Rayleigh-Benard Natural Convection Cell Formation and Nusselt number
International Nuclear Information System (INIS)
Moon, Je Young; Chung, Bum Jin
2013-01-01
The experimental results lie within the predictions of the existing heat transfer correlations for the Rayleigh-Benard natural convections even though the material properties were different. For shorter separation distances, the heat transfers enhance due to the active interaction between heated and cooled plumes. For a step temperature difference, the time dependent Nusselt number variations were investigated. Both experimental and numerical results showed that with time the Nusselt number decreases monotonically to a minimum point presenting the onset of convection. As the hot and cold plumes increase and convey the heat to the other plates, the Nusselt number increases to the local maximum point, presenting the vertical movements of the plumes. Then, the Nusselt number fluctuates with the formation of square cells and larger vortices. This also predicted by the mass transfer experiment. The experiments and calculations show similar trend but the timings were different. These discrepancies are caused by the disturbances inherent in both systems. The molten pool is formed in a hypothetical severe accident condition at the lower head of reactor vessel and is stratified into two layers by the density difference: an upper metallic layer and a lower oxide pool. Rayleigh-Benard natural convection occurs in the metallic layer of relocated molten pool. This study aimed at the investigation of the time-dependent cell formation and Nusselt number variation in Rayleigh-Benard natural convection. Time dependent variation of Nusselt number was also measured experimentally and analyzed numerically to investigate the relationship between the cell formation and Nusselt number. Based on the analogy, heat transfer experiments were replaced by mass transfer experiments using a sulfuric acid-copper sulfate (H 2 SO 4 -CuSO 4 ) electroplating system. Numerical analysis using the commercial CFD program FLUENT 6.3 were carried out with the same material properties and heating conditions
Universality in quasiperiodic Rayleigh-Benard convection
International Nuclear Information System (INIS)
Ecke, R.E.; Mainieri, R.; Sullivan, T.S.
1991-01-01
We study universal scaling properties of quasiperiodic Rayleigh-Benard convection in a 3 He--superfluid- 4 He mixture. The critical line is located in a parameter space of Rayleigh and Prandtl numbers using a transient-Poincare-section technique to identify transitions from nodal periodic points to spiral periodic points within resonance horns. We measure the radial and angular contraction rates and extract the linear-stability eigenvalues (Flouquet multipliers) of the periodic point. At the crossings of the critical line with the lines of fixed golden-mean-tail winding number we determine the universality class of our experimental dynamics using f(α) and trajectory-scaling-function analyses. A technique is used to obtain a robust five-scale approximation to the universal trajectory scaling function. Different methods of multifractal analysis are employed and an understanding of statistical and systematic errors in these procedures is developed. The power law of the inflection point of the map, determined for three golden-mean-tail winding numbers, is 2.9±0.3, corresponding to the universality class of the sine map
Large-scale patterns in Rayleigh-Benard convection
International Nuclear Information System (INIS)
Hardenberg, J. von; Parodi, A.; Passoni, G.; Provenzale, A.; Spiegel, E.A.
2008-01-01
Rayleigh-Benard convection at large Rayleigh number is characterized by the presence of intense, vertically moving plumes. Both laboratory and numerical experiments reveal that the rising and descending plumes aggregate into separate clusters so as to produce large-scale updrafts and downdrafts. The horizontal scales of the aggregates reported so far have been comparable to the horizontal extent of the containers, but it has not been clear whether that represents a limitation imposed by domain size. In this work, we present numerical simulations of convection at sufficiently large aspect ratio to ascertain whether there is an intrinsic saturation scale for the clustering process when that ratio is large enough. From a series of simulations of Rayleigh-Benard convection with Rayleigh numbers between 10 5 and 10 8 and with aspect ratios up to 12π, we conclude that the clustering process has a finite horizontal saturation scale with at most a weak dependence on Rayleigh number in the range studied
Three caveats for linear stability theory: Rayleigh-Benard convection
International Nuclear Information System (INIS)
Greenside, H.S.
1984-06-01
Recent theories and experiments challenge the applicability of linear stability theory near the onset of buoyancy-driven (Rayleigh-Benard) convection. This stability theory, based on small perturbations of infinite parallel rolls, is found to miss several important features of the convective flow. The reason is that the lateral boundaries have a profound influence on the possible wave numbers and flow patterns even for the largest cells studied. Also, the nonlinear growth of incoherent unstable modes distorts the rolls, leading to a spatially disordered and sometimes temporally nonperiodic flow. Finally, the relation of the skewed varicose instability to the onset of turbulence (nonperiodic time dependence) is examined. Linear stability theory may not suffice to predict the onset of time dependence in large cells close to threshold
An Experimental Study on Rayleigh-Benard Natural Convection
International Nuclear Information System (INIS)
Moon, Je Young; Chung, Bum Jin
2012-01-01
Core melt in a severe accident condition, forms a molten pool in the reactor vessel lower head. The molten pool is divided by a metallic pool (top) and an oxide pool (bottom) by the density difference. Due to the decay heat generated in oxide pool, Rayleigh- Benard natural convection heated from below and cooled from above occurs in the metallic pool. Experiments were performed to investigate Rayleigh- Benard natural convection as a preparatory study before an in-depth severe accident study. The natural convection heat transfers were measured varying the plate separation distance and the area of plate with and without the side wall. Using the analogy concept, heat transfer experiments were replaced by mass transfer experiments. A cupric acid.copper sulfate (H 2 SO 4 -CuSO 4 ) electroplating system was adopted as the mass transfer system and the electric currents were measured rather than the heat
Laser speckle velocimetry applied to Rayleigh-Benard convection
International Nuclear Information System (INIS)
Arroyo, M.P.; Yonte, T.; Quintanilla, M.; Saviron, J.M.
1986-01-01
An application of speckle velocimetry technique to Rayleigh-Benard convection is presented. A 5-mW He-Ne laser allows precise determination of the two-dimensional velocity flow field, up to several mm/sec. The digital techniques used to analyze automatically the multiexposed photographs and to generate velocity and vorticity fields are described. The obtained results are in good agreement with previously reported data. The ability of the technique to cover other experimental conditions is discussed. 14 references
Temperature boundary layer profiles in turbulent Rayleigh-Benard convection
Ching, Emily S. C.; Emran, Mohammad S.; Horn, Susanne; Shishkina, Olga
2017-11-01
Classical boundary-layer theory for steady flows cannot adequately describe the boundary layer profiles in turbulent Rayleigh-Benard convection. We have developed a thermal boundary layer equation which takes into account fluctuations in terms of an eddy thermal diffusivity. Based on Prandtl's mixing length ideas, we relate the eddy thermal diffusivity to the stream function. With this proposed relation, we can solve the thermal boundary layer equation and obtain a closed-form expression for the dimensionless mean temperature profile in terms of two independent parameters: θ(ξ) =1/b∫0b ξ [ 1 +3a3/b3(η - arctan(η)) ] - c dη , where ξ is the similarity variable and the parameters a, b, and c are related by the condition θ(∞) = 1 . With a proper choice of the parameters, our predictions of the temperature profile are in excellent agreement with the results of our direct numerical simulations for a wide range of Prandtl numbers (Pr), from Pr=0.01 to Pr=2547.9. OS, ME and SH acknowledge the financial support by the Deutsche Forschungsgemeinschaft (DFG) under Grants Sh405/4-2 (Heisenberg fellowship), Sh405/3-2 and Ho 5890/1-1, respectively.
Rayleigh-Benard convection as a Nambu-metriplectic problem
International Nuclear Information System (INIS)
Bihlo, A
2008-01-01
The traditional Hamiltonian structure of the equations governing conservative Rayleigh-Benard convection (RBC) is singular, i.e., its Poisson bracket possesses nontrivial Casimir functionals. We show that a special form of one of these Casimirs can be used to extend the bilinear Poisson bracket to a trilinear generalized Nambu bracket. It is further shown that the equations governing dissipative RBC can be written as the superposition of the conservative Nambu bracket with a dissipative symmetric bracket. This leads to a Nambu-metriplectic system, which completes the geometrical picture of RBC. (fast track communication)
Czech Academy of Sciences Publication Activity Database
Musilová, Věra; Králík, Tomáš; La Mantia, M.; Macek, Michal; Urban, Pavel; Skrbek, L.
2017-01-01
Roč. 832, OCT 26 (2017), s. 721-744 ISSN 0022-1120 R&D Projects: GA ČR(CZ) GA17-03572S; GA MŠk(CZ) LO1212 Institutional support: RVO:68081731 Keywords : Benard convection * turbulent convection * turbulent flows Subject RIV: BK - Fluid Dynamics OBOR OECD: Fluids and plasma physics (including surface physics) Impact factor: 2.821, year: 2016
Direct simulation of turbulent Rayleigh-Benard convection in liquid sodium
International Nuclear Information System (INIS)
Woerner, M.
1994-11-01
The numerical results are analysed to investigate both the structures and mechanisms of convection and the statistical features of turbulence in natural convection of liquid metals. The simulations are performed with the finite volume code TURBIT which is extended by a semi-implicit time integration scheme for the energy equation. Due to the implicit treatment of thermal diffusion the computational time for simulation of natural convection in liquid metals is reduced by about one order of magnitude, as compared to the original fully explicit code version. Results for Rayleigh-Benard convection in liquid sodium with Prandtl number Pr=0.006 are given for four different Rayleigh numbers: Ra=3 000, Ra=6 000, Ra=12 000, and Ra=24 000. At the Rayleigh number Ra=3 000 the inertial convection is identified. It is characterized by large two-dimensional vortices, which rotate like a solid body. These vortices are also observed in the simulations for Ra=6 000, Ra=12 000 and Ra=24 000, but, they only exist in certain regions and for short time intervals. The appearance of these two-dimensional structures in three-dimensional, time-dependent and turbulent convection is explained by the relative importance of the non-linear terms in the momentum and energy equation, which is totally different in both equations, and by the coupling of these equations by the buoyancy and the convective term. In order to improve and validate statistical turbulence model for application to natural convection in liquid metals, budgets of turbulence kinetic energy, turbulent heat flux and temperature variance are calculated from the numerical results. For several unknown correlations closure assumptions used in standard turbulence models are analyzed and model coefficients are determined. (orig./HP) [de
Reduced-Order Modeling of 3D Rayleigh-Benard Turbulent Convection
Hassanzadeh, Pedram; Grover, Piyush; Nabi, Saleh
2017-11-01
Accurate Reduced-Order Models (ROMs) of turbulent geophysical flows have broad applications in science and engineering; for example, to study the climate system or to perform real-time flow control/optimization in energy systems. Here we focus on 3D Rayleigh-Benard turbulent convection at the Rayleigh number of 106 as a prototype for turbulent geophysical flows, which are dominantly buoyancy driven. The purpose of the study is to evaluate and improve the performance of different model reduction techniques using this setting. One-dimensional ROMs for horizontally averaged temperature are calculated using several methods. Specifically, the Linear Response Function (LRF) of the system is calculated from a large DNS dataset using Dynamic Mode Decomposition (DMD) and Fluctuation-Dissipation Theorem (FDT). The LRF is also calculated using the Green's function method of Hassanzadeh and Kuang (2016, J. Atmos. Sci.), which is based on using numerous forced DNS runs. The performance of these LRFs in estimating the system's response to weak external forcings or controlling the time-mean flow are compared and contrasted. The spectral properties of the LRFs and the scaling of the accuracy with the length of the dataset (for the data-driven methods) are also discussed.
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
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.
Quasiperiodicity, mode-locking, and universal scaling in Rayleigh-Benard convection
International Nuclear Information System (INIS)
Ecke, R.E.
1990-01-01
This major review paper describes research on a model nonlinear dynamical system of small-aspect-ratio Rayleigh-Benard convection in 3 He - 4 He mixtures. The nonlinear effects of mode locking and quasiperiodic behavior are described. Analysis techniques for characterizing the state of the dynamical system include Fourier transforms, Poincare sections, phase differences, transients, multifractal f(∝) spectra and scaling function dynamics. Theoretical results such as the fractal staircase of mode-locked intervals and the Arnold tongues are reproduced in experimental data. New techniques for analyzing scaling dynamics are developed and discussed. This is a tutorial article that introduces the major important concepts in nonlinear dynamics and focuses on experimental problems and techniques. 77 refs
Energy Technology Data Exchange (ETDEWEB)
Martinand, D
2003-01-15
This analytical study deals with the spatio-temporal evolution of linear thermo-convective instabilities in a horizontal fluid layer heated from below (the Rayleigh--Benard system) and subject to a horizontal pressure gradient (Poiseuille flow). The novelty consists of a spatially inhomogeneous temperature, in the form of a two-dimensional bump imposed on the lower plate, while the upper plate is kept at a constant temperature. The inhomogeneous boundary temperature and the mean flow of the Rayleigh--Benard--Poiseuille system break the symmetries of the classical Rayleigh--Benard system. The instabilities of interest are therefore spatially localised packets of convection rolls. If a mode of this type is synchronized, it is called a global mode. Assuming that the characteristic scale of the spatial variation of the lower plate temperature is large compared to the wavelength of the rolls, global modes are sought in the form of Eigenmodes in the confined vertical direction, modulated by a two-dimensional WKBJ expansion in the slowly-varying horizontal directions. Such an expansion breaks down at points where the group velocity of the instability vanishes, i.e. at WKBJ turning points. In the neighbourhood of one such point, located at the top of the temperature bump, the boundedness of the solution imposes a selection criterion for the global modes which provides the growth rate (or equivalently the critical threshold), the frequency and the wave vector of the most amplified global mode. This study thus generalizes to two-dimensional cases the methods used and the results obtained for one-dimensional inhomogeneities. The analysis is first applied to a simplified governing equation obtained by an envelope formalism and the analytical results are compared with numerical solutions of the amplitude equation. The formalism is finally applied to the Rayleigh--Benard--Poiseuille system described by the Navier--Stokes equations with the Boussinesq approximation. (author)
International Nuclear Information System (INIS)
Gellert, M; Beltrame, P; Egbers, C
2005-01-01
Spherical Rayleigh-Benard convection under the influence of an artificial central force field produced by the so-called dielectrophoretic effect is studied as a simplified model of the flow in the outer earth core. The fluid motion there is most probably driving the earth's dynamo and the energy source for the earth's magnetic field. Studying convective flows in earth-like geometry could lead to a deeper understanding of the basics of these processes. This research is a preparatory study for the experiments on the International Space Station (ISS). A bifurcation-theoretical approach shows the existence of heteroclinic cycles between spherical modes (l, l + 1) for the non-rotating system. This behavior depends strong on the radius ratio of the spheres and will be hard to detect in the experiment. For slow rotations interactions of the azimuthal modes (m, m + 1) found in numerical simulations for supercritical states are supposed to be experimentally observable
Rayleigh-Benard convection in a Hele-Shaw cell - a numerical study
International Nuclear Information System (INIS)
Guenther, C.; Mueller, U.
1987-05-01
Free convection in narrow vertical gaps heated from below gives rise to several different flow patterns as has been demonstrated by previous experimental investigations. A numerical study is presented aimed at simulating the observed flow phenomena in Hele-Shaw cells of small lateral extend. The numerical study is based on the assumption that the flow is essentially two-dimensional. This allows an approach using a one-term Galerkin approximation with respect to the direction perpendicular to the gap and a finite difference scheme with regard to the coordinates in the plane of the gap. The calculations result in realistic values of the critical Rayleigh numbers for the onset of steady and oscillatory convection. Most of the observed unsteady flow patterns can be simulated numerically. It is shown that five different stable flow patterns can occur at one particular Rayleigh number. The different stable flow patterns are coupled by a variety of complex transitions. Moreover the calculations show that a realistic description of the observed flow phenomena can not be obtained by a simplified model using the Darcy law in the momentum equation and implying slip flow at the small confining boundaries. (orig.) [de
Supercritical Quasi-Conduction States in Stochastic Rayleigh-Benard Convection
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
The dynamics of droplets in moist Rayleigh-Benard turbulence
Chandrakar, Kamal Kant; van der Voort, Dennis; Kinney, Greg; Cantrell, Will; Shaw, Raymond
2017-11-01
Clouds are an intricate part of the climate, and strongly influence atmospheric dynamics and radiative balances. While properties such as cloud albedo and precipitation rate are large scale effects, these properties are determined by dynamics on the microscale, such droplet sizes, liquid water content, etc. The growth of droplets from condensation is dependent on a multitude of parameters, such as aerosol concentration (nucleation sites) and turbulence (scalar fluctuations and coalescence). However, the precise mechanism behind droplet growth and clustering in a cloud environment is still unclear. In this investigation we use a facility called the Pi Chamber to generate a (miniature) cloud in a laboratory setting with known boundary conditions, such as aerosol concentration, temperature, and humidity. Through the use of particle imaging velocimetry (PIV) on the droplets generated in the cloud, we can investigate the dynamics of these cloud droplets in the convective (Rayleigh-Benard) turbulence generated through an induced temperature gradient. We show the influence of the temperature gradient and Froude number (gravity forces) on the changing turbulence anisotropy, large scale circulation, and small-scale dissipation rates. This work was supported by National Science Foundation Grant AGS-1623429.
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.
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)
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)
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.
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.
Boundary layers and scaling relations in natural thermal convection
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.
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
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.
GPU Implementation of High Rayleigh Number Three-Dimensional Mantle Convection
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.
Boundary layers in turbulent convection for air, liquid gallium and liquid sodium
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.
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)
Non-Oberbeck-Boussinesq effects in two-dimensional Rayleigh-Bénard convection in glycerol
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 Î�
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
Boundary Layer Control of Rotating Convection Systems
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.
Direct numerical simulation and statistical analysis of turbulent convection in lead-bismuth
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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)
Heat Transport Enhancement of Turbulent Thermal Convection by Inserted Channels
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).
Extend of magnetic field interference in the natural convection of diamagnetic nanofluid
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.
Boundary-modulated Thermal Convection Model in the Mantle
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
Penetrative convection at high Rayleigh numbers
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.
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
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)
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
Thermal convection for large Prandtl numbers
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
Rotating Rayleigh-Bénard convection at low Prandtl number
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 .
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
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
Rotating thermal convection at very large Rayleigh numbers
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.
Effect of Brinkman number and magnetic field on laminar convection ...
African Journals Online (AJOL)
The effect of Brinkman number and magnetic field on laminar convection in a vertical plate channel with uniform and asymmetric temperatures has been studied. The dimensionless form of momentum and energy balanced equations has been solved using one term perturbation series solution. The solution of the ...
Effects of Brinkman number on thermal-driven convective spherical ...
African Journals Online (AJOL)
Michael Horsfall
KEYWORDS: Magnetic field generation, Thermal-driven convection, Brinkman number, Dynamo action, Fluid outer core ... The problem considers conducting fluid motion in a rapidly rotating spherical shell. The ... is, that the energy lost by the electric currents must be ... which are sources of free electrons and basically due.
Plume structure in high-Rayleigh-number convection
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.
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 ...
Prandtl-number Effects in High-Rayleigh-number Spherical Convection
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.
Turbulent boundary layer in high Rayleigh number convection in air.
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.
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
Convection in an ideal gas at high Rayleigh numbers.
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.
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)
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
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)
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)
Effects of external environment on thermocapillary convection of high prandtl number fluid
Directory of Open Access Journals (Sweden)
Liang Ruquan
2016-01-01
Full Text Available Numerical simulations have been carried out to investigate the influence of external environment on thermocapillary convection in high Prandtl number (Pr=68 liquid. The geometric model of physical problem is that the the liquid bridge surrounded by ambient air under zero or ground gravity. The interface velocity, temperature, heat flux and flow pattern in the liquid bridge are presented and discussed under different conditions by changing the external environment. The buoyancy convection produces a symmetrical vortex in the liquid bridge. The ambient air affects the distributions of the temperature velocity and heat flux on the interface by changing the thermocapillary convection.
Consequences of high effective Prandtl number on solar differential rotation and convective velocity
Karak, Bidya Binay; Miesch, Mark; Bekki, Yuto
2018-04-01
Observations suggest that the large-scale convective velocities obtained by solar convection simulations might be over-estimated (convective conundrum). One plausible solution to this could be the small-scale dynamo which cannot be fully resolved by global simulations. The small-scale Lorentz force suppresses the convective motions and also the turbulent mixing of entropy between upflows and downflows, leading to a large effective Prandtl number (Pr). We explore this idea in three-dimensional global rotating convection simulations at different thermal conductivity (κ), i.e., at different Pr. In agreement with previous non-rotating simulations, the convective velocity is reduced with the increase of Pr as long as the thermal conductive flux is negligible. A subadiabatic layer is formed near the base of the convection zone due to continuous deposition of low entropy plumes in low-κ simulations. The most interesting result of our low-κ simulations is that the convective motions are accompanied by a change in the convection structure that is increasingly influenced by small-scale plumes. These plumes tend to transport angular momentum radially inward and thus establish an anti-solar differential rotation, in striking contrast to the solar rotation profile. If such low diffusive plumes, driven by the radiative-surface cooling, are present in the Sun, then our results cast doubt on the idea that a high effective Pr may be a viable solution to the solar convective conundrum. Our study also emphasizes that any resolution of the conundrum that relies on the downward plumes must take into account the angular momentum transport and heat transport.
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)
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)
Ultimate regime of high Rayleigh number convection in a porous medium.
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).
Multigrid solution of the convection-diffusion equation with high-Reynolds number
Energy Technology Data Exchange (ETDEWEB)
Zhang, Jun [George Washington Univ., Washington, DC (United States)
1996-12-31
A fourth-order compact finite difference scheme is employed with the multigrid technique to solve the variable coefficient convection-diffusion equation with high-Reynolds number. Scaled inter-grid transfer operators and potential on vectorization and parallelization are discussed. The high-order multigrid method is unconditionally stable and produces solution of 4th-order accuracy. Numerical experiments are included.
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 multifractal nature of plume structure in high-Rayleigh-number convection
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.
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
Fully three dimensional simulations of rotating convection at low Prandtl number
Kaplan, E.; Schaeffer, N.; Cardin, P.
2016-12-01
Rotating thermal convection in spheres or spherical shells has been extensively studied for Prandtl number unity.However, planetary cores are made of liquid metals which have low Prandtl numbers Pr ≤ 0.1. Recently, using a quasi-geostrophic approximation, Guervilly & Cardin (2016) have studied nonlinear convection in rotating full sphere with internal heating at low Prandtl (0.01 ≤ Pr ≤ 0.1) and Ekman (10-8 ≤ Ek ≤ 10-5 ) numbers. They have found a bifurcation between a weak branch characterized by thermal Rossby waves and a strong branch characterized by a strong zonal flow with multiple jets. In these quasi-geostrophic simulations, where vorticity is defined to be constant along the axis of rotation, these bifurcations could be super- or sub-critical or exhibit hysteresis depending on the Ek and Prnumbers of the simulations. Here we present fully three dimensional simulations carried out over a portion of the parameter space (down to Ek = 10-6, Pr = 0.01) that confirm the scaling and bifurcations of the weak and strong branches found in the QG models. Additionally, by modeling the full flow we get information about the full meridional circulation of the convective fluid. The vigorous flows of the sub-critical strong branch may help to generate powerful dynamos before an inner-core has been formed, with a heat flux extracted from the mantle very close to the adiabatic flux.
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 flow in spiral tubes and effect of Prandtl number on a convective heat transfer
International Nuclear Information System (INIS)
Shistel', R.; Goss, Zh.
1976-01-01
Turbulent flow is analized of the fluid in the spiral tube with a pitch which is small enough as compared to the curvature radius. The effect of the curvature and the Prandtl number on the turbulent convection is studied. A description of three-dimensional model and its application for the spiral tubes is given. The example of heat convection in curved channels reveals the opportunity for employment of three-dimensional model to calculate the recirculating flows in complex-geometry channels, description of the turbulence field, and determination of the wall friction and heat transfer. The introduction of the wall functions into the numerical method affects adversely accuracy of calculations but ensures a considerable time saving and makes it possible to study the process in the first approximation. The example illustrates possible practical application of the calculation procedure
International Nuclear Information System (INIS)
Stalio, E.; Angeli, D.; Barozzi, G.S.
2011-01-01
Highlights: → We investigate laminar convective heat transfer in channels with periodic cavities. → Heat transfer rates are lower than for the flat channel. → This is ascribed to the steady circulating motion within the cavities. → Diffusion in a low Prandtl number fluid can locally overcome the heat transfer decrease due to advection only for isothermal boundary conditions. - Abstract: Convective heat transfer in laminar conditions is studied numerically for a Prandtl number Pr = 0.025, representative of liquid lead-bismuth eutectic (LBE). The geometry investigated is a channel with a periodic series of shallow cavities. Finite-volume simulations are carried out on structured orthogonal curvilinear grids, for ten values of the Reynolds number based on the hydraulic diameter between Re m = 24.9 and Re m = 2260. Flow separation and reattachment are observed also at very low Reynolds numbers and wall friction is found to be remarkably unequal at the two walls. In almost all cases investigated, heat transfer rates are smaller than the corresponding flat channel values. Low-Prandtl number heat transfer rates, investigated by comparison with Pr = 0.71 results, are large only for uniform wall temperature and very low Re. Influence of flow separation on local heat transfer rates is discussed, together with the effect of different thermal boundary conditions. Dependency of heat transfer performance on the cavity geometry is also considered.
Transitional boundary layer in low-Prandtl-number convection at high Rayleigh number
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.
Effect of thermo-solutal Marangoni convection on the azimuthal wave number in a liquid bridge
Minakuchi, H.; Okano, Y.; Dost, S.
2017-06-01
A numerical simulation study was carried out to investigate the effect of thermo-solutal Marangoni convection on the flow patterns and the azimuthal wave number (m) in a liquid bridge under zero-gravity. The liquid bridge in the model represents a three dimensional half-zone configuration of the Floating Zone (FZ) growth system. Three dimensional field equations of the liquid zone, i.e. continuity, momentum, energy, and diffusion equations, were solved by the PISO algorithm. The physical properties of the silicon-germanium melt were used (Pr=6.37×10-3 and Sc=14.0, where Pr and Sc stand for the Prandtl number and the Schmidt number). The aspect ratio Asp was set to 0.5 (Asp= L/a, where L and a stand for the length of free surface and the radius of liquid bridge). Computations were performed using the open source software OpenFOAM. The numerical simulation results show that the co-existence of thermal and solutal Marangoni convections significantly affects the azimuthal wave number m in the liquid bridge.
