.; Schram, D.C.; Jaegers, L.J.M.; Sanden, van de M.C.M.

1992-01-01

The difference in polarization for Rayleigh scattered radiation on spherically and nonspherically symmetric scattering objects has been used to obtain molecular species concentrations in plasmas of simple composition. Using a Rayleigh scattering diagnostic, the depolarized component of the scattered

Free diffusion of translation of macromolecules in solution with the rayleigh interferometer; Diffusion libre de translation des macromolecules en solution, par interferometrie de rayleigh

Energy Technology Data Exchange (ETDEWEB)

Leger, J J [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

1969-07-01

The aim of this study is to develop a rapid and accurate measurement, with the Rayleigh interferometer, of the free diffusion coefficient of translation of macromolecules in solution. After having explained the choice of a diffusion cell with laminar lateral flow, and explained the principle of the Rayleigh interferometer, a semi-automatic technique of free diffusion are then introduced. Solutions are proposed for systems composed of two or three components, such as biopolymers. The paper ends by drafting the possible treatment of recorded experimental data by means of electronic computer. (author) [French] Cette etude a ete entreprise pour mettre au point une methode precise et rapide de mesure, par interferometre de Rayleigh, du coefficient de diffusion libre de translation des macromolecules en solution. Apres avoir justifie le choix d'une cellule de diffusion a ecoulement laminaire lateral et explique le principe de l'interferometre de Rayleigh, l'auteur decrit une technique semi-automatique d'enregistrement des cliches d'interference. Il introduit ensuite les equations differentielles de diffusion libre et propose des solutions pour les systemes a deux et trois composants applicables aux biopolymeres. L'article se termine par une esquisse concernant le traitement des donnees experimentales enregistrees au moyen du calcul electronique. (auteur)

Rayleigh-Taylor instability of cylindrical jets with radial motion

International Nuclear Information System (INIS)

Chen, X.M.; Schrock, V.E.; Peterson, P.F.

1997-01-01

Rayleigh-Taylor instability of an interface between fluids with different densities subjected to acceleration normal to itself has interested researchers for almost a century. The classic analyses of a flat interface by Rayleigh and Taylor have shown that this type of instability depends on the direction of acceleration and the density differences of the two fluids. Plesset later analyzed the stability of a spherically symmetric flows (and a spherical interface) and concluded that the instability also depends on the velocity of the interface as well as the direction and magnitude of radial acceleration. The instability induced by radial motion in cylindrical systems seems to have been neglected by previous researchers. This paper analyzes the Rayleigh-Taylor type of instability for a cylindrical surface with radial motions. The results of the analysis show that, like the spherical case, the radial velocity also plays an important role. As an application, the example of a liquid jet surface in an Inertial Confinement Fusion (ICF) reactor design is analyzed. (orig.)

Dynamic stabilization of the imploding-shell Rayleigh-Taylor instability

International Nuclear Information System (INIS)

Boris, J.P.

1977-01-01

A method for dynamic stabilization of the Rayleigh-Taylor (R-T) instability on the surface of an imploding fusion pellet is discussed. The driving laser beams are modulated in intensity so the ablation layer is subject to a rapidly and strongly oscillating acceleration. A substantial band of the Rayleigh-Taylor instability spectrum can be stabilized by this oscillation even though the time average acceleration vector lies in the destabilizing direction. By adjusting the frequency, structure, and amplitude of the modulation, the band of dynamically stabilized modes can be made to include the most unstable and dangerous modes. Thus considerably higher aspect ratio shells (i.e., thinner shells) could implode successfully than had been previously considered stable enough. Both theory and numerical simulations support this conclusion for the case of laser-driven pellet implosions. Similar modulation via transverse beam oscillations or parallel bunching should also work to stabilize the most dangerous surface Rayleigh-Taylor modes in relativistic electron-, ion- and heavy ion-pellet fusion schemes. (U.K.)

Direct numerical simulation of the Rayleigh-Taylor instability with the spectral element method

International Nuclear Information System (INIS)

Zhang Xu; Tan Duowang

2009-01-01

A novel method is proposed to simulate Rayleigh-Taylor instabilities using a specially-developed unsteady three-dimensional high-order spectral element method code. The numerical model used consists of Navier-Stokes equations and a transport-diffusive equation. The code is first validated with the results of linear stability perturbation theory. Then several characteristics of the Rayleigh-Taylor instabilities are studied using this three-dimensional unsteady code, including instantaneous turbulent structures and statistical turbulent mixing heights under different initial wave numbers. These results indicate that turbulent structures of Rayleigh-Taylor instabilities are strongly dependent on the initial conditions. The results also suggest that a high-order numerical method should provide the capability of simulating small scale fluctuations of Rayleigh-Taylor instabilities of turbulent flows. (authors)

Evaluation of RANS and LES models for Natural Convection in High-Aspect-Ratio Parallel Plate Channels

Science.gov (United States)

Fradeneck, Austen; Kimber, Mark

2017-11-01

The present study evaluates the effectiveness of current RANS and LES models in simulating natural convection in high-aspect ratio parallel plate channels. The geometry under consideration is based on a simplification of the coolant and bypass channels in the very high-temperature gas reactor (VHTR). Two thermal conditions are considered, asymmetric and symmetric wall heating with an applied heat flux to match Rayleigh numbers experienced in the VHTR during a loss of flow accident (LOFA). RANS models are compared to analogous high-fidelity LES simulations. Preliminary results demonstrate the efficacy of the low-Reynolds number k- ɛ formulations and their enhancement to the standard form and Reynolds stress transport model in terms of calculating the turbulence production due to buoyancy and overall mean flow variables.