Ground Boundary Conditions for Thermal Convection Over Horizontal Surfaces at High Rayleigh Numbers
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.
Turbulent Superstructures in Rayleigh-Bénard convection at different Prandtl number
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.
Study of turbulent natural-circulation flow and low-Prandtl-number forced-convection flow
International Nuclear Information System (INIS)
Chung, K.S.; Thompson, D.H.
1980-01-01
Calculational methods and results are discussed for the coupled energy and momentum equations of turbulent natural circulation flow and low Prandtl number forced convection flow. The objective of this paper is to develop a calculational method for the study of the thermal-hydraulic behavior of coolant flowing in a liquid metal fast breeder reactor channel under natural circulation conditions. The two-equation turbulence model is used to evaluate the turbulent momentum transport property. Because the analogy between momentum transfer and heat transfer does not generally hold for low Prandtl number fluid and natural circulation flow conditions, the turbulent thermal conductivity is calculated independently using equations similar to the two-equation turbulence model. The numerical technique used in the calculation is the finite element method
Nusselt number and bulk temperature in turbulent Rayleigh-Bénard convection
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.
Homogeneous purely buoyancy driven turbulent flow
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.
Vilella, Kenny; Deschamps, Frederic
2018-04-01
Thermal evolution of terrestrial planets is controlled by heat transfer through their silicate mantles. A suitable framework for modelling this heat transport is a system including bottom heating (from the core) and internal heating, e.g., generated by secular cooling or by the decay of radioactive isotopes. The mechanism of heat transfer depends on the physical properties of the system. In systems where convection is able to operate, two different regimes are possible depending on the relative amount of bottom and internal heating. For moderate internal heating rates, the system is composed of active hot upwellings and cold downwellings. For large internal heating rates, the bottom heat flux becomes negative and the system is only composed of active cold downwellings. Here, we build theoretical scaling laws for both convective regimes following the approach of Vilella & Kaminski (2017), which links the surface heat flux and the temperature jump across both the top and bottom thermal boundary layer (TBL) to the Rayleigh number and the dimensionless internal heating rate. Theoretical predictions are then verified against numerical simulations performed in 2D and 3D-Cartesian geometry, and covering a large range of the parameter space. Our theoretical scaling laws are more successful in predicting the thermal structure of systems with large internal heating rates than that of systems with no or moderate internal heating. The differences between moderate and large internal heating rates are interpreted as differences in the mechanisms generating thermal instabilities. We identified three mechanisms: conductive growth of the TBL, instability impacting, and TBL erosion, the last two being present only for moderate internal heating rates, in which hot plumes are generated at the bottom of the system and are able to reach the surface. Finally, we apply our scaling laws to the evolution of the early Earth, proposing a new model for the cooling of the primordial magma ocean
Directory of Open Access Journals (Sweden)
S. Abdul Gaffar
2015-01-01
Full Text Available Magnetic polymers are finding increasing applications in diverse fields of chemical and mechanical engineering. In this paper, we investigate the nonlinear steady boundary layer flow and heat transfer of such fluids from a nonisothermal wedge. The incompressible Eyring-Powell non-Newtonian fluid model is employed and a magnetohydrodynamic body force is included in the simulation. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a second-order accurate implicit finite difference Keller Box technique. The numerical code is validated with previous studies. The influence of a number of emerging nondimensional parameters, namely, the Eyring-Powell rheological fluid parameter (ε, local non-Newtonian parameter based on length scale (δ, Prandtl number (Pr, Biot number (γ, pressure gradient parameter (m, magnetic parameter (M, mixed convection parameter (λ, and dimensionless tangential coordinate (ξ, on velocity and temperature evolution in the boundary layer regime is examined in detail. Furthermore, the effects of these parameters on surface heat transfer rate and local skin friction are also investigated.
Solutal convection induced by dissolution. Influence on erosion dynamics and interface shaping.
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
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
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
International Nuclear Information System (INIS)
Jackson, J.D.
2011-01-01
The early experimental studies of buoyancy-influenced turbulent convective heat transfer to fluids flowing upwards and downwards in long uniformly heated vertical tubes were mainly performed using water at atmospheric pressure as the working fluid. In addition, some experiments using air were reported and even some using mercury. At that time there was also quite a lot of interest in heat transfer to water at supercritical pressure and also carbon dioxide. More recently, experimental results have been obtained using liquid sodium. The Prandtl numbers in the studies referred to above cover a wide range of values, being well in excess of unity under some conditions in the case of the supercritical pressure fluids and atmospheric pressure water, just under unity in the case of air, much less than unity in the case of mercury and even lower in the case of liquid sodium. Over the years a good general understanding has gradually been achieved of the complex manner in which buoyancy affects heat transfer in conventional fluids such as water and air. Up to a point, the behaviour in the case of a liquid metal such as mercury can be reconciled with such arguments. However, this is certainly not so in the case of liquid sodium. In the present paper results from a number of experimental studies of buoyancy-influenced heat transfer in vertical tubes are reviewed. This is done with the aim of providing a picture of observed behaviour consistent with our understanding of the basic mechanisms of convective heat transfer, taking account of the complicated manner in which the mean motion, turbulence and the heat transfer are affected by buoyancy. The starting point is to view convective heat transfer in wall shear flows in terms of the local balance between diffusion of heat (turbulent and molecular) and advection of heat by the flowing fluid. Prandtl number affects the radial temperature profile and therefore the variation of density across the shear flow and, in turn, the extent
Entropy Analyses of Droplet Combustion in Convective Environment with Small Reynolds Number
Institute of Scientific and Technical Information of China (English)
ZHANG Xiaobin; ZHANG Wei; ZHANG Xuejun
2013-01-01
This paper analyzes the entropy generation rate of simple pure droplet combustion in a temperature-elevated air convective environment based on the solutions of flow,and heat and mass transfer between the two phases.The flow-field calculations are carried out by solving the respective conservation equations for each phase,accounting for the droplet deformation with the axisymmetric model.The effects of the temperature,velocity and oxygen fraction of the free stream air on the total entropy generation rate in the process of the droplet combustion are investigated.Special attention is given to analyze the quantitative effects of droplet deformation.The results reveal that the entropy generation rate due to chemical reaction occupies a large fraction of the total entropy generated,as a result of the large areas covered by the flame.Although,the magnitude of the entropy generation rate per volume due to heat transfer and combined mass and heat transfer has a magnitude of one order greater than that due to chemical reaction,they cover a very limited area,leading to a small fraction of the total entropy generated.The entropy generation rate due to mass transfer is negligible.High temperature and high velocity of the free stream are advantageous to increase the exergy efficiency in the range of small Reynolds number (＜1) from the viewpoint of the second-law analysis over the droplet lifetime.The effect of droplet deformation on the total entropy generation is the modest.
Thermal convection of a viscoplastic liquid with high Rayleigh and Bingham numbers
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.
Resolving both entrainment-mixing and number of activated CCN in deep convective clouds
Directory of Open Access Journals (Sweden)
E. Freud
2011-12-01
Full Text Available The number concentration of activated CCN (N_{a} is the most fundamental microphysical property of a convective cloud. It determines the rate of droplet growth with cloud depth and conversion into precipitation-sized particles and affects the radiative properties of the clouds. However, measuring N_{a} is not always possible, even in the cores of the convective clouds, because entrainment of sub-saturated ambient air deeper into the cloud lowers the concentrations by dilution and may cause partial or total droplet evaporation, depending on whether the mixing is homogeneous or extreme inhomogeneous, respectively.
Here we describe a methodology to derive N_{a} based on the rate of cloud droplet effective radius (R_{e} growth with cloud depth and with respect to the cloud mixing with the entrained ambient air. We use the slope of the tight linear relationship between the adiabatic liquid water mixing ratio and R_{e}^{3} (or R_{v}^{3} to derive an upper limit for N_{a} assuming extreme inhomogeneous mixing. Then we tune N_{a} down to find the theoretical relative humidity that the entrained ambient air would have for each horizontal cloud penetration, in case of homogeneous mixing. This allows us to evaluate both the entrainment and mixing process in the vertical dimension in addition to getting a better estimation for N_{a}.
We found that the derived N_{a} from the entire profile data is highly correlated with the independent CCN measurements from below cloud base. Moreover, it was found that mixing of sub-saturated ambient air into the cloud at scales of ~100 m and above is inclined towards the extreme inhomogeneous limit, i.e. that the time scale of droplet evaporation is significantly smaller than that for turbulent mixing. This means that ambient air that entrains
Directory of Open Access Journals (Sweden)
A. Abdullah
2018-04-01
Full Text Available Convection-diffusion problems, due to its fundamental nature, are found in various science and engineering applications. In this research, the importance of the relationship between grid structure and flow parameters in such problems is emphasized. In particular, we propose a systematic technique in the selection of the grid expansion factor based on its logarithmic relationship with low Peclet number. Such linear mathematical connection between the two non-dimensional parameters serves as a guideline for more structured decision-making and improves the heuristic process in the determination of the computational domain grid for the numerical solution of convection-diffusion equations especially in the prediction of the concentration of the scalar. Results confirm the effectiveness of the new approach.
International Nuclear Information System (INIS)
Ko, T.H.
2006-01-01
In the present paper, the entropy generation and optimal Reynolds number for developing forced convection in a double sine duct with various wall heat fluxes, which frequently occurs in plate heat exchangers, are studied based on the entropy generation minimization principle by analytical thermodynamic analysis as well as numerical investigation. According to the thermodynamic analysis, a very simple expression for the optimal Reynolds number for the double sine duct as a function of mass flow rate, wall heat flux, working fluid and geometric dimensions is proposed. In the numerical simulations, the investigated Reynolds number (Re) covers the range from 86 to 2000 and the wall heat flux (q'') varies as 160, 320 and 640 W/m 2 . From the numerical simulation of the developing laminar forced convection in the double sine duct, the effect of Reynolds number on entropy generation in the duct has been examined, through which the optimal Reynolds number with minimal entropy generation is detected. The optimal Reynolds number obtained from the analytical thermodynamic analysis is compared with the one from the numerical solutions and is verified to have a similar magnitude of entropy generation as the minimal entropy generation predicted by the numerical simulations. The optimal analysis provided in the present paper gives worthy information for heat exchanger design, since the thermal system could have the least irreversibility and best exergy utilization if the optimal Re can be used according to practical design conditions
Javed, Tariq; Ahmed, B.; Sajid, M.
2018-04-01
The current study focuses on the numerical investigation of the mixed convective peristaltic mechanism through a vertical tube for non-zero Reynolds and wave number. In the set of constitutional equations, energy equation contains the term representing heat generation parameter. The problem is formulated by dropping the assumption of lubrication theory that turns the model mathematically into a system of the nonlinear partial differential equations. The results of the long wavelength in a creeping flow are deduced from the present analysis. Thus, the current study explores the neglected features of peristaltic heat flow in the mixed convective model by considering moderate values of Reynolds and wave numbers. The finite element based on Galerkin’s weighted residual scheme is applied to solve the governing equations. The computed solution is presented in the form of contours of streamlines and isothermal lines, velocity and temperature profiles for variation of different involved parameters. The investigation shows that the strength of circulation for stream function increases by increasing the wave number and Reynolds number. Symmetric isotherms are reported for small values of time-mean flow. Linear behavior of pressure is noticed by vanishing inertial forces while the increase in pressure is observed by amplifying the Reynolds number.
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.
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.
International Nuclear Information System (INIS)
Su Jian; Silva Freire, Atila P.
2002-01-01
A simple analytical method was developed for the prediction of the friction factor, f, of fully developed turbulent flow and the Nusselt number, Nu, of fully developed turbulent forced convection in rod bundles arranged in square or hexagonal arrays. The friction factor equation for smooth rod bundles was presented in a form similar to the friction factor equation for turbulent flow in a circular pipe. An explicit equation for the Nusselt number of turbulent forced convection in rod bundles with smooth surface was developed. In addition, we extended the analysis to rod bundles with rough surface and provided a method for the prediction of the friction factor and the Nusselt number. The method was based on the law of the wall for velocity and the law of the wall for the temperature, which were integrated over the entire flow area to yield algebraic equations for the prediction of f and Nu. The present method is applicable to infinite rod bundles in square and hexagonal arrays with low pitch to rod diameter ratio, P/D<1.2
Study on the Instability of Two-Phase Flow in the Heat-Absorbing Tube of Trough Solar Collector
Directory of Open Access Journals (Sweden)
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.
International Nuclear Information System (INIS)
Lalizel, Gildas; Sultan, Qaiser; Fénot, Matthieu; Dorignac, Eva
2012-01-01
In actual gas turbine system, unsteadiness of the mainstream flow influences heat transfer and surface pressure distribution on the blade. In order to simulate these conditions, an experimental film cooling study with externally imposed pulsation is performed with purpose of characterizing both effects of turbine unsteadiness on film cooling (with frequency ranges typical to actual turbine), and also to figure out the range of Strouhal number pulsation under various blowing conditions, which could possibly deliver a performance improvement in film cooling. Influence of injection flow pulsation on adiabatic effectiveness and convective heat transfer coefficient are determined from IR-thermography of the wall for distances to the hole exit between 0 and 30 D.
Energy Technology Data Exchange (ETDEWEB)
Jacobs, A. M.; Zingale, M. [Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794-3800 (United States); Nonaka, A.; Almgren, A. S.; Bell, J. B. [Center for Computational Sciences and Engineering, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States)
2016-08-10
The dynamics of helium shell convection driven by nuclear burning establish the conditions for runaway in the sub-Chandrasekhar-mass, double-detonation model for SNe Ia, as well as for a variety of other explosive phenomena. We explore these convection dynamics for a range of white dwarf core and helium shell masses in three dimensions using the low Mach number hydrodynamics code MAESTRO. We present calculations of the bulk properties of this evolution, including time-series evolution of global diagnostics, lateral averages of the 3D state, and the global 3D state. We find a variety of outcomes, including quasi-equilibrium, localized runaway, and convective runaway. Our results suggest that the double-detonation progenitor model is promising and that 3D dynamic convection plays a key role.
Similarities between 2D and 3D convection for large Prandtl number
Indian Academy of Sciences (India)
2016-06-18
RBC), we perform a compara- tive study of the spectra and fluxes of energy and entropy, and the scaling of large-scale quantities for large and infinite Prandtl numbers in two (2D) and three (3D) dimensions. We observe close ...
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 × 10^{4} (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.
Yano, T.; Nishino, K.; Kawamura, H.; Ueno, I.; Matsumoto, S.
2015-02-01
This paper reports the experimental results on the instability and associated roll structures (RSs) of Marangoni convection in liquid bridges formed under the microgravity environment on the International Space Station. The geometry of interest is high aspect ratio (AR = height/diameter ≥ 1.0) liquid bridges of high Prandtl number fluids (Pr = 67 and 207) suspended between coaxial disks heated differentially. The unsteady flow field and associated RSs were revealed with the three-dimensional particle tracking velocimetry. It is found that the flow field after the onset of instability exhibits oscillations with azimuthal mode number m = 1 and associated RSs traveling in the axial direction. The RSs travel in the same direction as the surface flow (co-flow direction) for 1.00 ≤ AR ≤ 1.25 while they travel in the opposite direction (counter-flow direction) for AR ≥ 1.50, thus showing the change of traveling directions with AR. This traveling direction for AR ≥ 1.50 is reversed to the co-flow direction when the temperature difference between the disks is increased to the condition far beyond the critical one. This change of traveling directions is accompanied by the increase of the oscillation frequency. The characteristics of the RSs for AR ≥ 1.50, such as the azimuthal mode of oscillation, the dimensionless oscillation frequency, and the traveling direction, are in reasonable agreement with those of the previous sounding rocket experiment for AR = 2.50 and those of the linear stability analysis of an infinite liquid bridge.
Dong, Qingming; Sau, Amalendu
2016-06-01
Interfacial mass-transport and redistribution in the micro-scale liquid droplets are important in diverse fields of research interest. The role of the "inflow" and the "outflow" type convective eddy-pairs in the entrainment of outer solute and internal relocation are examined for different homogeneous and heterogeneous water droplet pairs appearing in a tandem arrangement. Two micro-droplets of pure (rain) water interact with an oncoming outer air stream (Re ≤ 100) contaminated by uniformly distributed SO2. By virtue of separation/attachment induced non-uniform interfacial shear-stress gradient, the well-defined inflow/outflow type pairs of recirculating eddy-based convective motion quickly develops, and the eddies effectively attract/repel the accumulated outer solute and control the physical process of mass-transport in the droplet-pair. The non-uniformly shear-driven flow interaction and bifurcation of the circulatory internal flow lead to growth of important micro-scale "secondary" eddies which suitably regroup with the adjacent "primary" one to create the sustained inflow/outflow type convective dynamics. The presently derived flow characteristics and in-depth analysis help to significantly improve our understanding of the micro-droplet based transport phenomena in a wider context. By tuning "Re" (defined in terms of the droplet diameter and the average oncoming velocity of the outer air) and gap-ratio "α," the internal convective forcing and the solute entrainment efficiency could be considerably enhanced. The quantitative estimates for mass entrainment, convective strength, and saturation characteristics for different coupled micro-droplet pairs are extensively examined here for 0.2 ≤ α ≤ 2.0 and 30 ≤ Re ≤ 100. Interestingly, for the compound droplets, with suitably tuned radius-ratio "B" (of upstream droplet with respect to downstream one) the generated "inflow" type coherent convective dynamics helped to significantly augment the centre
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.
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 ...
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 ...
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
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.
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
Renard , N.; Deck , S.; Sagaut , P.
2014-01-01
International audience; A method inspired by del Alamo et al. [1] is derived to assess the wavelength-dependent convection velocity in a zero pressure gradient spatially developing flat plate turbulent boundary layer at Retheta = 13 000 for all wavelengths and all wall distances, using only estimates of the time power spectral density of the streamwise velocity and of its local spatial derivative. The resulting global convection velocity has a least-squares interpretation and is easily relate...
Charbonnel, C.; Decressin, T.; Lagarde, N.; Gallet, F.; Palacios, A.; Aurière, M.; Konstantinova-Antova, R.; Mathis, S.; Anderson, R. I.; Dintrans, B.
2017-09-01
Context. Recent spectropolarimetric observations of otherwise ordinary (in terms e.g. of surface rotation and chemical properties) G, K, and M giants have revealed localized magnetic strips in the Hertzsprung-Russell diagram coincident with the regions where the first dredge-up and core helium burning occur. Aims: We seek to understand the origin of magnetic fields in such late-type giant stars, which is currently unexplained. In analogy with late-type dwarf stars, we focus primarily on parameters known to influence the generation of magnetic fields in the outer convective envelope. Methods: We compute the classical dynamo parameters along the evolutionary tracks of low- and intermediate-mass stars at various metallicities using stellar models that have been extensively tested by spectroscopic and asteroseismic observations. Specifically, these include convective turnover timescales and convective Rossby numbers, computed from the pre-main sequence (PMS) to the tip of the red giant branch (RGB) or the early asymptotic giant branch (AGB) phase. To investigate the effects of the very extended outer convective envelope, we compute these parameters both for the entire convective envelope and locally, that is, at different depths within the envelope. We also compute the turnover timescales and corresponding Rossby numbers for the convective cores of intermediate-mass stars on the main sequence. Results: Our models show that the Rossby number of the convective envelope becomes lower than unity in the well-delimited locations of the Hertzsprung-Russell diagram where magnetic fields have indeed been detected. Conclusions: We show that α - Ω dynamo processes might not be continuously operating, but that they are favored in the stellar convective envelope at two specific moments along the evolution tracks, that is, during the first dredge-up at the base of the RGB and during central helium burning in the helium-burning phase and early-AGB. This general behavior can explain
Jiji, Latif M.
Professor Jiji's broad teaching experience lead him to select the topics for this book to provide a firm foundation for convection heat transfer with emphasis on fundamentals, physical phenomena, and mathematical modelling of a wide range of engineering applications. Reflecting recent developments, this textbook is the first to include an introduction to the challenging topic of microchannels. The strong pedagogic potential of Heat Convection is enhanced by the follow ing ancillary materials: (1) Power Point lectures, (2) Problem Solutions, (3) Homework Facilitator, and, (4) Summary of Sections and Chapters.
International Nuclear Information System (INIS)
Le Quere, P.; Weisman, C.; Paillere, H.; Vierendeels, J.; Dick, E.; Becker, R.; Braack, M.; Locke, J.
2005-01-01
Heat transfer by natural convection and conduction in enclosures occurs in numerous practical situations including the cooling of nuclear reactors. For large temperature difference, the flow becomes compressible with a strong coupling between the continuity, the momentum and the energy equations through the equation of state, and its properties (viscosity, heat conductivity) also vary with the temperature, making the Boussinesq flow approximation inappropriate and inaccurate. There are very few reference solutions in the literature on non-Boussinesq natural convection flows. We propose here a test case problem which extends the well-known De Vahl Davis differentially heated square cavity problem to the case of large temperature differences for which the Boussinesq approximation is no longer valid. The paper is split in two parts: in this first part, we propose as yet unpublished reference solutions for cases characterized by a non-dimensional temperature difference of 0.6, Ra 10 6 (constant property and variable property cases) and Ra = 10 7 (variable property case). These reference solutions were produced after a first international workshop organized by Cea and LIMSI in January 2000, in which the above authors volunteered to produce accurate numerical solutions from which the present reference solutions could be established. (authors)
Stellar convection and dynamo theory
Energy Technology Data Exchange (ETDEWEB)
Jennings, R L
1989-10-01
In considering the large scale stellar convection problem the outer layers of a star are modelled as two co-rotating plane layers coupled at a fluid/fluid interface. Heating from below causes only the upper fluid to convect, although this convection can penetrate into the lower fluid. Stability analysis is then used to find the most unstable mode of convection. With parameters appropriate to the Sun the most unstable mode is steady convection in thin cells (aspect ratio {approx equal} 0.2) filling the convection zone. There is negligible vertical motion in the lower fluid, but considerable thermal penetration, and a large jump in helicity at the interface, which has implications for dynamo theory. An {alpha}{omega} dynamo is investigated in isolation from the convection problem. Complexity is included by allowing both latitudinal and time dependence in the magnetic fields. The nonlinear dynamics of the resulting partial differential equations are analysed in considerable detail. On varying the main control parameter D (the dynamo number), many transitions of behaviour are found involving many forms of time dependence, but not chaos. Further, solutions which break equatorial symmetry are common and provide a theoretical explanation of solar observations which have this symmetry. Overall the behaviour was more complicated than expected. In particular, there were multiple stable solutions at fixed D, meaning that similar stars can have very different magnetic patterns, depending upon their history. (author).
National Convective Weather Diagnostic
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...
Convective overshoot at the solar tachocline
Brown, Benjamin; Oishi, Jeffrey S.; Anders, Evan H.; Lecoanet, Daniel; Burns, Keaton; Vasil, Geoffrey M.
2017-08-01
At the base of the solar convection zone lies the solar tachocline. This internal interface is where motions from the unstable convection zone above overshoot and penetrate downward into the stiffly stable radiative zone below, driving gravity waves, mixing, and possibly pumping and storing magnetic fields. Here we study the dynamics of convective overshoot across very stiff interfaces with some properties similar to the internal boundary layer within the Sun. We use the Dedalus pseudospectral framework and study fully compressible dynamics at moderate to high Peclet number and low Mach number, probing a regime where turbulent transport is important, and where the compressible dynamics are similar to those of convective motions in the deep solar interior. We find that the depth of convective overshoot is well described by a simple buoyancy equilibration model, and we consider implications for dynamics at the solar tachocline and for the storage of magnetic fields there by overshooting convection.
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.
The pattern of convection in the Sun
International Nuclear Information System (INIS)
Weiss, N.O.
1976-01-01
The structure of solar magnetic fields is dominated by the effects of convection, which should be incorporated in any model of the solar cycle. Although mixing length theory is adequate for calculating the structure of main sequence stars, a better description of convection is needed for any detailed dynamo model. Recent work on nonlinear convection at low Prandt numbers is reviewed. There has been some progress towards a theory of compressible convection, though there is still no firm theoretical evidence for cells with scales less than the depth of the convecting layer. However, it remains likely that the pattern of solar convection is dominated by granules, supergranules and giant cells. The effects of rotation on these cells are briefly considered. (Auth.)
Vertical natural convection: application of the unifying theory of thermal convection
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
Novel Natural Convection Heat Sink Design Concepts From First Principles
2016-06-01
CONVECTION HEAT SINK DESIGN CONCEPTS FROM FIRST PRINCIPLES by Derek E. Fletcher June 2016 Thesis Advisor: Garth Hobson Second Reader...COVERED Master’s Thesis 4. TITLE AND SUBTITLE NOVEL NATURAL CONVECTION HEAT SINK DESIGN CONCEPTS FROM FIRST PRINCIPLES 5. FUNDING NUMBERS 6...CONVECTION HEAT SINK DESIGN CONCEPTS FROM FIRST PRINCIPLES Derek E. Fletcher Lieutenant Commander, United States Navy B.S., Southwestern
National Convective Weather Forecast
National Oceanic and Atmospheric Administration, Department of Commerce — The NCWF is an automatically generated depiction of: (1) current convection and (2) extrapolated signficant current convection. It is a supplement to, but does NOT...
Hristova-Veleva, S. M.; Chen, H.; Gopalakrishnan, S.; Haddad, Z. S.
2017-12-01
Tropical cyclones (TCs) are the product of complex multi-scale processes and interactions. The role of the environment has long been recognized. However, recent research has shown that convective-scale processes in the hurricane core might also play a crucial role in determining TCs intensity and size. Several studies have linked Rapid Intensification to the characteristics of the convective clouds (shallow versus deep), their organization (isolated versus wide-spread) and their location with respect to dynamical controls (the vertical shear, the radius of maximum wind). Yet a third set of controls signifies the interaction between the storm-scale and large-scale processes. Our goal is to use observations and models to advance the still-lacking understanding of these processes. Recently, hurricane models have improved significantly. However, deterministic forecasts have limitations due to the uncertainty in the representation of the physical processes and initial conditions. A crucial step forward is the use of high-resolution ensembles. We adopt the following approach: i) generate a high resolution ensemble forecast using HWRF; ii) produce synthetic data (e.g. brightness temperature) from the model fields for direct comparison to satellite observations; iii) develop metrics to allow us to sub-select the realistic members of the ensemble, based on objective measures of the similarity between observed and forecasted structures; iv) for these most-realistic members, determine the skill in forecasting TCs to provide"guidance on guidance"; v) use the members with the best predictive skill to untangle the complex multi-scale interactions. We will report on the first three goals of our research, using forecasts and observations of hurricane Edouard (2014), focusing on RI. We will focus on describing the metrics for the selection of the most appropriate ensemble members, based on applying low-wave number analysis (WNA - Hristova-Veleva et al., 2016) to the observed and
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
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.
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.
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
CRUCIB: an axisymmetric convection code
International Nuclear Information System (INIS)
Bertram, L.A.
1975-03-01
The CRUCIB code was written in support of an experimental program aimed at measurement of thermal diffusivities of refractory liquids. Precise values of diffusivity are necessary to realistic analysis of reactor safety problems, nuclear waste disposal procedures, and fundamental metal forming processes. The code calculates the axisymmetric transient convective motions produced in a right circular cylindrical crucible, which is surface heated by an annular heat pulse. Emphasis of this report is placed on the input-output options of the CRUCIB code, which are tailored to assess the importance of the convective heat transfer in determining the surface temperature distribution. Use is limited to Prandtl numbers less than unity; larger values can be accommodated by replacement of a single block of the code, if desired. (U.S.)
Convective Radio Occultations Final Campaign Summary
Energy Technology Data Exchange (ETDEWEB)
Biondi, R. [Atmospheric Radiation Measurement, Washington, DC (United States)
2016-03-01
Deep convective systems are destructive weather phenomena that annually cause many deaths and injuries as well as much damage, thereby accounting for major economic losses in several countries. The number and intensity of such phenomena have increased over the last decades in some areas of the globe. Damage is mostly caused by strong winds and heavy rain parameters that are strongly connected to the structure of the particular storm. Convection over land is usually stronger and deeper than over the ocean and some convective systems, known as supercells, also develop tornadoes through processes that remain mostly unclear. The intensity forecast and monitoring of convective systems is one of the major challenges for meteorology because in situ measurements during extreme events are too sparse or unreliable and most ongoing satellite missions do not provide suitable time/space coverage.
Observing Convective Aggregation
Holloway, Christopher E.; Wing, Allison A.; Bony, Sandrine; Muller, Caroline; Masunaga, Hirohiko; L'Ecuyer, Tristan S.; Turner, David D.; Zuidema, Paquita
2017-11-01
Convective self-aggregation, the spontaneous organization of initially scattered convection into isolated convective clusters despite spatially homogeneous boundary conditions and forcing, was first recognized and studied in idealized numerical simulations. While there is a rich history of observational work on convective clustering and organization, there have been only a few studies that have analyzed observations to look specifically for processes related to self-aggregation in models. Here we review observational work in both of these categories and motivate the need for more of this work. We acknowledge that self-aggregation may appear to be far-removed from observed convective organization in terms of time scales, initial conditions, initiation processes, and mean state extremes, but we argue that these differences vary greatly across the diverse range of model simulations in the literature and that these comparisons are already offering important insights into real tropical phenomena. Some preliminary new findings are presented, including results showing that a self-aggregation simulation with square geometry has too broad distribution of humidity and is too dry in the driest regions when compared with radiosonde records from Nauru, while an elongated channel simulation has realistic representations of atmospheric humidity and its variability. We discuss recent work increasing our understanding of how organized convection and climate change may interact, and how model discrepancies related to this question are prompting interest in observational comparisons. We also propose possible future directions for observational work related to convective aggregation, including novel satellite approaches and a ground-based observational network.
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)
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
Some problems of free convection in a macrocapillary
Energy Technology Data Exchange (ETDEWEB)
Luikov, A V; Berkovsky, B M; Kolpashchikov, V L
1971-01-01
Solution is given to a number of problems of free convection in incompressible viscous fluid in elementary macrocapillaries with nonuniform temperature distribution at the boundary. The fluid flow structure and effect of a magnetic field on convection in the case of conducting fluid has been studied in detail. The influence of macrocapillary properties on the flow structure, rate of convection, and temperature distribution has been estimated.
Kakac, Sadik; Pramuanjaroenkij, Anchasa
2014-01-01
Intended for readers who have taken a basic heat transfer course and have a basic knowledge of thermodynamics, heat transfer, fluid mechanics, and differential equations, Convective Heat Transfer, Third Edition provides an overview of phenomenological convective heat transfer. This book combines applications of engineering with the basic concepts of convection. It offers a clear and balanced presentation of essential topics using both traditional and numerical methods. The text addresses emerging science and technology matters, and highlights biomedical applications and energy technologies. What’s New in the Third Edition: Includes updated chapters and two new chapters on heat transfer in microchannels and heat transfer with nanofluids Expands problem sets and introduces new correlations and solved examples Provides more coverage of numerical/computer methods The third edition details the new research areas of heat transfer in microchannels and the enhancement of convective heat transfer with nanofluids....
Introductory analysis of Benard-Marangoni convection
International Nuclear Information System (INIS)
Maroto, J A; Perez-Munuzuri, V; Romero-Cano, M S
2007-01-01
We describe experiments on Benard-Marangoni convection which permit a useful understanding of the main concepts involved in this phenomenon such as, for example, Benard cells, aspect ratio, Rayleigh and Marangoni numbers, Crispation number and critical conditions. In spite of the complexity of convection theory, we carry out a simple and introductory analysis which has the additional advantage of providing very suggestive experiments. As a consequence, we recommend our device for use as a laboratory experiment for undergraduate students of the thermodynamics of nonlinear and fluid physics
Introductory analysis of Benard-Marangoni convection
Energy Technology Data Exchange (ETDEWEB)
Maroto, J A [Group of Physics and Chemistry of Linares, Escuela Politecnica Superior, St Alfonso X El Sabio, 28, University of Jaen, E-23700 Linares, Jaen (Spain); Perez-Munuzuri, V [Group of Nonlinear Physics, University of Santiago de Compostela, E-15782 Santiago de Compostela (Spain); Romero-Cano, M S [Group of Complex Fluids Physics, Department of Applied Physics, University of Almeria, E-04120 Almeria (Spain)
2007-03-15
We describe experiments on Benard-Marangoni convection which permit a useful understanding of the main concepts involved in this phenomenon such as, for example, Benard cells, aspect ratio, Rayleigh and Marangoni numbers, Crispation number and critical conditions. In spite of the complexity of convection theory, we carry out a simple and introductory analysis which has the additional advantage of providing very suggestive experiments. As a consequence, we recommend our device for use as a laboratory experiment for undergraduate students of the thermodynamics of nonlinear and fluid physics.
Scale analysis of convective clouds
Directory of Open Access Journals (Sweden)
Micha Gryschka
2008-12-01
Full Text Available The size distribution of cumulus clouds due to shallow and deep convection is analyzed using satellite pictures, LES model results and data from the German rain radar network. The size distributions found can be described by simple power laws as has also been proposed for other cloud data in the literature. As the observed precipitation at ground stations is finally determined by cloud numbers in an area and individual sizes and rain rates of single clouds, the cloud size distributions might be used for developing empirical precipitation forecasts or for validating results from cloud resolving models being introduced to routine weather forecasts.
Convective losses through an air-filled gap
Energy Technology Data Exchange (ETDEWEB)
Baum, V A; Ovezsakhatov, N
1976-01-01
Simplified formulas for the heat fluxes with given parameters of the air are used to calculate the specific heat losses by convection in a number of solar-energy systems (water heater, thermal generator, double-glazed window, and still). Heat losses by convection and radiation are compared.
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.
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.)
Convection and stellar oscillations
DEFF Research Database (Denmark)
Aarslev, Magnus Johan
2017-01-01
for asteroseismology, because of the challenges inherent in modelling turbulent convection in 1D stellar models. As a result of oversimplifying the physics near the surface, theoretical calculations systematically overestimate the oscillation frequencies. This has become known as the asteroseismic surface effect. Due...... to lacking better options, this frequency difference is typically corrected for with ad-hoc formulae. The topic of this thesis is the improvement of 1D stellar convection models and the effects this has on asteroseismic properties. The source of improvements is 3D simulations of radiation...... atmospheres to replace the outer layers of stellar models. The additional turbulent pressure and asymmetrical opacity effects in the atmosphere model, compared to convection in stellar evolution models, serve to expand the atmosphere. The enlarged acoustic cavity lowers the pulsation frequencies bringing them...
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.
Convective transport in tokamaks
International Nuclear Information System (INIS)
D'Ippolito, D.A.; Myra, J.R.; Russell, D.A.; Krasheninnikov, S.I.; Pigarov, A.Yu.; Yu, G.Q.; Xu, X.Q.; Nevins, W.M.
2005-01-01
Scrape-off-layer (SOL) convection in fusion experiments appears to be a universal phenomenon that can 'short-circuit' the divertor in some cases. The theory of 'blob' transport provides a simple and robust physical paradigm for studying convective transport. This paper summarizes recent advances in the theory of blob transport and its comparison with 2D and 3D computer simulations. We also discuss the common physical basis relating radial transport of blobs, pellets, and ELMs and a new blob regime that may lead to a connection between blob transport and the density limit. (author)
Arnett, W. David
2009-05-01
We review recent progress using numerical simulations as a testbed for development of a theory of stellar convection, much as envisaged by John von Newmann. Necessary features of the theory, non-locality and fluctuations, are illustrated by computer movies. It is found that the common approximation of convection as a diffusive process presents the wrong physical picture, and improvements are suggested. New observational results discussed at the conference are gratifying in their validation of some of our theoretical ideas, especially the idea that SNIb and SNIc events are related to the explosion of massive star cores which have been stripped by mass loss and binary interactions [1
Parameterizing convective organization
Directory of Open Access Journals (Sweden)
Brian Earle Mapes
2011-06-01
Full Text Available Lateral mixing parameters in buoyancy-driven deep convection schemes are among the most sensitive and important unknowns in atmosphere models. Unfortunately, there is not a true optimum value for plume mixing rate, but rather a dilemma or tradeoff: Excessive dilution of updrafts leads to unstable stratification bias in the mean state, while inadequate dilution allows deep convection to occur too easily, causing poor space and time distributions and variability. In this too-small parameter space, compromises are made based on competing metrics of model performance. We attempt to escape this “entrainment dilemma” by making bulk plume parameters (chiefly entrainment rate depend on a new prognostic variable (“organization,” org meant to reflect the rectified effects of subgrid-scale structure in meteorological fields. We test an org scheme in the Community Atmosphere Model (CAM5 with a new unified shallow-deep convection scheme (UW-ens, a 2-plume version of the University of Washington scheme. Since buoyant ascent involves natural selection, subgrid structure makes convection systematically deeper and stronger than the pure unorganized case: plumes of average (or randomly sampled air rising in the average environment. To reflect this, org is nonnegative, but we leave it dimensionless. A time scale characterizes its behavior (here ∼3 h for a 2o model. Currently its source is rain evaporation, but other sources can be added easily. We also let org be horizontally transported by advection, as a mass-weighted mean over the convecting layer. Linear coefficients link org to a plume ensemble, which it assists via: 1 plume base warmth above the mean temperature 2 plume radius enhancement (reduced mixing, and 3 increased probability of overlap in a multi-plume scheme, where interactions benefit later generations (this part has only been implemented in an offline toy column model. Since rain evaporation is a source for org, it functions as a time
Mathematical models of convection
Andreev, Victor K; Goncharova, Olga N; Pukhnachev, Vladislav V
2012-01-01
Phenomena of convection are abundant in nature as well as in industry. This volume addresses the subject of convection from the point of view of both, theory and application. While the first three chapters provide a refresher on fluid dynamics and heat transfer theory, the rest of the book describes the modern developments in theory. Thus it brings the reader to the ""front"" of the modern research. This monograph provides the theoretical foundation on a topic relevant to metallurgy, ecology, meteorology, geo-and astrophysics, aerospace industry, chemistry, crystal physics, and many other fiel
Convective aggregation in realistic convective-scale simulations
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...
Vortex statistics in turbulent rotating convection
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
Terminal project heat convection in thin cylinders
International Nuclear Information System (INIS)
Morales Corona, J.
1992-01-01
Heat convection in thin cylinders and analysis about natural convection for straight vertical plates, and straight vertical cylinders submersed in a fluid are presented some works carry out by different authors in the field of heat transfer. In the part of conduction, deduction of the equation of heat conduction in cylindrical coordinates by means of energy balance in a control volume is presented. Enthalpy and internal energy are used for the outlining of the equation and finally the equation in its vectorial form is obtained. In the convection part development to calculate the Nusselt number for a straight vertical plate by a forces analysis, an energy balance and mass conservation over a control volume is outlined. Several empiric correlations to calculate the Nusselt number and its relations with other dimensionless numbers are presented. In the experimental part the way in which a prototype rode is assembled is presented measurements of temperatures attained in steady state and in free convection for working fluids as air and water are showed in tables. Also graphs of Nusselt numbers obtained in the experimental way through some empiric correlations are showed (Author)
Energy Technology Data Exchange (ETDEWEB)
Ghalambaz, M.; Noghrehabadi, A.; Ghanbarzadeh, A., E-mail: m.ghalambaz@gmail.com, E-mail: ghanbarzadeh.a@scu.ac.ir [Department of Mechanical Engineering, Shahid Chamran University of Ahvaz, Ahvaz (Iran, Islamic Republic of)
2014-04-15
In this paper, the natural convective flow of nanofluids over a convectively heated vertical plate in a saturated Darcy porous medium is studied numerically. The governing equations are transformed into a set of ordinary differential equations by using appropriate similarity variables, and they are numerically solved using the fourth-order Runge-Kutta method associated with the Gauss-Newton method. The effects of parametric variation of the Brownian motion parameter (Nb), thermophoresis parameter (Nt) and the convective heating parameter (Nc) on the boundary layer profiles are investigated. Furthermore, the variation of the reduced Nusselt number and reduced Sherwood number, as important parameters of heat and mass transfer, as a function of the Brownian motion, thermophoresis and convective heating parameters is discussed in detail. The results show that the thickness of the concentration profiles is much lower than the temperature and velocity profiles. For low values of the convective heating parameter (Nc), as the Brownian motion parameter increases, the non-dimensional wall temperature increases. However, for high values of Nc, the effect of the Brownian motion parameter on the non-dimensional wall temperature is not significant. As the Brownian motion parameter increases, the reduced Sherwood number increases and the reduced Nusselt number decreases. (author)
Forced and free convection hydromagnetic flow past a vertical flat plate
International Nuclear Information System (INIS)
Abdelkhalek, M.M.
2004-01-01
The effects of magnetic field and temperature heat source on the free and forced convection flow past an infinite vertical plate is studied analytically. Solutions of the reduced equation appropriate in the forced convection and free convection regime are obtained using perturbation technique. The expression for the velocity field, skin friction and Nusselt number have been obtained
CDM Convective Forecast Planning guidance
National Oceanic and Atmospheric Administration, Department of Commerce — The CDM Convective Forecast Planning (CCFP) guidance product provides a foreast of en-route aviation convective hazards. The forecasts are updated every 2 hours and...
Presentation on Tropical Mesoscale convective Systems and ...
Indian Academy of Sciences (India)
IAS Admin
Shallow convection- 70% of the storm heights are below 6 km. ♢ Deep convection ... Decay convection, the convective top is found at a higher altitude than deep .... Stratospheric Fountain – Two step process. Warm tropopause- preferable for.
Convective overshooting in stars
Andrássy, R.
2015-01-01
Numerous observations provide evidence that the standard picture, in which convective mixing is limited to the unstable layers of a star, is incomplete. The mixing layers in real stars are significantly more extended than what the standard models predict. Some of the observations require changing
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 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
International Nuclear Information System (INIS)
Aziz, Abdul; Beers-Green, Arlen B.
2009-01-01
This paper investigates the performance and optimum design of a longitudinal rectangular fin attached to a convectively heated wall of finite thickness. The exposed surfaces of the fin lose heat to the environmental sink by simultaneous convection and radiation. The tip of the fin is assumed to lose heat by convection and radiation to the same sink. The analysis and optimization of the fin is conducted numerically using the symbolic algebra package Maple. The temperature distribution, the heat transfer rates, and the fin efficiency data is presented illustrating how the thermal performance of the fin is affected by the convection-conduction number, the radiation-conduction number, the base convection Biot number, the convection and radiation Biot numbers at the tip, and the dimensionless sink temperature. Charts are presented showing the relationship between the optimum convection-conduction number and the optimum radiation-conduction number for different values of the base convection Biot number and dimensionless sink temperature and fixed values of the convection and radiation Biot numbers at the tip. Unlike the few other papers which have applied the Adomian's decomposition and the differential quadrature element method to this problem but give illustrative results for specific fin geometry and thermal variables, the present graphical data are generally applicable and can be used by fin designers without delving into the mathematical details of the computational techniques.
Convective Propagation Characteristics Using a Simple Representation of Convective Organization
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.
Experimental study of laminar mixed convection in a rod bundle with mixing vane spacer grids
Energy Technology Data Exchange (ETDEWEB)
Mohanta, Lokanath, E-mail: lxm971@psu.edu [Department of Mechanical and Nuclear Engineering, Pennsylvania State University, University Park, PA 16802 (United States); Cheung, Fan-Bill [Department of Mechanical and Nuclear Engineering, Pennsylvania State University, University Park, PA 16802 (United States); Bajorek, Stephen M.; Tien, Kirk; Hoxie, Chris L. [Office of Nuclear Regulatory Research, U.S. Nuclear Regulatory Commission, Washington, DC 20555-0001 (United States)
2017-02-15
Highlights: • Investigated the heat transfer during mixed laminar convection in a rod bundle with linearly varying heat flux. • The Nusselt number increases downstream of the inlet with increasing Richardson number. • Developed an enhancement factor to account for the effects of mixed convection over the forced laminar heat transfer. - Abstract: Heat transfer by mixed convection in a rod bundle occurs when convection is affected by both the buoyancy and inertial forces. Mixed convection can be assumed when the Richardson number (Ri = Gr/Re{sup 2}) is on the order of unity, indicating that both forced and natural convection are important contributors to heat transfer. In the present study, data obtained from the Rod Bundle Heat Transfer (RBHT) facility was used to determine the heat transfer coefficient in the mixed convection regime, which was found to be significantly larger than those expected assuming purely forced convection based on the inlet flow rate. The inlet Reynolds (Re) number for the tests ranged from 500 to 1300, while the Grashof (Gr) number varied from 1.5 × 10{sup 5} to 3.8 × 10{sup 6} yielding 0.25 < Ri < 4.3. Using results from RBHT test along with the correlation from the FLECHT-SEASET test program for laminar forced convection, a new correlation is proposed for mixed convection in a rod bundle. The new correlation accounts for the enhancement of heat transfer relative to laminar forced convection.
Two-dimensional turbulent convection
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)].
Oscillatory Convection in Rotating Liquid Metals
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.
Bejan, Adrian
2013-01-01
Written by an internationally recognized authority on heat transfer and thermodynamics, this second edition of Convection Heat Transfer contains new and updated problems and examples reflecting real-world research and applications, including heat exchanger design. Teaching not only structure but also technique, the book begins with the simplest problem solving method (scale analysis), and moves on to progressively more advanced and exact methods (integral method, self similarity, asymptotic behavior). A solutions manual is available for all problems and exercises.
Cheng, W. Y.; Kim, D.; Rowe, A.; Park, S.
2017-12-01
Despite the impact of mesoscale convective organization on the properties of convection (e.g., mixing between updrafts and environment), parameterizing the degree of convective organization has only recently been attempted in cumulus parameterization schemes (e.g., Unified Convection Scheme UNICON). Additionally, challenges remain in determining the degree of convective organization from observations and in comparing directly with the organization metrics in model simulations. This study addresses the need to objectively quantify the degree of mesoscale convective organization using high quality S-PolKa radar data from the DYNAMO field campaign. One of the most noticeable aspects of mesoscale convective organization in radar data is the degree of convective clustering, which can be characterized by the number and size distribution of convective echoes and the distance between them. We propose a method of defining contiguous convective echoes (CCEs) using precipitating convective echoes identified by a rain type classification algorithm. Two classification algorithms, Steiner et al. (1995) and Powell et al. (2016), are tested and evaluated against high-resolution WRF simulations to determine which method better represents the degree of convective clustering. Our results suggest that the CCEs based on Powell et al.'s algorithm better represent the dynamical properties of the convective updrafts and thus provide the basis of a metric for convective organization. Furthermore, through a comparison with the observational data, the WRF simulations driven by the DYNAMO large-scale forcing, similarly applied to UNICON Single Column Model simulations, will allow us to evaluate the ability of both WRF and UNICON to simulate convective clustering. This evaluation is based on the physical processes that are explicitly represented in WRF and UNICON, including the mechanisms leading to convective clustering, and the feedback to the convective properties.
Concepts of magnetospheric convection
International Nuclear Information System (INIS)
Vasyliunas, V.M.
1975-01-01
Magnetospheric physics, which grew out of attempts to understand the space environment of the Earth, is becoming increasingly applicable to other systems in the Universe. Among the planets, in addition to the Earth, Jupiter, Mercury, Mars and (in a somewhat different way) Venus are now known to have magnetospheres. The magnetospheres of pulsars have been regarded as an essential part of the pulsar phenomenon. Other astrophysical systems, such as supernova remnant shells or magnetic stars and binary star systems, may be describable as magnetospheres. The major concepts of magnetospheric physics thus need to be formulated in a general way not restricted to the geophysical context in which they may have originated. Magnetospheric convection has been one of the most important and fruitful concepts in the study of the Earth's magnetosphere. This paper describes the basic theoretical notions of convection in a manner applicable to magnetospheres generally and discusses the relative importance of convective corotational motions, with particular reference to the comparison of the Earth and Jupiter. (Auth.)
Lattice Boltzmann model for melting with natural convection
International Nuclear Information System (INIS)
Huber, Christian; Parmigiani, Andrea; Chopard, Bastien; Manga, Michael; Bachmann, Olivier
2008-01-01
We develop a lattice Boltzmann method to couple thermal convection and pure-substance melting. The transition from conduction-dominated heat transfer to fully-developed convection is analyzed and scaling laws and previous numerical results are reproduced by our numerical method. We also investigate the limit in which thermal inertia (high Stefan number) cannot be neglected. We use our results to extend the scaling relations obtained at low Stefan number and establish the correlation between the melting front propagation and the Stefan number for fully-developed convection. We conclude by showing that the model presented here is particularly well-suited to study convection melting in geometrically complex media with many applications in geosciences
Impairment of Heat Transfer in the Passive Cooling System due to Mixed Convection
Energy Technology Data Exchange (ETDEWEB)
Chae Myeong Seon; Chung, Bum Jin [Kyunghee University, Yongin (Korea, Republic of); Kim, Jong Hwan [KAERI, Daejeon (Korea, Republic of)
2016-05-15
In the passive cooling devices, the buoyant flows are induced. However the local Nusselt number of natural convective flow can be partly impaired due to the development of the mixed convective flows. This paper discusses impairment of heat transfer in the passive cooling system in relation to the development of mixed convection. The present work describes the preliminary plan to explore the phenomena experimentally. This paper is to discuss and make the plan to experiment the impairment of heat transfer in the passive cooling system due to mixed convection. In the sufficiently high passive cooling devices, the natural convection flow behavior can be mixed convection. The local Nusselt number distribution exhibits the non-monotonic behavior as axial position, since the buoyancy-aided with mixed convection was appeared. This is the part of the experimental work.
Basal melting driven by turbulent thermal convection
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.
An application of the unifying theory of thermal convection in vertical natural convection
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.
Convection with local thermal non-equilibrium and microfluidic effects
Straughan, Brian
2015-01-01
This book is one of the first devoted to an account of theories of thermal convection which involve local thermal non-equilibrium effects, including a concentration on microfluidic effects. The text introduces convection with local thermal non-equilibrium effects in extraordinary detail, making it easy for readers newer to the subject area to understand. This book is unique in the fact that it addresses a large number of convection theories and provides many new results which are not available elsewhere. This book will be useful to researchers from engineering, fluid mechanics, and applied mathematics, particularly those interested in microfluidics and porous media.
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
Bidispersive-inclined convection
Mulone, Giuseppe; Straughan, Brian
2016-01-01
A model is presented for thermal convection in an inclined layer of porous material when the medium has a bidispersive structure. Thus, there are the usual macropores which are full of a fluid, but there are also a system of micropores full of the same fluid. The model we employ is a modification of the one proposed by Nield & Kuznetsov (2006 Int. J. Heat Mass Transf. 49, 3068–3074. (doi:10.1016/j.ijheatmasstransfer.2006.02.008)), although we consider a single temperature field only. PMID:27616934
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
Scaling of Convection and Plate Tectonics in Super-Earths
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.
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)
Turbulent convection in liquid metal with and without rotation
King, Eric M.; Aurnou, Jonathan M.
2013-01-01
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, . Most analog models of planetary dynamos, however, use moderate fluids, and the systematic influence of reducing is not well understood. We perform rotating Rayleigh–Bénard convection experiments in the liquid metal gallium over a range of nondimensional bu...
Heat transport in bubbling turbulent convection.
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.
Convective mass transfer around a dissolving bubble
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.
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.
Quantifying near-wall coherent structures in turbulent convection
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.
Improved nowcasting of precipitation based on convective analysis fields
Directory of Open Access Journals (Sweden)
T. Haiden
2007-04-01
Full Text Available The high-resolution analysis and nowcasting system INCA (Integrated Nowcasting through Comprehensive Analysis developed at the Austrian national weather service provides three-dimensional fields of temperature, humidity, and wind on an hourly basis, and two-dimensional fields of precipitation rate in 15 min intervals. The system operates on a horizontal resolution of 1 km and a vertical resolution of 100–200 m. It combines surface station data, remote sensing data (radar, satellite, forecast fields of the numerical weather prediction model ALADIN, and high-resolution topographic data. An important application of the INCA system is nowcasting of convective precipitation. Based on fine-scale temperature, humidity, and wind analyses a number of convective analysis fields are routinely generated. These fields include convective boundary layer (CBL flow convergence and specific humidity, lifted condensation level (LCL, convective available potential energy (CAPE, convective inhibition (CIN, and various convective stability indices. Based on the verification of areal precipitation nowcasts it is shown that the pure translational forecast of convective cells can be improved by using a decision algorithm which is based on a subset of the above fields, combined with satellite products.