Rayleigh Taylor instability of two superposed compressible fluids in un-magnetized plasma

International Nuclear Information System (INIS)

Sharma, P K; Tiwari, A; Argal, S; Chhajlani, R K

2014-01-01

The linear Rayleigh Taylor instability of two superposed compressible Newtonian fluids is discussed with the effect of surface tension which can play important roles in space plasma. As in both the superposed Newtonian fluids, the system is stable for potentially stable case and unstable for potentially unstable case in the present problem also. The equations of the problem are solved by normal mode method and a dispersion relation is obtained for such a system. The behaviour of growth rate is examined in the presence of surface tension and it is found that the surface tension has stabilizing influence on the Rayleigh Taylor instability of two superposed compressible fluids. Numerical analysis is performed to show the effect of sound velocity and surface tension on the growth rate of Rayleigh Taylor instability. It is found that both parameters have stabilizing influence on the growth rate of Rayleigh Taylor instability.

Thresholds for the onset of fluid and magnetofluid turbulence

International Nuclear Information System (INIS)

Montgomery, D.

1982-01-01

Hydrodynamic stability theory has focussed on a few simple test cases to obtain the sharpest possible confrontations between theory and experiment. Six of these are briefly reviewed: plane Poiseuille and Couette flow, pipe flow, rotating Couette flow, thermally-driven Benard convection, and the Blasius laminar boundary layer. Linear perturbation theory seems inadequate in the first three cases, and satisfactory in the last three. Insufficient information, experimental or theoretical, exists in magnetohydrodynamics to make any comparably decisive tests

Passive retrieval of Rayleigh waves in disordered elastic media

International Nuclear Information System (INIS)

Larose, Eric; Derode, Arnaud; Clorennec, Dominique; Margerin, Ludovic; Campillo, Michel

2005-01-01

When averaged over sources or disorder, cross correlation of diffuse fields yields the Green's function between two passive sensors. This technique is applied to elastic ultrasonic waves in an open scattering slab mimicking seismic waves in the Earth's crust. It appears that the Rayleigh wave reconstruction depends on the scattering properties of the elastic slab. Special attention is paid to the specific role of bulk to Rayleigh wave coupling, which may result in unexpected phenomena, such as a persistent time asymmetry in the diffuse regime

In situ nanoparticle diagnostics by multi-wavelength Rayleigh-Mie scattering ellipsometry

CERN Document Server

Gebauer, G

2003-01-01

We present and discuss the method of multiple-wavelength Rayleigh-Mie scattering ellipsometry for the in situ analysis of nanoparticles. It is applied to the problem of nanoparticles suspended in low-pressure plasmas. We discuss experimental results demonstrating that the size distribution and the complex refractive index can be determined with high accuracy and present a study on the in situ analysis of etching of melamine-formaldehyde nanoparticles suspended in an oxygen plasma. It is also shown that particles with a shell structure (core plus mantle) can be analysed by Rayleigh-Mie scattering ellipsometry. Rayleigh-Mie scattering ellipsometry is also applicable to in situ analysis of nanoparticles under high gas pressures and in liquids.

Parameter identification in a generalized time-harmonic Rayleigh damping model for elastography.

Directory of Open Access Journals (Sweden)

Elijah E W Van Houten

Full Text Available The identifiability of the two damping components of a Generalized Rayleigh Damping model is investigated through analysis of the continuum equilibrium equations as well as a simple spring-mass system. Generalized Rayleigh Damping provides a more diversified attenuation model than pure Viscoelasticity, with two parameters to describe attenuation effects and account for the complex damping behavior found in biological tissue. For heterogeneous Rayleigh Damped materials, there is no equivalent Viscoelastic system to describe the observed motions. For homogeneous systems, the inverse problem to determine the two Rayleigh Damping components is seen to be uniquely posed, in the sense that the inverse matrix for parameter identification is full rank, with certain conditions: when either multi-frequency data is available or when both shear and dilatational wave propagation is taken into account. For the multi-frequency case, the frequency dependency of the elastic parameters adds a level of complexity to the reconstruction problem that must be addressed for reasonable solutions. For the dilatational wave case, the accuracy of compressional wave measurement in fluid saturated soft tissues becomes an issue for qualitative parameter identification. These issues can be addressed with reasonable assumptions on the negligible damping levels of dilatational waves in soft tissue. In general, the parameters of a Generalized Rayleigh Damping model are identifiable for the elastography inverse problem, although with more complex conditions than the simpler Viscoelastic damping model. The value of this approach is the additional structural information provided by the Generalized Rayleigh Damping model, which can be linked to tissue composition as well as rheological interpretations.

Rayleigh-Taylor instability and mushroom-pattern formation in a two-component Bose-Einstein condensate

International Nuclear Information System (INIS)

Sasaki, Kazuki; Suzuki, Naoya; Saito, Hiroki; Akamatsu, Daisuke

2009-01-01

The Rayleigh-Taylor instability at the interface in an immiscible two-component Bose-Einstein condensate is investigated using the mean field and Bogoliubov theories. Rayleigh-Taylor fingers are found to grow from the interface and mushroom patterns are formed. Quantized vortex rings and vortex lines are then generated around the mushrooms. The Rayleigh-Taylor instability and mushroom-pattern formation can be observed in a trapped system.

Suppression of instability in rotatory hydromagnetic convection

Indian Academy of Sciences (India)

first time by Lord Rayleigh [9] for the idealized case of two free boundaries. Rayleigh's theory shows that the gravity-dominated thermal instability in liquid layer ... suppressed for oscillatory perturbations by the simultaneous application of a ...

On Amplify-and-Forward Relaying Over Hyper-Rayleigh Fading Channels

Directory of Open Access Journals (Sweden)

S. H. Alvi

2014-12-01

Full Text Available Relayed transmission holds promise for the next generation of wireless communication systems due to the performance gains it can provide over non-cooperative systems. Recently hyper-Rayleigh fading, which represents fading conditions more severe than Rayleigh fading, has received attention in the context of many practical communication scenarios. Though power allocation for Amplify-and-Forward (AF relaying networks has been studied in the literature, a theoretical analysis of the power allocation problem for hyper-Rayleigh fading channels is a novel contribution of this work. We develop an optimal power allocation (OPA strategy for a dual-hop AF relaying network in which the relay-destination link experiences hyper-Rayleigh fading. A new closed-form expression for the average signal-to-noise ratio (SNR at destination is derived and it is shown to provide a new upper-bound on the average SNR at destination, which outperforms a previously proposed upper-bound based on the well-known harmonic-geometric mean inequality. An OPA across the source and relay nodes, subject to a sum-power constraint, is proposed and it is shown to provide measurable performance gains in average SNR and SNR outage at the destination relative to the case of equal power allocation.

Mixed convective magnetohydrodynamic flow in a vertical channel filled with nanofluids

Directory of Open Access Journals (Sweden)

S. Das

2015-06-01

Full Text Available The fully developed mixed convection flow in a vertical channel filled with nanofluids in the presence of a uniform transverse magnetic field has been studied. Closed form solutions for the fluid temperature, velocity and induced magnetic field are obtained for both the buoyancy-aided and -opposed flows. Three different water-based nanofluids containing copper, aluminium oxide and titanium dioxide are taken into consideration. Effects of the pertinent parameters on the nanofluid temperature, velocity, and induced magnetic field as well as the shear stress and the rate of heat transfer at the channel wall are shown in figures and tables followed by a quantitative discussion. It is found that the magnetic field tends to enhance the nanofluid velocity in the channel. The induced magnetic field vanishes in the cental region of the channel. The critical Rayleigh number at onset of instability of flow is strongly dependent on the volume fraction of nanoparticles and the magnetic field.

Thermal convection for large Prandtl numbers

NARCIS (Netherlands)

Grossmann, Siegfried; Lohse, Detlef

2001-01-01

The Rayleigh-Bénard theory by Grossmann and Lohse [J. Fluid Mech. 407, 27 (2000)] is extended towards very large Prandtl numbers Pr. The Nusselt number Nu is found here to be independent of Pr. However, for fixed Rayleigh numbers Ra a maximum in the Nu(Pr) dependence is predicted. We moreover offer

Experimental investigation of quantum effects in time-resolved resonance Rayleigh scattering from quantum well excitons

DEFF Research Database (Denmark)

Birkedal, Dan; Shah, Jagdeep; Shchegrov, Andrei V.

2000-01-01

Resonant Rayleigh scattering from quantum well excitons is investigated using ultrafast spectral interferometry. We isolate the coherent Rayleigh scattering from incoherent luminescence in a single speckle. Averaging the resonant Rayleigh intensity over several speckles allows us to identify...... features in support of quantum corrections to the classical description of the underlying scattering process....

The effect of pressure on spontaneous Rayleigh-Brillouin scattering spectrum in nitrogen

Science.gov (United States)

Yang, Chuanyin; Wu, Tao; Shang, Jingcheng; Zhang, Xinyi; Hu, Rongjing; He, XingDao

2018-05-01

In order to study the effect of gas pressure on spontaneous Rayleigh-Brillouin scattering spectrum and verify the validity of Tenti S6 model at pressures up to 8 atm, the spontaneous Rayleigh-Brillouin scattering experiment in nitrogen was performed for a wavelength of 532 nm at the constant room temperature of 296 K and a 90° scattering angle. By comparing the experimental spectrum with the theoretical spectrum, the normalized root mean square deviation was calculated and found less than 2.2%. It is verified that Tenti S6 model can be applied to the spontaneous Rayleigh-Brillion scattering of nitrogen under higher pressures. The results of the experimental data analysis demonstrate that pressure has more effect on Brillouin peak intensity and has negligible effect on Brillouin frequency shift, and pressure retrieval based on spontaneous Rayleigh-Brillouin scattering profile is a promising method for remote of pressure, such as harsh environment applications. Some factors that caused experiment deviations are also discussed.

Measurement of unsteady convection in a complex fenestration using laser interferometry

Energy Technology Data Exchange (ETDEWEB)

Poulad, M.E.; Naylor, D. [Ryerson Univ., Toronto, ON (Canada). Dept. of Mechanical and Industrial Engineering; Oosthuizen, P.H. [Queen' s Univ., Kingston, ON (Canada). Dept. of Mechanical and Materials Engineering

2009-06-15

Complex fenestration involving windows with between-panes louvered blinds is gaining interest as a means to control solar gains in buildings. However, the heat transfer performance of this type of shading system is not well understood, especially at high Rayleigh numbers. A Mach-Zehnder interferometer was used in this study to measure the unsteady convective heat transfer in a tall enclosure with between-panes blind that was heated to simulate absorbed solar radiation. Digital cinematography was combined with laser interferometry to make time-averaged measurements of unsteady and turbulent free convective heat transfer. This paper described the procedures used to measure the time-average local heat flux. Under strongly turbulent conditions, the average Nusselt number for the enclosure was found to compare well with empirical correlations. A total sampling time of about ten seconds was needed in this experiment to obtain a stationary time-average heat flux. The time-average heat flux was found to be relatively insensitive to the camera frame rate. The local heat flux was found to be unsteady and periodic. Heating of the blind made the flow more unstable, producing a higher amplitude heat flux variation than for the unheated blind condition. This paper reported on only a small set of preliminary measurements. This study is being extended to other blind angles and glazing spacings. The next phase will focus on flow visualization studies to characterize the nature of the flow. 8 refs., 2 tabs., 7 figs.