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)
Combined convective heat transfer of liquid sodium flowing across tube banks
International Nuclear Information System (INIS)
Ma, Ying; Sugiyama, Ken-ichiro; Ishiguro, Ryoji
1989-01-01
In order to clarify the heat transfer characteristics of combined convection of liquid sodium, a numerical analysis is performed for liquid sodium which flows through a single horizontal row of tubes in the direction of gravity. The correlation of heat transfer characteristics between liquid sodium and ordinary fluids is also discussed. The heat transfer characteristics at large Reynolds numbers are improved when the Richardson number is increased, and the improvement rate is enlarged with increase in p/d value, since convection effect is relatively large. However heat transfer coefficients do not differ from those of forced convection at small Reynolds numbers even when the Richardson number reaches a high value because of conduction effect. A good consistence of heat transfer characteristics of combined convection between liquid sodium and air is obtained at the same Peclet number and Richardson number. This means that the fundamental heat transfer characteristics of combined convection of liquid sodium can be investigated with ordinary fluids. (author)
Counterintuitive Constraints on Chaos Formation Set by Heat Flux through Europa's Ocean
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
Panosetti, Davide; Schlemmer, Linda; Schär, Christoph
2018-05-01
Convection-resolving models (CRMs) can explicitly simulate deep convection and resolve interactions between convective updrafts. They are thus increasingly used in numerous weather and climate applications. However, the truncation of the continuous energy cascade at scales of O (1 km) poses a serious challenge, as in kilometer-scale simulations the size and properties of the simulated convective cells are often determined by the horizontal grid spacing (Δ x ).In this study, idealized simulations of deep moist convection over land are performed to assess the convergence behavior of a CRM at Δ x = 8, 4, 2, 1 km and 500 m. Two types of convergence estimates are investigated: bulk convergence addressing domain-averaged and integrated variables related to the water and energy budgets, and structural convergence addressing the statistics and scales of individual clouds and updrafts. Results show that bulk convergence generally begins at Δ x =4 km, while structural convergence is not yet fully achieved at the kilometer scale, despite some evidence that the resolution sensitivity of updraft velocities and convective mass fluxes decreases at finer resolution. In particular, at finer grid spacings the maximum updraft velocity generally increases, and the size of the smallest clouds is mostly determined by Δ x . A number of different experiments are conducted, and it is found that the presence of orography and environmental vertical wind shear yields more energetic structures at scales much larger than Δ x , sometimes reducing the resolution sensitivity. Overall the results lend support to the use of kilometer-scale resolutions in CRMs, despite the inability of these models to fully resolve the associated cloud field.
Nield, Donald A
2013-01-01
Convection in Porous Media, 4th Edition, provides a user-friendly introduction to the subject, covering a wide range of topics, such as fibrous insulation, geological strata, and catalytic reactors. The presentation is self-contained, requiring only routine mathematics and the basic elements of fluid mechanics and heat transfer. The book will be of use not only to researchers and practicing engineers as a review and reference, but also to graduate students and others entering the field. The new edition features approximately 1,750 new references and covers current research in nanofluids, cellular porous materials, strong heterogeneity, pulsating flow, and more. Recognized as the standard reference in the field Includes a comprehensive, 250-page reference list Cited over 2300 times to date in its various editions Serves as an introduction for those entering the field and as a comprehensive reference for experienced researchers Features new sections on nanofluids, carbon dioxide sequestration, and applications...
Bohan, Richard J.; Vandegrift, Guy
2003-02-01
Warm air aloft is stable. This explains the lack of strong winds in a warm front and how nighttime radiative cooling can lead to motionless air that can trap smog. The stability of stratospheric air can be attributed to the fact that it is heated from above as ultraviolet radiation strikes the ozone layer. On the other hand, fluid heated from below is unstable and can lead to Bernard convection cells. This explains the generally turbulent nature of the troposphere, which receives a significant fraction of its heat directly from the Earth's warmer surface. The instability of cold fluid aloft explains the violent nature of a cold front, as well as the motion of Earth's magma, which is driven by radioactive heating deep within the Earth's mantle. This paper describes how both effects can be demonstrated using four standard beakers, ice, and a bit of food coloring.
Nield, Donald A
1992-01-01
This book provides a user-friendly introduction to the topic of convection in porous media The authors as- sume that the reader is familiar with the basic elements of fluid mechanics and heat transfer, but otherwise the book is self-contained The book will be useful both as a review (for reference) and as a tutorial work, suitable as a textbook in a graduate course or seminar The book brings into perspective the voluminous research that has been performed during the last two decades The field has recently exploded because of worldwide concern with issues such as energy self-sufficiency and pollution of the environment Areas of application include the insulation of buildings and equipment, energy storage and recovery, geothermal reservoirs, nuclear waste disposal, chemical reactor engineering, and the storage of heat-generating materials such as grain and coal Geophysical applications range from the flow of groundwater around hot intrusions to the stability of snow against avalanches
A Stochastic Framework for Modeling the Population Dynamics of Convective Clouds
Hagos, Samson; Feng, Zhe; Plant, Robert S.; Houze, Robert A.; Xiao, Heng
2018-02-01
A stochastic prognostic framework for modeling the population dynamics of convective clouds and representing them in climate models is proposed. The framework follows the nonequilibrium statistical mechanical approach to constructing a master equation for representing the evolution of the number of convective cells of a specific size and their associated cloud-base mass flux, given a large-scale forcing. In this framework, referred to as STOchastic framework for Modeling Population dynamics of convective clouds (STOMP), the evolution of convective cell size is predicted from three key characteristics of convective cells: (i) the probability of growth, (ii) the probability of decay, and (iii) the cloud-base mass flux. STOMP models are constructed and evaluated against CPOL radar observations at Darwin and convection permitting model (CPM) simulations. Multiple models are constructed under various assumptions regarding these three key parameters and the realisms of these models are evaluated. It is shown that in a model where convective plumes prefer to aggregate spatially and the cloud-base mass flux is a nonlinear function of convective cell area, the mass flux manifests a recharge-discharge behavior under steady forcing. Such a model also produces observed behavior of convective cell populations and CPM simulated cloud-base mass flux variability under diurnally varying forcing. In addition to its use in developing understanding of convection processes and the controls on convective cell size distributions, this modeling framework is also designed to serve as a nonequilibrium closure formulations for spectral mass flux parameterizations.
Convective behaviour in vapour-gas-aerosol mixtures
International Nuclear Information System (INIS)
Clement, C.F.
1986-01-01
Unusual convective behaviour can occur in mixtures of gases and heavy vapour, including stabilization of mixtures hot at the base and 'upside-down' convection in mixtures hot at the top. Previous work produced a criterion for this behaviour which ignored the necessary presence of an aerosol. Modification arising from aerosol condensation is derived and is shown to involve the Lewis and condensation numbers of the mixture, as well as a quantity involving the temperature drop across a boundary layer. It becomes negligible at high temperatures, but can crucially affect the temperature for the onset of unusual behaviour. Aerosol formation produces an asymmetry between the convective forces in boundary layers in which the mixture is being heated and cooled, respectively, for example at the base and roof of a cavity. The convective behaviour discussed could occur in situations relevant to nuclear safety. (author)
Turbulent convection in liquid metal with and without rotation.
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.
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
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.
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.
Breakdown of large-scale circulation in turbulent rotating convection
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
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 %.
Convection in the Labrador Sea
National Research Council Canada - National Science Library
Davis, R
1997-01-01
The long-term goal of this grant was to describe the process of deep oceanic convection well enough to provide critical tests of, and guidance to, models used to predict subsurface ocean conditions...
Dunn, James C.; Hardee, Harry C.; Striker, Richard P.
1985-01-01
A convective heat flow probe device is provided which measures heat flow and fluid flow magnitude in the formation surrounding a borehole. The probe comprises an elongate housing adapted to be lowered down into the borehole; a plurality of heaters extending along the probe for heating the formation surrounding the borehole; a plurality of temperature sensors arranged around the periphery of the probe for measuring the temperature of the surrounding formation after heating thereof by the heater elements. The temperature sensors and heater elements are mounted in a plurality of separate heater pads which are supported by the housing and which are adapted to be radially expanded into firm engagement with the walls of the borehole. The heat supplied by the heater elements and the temperatures measured by the temperature sensors are monitored and used in providing the desired measurements. The outer peripheral surfaces of the heater pads are configured as segments of a cylinder and form a full cylinder when taken together. A plurality of temperature sensors are located on each pad so as to extend along the length and across the width thereof, with a heating element being located in each pad beneath the temperature sensors. An expansion mechanism driven by a clamping motor provides expansion and retraction of the heater pads and expandable packer-type seals are provided along the probe above and below the heater pads.
An experimental study of mixed convection
International Nuclear Information System (INIS)
Saez, Manuel
1998-01-01
The aim of our study is to establish a reliable data base for improving thermal-hydraulic codes, in the field of turbulent flows with buoyancy forces. The flow considered is mixed convection in the Reynolds and Richardson number range: Re=10"3 to 6*10"4 and Ri=10"-"4 to 1. Experiments are carried out in an upward turbulent flow between vertical parallel plates at different wall temperatures. Part 1 gives a detailed data base of turbulent mixed flow of free and forced convection. Part II presents the installation and the calibration system intended for probes calibration. Part III describes the measurement technique (constant-temperature probe and cold-wire probe) and the method for measuring the position of the hot-wire anemometer from the wall surface. The measurement accuracy is within 0.001 mm in the present system. Part IV relates the development of a method for near wall measurements. This correction procedure for hot-wire anemometer close to wall has been derived on the basis of a two-dimensional numerical study. The method permits to obtain a quantitative correction of the wall influence on hot-wires and takes into account the velocity profile and the effects the wall material has on the heat loss. Part V presents the experimental data obtained in the channel in forced and mixed convection. Results obtained in the forced convection regime serve as a verification of the measurement technique close to the wall and give the conditions at the entrance of the test section. The effects of the buoyancy force on the mean velocity and temperature profiles are confirmed. The buoyancy strongly affects the flow structure and deforms the distribution of mean velocity. The velocity profiles are asymmetric. The second section of part V gives an approach of analytical wall functions with buoyancy forces, on the basis of the experimental data obtained in the test section. (author) [fr
Convection-enhanced water evaporation
B. M. Weon; J. H. Je; C. Poulard
2011-01-01
Water vapor is lighter than air; this can enhance water evaporation by triggering vapor convection but there is little evidence. We directly visualize evaporation of nanoliter (2 to 700 nL) water droplets resting on silicon wafer in calm air using a high-resolution dual X-ray imaging method. Temporal evolutions of contact radius and contact angle reveal that evaporation rate linearly changes with surface area, indicating convective (instead of diffusive) evaporation in nanoliter water droplet...
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.
The Oscillatory Nature of Rotating Convection in Liquid Metal
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.
Transitions in rapidly rotating convection dynamos
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.
Heat Transfer Convection in The Cooking of Apple Using a Solar Cooker Box-Type
International Nuclear Information System (INIS)
Terres, H; Chávez, S; Lizardi, A; López, R; Vaca, M; Flores, J; Salazar, A
2015-01-01
In this work, experimental results to determine the convection heat transfer coefficient in the cooking process of apple using a solar cooker box-type are presented. Experimental data of temperatures for water, surface and central point of the apple were used. To determine the convection coefficient, the apple was modelled as a sphere. The temperatures evolution was defined using thermocouples located at water, surface and central point in the vegetables. Using heat transfer convection equations in transitory state and the temperatures measured, the Biot number and the convection coefficient were determined
Heat Transfer Convection in The Cooking of Apple Using a Solar Cooker Box-Type
Terres, H.; Chávez, S.; Lizardi, A.; López, R.; Vaca, M.; Flores, J.; Salazar, A.
2015-01-01
In this work, experimental results to determine the convection heat transfer coefficient in the cooking process of apple using a solar cooker box-type are presented. Experimental data of temperatures for water, surface and central point of the apple were used. To determine the convection coefficient, the apple was modelled as a sphere. The temperatures evolution was defined using thermocouples located at water, surface and central point in the vegetables. Using heat transfer convection equations in transitory state and the temperatures measured, the Biot number and the convection coefficient were determined.
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.
Calibrating convective properties of solar-like stars in the Kepler field of view
Bonaca, A.; Tanner, J.D.; Basu, S.; Chaplin, W.J.; Metcalfe, T.S.; Monteiro, M.J.P.F.G.; Ballot, J.; Bedding, T.R.; Bonanno, A.; Broomhall, A.M.; Bruntt, H.; Campante, T.L.; Christensen-Dalsgaard, J.; Corsaro, E.; Elsworth, Y.; García, R.A.; Hekker, S.; Karoff, C.; Kjeldsen, H.; Mathur, S.; Régulo, C.; Roxburgh, I.; Stello, D.; Trampedach, R.; Barclay, T.; Burke, C.J.; Caldwell, D.A.
2012-01-01
Stellar models generally use simple parameterizations to treat convection. The most widely used parameterization is the so-called mixing-length theory where the convective eddy sizes are described using a single number, α, the mixing-length parameter. This is a free parameter, and the general
Analysis of the convective heat transfer of a fluid flow over an ...
African Journals Online (AJOL)
Convective heat transfer in a homogeneous fluid flow Reynolds number of order less than 2000 over an immersed axi-symmetrical body with curved surfaces has been investigated. The fluid flow in consideration was unsteady and of constant density .This study analysed the extent to which convective heat transfer has on ...
Mantle Convection on Modern Supercomputers
Weismüller, J.; Gmeiner, B.; Huber, M.; John, L.; Mohr, M.; Rüde, U.; Wohlmuth, B.; Bunge, H. P.
2015-12-01
Mantle convection is the cause for plate tectonics, the formation of mountains and oceans, and the main driving mechanism behind earthquakes. The convection process is modeled by a system of partial differential equations describing the conservation of mass, momentum and energy. Characteristic to mantle flow is the vast disparity of length scales from global to microscopic, turning mantle convection simulations into a challenging application for high-performance computing. As system size and technical complexity of the simulations continue to increase, design and implementation of simulation models for next generation large-scale architectures is handled successfully only in an interdisciplinary context. A new priority program - named SPPEXA - by the German Research Foundation (DFG) addresses this issue, and brings together computer scientists, mathematicians and application scientists around grand challenges in HPC. Here we report from the TERRA-NEO project, which is part of the high visibility SPPEXA program, and a joint effort of four research groups. TERRA-NEO develops algorithms for future HPC infrastructures, focusing on high computational efficiency and resilience in next generation mantle convection models. We present software that can resolve the Earth's mantle with up to 1012 grid points and scales efficiently to massively parallel hardware with more than 50,000 processors. We use our simulations to explore the dynamic regime of mantle convection and assess the impact of small scale processes on global mantle flow.
effect of brinkman number and magnetic field on laminar convection ...
African Journals Online (AJOL)
Joseph et al.
Science World Journal Vol 12(No 4) 2017 ... Joule heating on the fully developed MHD flow with heat transfer .... fluid in a vertical parallel – plate with effect of magnetic field and ..... Plates Channel, Proceedings of the 2013 International.
Prandtl number variation on transient forced convection flow in a ...
African Journals Online (AJOL)
user
2Manufacturing Engineering Department, The Public Authority for Applied Education and ... A transient numerical study is conducted to investigate the transport .... The model describes a valve where it is possible to direct the flow into one.
Model for modulated and chaotic waves in zero-Prandtl-number ...
Indian Academy of Sciences (India)
KCD) [20] for thermal convection in zero-Prandtl-number fluids in the presence of Coriolis force showed the possibility of self-tuned temporal quasiperiodic waves at the onset of thermal convection. However, the effect of modulation when the.
Convective behaviour in severe accidents
International Nuclear Information System (INIS)
Clement, C.F.
1988-01-01
The nature and magnitude of the hazard from radioactivity posed by a possible nuclear accident depend strongly on convective behaviour within and immediately adjacent to the plant in question. This behaviour depends upon the nature of the vapour-gas-aerosol mixture concerned, and can show unusual properties such as 'upside-down' convection in which hot mixtures fall and cold mixtures rise. Predictions and criteria as to the types of behaviour which could possibly occur are summarised. Possible applications to present reactors are considered, and ways in which presently expected convection could be drastically modified are described. In some circumstances these could be used to suppress the radioactive source term or to switch its effect between distant dilute contamination and severe local contamination. (author). 8 refs, 2 figs, 2 tabs
Topology Optimization for Convection Problems
DEFF Research Database (Denmark)
Alexandersen, Joe
2011-01-01
This report deals with the topology optimization of convection problems.That is, the aim of the project is to develop, implement and examine topology optimization of purely thermal and coupled thermomechanical problems,when the design-dependent eects of convection are taken into consideration.......This is done by the use of a self-programmed FORTRAN-code, which builds on an existing 2D-plane thermomechanical nite element code implementing during the course `41525 FEM-Heavy'. The topology optimizationfeatures have been implemented from scratch, and allows the program to optimize elastostatic mechanical...
Experimental methods in natural convection
International Nuclear Information System (INIS)
Koster, J.N.
1982-11-01
Some common experimental techniques to determine local velocities and to visualize temperature fields in natural convection research are discussed. First the physics and practice of anemometers are discussed with emphasis put on optical anemometers. In the second and third case the physics and practice of the most developed interferometers are discussed; namely differential interferometry for visualization of temperature gradient fields and holographic interferometry for visualization of temperature fields. At the Institut fuer Reaktorbauelemente these three measuring techniques are applied for convection and pipe flow studies. (orig.) [de
Magnetohydrodynamic free convection in a strong cross field
Kuiken, H.K.
1970-01-01
The problem of magnetohydrodynamic free convection of an electrically conducting fluid in a strong cross field is investigated. It is solved by using a singular perturbation technique. The solutions presented cover the range of Prandtl numbers from zero to order one. This includes both the important
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
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
Segregation and convection in dendritic alloys
Poirier, D. R.
1990-01-01
Microsegregation in dentritic alloys is discussed, including solidification with and without thermal gradient, the convection of interdendritic liquid. The conservation of momentum, energy, and solute is considered. Directional solidification and thermosolutal convection are discussed.
Oscillatory magneto-convection under magnetic field modulation
Directory of Open Access Journals (Sweden)
Palle Kiran
2018-03-01
Full Text Available In this paper we investigate an oscillatory mode of nonlinear magneto-convection under time dependant magnetic field. The time dependant magnetic field consists steady and oscillatory parts. The oscillatory part of the imposed magnetic field is assumed to be of third order. An externally imposed vertical magnetic field in an electrically conducting horizontal fluid layer is considered. The finite amplitude analysis is discussed while perturbing the system. The complex Ginzburg-Landau model is used to derive an amplitude of oscillatory convection for weakly nonlinear mode. Heat transfer is quantified in terms of the Nusselt number, which is governed by the Landau equation. The variation of the modulation excitation of the magnetic field alternates heat transfer in the layer. The modulation excitation of the magnetic field is used either to enhance or diminish the heat transfer in the system. Further, it is found that, oscillatory mode of convection enhances the heat transfer and than stationary convection. The results have possible technological applications in magnetic fluid based systems involving energy transmission. Keywords: Weakly nonlinear theory, Oscillatory convection, Complex Ginzburg Landau model, Magnetic modulation
Extended Subadiabatic Layer in Simulations of Overshooting Convection
Energy Technology Data Exchange (ETDEWEB)
Käpylä, Petri J.; Arlt, Rainer [Leibniz-Institut für Astrophysik, An der Sternwarte 16, D-14482 Potsdam (Germany); Rheinhardt, Matthias; Käpylä, Maarit J.; Olspert, Nigul [ReSoLVE Centre of Excellence, Department of Computer Science, P.O. Box 15400, FI-00076 Aalto (Finland); Brandenburg, Axel [NORDITA, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-10691 Stockholm (Sweden); Lagg, Andreas; Warnecke, Jörn [Max-Planck-Institut für Sonnensystemforschung, Justus-von-Liebig-Weg 3, D-37077 Göttingen (Germany)
2017-08-20
We present numerical simulations of hydrodynamic overshooting convection in local Cartesian domains. We find that a substantial fraction of the lower part of the convection zone (CZ) is stably stratified according to the Schwarzschild criterion while the enthalpy flux is outward directed. This occurs when the heat conduction profile at the bottom of the CZ is smoothly varying, based either on a Kramers-like opacity prescription as a function of temperature and density or a static profile of a similar shape. We show that the subadiabatic layer arises due to nonlocal energy transport by buoyantly driven downflows in the upper parts of the CZ. Analysis of the force balance of the upflows and downflows confirms that convection is driven by cooling at the surface. We find that the commonly used prescription for the convective enthalpy flux being proportional to the negative entropy gradient does not hold in the stably stratified layers where the flux is positive. We demonstrate the existence of a non-gradient contribution to the enthalpy flux, which is estimated to be important throughout the convective layer. A quantitative analysis of downflows indicates a transition from a tree-like structure where smaller downdrafts merge into larger ones in the upper parts to a structure in the deeper parts where a height-independent number of strong downdrafts persist. This change of flow topology occurs when a substantial subadiabatic layer is present in the lower part of the CZ.
Vigorous convection as the explanation for Pluto's polygonal terrain.
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.
Boiling Suppression in Convective Flow
International Nuclear Information System (INIS)
Aounallah, Y.
2004-01-01
The development of convective boiling heat transfer correlations and analytical models has almost exclusively been based on measurements of the total heat flux, and therefore on the overall two-phase heat transfer coefficient, when the well-known heat transfer correlations have often assumed additive mechanisms, one for each mode of heat transfer, convection and boiling. While the global performance of such correlations can readily be assessed, the predictive capability of the individual components of the correlation has usually remained elusive. This becomes important when, for example, developing mechanistic models for subcooled void formation based on the partitioning of the wall heat flux into a boiling and a convective component, or when extending a correlation beyond its original range of applications where the preponderance of the heat transfer mechanisms involved can be significantly different. A new examination of existing experimental heat transfer data obtained under fixed hydrodynamic conditions, whereby the local flow conditions are decoupled from the local heat flux, has allowed the unequivocal isolation of the boiling contribution over a broad range of thermodynamic qualities (0 to 0.8) for water at 7 MPa. Boiling suppression, as the quality increases, has consequently been quantified, thus providing valuable new insights on the functionality and contribution of boiling in convective flows. (author)
Mixed convection flow past a horizontal plate
Directory of Open Access Journals (Sweden)
Savić Lj.
2005-01-01
Full Text Available The mixed convection flow past a horizontal plate being aligned through a small angle of attack to a uniform free stream will be considered in the limit of large Reynolds number and small Richardson number. Even a small angle of inclination of the wake is sufficient for the buoyancy force to accelerate the flow in the wake which causes a velocity overshoot in the wake. Moreover a hydrostatic pressure difference across the wake induces a correction to the potential flow which influences the inclination of the wake. Thus the wake and the correction of the potential flow have to be determined simultaneously. However, it turns out that solutions exist only if the angle of attack is sufficiently large. Solutions are computed numerically and the influence of the buoyancy on the lift coefficient is determined.
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)
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)
Mixing in heterogeneous internally-heated convection
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
On the Lyapunov stability of a plane parallel convective flow of a binary mixture
Directory of Open Access Journals (Sweden)
Giuseppe Mulone
1991-05-01
Full Text Available The nonlinear stability of plane parallel convective flows of a binary fluid mixture in the Oberbeck-Boussinesq scheme is studied in the stress-free boundary case. Nonlinear stability conditions independent of Reynolds number are proved.
A transilient matrix for moist convection
Energy Technology Data Exchange (ETDEWEB)
Romps, D.; Kuang, Z.
2011-08-15
A method is introduced for diagnosing a transilient matrix for moist convection. This transilient matrix quantifies the nonlocal transport of air by convective eddies: for every height z, it gives the distribution of starting heights z{prime} for the eddies that arrive at z. In a cloud-resolving simulation of deep convection, the transilient matrix shows that two-thirds of the subcloud air convecting into the free troposphere originates from within 100 m of the surface. This finding clarifies which initial height to use when calculating convective available potential energy from soundings of the tropical troposphere.
Nield, Donald A
2017-01-01
This updated edition of a widely admired text provides a user-friendly introduction to the field that requires only routine mathematics. The book starts with the elements of fluid mechanics and heat transfer, and covers a wide range of applications from fibrous insulation and catalytic reactors to geological strata, nuclear waste disposal, geothermal reservoirs, and the storage of heat-generating materials. As the standard reference in the field, this book will be essential to researchers and practicing engineers, while remaining an accessible introduction for graduate students and others entering the field. The new edition features 2700 new references covering a number of rapidly expanding fields, including the heat transfer properties of nanofluids and applications involving local thermal non-equilibrium and microfluidic effects. Recognized as the standard reference in the field Includes a comprehensive, 350-page reference list Cited over 5900 times to date in its various editions Serves as an introduction ...
Natural convection type reactor
International Nuclear Information System (INIS)
Nakayama, Takafumi; Horiuchi, Tetsuo; Moriya, Kimiaki; Matsumoto, Masayoshi; Akita, Minoru.
1988-01-01
Purpose: To improve the reliability by decreasing the number of dynamic equipments and safely shutdown the reactor core upon occurrence of accidents. Constitution: A pressure relief valve and a pressurizing tank or gravitational water falling tank disposed to the main steam pipe of a reactor are installed in combination. Upon loss-of-coolant accident, the pressure relief valve is opened to reduce the pressure in the reactor pressure vessel to the operation pressure for each of the tanks, thereby enabling to inject water in the pressurizing tank at first and, thereafter, water in the gravitational water falling tank successively to the inside of the pressure vessel. By utilizing the natural force in this way, the reliability can be improved as compared with the case of pumped water injection. Further, by injecting an aqueous boric acid to a portion of a plurality of tanks, if the control rod insertion becomes impossible, aqueous boric acid can be injected. (Takahashi, M.)
Perović Bojan D.; Klimenta Jelena Lj.; Tasić Dragan S.; Peuteman Joan L.G.; Klimenta Dardan O.; Anđelković Ljiljana N.