Rayleigh-Taylor/gravitational instability in dense magnetoplasmas

Energy Technology Data Exchange (ETDEWEB)

Ali, S., E-mail: shahid.ali@ncp.edu.p [National Centre for Physics, Quaid-i-Azam University Campus, Islamabad (Pakistan); IPFN, Instituto Superior Tecnico, Av. Rovisco Pais, 1049-001 Lisboa (Portugal); Ahmed, Z. [COMSATS Institute of Information Technology, Department of Physics, Wah Campus (Pakistan); Mirza, Arshad M. [Theoretical Plasma Physics Group, Physics Department, Quaid-i-Azam University, Islamabad 45320 (Pakistan); Ahmad, I. [COMSATS Institute of Information Technology, Department of Physics, Islamabad Campus (Pakistan)

2009-08-10

The Rayleigh-Taylor instability is investigated in a nonuniform dense quantum magnetoplasma. For this purpose, a quantum hydrodynamical model is used for the electrons whereas the ions are assumed to be cold and classical. The dispersion relation for the Rayleigh-Taylor instability becomes modified with the quantum corrections associated with the Fermi pressure law and the quantum Bohm potential force. Numerically, it is found that the quantum speed and density gradient significantly modify the growth rate of RT instability. In a dense quantum magnetoplasma case, the linear growth rate of RT instability becomes significantly higher than its classical value and the modes are found to be highly localized. The present investigation should be useful in the studies of dense astrophysical magnetoplasmas as well as in laser-produced plasmas.

Rayleigh-Taylor/gravitational instability in dense magnetoplasmas

International Nuclear Information System (INIS)

Ali, S.; Ahmed, Z.; Mirza, Arshad M.; Ahmad, I.

2009-01-01

The Rayleigh-Taylor instability is investigated in a nonuniform dense quantum magnetoplasma. For this purpose, a quantum hydrodynamical model is used for the electrons whereas the ions are assumed to be cold and classical. The dispersion relation for the Rayleigh-Taylor instability becomes modified with the quantum corrections associated with the Fermi pressure law and the quantum Bohm potential force. Numerically, it is found that the quantum speed and density gradient significantly modify the growth rate of RT instability. In a dense quantum magnetoplasma case, the linear growth rate of RT instability becomes significantly higher than its classical value and the modes are found to be highly localized. The present investigation should be useful in the studies of dense astrophysical magnetoplasmas as well as in laser-produced plasmas.

Quantum effects on the Rayleigh-Taylor instability in a horizontal inhomogeneous rotating plasma

International Nuclear Information System (INIS)

Hoshoudy, G. A.

2009-01-01

The Rayleigh-Taylor instability is studied analytically in inhomogeneous plasma rotating uniformly in an external transverse magnetic field. The influence of the quantum mechanism is considered. For a stratified layer the linear growth rate is obtained. Some special cases that isolate the effect of various parameters on the growth rate of the Rayleigh-Taylor instability are discussed. It is shown that for some cases, the presence of the external transverse magnetic field beside the quantum effect will bring about more stability on the Rayleigh-Taylor instability.

probing the atmosphere with high power, high resolution radars

Science.gov (United States)

Hardy, K. R.; Katz, I.

1969-01-01

Observations of radar echoes from the clear atmosphere are presented and the scattering mechanisms responsible for the two basic types of clear-air echoes are discussed. The commonly observed dot echo originates from a point in space and usually shows little variation in echo intensity over periods of about 0.1 second. The second type of clear-air radar echo appears diffuse in space, and signal intensities vary considerably over periods of less than 0.1 second. The echoes often occur in thin horizontal layers or as boundaries of convective activity; these are characterized by sharp gradients of refractive index. Some features of clear-air atmospheric structures as observed with radar are presented. These structures include thin stable inversions, convective thermals, Benard convection cells, breaking gravity waves, and high tropospheric layers which are sufficiently turbulent to affect aircraft.

Computational simulation of natural convection of a molten core in lower head of a PWR pressure vessel

International Nuclear Information System (INIS)

Vieira, Camila Braga; Romero, Gabriel Alves; Jian Su

2010-01-01

Computational simulation of natural convection in a molten core during a hypothetical severe accident in the lower head of a typical PWR pressure vessel was performed for two-dimensional semi-circular geometry with isothermal walls. Transient turbulent natural convection heat transfer of a fluid with uniformly distributed volumetric heat generation rate was simulated by using a commercial computational fluid dynamics software ANSYS CFX 12.0. The Boussinesq model was used for the buoyancy effect generated by the internal heat source in the flow field. The two-equation k-ω based SST (Shear Stress Transport) turbulence model was used to mould the turbulent stresses in the Reynolds-Average Navier-Stokes equations (RANS). Two Prandtl numbers, 6:13 and 7:0, were considered. Five Rayleigh numbers were simulated for each Prandtl number used (109, 1010, 1011, 1012, and 1013). The average Nusselt numbers on the bottom surface of the semicircular cavity were in excellent agreement with Mayinger et al. (1976) correlation and only at Ra = 109 the average Nusselt number on the top flat surface was in agreement with Mayinger et al. (1976) and Kulacki and Emara (1975) correlations. (author)

Effects of thermal conduction and compressibility on Rayleigh-Taylor instability

International Nuclear Information System (INIS)

Takabe, Hideaki; Mima, Kunioki.

1980-01-01

In order to study the stability of the ablation front in laser driven implosion, the thermal conduction and compressibility effects on the Rayleigh-Taylor instability are considered. It is found that the thermal conduction effect cannot stabilize the Rayleigh-Taylor mode, but reduce the growth rate in the short wavelength case. But, the growth rate is found not to differ from the classical value √gk in the long wavelength limit, where the compressibility is essential. (author)

Dynamics and mass transport of solutal convection in a closed porous media system

Science.gov (United States)

Wen, Baole; Akhbari, Daria; Hesse, Marc

2016-11-01

Most of the recent studies of CO2 sequestration are performed in open systems where the constant partial pressure of CO2 in the vapor phase results in a time-invariant saturated concentration of CO2 in the brine (Cs). However, in some closed natural CO2 reservoirs, e.g., Bravo Dome in New Mexico, the continuous dissolution of CO2 leads to a pressure drop in the gas that is accompanied by a reduction of Cs and thereby affects the dynamics and mass transport of convection in the brine. In this talk, I discuss the characteristics of convective CO2 dissolution in a closed system. The gas is assumed to be ideal and its solubility given by Henry's law. An analytical solution shows that the diffusive base state is no longer self-similar and that diffusive mass transfer declines rapidly. Scaling analysis reveals that the volume ratio of brine and gas η determines the behavior of the system. DNS show that no constant flux regime exists for η > 0 nevertheless, the quantity F /Cs2 remains constant, where F is the dissolution flux. The onset time is only affected by η when the Rayleigh number Ra is small. In this case, the drop in Cs during the initial diffusive regime significantly reduces the effective Ra and therefore delays the onset.

Experimental investigation of natural convection in a core of a marine reactor in rolling motion

International Nuclear Information System (INIS)

Murata, Hiroyuki; Sawada, Ken-ichi; Kobayashi, Michiyuki

2000-01-01

A series of single-phase natural circulation experiments in a simulated marine reactor mounted on a rolling bed was performed and the average Nusselt number in the core was evaluated in order to investigate effects of the rolling motion on the heat transfer in the core. Heat transfer with an upright attitude is well correlated with the Rayleigh number and is slightly lower than El-Genk's correlation. Heat transfer in the core is not affected by the inclination angle because the inclination of the present experiment is not large enough to cause any remarkable changes in the flow pattern of the core. Heat transfer in the core is enhanced by the rolling motion which is thought to cause internal flow in the core. Heat transfer during the rolling motion is correlated with the Richardson number for rolling motion, Ri R , and is classified into three regimes: (1) region A (0.05 R ≤0.3) where heat transfer is dominated by the inertial force due to the rolling motion; (2) region B (0.3 R ≤2) where heat transfer is affected by the combined effect of the inertial force and natural convection; and (3) region C (Ri R >2) where heat transfer is affected only by the natural convection. (author)

Natural convection and radiation heat transfer in a vertical porous layer with a hexagonal honeycomb core. 1st Report. Numerical analysis; Honeycomb core de shikirareta enchoku takoshitsu sonai no shizen tairyu - fukusha fukugo netsu dentatsu. 1. Suchi kaiseki

Energy Technology Data Exchange (ETDEWEB)

Yamaguchi, Y; Asako, Y [Tokyo Metropolitan Univ., Tokyo (Japan). Faculty of Technology; Faghri, M [University of Rhode Island, Kingston, RI (United States)

1997-06-25

Combined heat transfer characteristics are obtained numerically for three-dimensional natural convection and thermal radiation in a long and wide vertical porous layer with a hexagonal honeycomb core. The porous layer is assumed to be both homogeneous and isotropic. The pure Darcy law for the fluid flow and Rosseland`s approximation for the radiation are employed. The numerical methodology is based on an algebraic coordinate transformation technique and the transformed governing equations are solved using the SIMPLE algorithm. The effect of radiation on the beat transfer characteristics is investigated in a wide range of radiation numbers and temperature ratios, for two Darcy-Rayleigh number values (Ra*=100, 1000), and for a fixed aspect ratio of H/L=1. The results are presented in the form of combined and convection heat transfer coefficients, and are compared with the corresponding values for pure natural convection. 7 refs., 12 figs., 1 tab.

Analytical and numerical analysis of finite amplitude Rayleigh-Taylor instability

International Nuclear Information System (INIS)

Meiron, D.I.; Saffman, P.G.