2017-01-01
The main purpose of this paper is to show how the inclination angle affects natural convection from a flat-plate photovoltaic module which is mounted on the ground surface. In order to model this effect, novel correlations for natural convection from isothermal flat plates are developed by using the fundamental dimensionless number. On the basis of the available experimental and numerical results, it is shown that the natural convection correlations correspond well with the existing empirical...
Heat convection in a set of three vertical cylinders
International Nuclear Information System (INIS)
Serrano Ramirez, M.L. de.
1993-01-01
Experimental results on temperature and heat flow in a set of three vertical cylinders with internal generation of heat, water submerged and in free convection are presented in this work . Temperature distribution, Nusselt number and convective coefficient (h) for each rod, developed for the distance between the axis of cylinders in vertical position, as a consequence of the application of power in its outside, are analyzed. Experimental information about heat transfer by free convection in vertical cylinders and surfaces is analyzed. Information of the several author who have carried out studies about the heat transfer on vertical cylinders was compiled, and the proposed equations with the experimental data obtained in the thermo fluids laboratory of National Institute of Nuclear Research (ININ) were tested. The way in which separation distance, s, distribution temperature array, Nusselt number, and convective coefficient calculated for the proposed channel with the Keyhani, Dutton and experimental equations are tabulated and they are plotted for each power value and for each separation between rods. The scheme of the used equipment and the experimentation description as well as the observations of tests and graphical results are included. (Author)
Seasonal Scale Convective-Stratiform Pricipitation Variabilities at Tropics
S, Sreekanth T.
begin{center} Large Seasonal Scale Convective-Stratiform Pricipitation Variabilities at Tropics Sreekanth T S*, Suby Symon*, G. Mohan Kumar (1) and V Sasi Kumar (2) *Centre for Earth Science Studies, Akkulam, Thiruvananthapuram (1) D-330, Swathi Nagar, West Fort, Thiruvananthapuram 695023 (2) 32. NCC Nagar Peroorkada, Thiruvananthapuram ABSTRACT This study investigates the variabilities of convective and stratiform rainfall from 2011 to 2013 at a tropical coastal station in three seasons viz Pre-Monsoon (March-May), Monsoon (June-September) and Post-Monsoon (October-December). Understanding the climatological variability of these two dominant forms of precipitation and their implications in the total rainfall were the main objectives of this investigation. Variabilities in the frequency & duration of events, rain rate & total number of rain drops distribution in different events and the accumulated amount of rain water were analysed. Based on the ground & radar observations from optical & impact disdrometers, Micro Rain Radar and Atmospheric Electric Field Mill, precipitation events were classified into convective and stratiform in three seasons. Classification was done by the method followed by Testud et al (2001) and as an additional information electrical behaviour of clouds from Atmospheric Electric Field Mill is also used. Events which could not be included in both types were termed as 'mixed precipitation' and were included separately. Diurnal variability of the total rainfall in each seasons were also examined. For both convective and stratiform rainfall there exist distinct day-night differences. During nocturnal hours convective rain draged more attention. In all seasons almost 70% of rain duration and 60% of rain events of convective origin were confined to nocturnal hours. But stratiform rain was not affected by diurnal variations greatly because night time occurrences of stratiform duration and events were less than 50%. Also in Monsoon above 35% of
Convective aggregation in realistic convective-scale simulations
Holloway, Christopher E.
2017-06-01
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 equilibrium. Analysis of the budget of the spatial variance of column-integrated frozen moist static energy shows that control runs have significant positive contributions to organization from radiation and negative contributions from surface fluxes and transport, similar to idealized runs once they become aggregated. Despite identical lateral boundary conditions for all experiments in each case, systematic differences in mean column water vapor (CWV), CWV distribution shape, and CWV autocorrelation length scale are found between the different sensitivity runs, particularly for those without interactive radiation, showing that there are at least some similarities in sensitivities to these feedbacks in both idealized and realistic simulations (although the organization of precipitation shows less sensitivity to interactive radiation). The magnitudes and signs of these systematic differences are consistent with a rough equilibrium between (1) equalization due to advection from the lateral boundaries and (2) disaggregation due to the absence of interactive radiation, implying disaggregation rates comparable to those in idealized runs with aggregated initial conditions and noninteractive radiation. This points to a plausible similarity in the way that radiation feedbacks maintain aggregated convection in both idealized simulations and the real world.Plain Language SummaryUnderstanding the processes that lead to the organization of tropical rainstorms is an important challenge for weather
Subcritical thermal convection of liquid metals in a rapidly rotating sphere
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.
Fluid convection, constraint and causation
Bishop, Robert C.
2012-01-01
Complexity—nonlinear dynamics for my purposes in this essay—is rich with metaphysical and epistemological implications but is receiving sustained philosophical analysis only recently. I will explore some of the subtleties of causation and constraint in Rayleigh–Bénard convection as an example of a complex phenomenon, and extract some lessons for further philosophical reflection on top-down constraint and causation particularly with respect to causal foundationalism. PMID:23386955
Turbulent mixed convection in asymmetrically heated vertical channel
Directory of Open Access Journals (Sweden)
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.
Direct simulation of natural convection in square porous enclosure
International Nuclear Information System (INIS)
Pourshaghaghy, A.; Hakkaki-Fard, A.; Mahdavi-Nejad, A.
2007-01-01
In this article, natural convection in a square porous enclosure is simulated by a direct numerical method. The solution method is based on a random distribution of solid blocks, which resembles the porous media within the cavity. The Navier-Stokes equations are solved directly in the fluid region without the assumption of volume averaging. The no-slip condition is applied on the surface of any solid particle, and the energy transport equation is solved separately for the solid phase and fluid flow. The local and average Nusselt numbers are presented for steady state for two different cases of thermal boundary conditions of the cavity walls. An oscillatory solution is observed for the local Nu number on the surface of the enclosure, and the critical Ra numbers are found in which natural convection flow is started within the cavity
Thermosolutal convection during dendritic solidification
Heinrich, J. C.; Nandapurkar, P.; Poirier, D. R.; Felicelli, S.
1989-01-01
This paper presents a mathematical model for directional solidification of a binary alloy including a dendritic region underlying an all-liquid region. It is assumed initially that there exists a nonconvecting state with planar isotherms and isoconcentrates solidifying at a constant velocity. The stability of this system has been analyzed and nonlinear calculations are performed that show the effect of convection in the solidification process when the system is unstable. Results of calculations for various cases defined by the initial temperature gradient at the dendrite tips and varying strength of the gravitational field are presented for systems involving lead-tin alloys. The results show that the systems are stable for a gravitational constant of 0.0001 g(0) and that convection can be suppressed by appropriate choice of the container's size for higher values of the gravitational constant. It is also concluded that for the lead-tin systems considered, convection in the mushy zone is not significant below the upper 20 percent of the dendritic zone, if al all.
Heat transfer and large scale dynamics in turbulent Rayleigh-Bénard convection
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
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)
Mixed convection heat transfer experiments using analogy concept
International Nuclear Information System (INIS)
Ko, Bong Jin; Chung, Bum Jin; Lee, Won Jea
2009-01-01
A Series of the turbulent mixed convective heat transfer experiments in a vertical cylinder was carried out. In order to achieve high Gr and/or Ra with small scale test rigs, the analogy concept was adopted. Using the concept, heat transfer systems were simulated by mass transfer systems, and large Grashof numbers could be achieved with reasonable facility heights. The tests were performed with buoyancy-aided flow and opposed flow for Reynolds numbers from 4,000 to 10,000 with a constant Grashof number, Gr H of 6.2 x 10 9 and Prandtl number of about 2,000. The test results reproduced the typical of the mixed convection heat transfer phenomena in a turbulent situation and agree well with the experimental study performed by Y. Palratan et al. The analogy experimental method simulated the mixed convection heat transfer phenomena successfully and seems to be a useful tool for heat transfer studies for VHTR as well as the systems with high buoyancy condition and high Prandtl number
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)
Convectively Induced Meanflow in a Long Channel.
Grimm, Th.; Maxworthy, T.
1997-11-01
The similarity theory of Phillips (Deep Sea Res. 13, 1966) for the convectively induced motion in the Red Sea, predicts that the outflow buoyancy difference should scale as (B _0L) ^2/3/h :: , where B 0 is the surface buoyancy flux and L and h are the length and height of the channel above the sill crest, respectively. A friction-buoyancy balance leads to a modified expression [(B _0L) ^2/3/h][fracLh]^1/3 :: (2). The results can be applied also to a number of other natural flows including freezing-induced convection in fjords and polar seas. A series of Experiments have been conducted to check the predictions. A channel 300 cm long and 21 cm wide has been constructed. Within it segmented salt-water sources have been placed over a length of 250 cm. Their depth varied from 2 to 12 cm. A sill was placed in the exit region and its height was at least half the total depth of water in the channel. Density data were taken by withdrawing samples while velocity profiles were found by a DPIV technique. The meanflow consists of a two-layer stratification over a large fraction of the length of the channel. Our results suggest that the scaling (2) above is most closely realized with a constant of value 1.1. Analysis of the Red Sea data suggests a constant between 1.1 and 1.4 depending on the data set used. The exit Fr-number is unity. The amount of mixing within the channel is less than that predicted for the 'overmixed' state. Supported by the German Acad. Exchge. Serv. and the NSF Polar Programs.
Land surface sensitivity of mesoscale convective systems
Tournay, Robert C.
the high plains in the east of regions. Examining the covariance of SM and vegetation at CI points revealed that July and August showed expected covariance relationships with concurrently measured convective variables (i.e., high SM/vegetation associated with high CAPE and vice versa for low SM/vegetation) while May and June higher CAPE and CIN over low vegetation anomalies. A climatology of elevated mixed layers in the central GP was conducted, revealing that the greatest number of EMLS occurred in the northern GP. Back trajectories (BT) were conducted from the radiosonde point of detection for 18 and 36 hours, revealing that the BT point mean for days with severe weather were further west and south from the origin point. The SM and vegetation was sampled at the BT point, revealing a negative, significant correlation with EML depth when pooling the northern stations in 18-hr BTs, and a significant, negative correlation with EVI when pooling the southern sites. A modeling case study was conducted in which an idealized SM anomaly was imposed over the EML origin region. Experiments were also conducted to test the sensitivity of ML formation and EML transport using different PBL parameterizations. While the YSU PBL parameterization produced the deeper PBL over anonymously dry soils in the EML origin region, the EML was not transported to the east as it was in those experiments using the MYNN parameterization, impacting the timing and extent of precipitation in the model runs.
Heat and momentum transport scalings in vertical convection
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.
The convection electric field in auroral substorms
DEFF Research Database (Denmark)
Gjerløv, Jesper Wittendorff; Hoffman, R.A.
2001-01-01
Dynamics Explorer 2 (DE 2) electric field and ion drift data are used in a statistical study of the ionospheric convection electric field in bulge-type auroral substorms. Thirty-one individual DE 2 substorm crossings were carefully selected and organized by the use of global auroral images obtained...... this database enabled us to compile a model of the ionospheric convection electric field. The characteristics of the premidnight convection reversal show a pronounced local time dependency. Far west of the surge it is a fairly well defined point reversal or convection shear. Approaching the surge and within...... the surge it is a region of weak electric fields increasing in width toward midnight that separates regions of equatorward and poleward electric fields. Therefore we adopt the term Harang region rather than the Harang discontinuity for the premidnight convection reversal. A relatively narrow convection...
Spectrally-consistent regularization modeling of turbulent natural convection flows
International Nuclear Information System (INIS)
Trias, F Xavier; Gorobets, Andrey; Oliva, Assensi; Verstappen, Roel
2012-01-01
The incompressible Navier-Stokes equations constitute an excellent mathematical modelization of turbulence. Unfortunately, attempts at performing direct simulations are limited to relatively low-Reynolds numbers because of the almost numberless small scales produced by the non-linear convective term. Alternatively, a dynamically less complex formulation is proposed here. Namely, regularizations of the Navier-Stokes equations that preserve the symmetry and conservation properties exactly. To do so, both convective and diffusive terms are altered in the same vein. In this way, the convective production of small scales is effectively restrained whereas the modified diffusive term introduces a hyperviscosity effect and consequently enhances the destruction of small scales. In practice, the only additional ingredient is a self-adjoint linear filter whose local filter length is determined from the requirement that vortex-stretching must stop at the smallest grid scale. In the present work, the performance of the above-mentioned recent improvements is assessed through application to turbulent natural convection flows by means of comparison with DNS reference data.
Extreme value statistics for two-dimensional convective penetration in a pre-main sequence star
Pratt, J.; Baraffe, I.; Goffrey, T.; Constantino, T.; Viallet, M.; Popov, M. V.; Walder, R.; Folini, D.
2017-08-01
Context. In the interior of stars, a convectively unstable zone typically borders a zone that is stable to convection. Convective motions can penetrate the boundary between these zones, creating a layer characterized by intermittent convective mixing, and gradual erosion of the density and temperature stratification. Aims: We examine a penetration layer formed between a central radiative zone and a large convection zone in the deep interior of a young low-mass star. Using the Multidimensional Stellar Implicit Code (MUSIC) to simulate two-dimensional compressible stellar convection in a spherical geometry over long times, we produce statistics that characterize the extent and impact of convective penetration in this layer. Methods: We apply extreme value theory to the maximal extent of convective penetration at any time. We compare statistical results from simulations which treat non-local convection, throughout a large portion of the stellar radius, with simulations designed to treat local convection in a small region surrounding the penetration layer. For each of these situations, we compare simulations of different resolution, which have different velocity magnitudes. We also compare statistical results between simulations that radiate energy at a constant rate to those that allow energy to radiate from the stellar surface according to the local surface temperature. Results: Based on the frequency and depth of penetrating convective structures, we observe two distinct layers that form between the convection zone and the stable radiative zone. We show that the probability density function of the maximal depth of convective penetration at any time corresponds closely in space with the radial position where internal waves are excited. We find that the maximal penetration depth can be modeled by a Weibull distribution with a small shape parameter. Using these results, and building on established scalings for diffusion enhanced by large-scale convective motions, we
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
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.
Feedback control and heat transfer measurements in a Rayleigh-Bénard convection cell
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.
Heat-transfer correlations for natural convection boiling
International Nuclear Information System (INIS)
Stephan, K.; Abdelsalam, M.
1980-01-01
To-date there exists no comprehensive theory allowing the prediction of heat-transfer coefficients in natural convection boiling, in spite of the many efforts made in this field. In order to establish correlations with wide application, the methods of regression analysis were applied to the nearly 500 existing experimental data points for natural convection boiling heat transfer. As demonstrated by the analysis, these data can best be represented by subdividing the substances into four groups (water, hydrocarbons, cryogenic fluids and refrigerants) and employing a different set of dimensionless numbers for each group of substances, because certain dimensionless numbers important for one group of substances are unimportant to another. One equation valid for all substances could be built up, but its accuracy would be less than that obtained for the individual correlations without adding undesirable complexity. (author)
Titan Balloon Convection Model, Phase I
National Aeronautics and Space Administration — This innovative research effort is directed at determining, quantitatively, the convective heat transfer coefficients applicable to a Montgolfiere balloon operating...
REVERSALS IN THE 6-CELLS CONVECTION DRIVEN
Directory of Open Access Journals (Sweden)
G.M. Vodinchar
2015-12-01
Full Text Available We describe the large-scale model geodynamo, which based on indirect data of inhomogeneities in the density of the Earth’s core. Convection structure is associated with spherical harmonic Y24 , which defines the basic poloidal component of velocity. Coriolis drift of this mode determines the toroidal component of velocity. Thus, 6 convective cells are formed. The model takes into account the feedback effect of the magnetic field on convection. It was ascertained that the model contains stable regimes of field generation. The velocity of convection and the dipole component of the magnetic field are close to the observed ones.
Characterizing Convection in Stellar Atmospheres
International Nuclear Information System (INIS)
Tanner, Joel; Basu, Sarbani; Demarque, Pierre; Robinson, Frank
2011-01-01
We perform 3D radiative hydrodynamic simulations to study the properties of convection in the superadiabatic layer of stars. The simulations show differences in both the stratification and turbulent quantities for different types of stars. We extract turbulent pressure and eddy sizes, as well as the T-τ relation for different stars and find that they are sensitive to the energy flux and gravity. We also show that contrary to what is usually assumed in the field of stellar atmospheres, the structure and gas dynamics of simulations of turbulent atmospheres cannot be parameterized with T eff and log(g) alone.
Soret-driven double diffusive magneto-convection in couple stress liquid
Directory of Open Access Journals (Sweden)
Mishra P.
2012-07-01
Full Text Available The stability analysis of Soret driven double diffusive convection for electrically conducting couple stress liquid is investigated theoretically. The couple stress liquid is confined between two horizontal surfaces and a constant vertical magnetic field is applied across the surfaces. Linear stability analysis is used to investigate the effect of various parameters on the onset of convection. Effect of magnetic field on the onset of convection is presented by means of Chandrasekhar number. The problem is analyzed as a function of Chandrasekhar number (Q, positive and negative Soret parameter (S r and couple stress parameter (C, mainly. The results show that the Q, both positive and negative Sr and C delay the onset of convection. The effect of other parameters is also discussed in paper and shown by graphs.
Criteria for analysis and optimization of longitudinal fins with convective tip
International Nuclear Information System (INIS)
Gomes, E.S.
1983-01-01
The problem of heat transfer in longitudinal fins with the main geometries used in equipaments of heat transfer by convection is analyzed. The equation of energy is solved analytically of several geometries fins, with unidimensional formulation, through the use of the convective heat transfer coefficient. The problem of fin optimization is approached analytically yielding the parameters which allow the maximum heat transfer for each particular material waste in the fin. The use of the insulated tip model suggests the use of fins and its optimization for any Biot number of the fin. The use of the convective tip model allows us to determine when is vantageous or disadvantageous to use fins and when fin optimization is possible according to the value of the Biot number and to a convection parameter on the fin tip. (Author) [pt
Bounds on poloidal kinetic energy in plane layer convection
Tilgner, A.
2017-12-01
A numerical method is presented that conveniently computes upper bounds on heat transport and poloidal energy in plane layer convection for infinite and finite Prandtl numbers. The bounds obtained for the heat transport coincide with earlier results. These bounds imply upper bounds for the poloidal energy, which follow directly from the definitions of dissipation and energy. The same constraints used for computing upper bounds on the heat transport lead to improved bounds for the poloidal energy.
Nonlinear Multiplicative Schwarz Preconditioning in Natural Convection Cavity Flow
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.
Pattern formation in rotating Bénard convection
Fantz, M.; Friedrich, R.; Bestehorn, M.; Haken, H.
1992-12-01
Using an extension of the Swift-Hohenberg equation we study pattern formation in the Bénard experiment close to the onset of convection in the case of rotating cylindrical fluid containers. For small Taylor numbers we emphasize the existence of slowly rotating patterns and describe behaviour exhibiting defect motion. Finally, we study pattern formation close to the Küppers-Lortz instability. The instability is nucleated at defects and proceeds through front propagation into the bulk patterns.
Nonlinear Multiplicative Schwarz Preconditioning in Natural Convection Cavity Flow
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.
Engineering photochemical smog through convection towers
Energy Technology Data Exchange (ETDEWEB)
Elliott, S.; Prueitt, M.L.; Bossert, J.E.; Mroz, E.J.; Krakowski, R.A.; Miller, R.L. [Los Alamos National Lab., NM (United States); Jacobson, M.Z.; Turco, R.P. [Los Alamos National Lab., NM (United States)]|[Univ. of California, Los Angeles, CA (United States). Atmospheric Sciences Dept.
1995-02-01
Reverse convection towers have attracted attention as a medium for cleansing modern cities. Evaporation of an aqueous mist injected at the tower opening could generate electrical power by creating descent, and simultaneously scavenge unsightly and unhealthful particulates. The study offered here assesses the influence to tower water droplets on the photochemical component of Los Angeles type smog. The primary radical chain initiator OH is likely removed into aqueous phases well within the residence time of air in the tower, and then reacts away rapidly. Organics do not dissolve, but nighttime hydrolysis of N{sub 2}O{sub 5} depletes the nitrogen oxides. A lack of HOx would slow hydrocarbon oxidation and so also ozone production. Lowering of NOx would also alter ozone production rates, but the direction is uncertain. SO{sub 2} is available in sufficient quantities in some urban areas to react with stable oxidants, and if seawater were the source of the mist, the high pH would lead to fast sulfur oxidation kinetics. With an accommodation coefficient of 10{sup {minus}3}, however, ozone may not enter the aqueous phase efficiently. Even if ozone is destroyed or its production suppressed, photochemical recovery times are on the order of hours, so that tower processing must be centered on a narrow midday time window. The cost of building the number of structures necessary for this brief turnover could be prohibitive. The increase in humidity accompanying mist evaporation could be controlled with condensers, but might otherwise counteract visibility enhancements by recreating aqueous aerosols. Quantification of the divergent forcings convection towers must exert upon the cityscape would call for coupled three dimensional modeling of transport, microphysics, and photochemistry. 112 refs.
Constraints on the properties of Pluto's nitrogen-ice rich layer from convection simulations
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.
Directory of Open Access Journals (Sweden)
J. M. Jawdat
2012-01-01
Full Text Available The effect of nanofluids on chaotic convection in a fluid layer heated from below was studied in this paper for low Prandtl number based on the theory of dynamical systems. A low-dimensional, Lorenz-like model was obtained using Galerkin-truncated approximations. The fourth-order Runge-Kutta method was employed to solve the nonlinear system. The results show that inhibition of chaotic convection can be observed when using nanofluids.
Experimental StudyHigh Altitude Forced Convective Cooling of Electromechanical Actuation Systems
2016-01-01
34 Massachusetts Institute of Technology , 1989. [3] FedBizOps.Gov, " Integrated Vehicle Energy Technology (INVENT) Development Program for the 6th...AFRL-RQ-WP-TR-2016-0043 EXPERIMENTAL STUDY—HIGH ALTITUDE FORCED CONVECTIVE COOLING OF ELECTROMECHANICAL ACTUATION SYSTEMS Evan M. Racine...TITLE AND SUBTITLE EXPERIMENTAL STUDY—HIGH ALTITUDE FORCED CONVECTIVE COOLING OF ELECTROMECHANICAL ACTUATION SYSTEMS 5a. CONTRACT NUMBER In-house
True polar wander on convecting planets
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
Directory of Open Access Journals (Sweden)
Hanafi Abdalla S.
2008-01-01
Full Text Available This paper presents experimental and numerical studies for the case of turbulent forced and mixed convection flow of water through narrow vertical rectangular channel. The channel is composed of two parallel plates which are heated at a uniform heat flux, whereas, the other two sides of the channel are thermally insulated. The plates are of 64 mm in width, 800 mm in height, and separated from each other at a narrow gap of 2.7 mm. The Nusselt number distribution along the flow direction normalized by the Nusselt number for the case of turbulent forced convection flow is obtained experimentally with a comparison with the numerical results obtained from a commercial computer code. The quantitative determination of the nor- malized Nusselt number with respect to the dimension-less number Z = (Gr/Re21/8Pr0.5 is presented with a comparison with previous experimental results. Qualitative results are presented for the normalized temperature and velocity profiles in the transverse direction with a comparison between the forced and mixed convection flow for both the cases of upward and downward flow directions. The effect of the axial locations and the parameter Gr/Re on the variation of the normalized temperature profiles in the transverse direction for both the regions of forced and mixed convection and for both of the upward and downward flow directions are obtained. The normalized velocity profiles in the transverse directions are also determined at different inlet velocity and heat fluxes for the previous cases. It is found that the normalized Nusselt number is greater than one in the mixed convection region for both the cases of upward and downward flow and correlated well with the dimension-less parameter Z for both of the forced and mixed convection regions. The temperature profiles increase with increasing the axial location along the flow direction or the parameter Gr/Re for both of the forced and mixed convection regions, but this increase is
Examining Chaotic Convection with Super-Parameterization Ensembles
Jones, Todd R.
This study investigates a variety of features present in a new configuration of the Community Atmosphere Model (CAM) variant, SP-CAM 2.0. The new configuration (multiple-parameterization-CAM, MP-CAM) changes the manner in which the super-parameterization (SP) concept represents physical tendency feedbacks to the large-scale by using the mean of 10 independent two-dimensional cloud-permitting model (CPM) curtains in each global model column instead of the conventional single CPM curtain. The climates of the SP and MP configurations are examined to investigate any significant differences caused by the application of convective physical tendencies that are more deterministic in nature, paying particular attention to extreme precipitation events and large-scale weather systems, such as the Madden-Julian Oscillation (MJO). A number of small but significant changes in the mean state climate are uncovered, and it is found that the new formulation degrades MJO performance. Despite these deficiencies, the ensemble of possible realizations of convective states in the MP configuration allows for analysis of uncertainty in the small-scale solution, lending to examination of those weather regimes and physical mechanisms associated with strong, chaotic convection. Methods of quantifying precipitation predictability are explored, and use of the most reliable of these leads to the conclusion that poor precipitation predictability is most directly related to the proximity of the global climate model column state to atmospheric critical points. Secondarily, the predictability is tied to the availability of potential convective energy, the presence of mesoscale convective organization on the CPM grid, and the directive power of the large-scale.
Thermal-chemical Mantle Convection Models With Adaptive Mesh Refinement
Leng, W.; Zhong, S.
2008-12-01
In numerical modeling of mantle convection, resolution is often crucial for resolving small-scale features. New techniques, adaptive mesh refinement (AMR), allow local mesh refinement wherever high resolution is needed, while leaving other regions with relatively low resolution. Both computational efficiency for large- scale simulation and accuracy for small-scale features can thus be achieved with AMR. Based on the octree data structure [Tu et al. 2005], we implement the AMR techniques into the 2-D mantle convection models. For pure thermal convection models, benchmark tests show that our code can achieve high accuracy with relatively small number of elements both for isoviscous cases (i.e. 7492 AMR elements v.s. 65536 uniform elements) and for temperature-dependent viscosity cases (i.e. 14620 AMR elements v.s. 65536 uniform elements). We further implement tracer-method into the models for simulating thermal-chemical convection. By appropriately adding and removing tracers according to the refinement of the meshes, our code successfully reproduces the benchmark results in van Keken et al. [1997] with much fewer elements and tracers compared with uniform-mesh models (i.e. 7552 AMR elements v.s. 16384 uniform elements, and ~83000 tracers v.s. ~410000 tracers). The boundaries of the chemical piles in our AMR code can be easily refined to the scales of a few kilometers for the Earth's mantle and the tracers are concentrated near the chemical boundaries to precisely trace the evolvement of the boundaries. It is thus very suitable for our AMR code to study the thermal-chemical convection problems which need high resolution to resolve the evolvement of chemical boundaries, such as the entrainment problems [Sleep, 1988].
Energy Technology Data Exchange (ETDEWEB)
Pelce, J [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1960-02-15
This report deals with the experimental study of forced heat convection in annular spaces through which flow of air is passing when a uniform heat flux is dissipated across the inner wall. These observations took place chiefly in the region where thermal equilibrium are not yet established. Amongst other things it became apparent that, both in the region where thermal equilibrium conditions are on the way to establishment and where they are already established, the following relationship held good: the longitudinal temperature gradient, either on the wall or in the fluid stream, is proportional to the heat flux dissipated q, and inversely proportional to the average flow rate V: dT/dx = B (q/V). From this result the next step is to express the variations of the local convection coefficient {alpha} (or of the Margoulis number M) in a relationship of the form: 1/M = {psi}(V) + F(x). If this relationship is compared with the classical empirical relationship {alpha} = KV{sup n} (where n is close to 0.8), the relationship: 1/M = {xi}V{sup 1-n} + F(x) is obtained ({xi} is a constant for a given annular space); from this it was possible to coordinate the whole set of experimental results. (author) [French] Il s'agit precisement de l'etude experimentale de la convection forcee de la chaleur dans des espaces annulaires parcourus par de l'air en ecoulement turbulent, lorsqu'on dissipe a travers la paroi interieure un flux de chaleur uniforme. Ces observations ont eu lieu principalement dans la region ou le regime thermique n'est pas encore etabli. Il est apparu, entre autre, qu'il existait, tant dans la region ou le regime thermique est en voie d'etablissement qu'en regime etabli, la relation suivante: le gradient longitudinal des temperatures, que ce soit sur la paroi ou dans l'ecoulement fluide, est proportionnel au flux de la chaleur dissipee q, et inversement proportionnel a la vitesse moyenne V de l'ecoulement: dT/dx = B (q/V). Ce resultat a pour consequence de traduire
Hayat, T.; Khan, M. Waleed Ahmed; Khan, M. Ijaz; Waqas, M.; Alsaedi, A.
2018-06-01
Flow of magnetohydrodynamic (MHD) viscous fluid between two rotating disks is modeled. Angular velocities of two disks are different. Flow is investigated for nonlinear mixed convection. Heat transfer is analyzed for nonlinear thermal radiation and heat generation/absorption. Chemical reaction is also implemented. Convective conditions of heat and mass transfer are studied. Transformations used lead to reduction of PDEs into the ODEs. The impacts of important physical variables like Prandtl number, Reynold number, Hartman number, mixed convection parameter, chemical reaction and Schmidt number on velocities, temperature and concentration are elaborated. In addition velocity and temperature gradients are physically interpreted. Our obtained results indicate that radial, axial and tangential velocities decrease for higher estimation of Hartman number.
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.
Ostrowski, Ziemowit; Rojczyk, Marek
2017-11-01
The energy balance and heat exchange for newborn baby in radiant warmer environment are considered. The present study was performed to assess the body dry heat loss from an infant in radiant warmer, using copper cast anthropomorphic thermal manikin and controlled climate chamber laboratory setup. The total body dry heat losses were measured for varying manikin surface temperatures (nine levels between 32.5 °C and 40.1 °C) and ambient air temperatures (five levels between 23.5 °C and 29.7 °C). Radiant heat losses were estimated based on measured climate chamber wall temperatures. After subtracting radiant part, resulting convective heat loses were compared with computed ones (based on Nu correlations for common geometries). Simplified geometry of newborn baby was represented as: (a) single cylinder and (b) weighted sum of 5 cylinders and sphere. The predicted values are significantly overestimated relative to measured ones by: 28.8% (SD 23.5%) for (a) and 40.9% (SD 25.2%) for (b). This showed that use of adopted general purpose correlations for approximation of convective heat losses of newborn baby can lead to substantial errors. Hence, new Nu number correlating equation is proposed. The mean error introduced by proposed correlation was reduced to 1.4% (SD 11.97%), i.e. no significant overestimation. The thermal manikin appears to provide a precise method for the noninvasive assessment of thermal conditions in neonatal care.
Energy Technology Data Exchange (ETDEWEB)
Robin, M; Schwab, B [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1957-07-01
In the thermal study of a 'swimming-pool' type of pile, the flow of water between vertical plates of 'combustible' material must be investigated. Therefore starting from general equations of natural convection, we have determined, the law of distribution of velocities, then that of temperatures, and finally the value of the Biot-Nusselt number, assuming steady-state conditions (both dynamic and thermal) and a constant heat flow at the surface. An abacus (fig. 7, 8 and 9) allows working power to be related to the average velocity and to the heating of the water which passes through the pile. For purposes of comparison, the curves on the calculation presented by S. GLASSTONE (31) have been drawn. (author) [French] L'etude thermique d'une pile du type 'piscine' necessite l'etude de l'ecoulement de l'eau entre les plaques verticales de materiau 'combustible'. Nous avons donc, a partir des equations generales de la convection naturelle, determine la loi de repartition des vitesses, puis celle des temperatures et enfin la valeur du nombre de Biot-Niisselt, en supposant les regimes, dynamique et thermique, etablis et la densite de flux calorifique a la paroi constante. Un abaque (fig. 7, 8 et 9) permet de relier a la puissance de fonctionnement, la vitesse moyenne de l'echauffement de l'eau qui traverse la pile. On a trace a titre de comparaison, les courbes du calcul presente par S. GLASSTONE (3). (auteur)
Ten Year Analysis of Tropopause-Overshooting Convection Using GridRad Data
Cooney, John W.; Bowman, Kenneth P.; Homeyer, Cameron R.; Fenske, Tyler M.
2018-01-01
Convection that penetrates the tropopause (overshooting convection) rapidly transports air from the lower troposphere to the lower stratosphere, potentially mixing air between the two layers. This exchange of air can have a substantial impact on the composition, radiation, and chemistry of the upper troposphere and lower stratosphere (UTLS). In order to improve our understanding of the role convection plays in the transport of trace gases across the tropopause, this study presents a 10 year analysis of overshooting convection for the eastern two thirds of the contiguous United States for March through August of 2004 to 2013 based on radar observations. Echo top altitudes are estimated at hourly intervals using high-resolution, three-dimensional, gridded, radar reflectivity fields created by merging observations from available radars in the National Oceanic and Atmospheric Administration Next Generation Weather Radar (NEXRAD) network. Overshooting convection is identified by comparing echo top altitudes with tropopause altitudes derived from the ERA-Interim reanalysis. It is found that overshooting convection is most common in the central United States, with a weak secondary maximum along the southeast coast. The maximum number of overshooting events occur consistently between 2200 and 0200 UTC. Most overshooting events occur in May, June, and July when convection is deepest and the tropopause altitude is relatively low. Approximately 45% of the analyzed overshooting events (those with echo tops at least 1 km above the tropopause) have echo tops extending above the 380 K level into the stratospheric overworld.
Free surface deformation and heat transfer by thermocapillary convection
Fuhrmann, Eckart; Dreyer, Michael; Basting, Steffen; Bänsch, Eberhard
2016-04-01
Knowing the location of the free liquid/gas surface and the heat transfer from the wall towards the fluid is of paramount importance in the design and the optimization of cryogenic upper stage tanks for launchers with ballistic phases, where residual accelerations are smaller by up to four orders of magnitude compared to the gravity acceleration on earth. This changes the driving forces drastically: free surfaces become capillary dominated and natural or free convection is replaced by thermocapillary convection if a non-condensable gas is present. In this paper we report on a sounding rocket experiment that provided data of a liquid free surface with a nonisothermal boundary condition, i.e. a preheated test cell was filled with a cold but storable liquid in low gravity. The corresponding thermocapillary convection (driven by the temperature dependence of the surface tension) created a velocity field directed away from the hot wall towards the colder liquid and then in turn back at the bottom towards the wall. A deformation of the free surface resulting in an apparent contact angle rather different from the microscopic one could be observed. The thermocapillary flow convected the heat from the wall to the liquid and increased the heat transfer compared to pure conduction significantly. The paper presents results of the apparent contact angle as a function of the dimensionless numbers (Weber-Marangoni and Reynolds-Marangoni number) as well as heat transfer data in the form of a Nusselt number. Experimental results are complemented by corresponding numerical simulations with the commercial software Flow3D and the inhouse code Navier.
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.
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
Energy Technology Data Exchange (ETDEWEB)
Teamah, M.A. [Faculty of Engineering, Alexandria University, Mech. Eng. Dept, Alexandria (Egypt); El-Maghlany, W.M. [Faculty of Engineering, Suez Canal University, Ismailia (Egypt)
2010-09-15
The present study is concerned with the mixed convection in a rectangular lid-driven cavity under the combined buoyancy effects of thermal and mass diffusion. Double-diffusive convective flow in a rectangular enclosure with moving upper surface is studied numerically. Both upper and lower surfaces are being insulated and impermeable. Constant different temperatures and concentration are imposed along the vertical walls of the enclosure, steady state laminar regime is considered. The transport equations for continuity, momentum, energy and spices transfer are solved. The numerical results are reported for the effect of Richardson number, Lewis number, and buoyancy ratio on the iso-contours of stream line, temperature, and concentration. In addition, the predicted results for both local and average Nusselt and Sherwood numbers are presented and discussed for various parametric conditions. This study was done for 0.1 <= Le <= 50 and Prandtl number Pr = 0.7. Through out the study the Grashof number and aspect ratio are kept constant at 10{sup 4} and 2 respectively and -10 <= N <= 10, while Richardson number has been varied from 0.01 to 10 to simulate forced convection dominated flow, mixed convection and natural convection dominated flow. (authors)
Benard convection in gaps and cavities
International Nuclear Information System (INIS)
Mueller, U.
1981-04-01
The article contains two parts. In the first part a condensed review of the most striking phenomena in Benard convection in laterally confined fluid layers is given. In the second part recent experimental and theoretical work on Benard convection in gaps is presented an analysed. (orig.) [de
Convective mixing and accretion in white dwarfs
International Nuclear Information System (INIS)
Koester, D.
1976-01-01
The evolution of convection zones in cooling white dwarfs with helium envelopes and outer hydrogen layers is calculated with a complete stellar evolution code. It is shown that white dwarfs of spectral type DB cannot be formed from DA stars by convective mixing. However, for cooler temperatures (Tsub(e) [de
Southern Ocean Convection and tropical telleconnections
Marinov, I.; Cabre, A.; Gnanadesikan, A.
2014-12-01
We show that Southern Ocean (SO) temperatures in the latest generation of Earth System Models exhibit two major modes of variation, one driven by deep convection, the other by tropical variability. We perform a CMIP5 model intercomparison to understand why different climate models represent SO variability so differently in long, control simulations. We show that multiyear variability in Southern Ocean sea surface temperatures (SSTs) can in turn influence oceanic and atmospheric conditions in the tropics on short (atmospheric) time-scales. We argue that the strength and pattern of SO-tropical teleconnections depends on the intensity of SO deep convection. Periodic convection in the SO is a feature of most CMIP5 models under preindustrial forcing (deLavergne et al., 2014). Models show a wide distribution in the spatial extent, periodicity and intensity of their SO convection, with some models convecting most of the time, and some showing very little convection. In a highly convective coupled model, we find that multidecadal variability in SO and global SSTs, as well as SO heat storage are driven by Weddell Sea convective variability, with convective decades relatively warm due to the heat released from the deep southern ocean and non-convective decades cold due to the subsurface storage of heat. Furthermore, pulses of SO convection drive SST and sea ice variations, influencing absorbed shortwave and emitted longwave radiation, wind, cloud and precipitation patterns, with climatic implications for the low latitudes via fast atmospheric teleconnections. We suggest that these high-low latitude teleconnection mechanisms are relevant for understanding hiatus decades. Additionally, Southern Ocean deep convection varied significantly during past, natural climate changes such as during the last deglaciation. Weddell Sea open convection was recently weakened, likely as a consequence of anthropogenic forcing and the resulting surface freshening. Our study opens up the
Topology Optimisation for Coupled Convection Problems
DEFF Research Database (Denmark)
Alexandersen, Joe
This thesis deals with topology optimisation for coupled convection problems. The aim is to extend and apply topology optimisation to steady-state conjugate heat transfer problems, where the heat conduction equation governs the heat transfer in a solid and is coupled to thermal transport...... in a surrounding uid, governed by a convection-diffusion equation, where the convective velocity field is found from solving the isothermal incompressible steady-state Navier-Stokes equations. Topology optimisation is also applied to steady-state natural convection problems. The modelling is done using stabilised...... finite elements, the formulation and implementation of which was done partly during a special course as prepatory work for this thesis. The formulation is extended with a Brinkman friction term in order to facilitate the topology optimisation of fluid flow and convective cooling problems. The derived...
Convective penetration in a young sun
Pratt, Jane; Baraffe, Isabelle; Goffrey, Tom; MUSIC developers group
2018-01-01
To interpret the high-quality data produced from recent space-missions it is necessary to study convection under realistic stellar conditions. We describe the multi-dimensional, time implicit, fully compressible, hydrodynamic, implicit large eddy simulation code MUSIC. We use MUSIC to study convection during an early stage in the evolution of our sun where the convection zone covers approximately half of the solar radius. This model of the young sun possesses a realistic stratification in density, temperature, and luminosity. We approach convection in a stellar context using extreme value theory and derive a new model for convective penetration, targeted for one-dimensional stellar evolution calculations. This model provides a scenario that can explain the observed lithium abundance in the sun and in solar-like stars at a range of ages.
Numerical simulations of convectively excited gravity waves
International Nuclear Information System (INIS)
Glatzmaier, G.A.
1983-01-01
Magneto-convection and gravity waves are numerically simulated with a nonlinear, three-dimensional, time-dependent model of a stratified, rotating, spherical fluid shell heated from below. A Solar-like reference state is specified while global velocity, magnetic field, and thermodynamic perturbations are computed from the anelastic magnetohydrodynamic equations. Convective overshooting from the upper (superadiabatic) part of the shell excites gravity waves in the lower (subadiabatic) part. Due to differential rotation and Coriolis forces, convective cell patterns propagate eastward with a latitudinally dependent phase velocity. The structure of the excited wave motions in the stable region is more time-dependent than that of the convective motions above. The magnetic field tends to be concentrated over giant-cell downdrafts in the convective zone but is affected very little by the wave motion in the stable region
Non-linear thermal convection in a
Directory of Open Access Journals (Sweden)
Sachin Shaw
2016-06-01
Full Text Available Casson fluid flow has many practical applications such as food processing, metallurgy, drilling operations and bio-engineering operations. In this paper, we study Casson fluid flow through a plate with a convective boundary condition at the surface and quantify the effects of suction/injection, velocity ratio, and Soret and Dufour effects. Firstly we used a similarity transformation to change the governing equations to ordinary differential equations which were then solved numerically. The effect of the rheological parameters on the velocity, temperature, and concentration with skin friction, and heat and mass transfer are shown graphically and discussed briefly. It is observed that the velocity of the fluid at the surface decreases with increase of the velocity ratio while the nature of the flow is in opposite characteristics. The local Nusselt number decreases with increase in the velocity ratio. Skin friction at the surface is enhanced by buoyancy ratio and Casson number. Due to injection of the fluid in the system, the mass transfer rate at the surface increases while it decreases with the velocity ratio parameter.
Magnetic Fields in the Solar Convection Zone
Directory of Open Access Journals (Sweden)
Fan Yuhong
2004-07-01
Full Text Available Recent studies of the dynamic evolution of magnetic flux tubes in the solar convection zone are reviewed with focus on emerging flux tubes responsible for the formation of solar active regions. The current prevailing picture is that active regions on the solar surface originate from strong toroidal magnetic fields generated by the solar dynamo mechanism at the thin tachocline layer at the base of the solar convection zone. Thus the magnetic fields need to traverse the entire convection zone before they reach the photosphere to form the observed solar active regions. This review discusses results with regard to the following major topics: 1. the equilibrium properties of the toroidal magnetic fields stored in the stable overshoot region at the base of the convection zone, 2. the buoyancy instability associated with the toroidal magnetic fields and the formation of buoyant magnetic flux tubes, 3. the rise of emerging flux loops through the solar convective envelope as modeled by the thin flux tube calculations which infer that the field strength of the toroidal magnetic fields at the base of the solar convection zone is significantly higher than the value in equipartition with convection, 4. the minimum twist needed for maintaining cohesion of the rising flux tubes, 5. the rise of highly twisted kink unstable flux tubes as a possible origin of d -sunspots, 6. the evolution of buoyant magnetic flux tubes in 3D stratified convection, 7. turbulent pumping of magnetic flux by penetrative compressible convection, 8. an alternative mechanism for intensifying toroidal magnetic fields to significantly super-equipartition field strengths by conversion of the potential energy associated with the superadiabatic stratification of the solar convection zone, and finally 9. a brief overview of our current understanding of flux emergence at the surface and post-emergence evolution of the subsurface magnetic fields.
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)
Substantial convection and precipitation enhancements by ultrafine aerosol particles
Energy Technology Data Exchange (ETDEWEB)
Fan, Jiwen; Rosenfeld, Daniel; Zhang, Yuwei; Giangrande, Scott E.; Li, Zhanqing; Machado, Luiz A. T.; Martin, Scot T.; Yang, Yan; Wang, Jian; Artaxo, Paulo; Barbosa, Henrique M. J.; Braga, Ramon C.; Comstock, Jennifer M.; Feng, Zhe; Gao, Wenhua; Gomes, Helber B.; Mei, Fan; Pöhlker, Christopher; Pöhlker, Mira L.; Pöschl, Ulrich; de Souza, Rodrigo A. F.
2018-01-25
Aerosol-cloud interaction remains the largest uncertainty in climate projections. Ultrafine aerosol particles (UAP; size <50nm) are considered too small to serve as cloud condensation nuclei conventionally. However, this study provides observational evidence to accompany insights from numerical simulations to support that deep convective clouds (DCCs) over Amazon have strong capability of nucleating UAP from an urban source and forming greater numbers of droplets, because fast drop coalescence in these DCCs reduces drop surface area available for condensation, leading to high vapor supersaturation. The additional droplets subsequently decrease supersaturation and release more condensational latent heating, a dominant contributor to convection intensification, whereas enhanced latent heat from ice-related processes plays a secondary role. Therefore, the addition of anthropogenic UAP may play a much greater role in modulating clouds than previously believed over the Amazon region and possibly in other relatively pristine regions such as maritime and forest locations.
Transient Convection, Diffusion, and Adsorption in Surface-Based Biosensors
DEFF Research Database (Denmark)
Hansen, Rasmus; Bruus, Henrik; Callisen, Thomas H.
2012-01-01
This paper presents a theoretical and computational investigation of convection, diffusion, and adsorption in surface-based biosensors. In particular, we study the transport dynamics in a model geometry of a surface plasmon resonance (SPR) sensor. The work, however, is equally relevant for other...... microfluidic surface-based biosensors, operating under flow conditions. A widely adopted approximate quasi-steady theory to capture convective and diffusive mass transport is reviewed, and an analytical solution is presented. An expression of the Damköhler number is derived in terms of the nondimensional...... concentration to the maximum surface capacity is critical for reliable use of the quasi-steady theory. Finally, our results provide users of surface-based biosensors with a tool for correcting experimentally obtained adsorption rate constants....
Actively convected liquid metal divertor
International Nuclear Information System (INIS)
Shimada, Michiya; Hirooka, Yoshi
2014-01-01
The use of actively convected liquid metals with j × B force is proposed to facilitate heat handling by the divertor, a challenging issue associated with magnetic fusion experiments such as ITER. This issue will be aggravated even more for DEMO and power reactors because the divertor heat load will be significantly higher and yet the use of copper would not be allowed as the heat sink material. Instead, reduced activation ferritic/martensitic steel alloys with heat conductivities substantially lower than that of copper, will be used as the structural materials. The present proposal is to fill the lower part of the vacuum vessel with liquid metals with relatively low melting points and low chemical activities including Ga and Sn. The divertor modules, equipped with electrodes and cooling tubes, are immersed in the liquid metal. The electrode, placed in the middle of the liquid metal, can be biased positively or negatively with respect to the module. The j × B force due to the current between the electrode and the module provides a rotating motion for the liquid metal around the electrodes. The rise in liquid temperature at the separatrix hit point can be maintained at acceptable levels from the operation point of view. As the rotation speed increases, the current in the liquid metal is expected to decrease due to the v × B electromotive force. This rotating motion in the poloidal plane will reduce the divertor heat load significantly. Another important benefit of the convected liquid metal divertor is the fast recovery from unmitigated disruptions. Also, the liquid metal divertor concept eliminates the erosion problem. (letter)
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
Convective growth of broadband turbulence in the plasma sheet boundary layer
International Nuclear Information System (INIS)
Dusenbery, P.B.
1987-01-01
Convective growth of slow and fast beam acoustic waves in the plasma sheet boundary layer (PSBL) is investigated. It has been shown previously that a could ion population must be present in order to excite beam acoustic waves in the PSBL. However, growth rates are significantly enhanced when warm plasma sheet boundary layer ions are present. Net wave growth along a ray path is determined by convective growth. This quantity is calculated for particle distribution models consistent with the PSBL where the intensity of broadband turbulence is observed to peak. Total number density dependence on beam acoustic convective growth is evaluated, and it is found that even for low density conditions of ∼0.01 cm -3 , a measurable level of broadband turbulence is expected. Relative drift effects between cold and warm ion populations are also considered. In particular, it is found that slow mode convective growth can be enhanced when slowly streaming cold ions are present, compared to fast ion streams
Effect of perturbation of convective energy transport on the luminosity and radius of the sun
International Nuclear Information System (INIS)
Endal, A.S.; Twigg, L.W.
1982-01-01
The response of solar models to perturbations of the efficiency of convective energy transport is studied for a number of cases. Such perturbations primarily affect the shallow superadiabatic layer of the convective envelope (at depths 3 km below the photosphere). Independent of the details of the perturbation scheme, the resulting change in the solar radius (ΔR/R) is always very small compared to the change in luminosity (ΔL/L). This appears to be true for any physical mechanism of solar variability which operates in the outer layers of the convection zone. Changes of the solar radius have been inferred by Dunham et al. from historical observations of solar eclipses in 1715 and 1925. Considering the constraints on concurrent luminosity changes, this type of solar variability must be indicative of changes in the solar structure at substantial depths below the superadiabatic layer of the convective envelope
Directory of Open Access Journals (Sweden)
Adolfo Ribeiro
2015-03-01
Full Text Available Planets and stars are often capable of generating their own magnetic fields. This occurs through dynamo processes occurring via turbulent convective stirring of their respective molten metal-rich cores and plasma-based convection zones. Present-day numerical models of planetary and stellar dynamo action are not carried out using fluids properties that mimic the essential properties of liquid metals and plasmas (e.g., using fluids with thermal Prandtl numbers Pr < 1 and magnetic Prandtl numbers Pm ≪ 1. Metal dynamo simulations should become possible, though, within the next decade. In order then to understand the turbulent convection phenomena occurring in geophysical or astrophysical fluids and next-generation numerical models thereof, we present here canonical, end-member examples of thermally-driven convection in liquid gallium, first with no magnetic field or rotation present, then with the inclusion of a background magnetic field and then in a rotating system (without an imposed magnetic field. In doing so, we demonstrate the essential behaviors of convecting liquid metals that are necessary for building, as well as benchmarking, accurate, robust models of magnetohydrodynamic processes in Pm ≪ Pr < 1 geophysical and astrophysical systems. Our study results also show strong agreement between laboratory and numerical experiments, demonstrating that high resolution numerical simulations can be made capable of modeling the liquid metal convective turbulence needed in accurate next-generation dynamo models.
Second Law Analysis in Convective Heat and Mass Transfer
Directory of Open Access Journals (Sweden)
A. Ben Brahim
2006-02-01
Full Text Available This paper reports the numerical determination of the entropy generation due to heat transfer, mass transfer and fluid friction in steady state for laminar double diffusive convection, in an inclined enclosure with heat and mass diffusive walls, by solving numerically the mass, momentum, species conservation and energy balance equations, using a Control Volume Finite-Element Method. The influences of the inclination angle, the thermal Grashof number and the buoyancy ratio on total entropy generation were investigated. The irreversibilities localization due to heat transfer, mass transfer and fluid friction is discussed for three inclination angles at a fixed thermal Grashof number.
Group analysis for natural convection from a vertical plate
Rashed, A. S.; Kassem, M. M.
2008-12-01
The steady laminar natural convection of a fluid having chemical reaction of order n past a semi-infinite vertical plate is considered. The solution of the problem by means of one-parameter group method reduces the number of independent variables by one leading to a system of nonlinear ordinary differential equations. Two different similarity transformations are found. In each case the set of differential equations are solved numerically using Runge-Kutta and the shooting method. For each transformation different Schmidt numbers and chemical reaction orders are tested.
A thermodynamically general theory for convective vortices
Renno, Nilton O.
2008-08-01
Convective vortices are common features of atmospheres that absorb lower-entropy-energy at higher temperatures than they reject higher-entropy-energy to space. These vortices range from small to large-scale and play an important role in the vertical transport of heat, momentum, and tracer species. Thus, the development of theoretical models for convective vortices is important to our understanding of some of the basic features of planetary atmospheres. The heat engine framework is a useful tool for studying convective vortices. However, current theories assume that convective vortices are reversible heat engines. Since there are questions about how reversible real atmospheric heat engines are, their usefulness for studying real atmospheric vortices is somewhat controversial. In order to reduce this problem, a theory for convective vortices that includes irreversible processes is proposed. The paper's main result is that the proposed theory provides an expression for the pressure drop along streamlines that includes the effects of irreversible processes. It is shown that a simplified version of this expression is a generalization of Bernoulli's equation to convective circulations. It is speculated that the proposed theory not only explains the intensity, but also sheds light on other basic features of convective vortices such as their physical appearance.
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
Directory of Open Access Journals (Sweden)
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.
A numerical method for investigating crystal settling in convecting magma chambers
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.