1987-01-01

We summarize the results obtained in the last year. These include a simple model of bubble competition in Rayleigh-Taylor unstable flows which gives results which are in good agreement with experiment. In addition the model has been compared with two dimensional numerical simulations of inviscid Rayleigh-Taylor instability using the cloud-in-cell method. These simulations can now be run into the late time regime and can track the competition of as many as ten bubbles. The improvement in performance over previous applications of the cloud-in-cell approach is due to the application of finite difference techniques designed to handle shock-like structures in the vorticity of the interface which occur at late times. We propose to extend the research carried thus far to Rayleigh-Taylor problems in three dimensional and convergent geometries as well as to two-fluid instabilities in which interface roll-up is observed. Finally we present a budget for the fiscal year 1987-1988. 6 refs

Effect of Perpendicular Magnetic Field on Free Convection in a Rectangular Cavity

Directory of Open Access Journals (Sweden)

Anand Kumar

2015-12-01

Full Text Available The steady free convective flow of a viscous incompressible and electrically conducting fluid in a two-dimensional cavity in the presence of a magnetic field applied normal to the plane of the cavity is investigated. The side vertical walls of the cavity are heated differentially while the horizontal walls are assumed to be insulated. The governing equations are re-formulated in terms of vorticity and stream function. The resulting boundary value problem is solved numerically using an alternating direction implicit (ADI method. A number of plots illustrating the influence of Hartmann number and Rayleigh number on the streamlines and isotherms as well as the velocity and temperature profiles are shown. Furthermore, results for the average Nusselt number and the maximum absolute stream function have been obtained, and these are compared with the corresponding results in the literature when the magnetic field is applied along the cavity in the horizontal direction.

Effect of FLR correction on Rayleigh -Taylor instability of quantum and stratified plasma

International Nuclear Information System (INIS)

Sharma, P.K.; Tiwari, Anita; Argal, Shraddha; Chhajlani, R.K.

2013-01-01

The Rayleigh Taylor instability of stratified incompressible fluids is studied in presence of FLR Correction and quantum effects in bounded medium. The Quantum magneto hydrodynamic equations of the problem are solved by using normal mode analysis method. A dispersion relation is carried out for the case where plasma is bounded by two rigid planes z = 0 and z = h. The dispersion relation is obtained in dimensionless form to discuss the growth rate of Rayleigh Taylor instability in presence of FLR Correction and quantum effects. The stabilizing or destabilizing behavior of quantum effect and FLR correction on the Rayleigh Taylor instability is analyzed. (author)

Generalized modification in the lattice Bhatnagar-Gross-Krook model for incompressible Navier-Stokes equations and convection-diffusion equations.

Science.gov (United States)

Yang, Xuguang; Shi, Baochang; Chai, Zhenhua

2014-07-01

In this paper, two modified lattice Boltzmann Bhatnagar-Gross-Krook (LBGK) models for incompressible Navier-Stokes equations and convection-diffusion equations are proposed via the addition of correction terms in the evolution equations. Utilizing this modification, the value of the dimensionless relaxation time in the LBGK model can be kept in a proper range, and thus the stability of the LBGK model can be improved. Although some gradient operators are included in the correction terms, they can be computed efficiently using local computational schemes such that the present LBGK models still retain the intrinsic parallelism characteristic of the lattice Boltzmann method. Numerical studies of the steady Poiseuille flow and unsteady Womersley flow show that the modified LBGK model has a second-order convergence rate in space, and the compressibility effect in the common LBGK model can be eliminated. In addition, to test the stability of the present models, we also performed some simulations of the natural convection in a square cavity, and we found that the results agree well with those reported in the previous work, even at a very high Rayleigh number (Ra = 10(12)).

Natural convection flow and heat transfer between a fluid layer and a porous layer inside a rectangular enclosure

International Nuclear Information System (INIS)

Beckermann, C.; Ramadhyani, S.; Viskanta, R.

1986-01-01

A numerical and experimental study is performed to analyze the steady-state natural convection fluid flow and heat transfer in a vertical rectangular enclosure that is partially filled with a vertical layer of a fluid-saturated porous medium. The flow in the porous layer is modeled utilizing the Brinkman-Forchheimer-extended Darcy equations. The numerical model is verified by conducting a number of experiments with spherical glass beads as the porous medium and water and glycerin as the fluids in rectangular test-cells. The agreement between the flow visualization results and temperature measurements and the numerical model is, in general, good. It is found that the amount of fluid penetrating from the fluid region into the porous layer depends strongly on the Darcy (Da) and Rayleigh (Ra) numbers. For a relatively low product of Ra x Da, the flow takes place primarily in the fluid layer, and heat transfer in the porous layer is by conduction only. On the other hand, fluid penetrating into a relatively highly permeable porous layer has a significant impact on the natural convection flow patterns in the entire enclosure

Study on Rayleigh Wave Inversion for Estimating Shear-wave Velocity Profile

Directory of Open Access Journals (Sweden)

T.A. Sanny

2003-05-01

Full Text Available Rayleigh wave or ground roll is a noise in seismic body waves. However, how to use this noise for soil characterization is very interesting since Rayleigh wave phase velocity is a function of compression-wave velocity, shear-wave velocity, density and layer thickness. In layered-medium Rayleigh wave velocity also depends on wavelength or frequency, and this phenomenon is called dispersion. Inversion procedure to get shear-wave velocity profile needs a priori information about the solution of the problem to limit the unknown parameters. The Lagrange multiplier method was used to solve the constrained optimization problems or well known as a smoothing parameter in inversion problems. The advantage of our inversion procedure is that it can guarantee the convergence of solution even though the field data is incomplete, insufficient, and inconsistent. The addition of smoothing parameter can reduce the time to converge. Beside numerical stability, the statistical stability is also involved in inversion procedure. In field experiment we extracted ground roll data from seismic refraction record. The dispersion curves had been constructed by applying f-k analysis and f-k dip filtering. The dispersion curves show the dependence of Rayleigh wave phase velocities in layered media to frequency. The synthetic models also demonstrate the stability and the speed of inversion procedure.

National Convective Weather Diagnostic

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National Oceanic and Atmospheric Administration, Department of Commerce — Current convective hazards identified by the National Convective Weather Detection algorithm. The National Convective Weather Diagnostic (NCWD) is an automatically...