Measuring Convective Mass Fluxes Over Tropical Oceans
Raymond, David
2017-04-01
Deep convection forms the upward branches of all large-scale circulations in the tropics. Understanding what controls the form and intensity of vertical convective mass fluxes is thus key to understanding tropical weather and climate. These mass fluxes and the corresponding conditions supporting them have been measured by recent field programs (TPARC/TCS08, PREDICT, HS3) in tropical disturbances considered to be possible tropical storm precursors. In reality, this encompasses most strong convection in the tropics. The measurements were made with arrays of dropsondes deployed from high altitude. In some cases Doppler radar provided additional measurements. The results are in some ways surprising. Three factors were found to control the mass flux profiles, the strength of total surface heat fluxes, the column-integrated relative humidity, and the low to mid-tropospheric moist convective instability. The first two act as expected, with larger heat fluxes and higher humidity producing more precipitation and stronger lower tropospheric mass fluxes. However, unexpectedly, smaller (but still positive) convective instability produces more precipitation as well as more bottom-heavy convective mass flux profiles. Furthermore, the column humidity and the convective instability are anti-correlated, at least in the presence of strong convection. On spatial scales of a few hundred kilometers, the virtual temperature structure appears to be in dynamic balance with the pattern of potential vorticity. Since potential vorticity typically evolves on longer time scales than convection, the potential vorticity pattern plus the surface heat fluxes then become the immediate controlling factors for average convective properties. All measurements so far have taken place in regions with relatively flat sea surface temperature (SST) distributions. We are currently seeking funding for a measurement program in the tropical east Pacific, a region that exhibits strong SST gradients and
Transient Mixed Convection Validation for NGNP
Energy Technology Data Exchange (ETDEWEB)
Smith, Barton [Utah State Univ., Logan, UT (United States); Schultz, Richard [Idaho National Lab. (INL), Idaho Falls, ID (United States)
2015-10-19
The results of this project are best described by the papers and dissertations that resulted from the work. They are included in their entirety in this document. They are: (1) Jeff Harris PhD dissertation (focused mainly on forced convection); (2) Blake Lance PhD dissertation (focused mainly on mixed and transient convection). This dissertation is in multi-paper format and includes the article currently submitted and one to be submitted shortly; and, (3) JFE paper on CFD Validation Benchmark for Forced Convection.
Convective cells and transport in toroidal plasmas
International Nuclear Information System (INIS)
Hassam, A.B.; Kulsrud, R.M.
1978-12-01
The properties of convective cells and the diffusion resulting from such cells are significantly influenced by an inhomogeneity in the extermal confining magnetic field, such as that in toroidal plasmas. The convective diffusion in the presence of a field inhomogeneity is estimated. For a thermal background, this diffusion is shown to be substantially smaller than classical collisional diffusion. For a model nonthermal background, the diffusion is estimated, for typical parameters, to be at most of the order of collisional diffusion. The model background employed is based on spectra observed in numerical simulations of drift-wave-driven convective cells
Transient Mixed Convection Validation for NGNP
International Nuclear Information System (INIS)
Smith, Barton; Schultz, Richard
2015-01-01
The results of this project are best described by the papers and dissertations that resulted from the work. They are included in their entirety in this document. They are: (1) Jeff Harris PhD dissertation (focused mainly on forced convection); (2) Blake Lance PhD dissertation (focused mainly on mixed and transient convection). This dissertation is in multi-paper format and includes the article currently submitted and one to be submitted shortly; and, (3) JFE paper on CFD Validation Benchmark for Forced Convection.
Mixed convection heat transfer from confined tandem square cylinders in a horizontal channel
Huang, Zhu; Xi, Guang; Zhang, Wei; Wen, Suping
2013-01-01
with four widths of the cylinder and the blockage ratio and the Prandtl number are fixed at 0.1 and 0.7 respectively. The mixed convective flow and heat transfer is simulated by high accuracy multidomain pseudospectral method. The Reynolds number (Re
MHD free convection flow of a non-Newtonian power-law fluid over ...
African Journals Online (AJOL)
... flow have been presented for various parameters such as Prandtl number, flow behavior index (n), porous plate parameter and magnetic parameter. The local Nusselt number and skin friction coefficient is also presented graphically. Keywords: Magnetohydrodynamic flow; free convection flow; Non-Newtonian power-law
Asymptotic solution of natural convection problem in a square cavity heated from below
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
Non-Oberbeck-Boussinesq effects in strongly turbulent Rayleigh-Bénard convection
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
Multicomponent droplet vaporization in a convecting environment
International Nuclear Information System (INIS)
Megaridis, C.M.; Sirignano, W.A.
1990-01-01
In this paper a parametric study of the fundamental exchange processes for energy, mass and momentum between the liquid and gas phases of multicomponent liquid vaporizing droplets is presented. The model, which examines an isolated, vaporizing, multicomponent droplet in an axisymmetric, convecting environment, considers the different volatilities of the liquid components, the alteration of the liquid-phase properties due to the spatial/temporal variations of the species concentrations and also the effects of multicomponent diffusion. In addition, the model accounts for variable thermophysical properties, surface blowing and droplet surface regression due to vaporization, transient droplet heating with internal liquid circulation, and finally droplet deceleration with respect to the free flow due to drag. The numerical calculation employs finite-difference techniques and an iterative solution procedure that provides time-varying spatially-resolved data for both phases. The effects of initial droplet composition, ambient temperature, initial Reynolds number (based on droplet diameter), and volatility differential between the two liquid components are investigated for a liquid droplet consisting of two components with very different volatilities. It is found that mixtures with higher concentration of the less volatile substance actually vaporize faster on account of intrinsically higher liquid heating rates
Compressible Convection Experiment using Xenon Gas in a Centrifuge
Menaut, R.; Alboussiere, T.; Corre, Y.; Huguet, L.; Labrosse, S.; Deguen, R.; Moulin, M.
2017-12-01
We present here an experiment especially designed to study compressible convection in the lab. For significant compressible convection effects, the parameters of the experiment have to be optimized: we use xenon gaz in a cubic cell. This cell is placed in a centrifuge to artificially increase the apparent gravity and heated from below. With these choices, we are able to reach a dissipation number close to Earth's outer core value. We will present our results for different heating fluxes and rotation rates. We success to observe an adiabatic gradient of 3K/cm in the cell. Studies of pressure and temperature fluctuations lead us to think that the convection takes place under the form of a single roll in the cell for high heating flux. Moreover, these fluctuations show that the flow is geostrophic due to the high rotation speed. This important role of rotation, via Coriolis force effects, in our experimental setup leads us to develop a 2D quasigeostrophic compressible model in the anelastic liquid approximation. We test numerically this model with the finite element solver FreeFem++ and compare its results with our experimental data. In conclusion, we will present our project for the next experiment in which the cubic cell will be replace by a annulus cell. We will discuss the new expected effects due to this geometry as Rossby waves and zonal flows.
Magnetospheric convection and current system in the dayside polar cap
International Nuclear Information System (INIS)
Nishida, A.; Mukai, T.; Tsuruda, K.; Hayakawa, H.
1992-01-01
Field and particle observations on EXOS-D (Akebono) have yielded new information on convection and current system in the dayside polar cap. Convection patterns are distinctly different depending upon whether IMF B z is northward or southward. The number of convection cells is two when B z is southward but four when B z is northward. Lobe cells in which plasma flows sunward in the region of open field lines are observed as a pair (of which one is in the dawn and the other in the dusk sector) for any polarity of IMF B y and B z . Ions in the keV range precipitate not only in the dayside cusp region but also along the sunward directed streamlines of the dawn and dusk lobe cells. These observations require reconsideration on the position and the extent of the reconnection region on the magnetopause. They also suggest that the magnetotail plays a vital role in some phenomena which have been ascribed to dayside magnetopause processes. We have not been able to find evidence to prove the presence of the viscous cell under southward IMF
Modeling the natural convective flow of micropolar nanofluids
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.
Application of supercomputers to 3-D mantle convection
International Nuclear Information System (INIS)
Baumgardner, J.R.
1986-01-01
Current generation vector machines are providing for the first time the computing power needed to treat planetary mantle convection in a fully three-dimensional fashion. A numerical technique known as multigrid has been implemented in spherical geometry using a hierarchy of meshes constructed from the regular icosahedron to yield a highly efficient three-dimensional compressible Eulerian finite element hydrodynamics formulation. The paper describes the numerical method and presents convection solutions for the mantles of both the earth and the Moon. In the case of the Earth, the convection pattern is characterized by upwelling in narrow circular plumes originating at the core-mantle boundary and by downwelling in sheets or slabs derived from the cold upper boundary layer. The preferred number of plumes appears to be on the order of six or seven. For the Moon, the numerical results indicate that development of a predominately L = 2 pattern in later lunar history is a plausible explanation for the present large second-degree non-hydrostatic component in the lunar figure
Study of liquid metal mixed convection in cavities
International Nuclear Information System (INIS)
Abadie, Philippe.
1979-10-01
This study has enabled some results to be obtained on the flow of liquid metals in cavities. The effects of different adimensional parameters characteristic of mixed convection flows were experimentally demonstrated. In the case of a roof heated cavity, three zones were distinguished: the mixing zone at the channel exit, a quasi constant temperature recirculation zone and a stratified zone at the top of the cavity. The thickness of this last region depends on natural convection effects: it disappears completely in a pure forced convection regime. A simple model using a critical Richardson number concept was developed in order to be able to predict the thickness of this region. Heat transfer correlation formulas were established both for the heated roof and forward direction heated wall cases. Some data was also obtained on temperature fluctuations for both cases. The different topics investigated are useful for defining heat transfers in certain regions of fast neutron sodium cooled reactors. A more extensive program is currently being developed in order to be able to investigate a wider range of variations in the above mentioned parameters and to more closely approximate reactor vessels [fr
Convection in complex shaped vessel; Convection dans des enceintes de forme complexe
Energy Technology Data Exchange (ETDEWEB)
NONE
2000-07-01
The 8 november 2000, the SFT (Societe Francaise de Thermique) organized a technical day on the convection in complex shaped vessels. Nine papers have been presented in the domains of the heat transfers, the natural convection, the fluid distribution, the thermosyphon effect, the steam flow in a sterilization cycle and the transformers cooling. Eight papers are analyzed in ETDE and one paper dealing with the natural convection in spent fuels depository is analyzed in INIS. (A.L.B.)
Thermal convection of liquid sodium in inclined cylinders
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
Ignition in Convective-Diffusive Systems
National Research Council Canada - National Science Library
Law, Chung
1999-01-01
... efficiency as well as the knock and emission characteristics. The ignition event is clearly controlled by the chemical reactions of fuel oxidation and the fluid mechanics of convective and diffusive transport...
Understanding and controlling plasmon-induced convection
Roxworthy, Brian J.; Bhuiya, Abdul M.; Vanka, Surya P.; Toussaint, Kimani C.
2014-01-01
The heat generation and fluid convection induced by plasmonic nanostructures is attractive for optofluidic applications. However, previously published theoretical studies predict only nanometre per second fluid velocities that are inadequate for microscale mass transport. Here we show both theoretically and experimentally that an array of plasmonic nanoantennas coupled to an optically absorptive indium-tin-oxide (ITO) substrate can generate >micrometre per second fluid convection. Crucially, the ITO distributes thermal energy created by the nanoantennas generating an order of magnitude increase in convection velocities compared with nanoantennas on a SiO2 base layer. In addition, the plasmonic array alters absorption in the ITO, causing a deviation from Beer-Lambert absorption that results in an optimum ITO thickness for a given system. This work elucidates the role of convection in plasmonic optical trapping and particle assembly, and opens up new avenues for controlling fluid and mass transport on the micro- and nanoscale.
What favors convective aggregation and why?
Muller, Caroline; Bony, Sandrine
2015-07-01
The organization of convection is ubiquitous, but its physical understanding remains limited. One particular type of organization is the spatial self-aggregation of convection, taking the form of cloud clusters, or tropical cyclones in the presence of rotation. We show that several physical processes can give rise to self-aggregation and highlight the key features responsible for it, using idealized simulations. Longwave radiative feedbacks yield a "radiative aggregation." In that case, sufficient spatial variability of radiative cooling rates yields a low-level circulation, which induces the upgradient energy transport and radiative-convective instability. Not only do vertically integrated radiative budgets matter but the vertical profile of cooling is also crucial. Convective aggregation is facilitated when downdrafts below clouds are weak ("moisture-memory aggregation"), and this is sufficient to trigger aggregation in the absence of longwave radiative feedbacks. These results shed some light on the sensitivity of self-aggregation to various parameters, including resolution or domain size.
Theoretical basis for convective invigoration due to increased aerosol concentration
Directory of Open Access Journals (Sweden)
Z. J. Lebo
2011-06-01
Full Text Available The potential effects of increased aerosol loading on the development of deep convective clouds and resulting precipitation amounts are studied by employing the Weather Research and Forecasting (WRF model as a detailed high-resolution cloud resolving model (CRM with both detailed bulk and bin microphysics schemes. Both models include a physically-based activation scheme that incorporates a size-resolved aerosol population. We demonstrate that the aerosol-induced effect is controlled by the balance between latent heating and the increase in condensed water aloft, each having opposing effects on buoyancy. It is also shown that under polluted conditions, increases in the CCN number concentration reduce the cumulative precipitation due to the competition between the sedimentation and evaporation/sublimation timescales. The effect of an increase in the IN number concentration on the dynamics of deep convective clouds is small and the resulting decrease in domain-averaged cumulative precipitation is shown not to be statistically significant, but may act to suppress precipitation. It is also shown that even in the presence of a decrease in the domain-averaged cumulative precipitation, an increase in the precipitation variance, or in other words, andincrease in rainfall intensity, may be expected in more polluted environments, especially in moist environments.
A significant difference exists between the predictions based on the bin and bulk microphysics schemes of precipitation and the influence of aerosol perturbations on updraft velocity within the convective core. The bulk microphysics scheme shows little change in the latent heating rates due to an increase in the CCN number concentration, while the bin microphysics scheme demonstrates significant increases in the latent heating aloft with increasing CCN number concentration. This suggests that even a detailed two-bulk microphysics scheme, coupled to a detailed activation scheme, may not be
Antartic observations of plasma convection
International Nuclear Information System (INIS)
Hansen, H.J.
1983-01-01
This thesis is concerned with the use of whistler duct tracking as a diagnostic for the behaviour of plasma in the plasmasphere. As a setting for the results given in the thesis, a broad review is presented which embraces pertinent aspects of previous experimental and theoretical studies of the plasmasphere. From a study of 24 hours of continuous whistler data recorded at Sanae, (L = 3,98), it is shown that associated with quiet magnetic conditions (Av Ksub(p)=1), there exists two plasmasphere bulges centred on about 1700 and 0100 UT. There is evidence that these plasmasphere bulge structures are part of a ground-state or reference base drift pattern. Electric field measurements provide some evidence that quiet time plasmasphere drift behaviour is controlled by the internal ionospheric current systems of dynamo origin, rather than being controlled by magnetospheric convection. Finally, this thesis describes an application of the whistler duct tracking technique to whistler data recorded simultaneously at two ground-based stations (Sanae (L = 3,98) and Halley (L = 4,23)). The identification of common whistler components on each station's data set provides a means of estimating the lifetimes of the associated whistler ducts. Duct lifetimes of as little as 30 minutes are found. Such short lived ducts have important implications for current theories of duct formation
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)
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)
Dynamics of acoustic-convective drying of sunflower cake
Zhilin, A. A.
2017-10-01
The dynamics of drying sunflower cake by a new acoustic-convective method has been studied. Unlike the conventional (thermal-convective) method, the proposed method allows moisture to be extracted from porous materials without applying heat to the sample to be dried. Kinetic curves of drying by the thermal-convective and acoustic-convective methods were obtained and analyzed. The advantages of the acoustic-convective extraction of moisture over the thermal-convective method are discussed. The relaxation times of drying were determined for both drying methods. An intermittent drying mode which improves the efficiency of acoustic-convective extraction of moisture is considered.
Energy Technology Data Exchange (ETDEWEB)
Li, K., E-mail: likai@imech.ac.cn [Key Laboratory of Microgravity, Chinese Academy of Sciences, Beijing 100190, China and National Microgravity Laboratory, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190 (China); University of Chinese Academy of Sciences, Beijing 100190 (China); Xun, B.; Hu, W. R. [Key Laboratory of Microgravity, Chinese Academy of Sciences, Beijing 100190, China and National Microgravity Laboratory, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190 (China)
2016-05-15
As a part of the preliminary studies for the future space experiment (Zona-K) in the Russian module of the International Space Station, some bifurcation routes to chaos of thermocapillary convection in two-dimensional liquid layers filled with 10 cSt silicone oil have been numerically studied in this paper. As the laterally applied temperature difference is raised, variations in the spatial structure and temporal evolution of the thermocapillary convection and a complex sequence of transitions are observed. The results show that the finite extent of the liquid layer significantly influences the tempo-spatial evolution of the thermocapillary convection. Moreover, the bifurcation route of the thermocapillary convection changes very sensitively by the aspect ratio of the liquid layer. With the increasing Reynolds number (applied temperature difference), the steady thermocapillary convection experiences two consecutive transitions from periodic oscillatory state to quasi-periodic oscillatory state with frequency-locking before emergence of chaotic convection in a liquid layer of aspect ratio 14.25, and the thermocapillary convection undergoes period-doubling cascades leading to chaotic convection in a liquid layer of aspect ratio 13.0.
International Nuclear Information System (INIS)
Li, K.; Xun, B.; Hu, W. R.
2016-01-01
As a part of the preliminary studies for the future space experiment (Zona-K) in the Russian module of the International Space Station, some bifurcation routes to chaos of thermocapillary convection in two-dimensional liquid layers filled with 10 cSt silicone oil have been numerically studied in this paper. As the laterally applied temperature difference is raised, variations in the spatial structure and temporal evolution of the thermocapillary convection and a complex sequence of transitions are observed. The results show that the finite extent of the liquid layer significantly influences the tempo-spatial evolution of the thermocapillary convection. Moreover, the bifurcation route of the thermocapillary convection changes very sensitively by the aspect ratio of the liquid layer. With the increasing Reynolds number (applied temperature difference), the steady thermocapillary convection experiences two consecutive transitions from periodic oscillatory state to quasi-periodic oscillatory state with frequency-locking before emergence of chaotic convection in a liquid layer of aspect ratio 14.25, and the thermocapillary convection undergoes period-doubling cascades leading to chaotic convection in a liquid layer of aspect ratio 13.0.
Evaporative and Convective Instabilities for the Evaporation of a Binary Mixture in a Bilayer System
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.
Clifford, Corey; Kimber, Mark
2017-11-01
Over the last 30 years, an industry-wide shift within the nuclear community has led to increased utilization of computational fluid dynamics (CFD) to supplement nuclear reactor safety analyses. One such area that is of particular interest to the nuclear community, specifically to those performing loss-of-flow accident (LOFA) analyses for next-generation very-high temperature reactors (VHTR), is the capacity of current computational models to predict heat transfer across a wide range of buoyancy conditions. In the present investigation, a critical evaluation of Reynolds-averaged Navier-Stokes (RANS) and large-eddy simulation (LES) turbulence modeling techniques is conducted based on CFD validation data collected from the Rotatable Buoyancy Tunnel (RoBuT) at Utah State University. Four different experimental flow conditions are investigated: (1) buoyancy-aided forced convection; (2) buoyancy-opposed forced convection; (3) buoyancy-aided mixed convection; (4) buoyancy-opposed mixed convection. Overall, good agreement is found for both forced convection-dominated scenarios, but an overly-diffusive prediction of the normal Reynolds stress is observed for the RANS-based turbulence models. Low-Reynolds number RANS models perform adequately for mixed convection, while higher-order RANS approaches underestimate the influence of buoyancy on the production of turbulence.
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.
Freitas, S.; Grell, G. A.; Molod, A.
2017-12-01
We implemented and began to evaluate an alternative convection parameterization for the NASA Goddard Earth Observing System (GEOS) global model. The parameterization (Grell and Freitas, 2014) is based on the mass flux approach with several closures, for equilibrium and non-equilibrium convection, and includes scale and aerosol awareness functionalities. Scale dependence for deep convection is implemented either through using the method described by Arakawa et al (2011), or through lateral spreading of the subsidence terms. Aerosol effects are included though the dependence of autoconversion and evaporation on the CCN number concentration.Recently, the scheme has been extended to a tri-modal spectral size approach to simulate the transition from shallow, congestus, and deep convection regimes. In addition, the inclusion of a new closure for non-equilibrium convection resulted in a substantial gain of realism in model simulation of the diurnal cycle of convection over the land. Also, a beta-pdf is employed now to represent the normalized mass flux profile. This opens up an additional venue to apply stochasticism in the scheme.
Subcritical thermal convection of liquid metals in a rotating sphere using a quasi-geostrophic model
Cardin, P.; Guervilly, C.
2016-12-01
We study non-linear convection in a rapidly rotating sphere with internal heating for values of the Prandtl number relevant for liquid metals (10-2-1). We use a numerical model based on the quasi-geostrophic approximation, in which variations of the axial vorticity along the rotation axis are neglected, whereas the temperature field is fully three-dimensional. We identify two separate branches of convection close to onset: (i) a well-known weak branch for Ekman numbers greater than 10-6, which is continuous at the onset (supercritical bifurcation) and consists of the interaction of thermal Rossby waves, and (ii) a novel strong branch at lower Ekman numbers, which is discontinuous at the onset. The strong branch becomes subcritical for Ekman numbers of the order of 10-8. On the strong branch, the Reynolds number of the flow is greater than 1000, and a strong zonal flow with multiple jets develops, even close to the non-linear onset of convection. We find that the subcriticality is amplified by decreasing the Prandtl number. The two branches can co-exist for intermediate Ekman numbers, leading to hysteresis (E = 10-6, Pr =10-2). Non-linear oscillations are observed near the onset of convection for E = 10-7 and Pr = 10-1.
Subcritical convection of liquid metals in a rotating sphere using a quasi-geostrophic model
Guervilly, Céline; Cardin, Philippe
2016-12-01
We study nonlinear convection in a rapidly rotating sphere with internal heating for values of the Prandtl number relevant for liquid metals ($Pr\\in[10^{-2},10^{-1}]$). We use a numerical model based on the quasi-geostrophic approximation, in which variations of the axial vorticity along the rotation axis are neglected, whereas the temperature field is fully three-dimensional. We identify two separate branches of convection close to onset: (i) a well-known weak branch for Ekman numbers greater than $10^{-6}$, which is continuous at the onset (supercritical bifurcation) and consists of thermal Rossby waves, and (ii) a novel strong branch at lower Ekman numbers, which is discontinuous at the onset. The strong branch becomes subcritical for Ekman numbers of the order of $10^{-8}$. On the strong branch, the Reynolds number of the flow is greater than $10^3$, and a strong zonal flow with multiple jets develops, even close to the nonlinear onset of convection. We find that the subcriticality is amplified by decreasing the Prandtl number. The two branches can co-exist for intermediate Ekman numbers, leading to hysteresis ($Ek=10^{-6}$, $Pr=10^{-2}$). Nonlinear oscillations are observed near the onset of convection for $Ek=10^{-7}$ and $Pr=10^{-1}$.
CONVECTION IN CONDENSIBLE-RICH ATMOSPHERES
Energy Technology Data Exchange (ETDEWEB)
Ding, F. [Department of the Geophysical Sciences, University of Chicago, Chicago, IL 60637 (United States); Pierrehumbert, R. T., E-mail: fding@uchicago.edu [Department of Physics, University of Oxford, Oxford OX1 3PU (United Kingdom)
2016-05-01
Condensible substances are nearly ubiquitous in planetary atmospheres. For the most familiar case—water vapor in Earth’s present climate—the condensible gas is dilute, in the sense that its concentration is everywhere small relative to the noncondensible background gases. A wide variety of important planetary climate problems involve nondilute condensible substances. These include planets near or undergoing a water vapor runaway and planets near the outer edge of the conventional habitable zone, for which CO{sub 2} is the condensible. Standard representations of convection in climate models rely on several approximations appropriate only to the dilute limit, while nondilute convection differs in fundamental ways from dilute convection. In this paper, a simple parameterization of convection valid in the nondilute as well as dilute limits is derived and used to discuss the basic character of nondilute convection. The energy conservation properties of the scheme are discussed in detail and are verified in radiative-convective simulations. As a further illustration of the behavior of the scheme, results for a runaway greenhouse atmosphere for both steady instellation and seasonally varying instellation corresponding to a highly eccentric orbit are presented. The latter case illustrates that the high thermal inertia associated with latent heat in nondilute atmospheres can damp out the effects of even extreme seasonal forcing.
Numerical Studies on Natural Convection Heat Losses from Open Cubical Cavities
Directory of Open Access Journals (Sweden)
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.
Energy Technology Data Exchange (ETDEWEB)
Saez, M.
1998-10-20
The aim of our study is to establish a reliable database for improving thermal hydraulic codes, in the field of turbulent flows with buoyancy forces. The flow considered is mixed convection in the Reynolds and Richardson number range: Re = 10{sup 3} to 6.10{sup 4} and Ri = 10{sup -4} to 1. Experiments are carried out in an upward turbulent flow between vertical parallel plates at different wall temperatures. Part 1 gives a detailed database of turbulent mixed flow of free and forced convection. Part 2 presents the installation and the calibration system intended for probes calibration. Part 3 describes the measurement technique (constant temperature probe and cold-wire probe) and the method for measuring the position of the hot-wire anemometer from the wall surface. The measurement accuracy is within 0.001 mm in the present system. Part 4 relates the development of a method for near wall measurements. This correction procedure for hot-wire anemometer close to wall has been derived on the basis of a two-dimensional numerical study. The method permits to obtain a quantitative correction of the wall influence on hot-wires and takes into account the velocity profile and the effects the wall material has on the heat loss. Part 5 presents the experimental data obtained in the channel in forced and mixed convection. Results obtained in the forced convection regime serve as a verification of the measurement technique close to the wall and give the conditions at the entrance of the test section. The effects of the buoyancy force on the mean velocity and temperature profiles are confirmed. The buoyancy strongly affects the fluid structure and deforms the distribution of mean velocity. The velocity profiles are asymmetric. The second section of part 5 gives an approach of analytical wall functions with buoyancy forces, on the basis of the experimental data obtained in the test section. (author)
Bennett, Ruth, Ed.; And Others
An introduction to the Hupa number system is provided in this workbook, one in a series of numerous materials developed to promote the use of the Hupa language. The book is written in English with Hupa terms used only for the names of numbers. The opening pages present the numbers from 1-10, giving the numeral, the Hupa word, the English word, and…
Indian Academy of Sciences (India)
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Triangular number, figurate num- ber, rangoli, Brahmagupta–Pell equation, Jacobi triple product identity. Figure 1. The first four triangular numbers. Left: Anuradha S Garge completed her PhD from. Pune University in 2008 under the supervision of Prof. S A Katre. Her research interests include K-theory and number theory.