Short Rayleigh length free electron lasers

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W. B. Colson

2006-03-01

Full Text Available Conventional free electron laser (FEL oscillators minimize the optical mode volume around the electron beam in the undulator by making the resonator Rayleigh length about one third to one half of the undulator length. This maximizes gain and beam-mode coupling. In compact configurations of high-power infrared FELs or moderate power UV FELs, the resulting optical intensity can damage the resonator mirrors. To increase the spot size and thereby reduce the optical intensity at the mirrors below the damage threshold, a shorter Rayleigh length can be used, but the FEL interaction is significantly altered. We model this interaction using a coordinate system that expands with the rapidly diffracting optical mode from the ends of the undulator to the mirrors. Simulations show that the interaction of the strongly focused optical mode with a narrow electron beam inside the undulator distorts the optical wave front so it is no longer in the fundamental Gaussian mode. The simulations are used to study how mode distortion affects the single-pass gain in weak fields, and the steady-state extraction in strong fields.

Study on evaluation methods for Rayleigh wave dispersion characteristic

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Shi, L.; Tao, X.; Kayen, R.; Shi, H.; Yan, S.

2005-01-01

The evaluation of Rayleigh wave dispersion characteristic is the key step for detecting S-wave velocity structure. By comparing the dispersion curves directly with the spectra analysis of surface waves (SASW) method, rather than comparing the S-wave velocity structure, the validity and precision of microtremor-array method (MAM) can be evaluated more objectively. The results from the China - US joint surface wave investigation in 26 sites in Tangshan, China, show that the MAM has the same precision with SASW method in 83% of the 26 sites. The MAM is valid for Rayleigh wave dispersion characteristic testing and has great application potentiality for site S-wave velocity structure detection.

Three-dimensional single-mode nonlinear ablative Rayleigh-Taylor instability

International Nuclear Information System (INIS)

Yan, R.; Aluie, H.; Betti, R.; Sanz, J.; Liu, B.; Frank, A.

2016-01-01

The nonlinear evolution of the single-mode ablative Rayleigh-Taylor instability is studied in three dimensions. As the mode wavelength approaches the cutoff of the linear spectrum (short-wavelength modes), it is found that the three-dimensional (3D) terminal bubble velocity greatly exceeds both the two-dimensional (2D) value and the classical 3D bubble velocity. Unlike in 2D, the 3D short-wavelength bubble velocity does not saturate. The growing 3D bubble acceleration is driven by the unbounded accumulation of vorticity inside the bubble. The vorticity is transferred by mass ablation from the Rayleigh-Taylor spikes to the ablated plasma filling the bubble volume

Rayleigh imaging in spectral mammography

Science.gov (United States)

Berggren, Karl; Danielsson, Mats; Fredenberg, Erik

2016-03-01

Spectral imaging is the acquisition of multiple images of an object at different energy spectra. In mammography, dual-energy imaging (spectral imaging with two energy levels) has been investigated for several applications, in particular material decomposition, which allows for quantitative analysis of breast composition and quantitative contrast-enhanced imaging. Material decomposition with dual-energy imaging is based on the assumption that there are two dominant photon interaction effects that determine linear attenuation: the photoelectric effect and Compton scattering. This assumption limits the number of basis materials, i.e. the number of materials that are possible to differentiate between, to two. However, Rayleigh scattering may account for more than 10% of the linear attenuation in the mammography energy range. In this work, we show that a modified version of a scanning multi-slit spectral photon-counting mammography system is able to acquire three images at different spectra and can be used for triple-energy imaging. We further show that triple-energy imaging in combination with the efficient scatter rejection of the system enables measurement of Rayleigh scattering, which adds an additional energy dependency to the linear attenuation and enables material decomposition with three basis materials. Three available basis materials have the potential to improve virtually all applications of spectral imaging.

NUMERICAL STUDY OF NON-DARCIAN NATURAL CONVECTION HEAT TRANSFER IN A RECTANGULAR ENCLOSURE FILLED WITH POROUS MEDIUM SATURATED WITH VISCOUS FLUID

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Mahmood H. Ali

2015-02-01

Full Text Available A numerical study of non-Darcian natural convection heat transfer in a rectangular enclosure filled with porous medium saturated with viscous fluid was carried out. The effects of medium Rayleigh number, porosity, particle to fluid thermal conductivity ratio, Darcy number and enclosure aspect ratio on heat transfer were examined to demonstrate the ability of using this construction in thermal insulation of buildings walls.A modified Brinkman-Forchheimer-extended Darcy flow model was used and no-slip boundary conditions were imposed for velocity at the walls and the governing equations were expressed in dimensionless stream function, vorticity, and temperature formulation. The resulting algebraic equations obtained from finite difference discritization of vorticity and temperature equations are solved using (ADI method which uses Three Diagonal Matrix Algorithm (TDMA in each direction, while that of the stream function equation solved using successive iteration method.The study was done for the range of enclosure aspect ratio ( which is in the tall layers region at medium Rayleigh number ( , Darcy number (Da=10-3, 10-4, 10-5 , porosity (e=0.35, 0.45, 0.55, particle to fluid thermal conductivity (kS/kf=5.77, 38.5, 1385.5.The results showed that the Nusselt number is direct proportional to medium Rayleigh number and porosity and reversely proportional to Darcy number, ratio of particle to fluid thermal conductivity and enclosure aspect ratio. The variables that affect the heat transfer in the above arrangement was correlated in a mathematical equation that account better for their affects on heat transfer which is represented by mean Nusselt number (Nu.

Natural convection in a horizontal channel provided with heat generating blocks: Discussion of the isothermal blocks validity

International Nuclear Information System (INIS)

Mouhtadi, D.; Amahmid, A.; Hasnaoui, M.; Bennacer, R.

2012-01-01

Highlights: ► We examine the validity of isothermal model for blocks with internal heat generation. ► Criteria based on comparison of total and local quantities are adopted. ► Thermal conductivity and Biot number required for the validity of the isothermal model are dependent on the Rayleigh number. ► The validity conditions are also affected by the multiplicity of solutions. - Abstract: This work presents a numerical study of air natural convection in a horizontal channel provided with heating blocks periodically distributed on its lower adiabatic surface. The blocks are submitted to a uniform heat generation and the channel upper surface is maintained at a cold constant temperature. The main objective of this study is to examine the validity of the model with isothermal blocks for the system under consideration. Then the calculations are performed using two different models. In the first (denoted Model 1 or M1) the calculations are performed by imposing a uniform volumetric heat generation inside the blocks. In the second model (denoted Model 2 or M2), the blocks are maintained isothermal at the average blocks surface temperature deduced from the Model 1. The controlling parameters of the present problem are the thermal conductivity ratio of the solid block and the fluid (0.1 ⩽ k* = k s /k a ⩽ 200) and the Rayleigh number (10 4 ⩽ Ra ⩽ 10 7 ). The validity of the isothermal model is examined for various Ra by using criteria based on local and mean heat transfer characteristics. It is found that some solutions of the isothermal model do not reproduce correctly the results of the first model even for very large conductivity ratios. The Biot number below which the Model 2 is valid depends strongly on the Rayleigh number and the type of solution.

Rayleigh scattering in coupled microcavities: theory.

Science.gov (United States)

Vörös, Zoltán; Weihs, Gregor

2014-12-03

In this paper we theoretically study how structural disorder in coupled semiconductor heterostructures influences single-particle scattering events that would otherwise be forbidden by symmetry. We extend the model of Savona (2007 J. Phys.: Condens. Matter 19 295208) to describe Rayleigh scattering in coupled planar microcavity structures, and find that effective filter theories can be ruled out.

Natural convection heat transfer in an anisotropic porous cavity heated from the side. 1st Report. Theory; Tosuiritsu ni ihosei wo yusuru howa takoshitsu sonai no sokuho kanetsu ni yoru shizen tairyu netsu dentatsu. 1. Riron kaiseki

Energy Technology Data Exchange (ETDEWEB)

Kimura, S [Kanazawa University, Ishikawa (Japan). Faculty of Engineering; Okajima, A [Kanazawa University, Ishikawa (Japan)

1998-02-25

Natural convection heat transfer and flow structure in an anisotropic porous medium of square cavity saturated with Boussinesq fluid has been studied analytically and numerically. Based on asymptotic analysis three distinctive regimes are found depending upon the magnitude of permeability ratio K. In the vicinity of K=1 the average Nusselt number and fluid velocity are scaled with (KRa){sup 1/2} when either K or the Rayleigh number Ra is varied. In the limit of K {yields} 0 the heat transfer across the cavity approaches to the conductive state, and the convecting velocity, which is primarily in the vertical direction, is scaled with KRa. In the other end of spectrum, namely K {yields} {infinity}, the average Nusselt number and the convecting velocity are scaled with Ra and independent of K. The asymptotic results are verified with two-dimensional numerical calculations. The ranges of K of the respective regimes are also determined based on the numerical results. 12 refs., 12 figs.

Pseudospectral modeling and dispersion analysis of Rayleigh waves in viscoelastic media

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Zhang, K.; Luo, Y.; Xia, J.; Chen, C.

2011-01-01

Multichannel Analysis of Surface Waves (MASW) is one of the most widely used techniques in environmental and engineering geophysics to determine shear-wave velocities and dynamic properties, which is based on the elastic layered system theory. Wave propagation in the Earth, however, has been recognized as viscoelastic and the propagation of Rayleigh waves presents substantial differences in viscoelastic media as compared with elastic media. Therefore, it is necessary to carry out numerical simulation and dispersion analysis of Rayleigh waves in viscoelastic media to better understand Rayleigh-wave behaviors in the real world. We apply a pseudospectral method to the calculation of the spatial derivatives using a Chebyshev difference operator in the vertical direction and a Fourier difference operator in the horizontal direction based on the velocity-stress elastodynamic equations and relations of linear viscoelastic solids. This approach stretches the spatial discrete grid to have a minimum grid size near the free surface so that high accuracy and resolution are achieved at the free surface, which allows an effective incorporation of the free surface boundary conditions since the Chebyshev method is nonperiodic. We first use an elastic homogeneous half-space model to demonstrate the accuracy of the pseudospectral method comparing with the analytical solution, and verify the correctness of the numerical modeling results for a viscoelastic half-space comparing the phase velocities of Rayleigh wave between the theoretical values and the dispersive image generated by high-resolution linear Radon transform. We then simulate three types of two-layer models to analyze dispersive-energy characteristics for near-surface applications. Results demonstrate that the phase velocity of Rayleigh waves in viscoelastic media is relatively higher than in elastic media and the fundamental mode increases by 10-16% when the frequency is above 10. Hz due to the velocity dispersion of P

Measurement of Rayleigh Wave Beams Using Angle Beam Wedge Transducers as the Transmitter and Receiver with Consideration of Beam Spreading.

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