Directory of Open Access Journals (Sweden)
Schwarzweller Christoph
2015-02-01
Full Text Available In this article we introduce Proth numbers and prove two theorems on such numbers being prime [3]. We also give revised versions of Pocklington’s theorem and of the Legendre symbol. Finally, we prove Pepin’s theorem and that the fifth Fermat number is not prime.
Directory of Open Access Journals (Sweden)
Nee Alexander
2016-01-01
Full Text Available Mathematical modeling of conjugate natural convection in a closed rectangular cavity with a radiant energy source in conditions of convective-radiative heat exchange at the external boundary was conducted. The radiant energy distribution was set by the Lambert’s law. Conduction and convection processes analysis showed that the air masses flow pattern is modified slightly over the time. The temperature increases in the gas cavity, despite the heat removal from the one of the external boundary. According to the results of the integral heat transfer analysis were established that the average Nusselt number (Nuav increasing occurs up to τ = 200 (dimensionless time. Further Nuav has changed insignificantly due to the temperature field equalization near the interfaces “gas – wall”.
Mendonça, J. Ricardo G.
2012-01-01
We define a new class of numbers based on the first occurrence of certain patterns of zeros and ones in the expansion of irracional numbers in a given basis and call them Sagan numbers, since they were first mentioned, in a special case, by the North-american astronomer Carl E. Sagan in his science-fiction novel "Contact." Sagan numbers hold connections with a wealth of mathematical ideas. We describe some properties of the newly defined numbers and indicate directions for further amusement.
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)
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.
DEFF Research Database (Denmark)
Le Dreau, Jerome; Heiselberg, Per; Jensen, Rasmus Lund
2015-01-01
-state and dynamic conditions. With the air-based cooling system, a dependency of the convective heat transfer on the air jet trajectory has been observed. New correlations have been developed, introducing a modified Archimedes number to account for the air flow pattern. The accuracy of the new correlations has been...... evaluated to±15%. Besides the study with an air-based cooling system, the convective heat transfer with a radiant cooling system has also been investigated. The convective flow at the activated surface is mainly driven by natural convection. For other surfaces, the complexity of the flow and the large......The complexity and diversity of airflow in buildings make the accurate definition of convective heat transfer coefficients (CHTCs) difficult. In a full-scale test facility, the convective heat transfer of two cooling systems (active chilled beam and radiant wall) has been investigated under steady...
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
Hence, Deanna A.; Houze, Robert A.
2008-08-01
Airborne Doppler radar data collected during the Hurricane Rainband and Intensity Change Experiment (RAINEX) show the convective-scale air motions embedded in the principal rainbands of hurricanes Katrina and Rita. These embedded convective cells have overturning updrafts and low-level downdrafts (originating at 2-4 km) that enter the rainband on its radially outward side and cross over each other within the rainband as well as a strong downdraft emanating from upper levels (6+ km) on the radially inward side. These vertical motion structures repeat from one convective cell to another along each rainband. The resulting net vertical mass transport is upward in the upwind portion of the band and greatest in the middle sector of the principal rainband, where the updraft motions contribute generally to an increase of potential vorticity below the 3-4 km level. Because the convective cells in the middle sector are systematically located radially just inside the secondary horizontal wind maximum (SHWM), the local increase in vorticity implied by the convective mass transport is manifest locally as an increase in the strength of the SHWM at midlevels (˜4 km). The overturning updrafts of the convective cells tilt, stretch, and vertically transport vorticity such that the convergence of the vertical flux of vorticity strengthens the vorticity anomaly associated with the SHWM. This process could strengthen the SHWM by several meters per second per hour, and may explain how high wave number convective-scale features can influence a low wave number feature such as the principal rainband, and subsequently influence the primary vortex.
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
Petersen, T Kyle
2015-01-01
This text presents the Eulerian numbers in the context of modern enumerative, algebraic, and geometric combinatorics. The book first studies Eulerian numbers from a purely combinatorial point of view, then embarks on a tour of how these numbers arise in the study of hyperplane arrangements, polytopes, and simplicial complexes. Some topics include a thorough discussion of gamma-nonnegativity and real-rootedness for Eulerian polynomials, as well as the weak order and the shard intersection order of the symmetric group. The book also includes a parallel story of Catalan combinatorics, wherein the Eulerian numbers are replaced with Narayana numbers. Again there is a progression from combinatorics to geometry, including discussion of the associahedron and the lattice of noncrossing partitions. The final chapters discuss how both the Eulerian and Narayana numbers have analogues in any finite Coxeter group, with many of the same enumerative and geometric properties. There are four supplemental chapters throughout, ...
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
Vansteelant, W.M.G.; Verhelst, B.; Shamoun-Baranes, J.; Bouten, W.; van Loon, E.E.; Bildstein, K.L.
2014-01-01
Every autumn, large numbers of raptors migrate through geographical convergence zones to avoid crossing large bodies of water. At coastal convergence zones, raptors may aggregate along coastlines because of convective or wind conditions. However, the effect of wind and thermal convection on
Convective transport resistance in the vitreous humor
Penkova, Anita; Sadhal, Satwindar; Ratanakijsuntorn, Komsan; Moats, Rex; Tang, Yang; Hughes, Patrick; Robinson, Michael; Lee, Susan
2012-11-01
It has been established by MRI visualization experiments that the convection of nanoparticles and large molecules with high rate of water flow in the vitreous humor will experience resistance, depending on the respective permeabilities of the injected solute. A set of experiments conducted with Gd-DTPA (Magnevist, Bayer AG, Leverkusen, Germany) and 30 nm gadolinium-based particles (Gado CELLTrackTM, Biopal, Worcester, MA) as MRI contrast agents showed that the degree of convective transport in this Darcy-type porous medium varies between the two solutes. These experiments consisted of injecting a mixture of the two (a 30 μl solution of 2% Magnevist and 1% nanoparticles) at the middle of the vitreous of an ex vivo whole bovine eye and subjecting the vitreous to water flow rate of 100 μl/min. The water (0.9% saline solution) was injected at the top of the eye, and was allowed to drain through small slits cut at the bottom of the eyeball. After 50 minutes of pumping, MRI images showed that the water flow carried the Gd-DTPA farther than the nanoparticles, even though the two solutes, being mixed, were subjected to the same convective flow conditions. We find that the convected solute lags the water flow, depending on the solute permeability. The usual convection term needs to be adjusted to allow for the filtration effect on the larger particles in the form (1- σ) u . ∇ c with important implications for the modeling of such systems.
Indian Academy of Sciences (India)
Transfinite Numbers. What is Infinity? S M Srivastava. In a series of revolutionary articles written during the last quarter of the nineteenth century, the great Ger- man mathematician Georg Cantor removed the age-old mistrust of infinity and created an exceptionally beau- tiful and useful theory of transfinite numbers. This is.
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)
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)
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.
Ji, Caleb; Khovanova, Tanya; Park, Robin; Song, Angela
2015-01-01
In this paper, we consider a game played on a rectangular $m \\times n$ gridded chocolate bar. Each move, a player breaks the bar along a grid line. Each move after that consists of taking any piece of chocolate and breaking it again along existing grid lines, until just $mn$ individual squares remain. This paper enumerates the number of ways to break an $m \\times n$ bar, which we call chocolate numbers, and introduces four new sequences related to these numbers. Using various techniques, we p...
Andrews, George E
1994-01-01
Although mathematics majors are usually conversant with number theory by the time they have completed a course in abstract algebra, other undergraduates, especially those in education and the liberal arts, often need a more basic introduction to the topic.In this book the author solves the problem of maintaining the interest of students at both levels by offering a combinatorial approach to elementary number theory. In studying number theory from such a perspective, mathematics majors are spared repetition and provided with new insights, while other students benefit from the consequent simpl
Convective mixing in helium white dwarfs
International Nuclear Information System (INIS)
Vauclair, G.; Fontaine, G.
1979-01-01
The conditions under which convective mixing episodes take place between the helium envelopes and the underlying carbon layers in helium-rich white dwarfs are investigated. It is found that, for essentially any value of the initial helium content less than the maximum mass a helium convection zone can have, mixing does occur, and leads, in the vast majority of cases, to an almost pure carbon superficial composition. Mixing products that show only traces of carbon while retaining helium-dominated envelopes are possible only if the initial helium content is quite close to the maximum possible mass of the helium convection zone. In the presence of turbulence, this restriction could be relaxed, however, and the helium-rich lambda4670 stars may possibly be explained in this fashion
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.)
Hamed K. Arzani; Hamid K. Arzani; S.N. Kazi; A. Badarudin
2016-01-01
Numerical investigation into convective heat transfer of CuO-Water based nanofluid in a pipe with return bend under laminar flow conditions has been done. The impacts of Reynolds number and the volume concentration of nanoparticles on the flow and the convective heat transfer behaviour are investigated. The results indicate that the increase in Reynolds number leads to the enhancement of average Nusselt number, and the increase in specific heat in the presence of the nanofluid results in impr...
The Impact of Reduced Gravity on Free Convective Heat Transfer from a Finite, Flat, Vertical Plate
Lotto, Michael A.; Johnson, Kirstyn M.; Nie, Christopher W.; Klaus, David M.
2017-10-01
Convective heat transfer is governed by a number of factors including various fluid properties, the presence of a thermal gradient, geometric configuration, flow condition, and gravity. Empirically-derived analytical relationships can be used to estimate convection as a function of these governing parameters. Although it is relatively straightforward to experimentally quantify the contributions of the majority of these variables, it is logistically difficult to assess the influence of reduced-gravity due to practical limitations of establishing this environment. Therefore, in order to explore this regime, a series of tests was conducted to evaluate convection under reduced-gravity conditions averaging 0.45 m/sec2 (0.05 g) achieved aboard a parabolic aircraft. The results showed a reduction in net heat transfer of approximately 61% in flight relative to a 1 g terrestrial baseline using the same setup. The average experimental Nusselt Number of 19.05 ± 1.41 statistically correlated with the predicted value of 18.90 ± 0.63 (N = 13), estimated using the Churchill-Chu correlation for free convective heat transfer from a finite, flat, vertical plate. Extrapolating this to similar performance in true microgravity (10-6 g) indicates that these conditions should yield a Nusselt Number of 1.27, which is 2.6% the magnitude of free convection at 1 g, or a reduction of 97.4%. With advection essentially eliminated, heat transfer becomes limited to diffusion and radiation, which are gravity-independent and nearly equivalent in magnitude in this case. These results offer a general guideline for integrating components that utilize natural (free) convective gas cooling in a spacecraft habitat and properly sizing the thermal control system.
Barnes, John
2016-01-01
In this intriguing book, John Barnes takes us on a journey through aspects of numbers much as he took us on a geometrical journey in Gems of Geometry. Similarly originating from a series of lectures for adult students at Reading and Oxford University, this book touches a variety of amusing and fascinating topics regarding numbers and their uses both ancient and modern. The author intrigues and challenges his audience with both fundamental number topics such as prime numbers and cryptography, and themes of daily needs and pleasures such as counting one's assets, keeping track of time, and enjoying music. Puzzles and exercises at the end of each lecture offer additional inspiration, and numerous illustrations accompany the reader. Furthermore, a number of appendices provides in-depth insights into diverse topics such as Pascal’s triangle, the Rubik cube, Mersenne’s curious keyboards, and many others. A theme running through is the thought of what is our favourite number. Written in an engaging and witty sty...
Natural Convective Heat Transfer from Narrow Plates
Oosthuizen, Patrick H
2013-01-01
Natural Convective Heat Transfer from Narrow Plates deals with a heat transfer situation that is of significant practical importance but which is not adequately dealt with in any existing textbooks or in any widely available review papers. The aim of the book is to introduce the reader to recent studies of natural convection from narrow plates including the effects of plate edge conditions, plate inclination, thermal conditions at the plate surface and interaction of the flows over adjacent plates. Both numerical and experimental studies are discussed and correlation equations based on the results of these studies are reviewed.
Might electrical earthing affect convection of light
International Nuclear Information System (INIS)
Budrikis, Z.L.
1982-01-01
Partial convection of light by moving media was predicted by Fresnel and verified by Fizeau, Zeeman and others. It is accepted as an important argument in favour of the Special Theory of Relativity. The suggestion is made here that the convection is partial only when the propagating medium is moved with respect to its electrically earthed surroundings and that it would be total if an earthed shield was co-moving with the medium. This is based on a reinterpretation of Maxwell's equations wherein they are seen as macroscopic relationships that are in each case valid only in respect of a particular inertial frame of reference, the local electrical earth frame. (Auth.)
Topology Optimisation for Coupled Convection Problems
DEFF Research Database (Denmark)
Alexandersen, Joe; Andreasen, Casper Schousboe; Aage, Niels
stabilised finite elements implemented in a parallel multiphysics analysis and optimisation framework DFEM [1], developed and maintained in house. Focus is put on control of the temperature field within the solid structure and the problems can therefore be seen as conjugate heat transfer problems, where heat...... conduction governs in the solid parts of the design domain and couples to convection-dominated heat transfer to a surrounding fluid. Both loosely coupled and tightly coupled problems are considered. The loosely coupled problems are convection-diffusion problems, based on an advective velocity field from...
Directory of Open Access Journals (Sweden)
Perović Bojan D.
2017-01-01
Full Text Available The main purpose of this paper is to show how the inclination angle affects natural convection from a flat-plate photovoltaic module which is mounted on the ground surface. In order to model this effect, novel correlations for natural convection from isothermal flat plates are developed by using the fundamental dimensionless number. On the basis of the available experimental and numerical results, it is shown that the natural convection correlations correspond well with the existing empirical correlations for vertical, inclined, and horizontal plates. Five additional correlations for the critical Grashof number are derived from the available data, three indicating the onset of transitional flow regime and two indicating the onset of flow separation. The proposed correlations cover the entire range of inclination angles and the entire range of Prandtl numbers. This paper also provides two worked examples, one for natural convection combined with radiation and one for natural convection combined with forced convection and radiation. [Project of the Serbian Ministry of Education, Science and Technological Development, Grant no. TR33046
Dhara, Chirag; Renner, Maik; Kleidon, Axel
2015-04-01
The convective transport of heat and moisture plays a key role in the climate system, but the transport is typically parameterized in models. Here, we aim at the simplest possible physical representation and treat convective heat fluxes as the result of a heat engine. We combine the well-known Carnot limit of this heat engine with the energy balances of the surface-atmosphere system that describe how the temperature difference is affected by convective heat transport, yielding a maximum power limit of convection. This results in a simple analytic expression for convective strength that depends primarily on surface solar absorption. We compare this expression with an idealized grey atmosphere radiative-convective (RC) model as well as Global Circulation Model (GCM) simulations at the grid scale. We find that our simple expression as well as the RC model can explain much of the geographic variation of the GCM output, resulting in strong linear correlations among the three approaches. The RC model, however, shows a lower bias than our simple expression. We identify the use of the prescribed convective adjustment in RC-like models as the reason for the lower bias. The strength of our model lies in its ability to capture the geographic variation of convective strength with a parameter-free expression. On the other hand, the comparison with the RC model indicates a method for improving the formulation of radiative transfer in our simple approach. We also find that the latent heat fluxes compare very well among the approaches, as well as their sensitivity to surface warming. What our comparison suggests is that the strength of convection and their sensitivity in the climatic mean can be estimated relatively robustly by rather simple approaches.
International Nuclear Information System (INIS)
D'Orazio, A; Karimipour, A; Nezhad, A H; Shirani, E
2014-01-01
Laminar mixed convective heat transfer in two-dimensional rectangular inclined driven cavity is studied numerically by means of a double population thermal Lattice Boltzmann method. Through the top moving lid the heat flux enters the cavity whereas it leaves the system through the bottom wall; side walls are adiabatic. The counter-slip internal energy density boundary condition, able to simulate an imposed non zero heat flux at the wall, is applied, in order to demonstrate that it can be effectively used to simulate heat transfer phenomena also in case of moving walls. Results are analyzed over a range of the Richardson numbers and tilting angles of the enclosure, encompassing the dominating forced convection, mixed convection, and dominating natural convection flow regimes. As expected, heat transfer rate increases as increases the inclination angle, but this effect is significant for higher Richardson numbers, when buoyancy forces dominate the problem; for horizontal cavity, average Nusselt number decreases with the increase of Richardson number because of the stratified field configuration
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.
Cell structures caused by settling particles in turbulent Rayleigh-Bénard convection
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.
Effect of plumes on measuring the large scale circulation in turbulent Rayleigh-Bénard convection
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
Laminar forced convective/conductive heat transfer by finite element method
International Nuclear Information System (INIS)
Kushwaha, H.S.; Kakodkar, A.
1982-01-01
The present study is directed at developing a finite element computer program for solution of decoupled convective/conductive heat transfer problems. Penalty function formulation has been used to solve momentum equations and subsequently transient energy equation is solved using modified Crank-Nicolson method. The optimal upwinding scheme has been employed in energy equation to remove oscillations at high Peclet number. (author)
Unsteady free convection MHD flow between two heated vertical parallel conducting plates
International Nuclear Information System (INIS)
Sanyal, D.C.; Adhikari, A.
2006-01-01
Unsteady free convection flow of a viscous incompressible electrically conducting fluid between two heated conducting vertical parallel plates subjected to a uniform transverse magnetic field is considered. The approximate analytical solutions for velocity, induced field and temperature distribution are obtained for small and large values of magnetic Reynolds number. The problem is also extended to thermometric case. (author)
The effect of Coriolis force on nonlinear convection in a porous medium
Directory of Open Access Journals (Sweden)
D. H. Riahi
1994-01-01
Full Text Available Nonlinear convection in a porous medium and rotating about vertical axis is studied in this paper. An upper bound to the heat flux is calculated by the method initiated first by Howard [6] for the case of infinite Prandtl number.
Dynamo Scaling Laws for Uranus and Neptune: The Role of Convective Shell Thickness on Dipolarity
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.
Stability analysis of natural convection in superposed fluid and porous layers
International Nuclear Information System (INIS)
Hirata, S.C.; Goyeau, B.; Gobin, D.; Cotta, R.M.
2005-01-01
A linear stability analysis of the onset of thermal natural convection in superposed fluid and porous layers is called out. The resulting eigenvalue problem is solved using a integral transformation technique. The effect of the variation of the Darcy number on the stability of the system is analyzed. (authors)
Stability analysis of natural convection in superposed fluid and porous layers
Energy Technology Data Exchange (ETDEWEB)
Hirata, S.C.; Goyeau, B.; Gobin, D. [Paris-11 Univ. - Paris-6, FAST - UMR CNRS 7608, 91 - Orsay (France); Cotta, R.M. [Rio de Janeiro Univ. (LTTC/PEM/EE/COPPE/UFRJ), RJ (Brazil)
2005-07-01
A linear stability analysis of the onset of thermal natural convection in superposed fluid and porous layers is called out. The resulting eigenvalue problem is solved using a integral transformation technique. The effect of the variation of the Darcy number on the stability of the system is analyzed. (authors)
A highly stable microchannel heat sink for convective boiling
International Nuclear Information System (INIS)
Lu, Chun Ting; Pan Chin
2009-01-01
To develop a highly stable two-phase microchannel heat sink, we experimented with convective boiling in diverging, parallel microchannels with different distributions of laser-etched artificial nucleation sites. Each microchannel had a mean hydraulic diameter of 120 µm. The two-phase flow visualization and the magnitudes of pressure drop and inlet temperature oscillations under boiling conditions demonstrated clearly the merits of using artificial nucleation sites to further stabilize the flow boiling in diverging, parallel microchannels. The stability map showed the plane of subcooling number versus phase change number. It illustrated that diverging, parallel microchannels with artificial nucleation cavities have a much wider stable region than parallel microchannels with uniform cross-sections or diverging, parallel microchannels without artificial nucleation cavities. In addition, the results revealed that the design with cavities distributed uniformly along the downstream half of the channel presented the best stability performance among the three distributions of nucleation sites. This particular design can be regarded as a highly stable microchannel heat sink for convective boiling
Dynamical role of Ekman pumping in rapidly rotating convection
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.
Optimization of fin geometry in heat convection with entransy theory
International Nuclear Information System (INIS)
Cheng Xue-Tao; Xu Xiang-Hua; Liang Xin-Gang; Zhang Qin-Zhao
2013-01-01
The entransy theory developed in recent years is used to optimize the aspect ratio of a plate fin in heat convection. Based on a two-dimensional model, the theoretical analysis shows that the minimum thermal resistance defined with the concept of entransy dissipation corresponds to the maximum heat transfer rate when the temperature of the heating surface is fixed. On the other hand, when the heat flux of the heating surface is fixed, the minimum thermal resistance corresponds to the minimum average temperature of the heating surface. The entropy optimization is also given for the heat transfer processes. It is observed that the minimum entropy generation, the minimum entropy generation number, and the minimum revised entropy generation number do not always correspond to the best heat transfer performance. In addition, the influence factors on the optimized aspect ratio of the plate fin are also discussed. The optimized ratio decreases with the enhancement of heat convection, while it increases with fin thermal conductivity increasing. (general)
Numerical simulation of natural convection in annuli with internal fins
International Nuclear Information System (INIS)
Ha, Man Yeong; Kim, Joo Goo
2004-01-01
The solution for the natural convection in internally finned horizontal annuli is obtained by using a numerical simulation of time-dependent and two-dimensional governing equations. The fins existing in annuli influence the flow pattern, temperature distribution and heat transfer rate. The variations of the fin configuration suppress or accelerate the free convective effects compared to those of the smooth tubes. The effects of fin configuration, number of fins and ratio of annulus gap width to the inner cylinder radius on the fluid flow and heat transfer in annuli are demonstrated by the distribution of the velocity vector, isotherms and streamlines. The governing equations are solved efficiently by using a parallel implementation. The technique is adopted for reduction of the computation cost. The parallelization is performed with the domain decomposition technique and message passing between sub-domains on the basis of the MPI library. The results from parallel computation reveal in consistency with those of the sequential program. Moreover, the speed-up ratio shows linearity with the number of processor
Convection index as a tool for trend analysis of intense summer storms in Switzerland
Gaal, Ladislav; Molnar, Peter; Szolgay, Jan
2013-04-01
Convective summer thunderstorms are generally responsible for the most devastating floods in urban and small natural catchments. In this study we focus on the identification of the nature and magnitude of changes in the properties of intense summer storms of convective character in Switzerland in the last three decades. The study is based on precipitation records from the SwissMetNet (MeteoSwiss) network at 63 stations that cover altitudes ranging from 200 up to 3300 m a.s.l. over the period 1981-2012 (32 years). Additionally, the same stations also measure the number of lightning strikes within a range of 30 km from each station. In an accompanying contribution we describe the method how intensive summer storms can be reliably selected out of all storms in long and high resolution precipitation time series. On the basis of the statistical distributions and dependence among key storm characteristics at the event scale (total rainfall depth R, storm duration D, and peak intensity I) and using high resolution lightning data as a surrogate we defined a threshold intensity I* that differentiates between the events accompanied with lightning with an acceptably small probability of misclassification. This allowed us to identify intense summer events with convective character as those where I > I* regardless of their duration or total rainfall depth. The current study makes use of the threshold intensity I* for the definition of a seasonal convection index at each station (Llasat, 2001). This index gives us a measure of 'convectiveness', i.e. the total precipitation depth coming from convective storms relative to the total precipitation depth of all summer storms. We computed the convection index at all 63 stations and analyzed the series for trends. We found that the seasonal convection index increases at most of the stations in Switzerland and in approximately 20% of the cases this increase is statistically significant. This is likely a consequence of the fact that the
International Nuclear Information System (INIS)
Vieira, Camila Braga; Jian Su
2010-01-01
Natural convection is a physical phenomenon that has been investigated in nuclear engineering so as to provide information about heat transfer in severe accident conditions involving nuclear reactors. This research reported transient natural convection of fluids with uniformly distributed volumetrically heat generation in square cavity with isothermal side walls and adiabatic top/bottom walls. Two Prandtl numbers were considered, 0:0321 and 0:71. Direct numerical simulations were applied in order to obtain results about the velocities of the fluid in directions x and y. These results were used in Fast Fourier Transform, which showed the periodic, quasi-chaotic and chaotic behavior of transient laminar flow. (author)
The effect of thermal conductance of vertical walls on natural convection in a rectangular enclosure
International Nuclear Information System (INIS)
Kikuchi, Y.; Yoshino, A.; Taii, K.
2004-01-01
This paper deals with the experimental results of natural convective heat transfer in a rectangular water layer bounded by vertical walls of different thermal conductance. The vertical walls were made of copper or stainless steel. A minimum was observed in the horizontal distribution of temperature near the heating wall since a secondary reverse flow occurred outside the boundary layer. For copper case the experimental results of Nusselt number agreed well with calculations under an isothermal wall condition. For stainless steel case, however, the measured values were lower than the calculations since a three-dimensional effect appeared in convection due to non-uniformity in wall temperature. (author)
El-Amin, Mohamed; Ebrahiem, N.A.; Salama, Amgad; Sun, S.
2011-01-01
The interaction of mixed convection with thermal radiation of an optical dense viscous fluid adjacent to an isothermal cone imbedded in a porous medium with Rosseland diffusion approximation incorporating the variation of permeability and thermal conductivity is numerically investigated. The transformed conservation laws are solved numerically for the case of variable surface temperature conditions. Numerical results are given for the dimensionless temperature profiles and the local Nusselt number for various values of the mixed convection parameter , the cone angle parameter ?, the radiation-conduction parameter R d, and the surface temperature parameter H. Copyright 2011 M. F. El-Amin et al.
Double-diffusive natural convection in an enclosure filled with nanofluid using ISPH method
Directory of Open Access Journals (Sweden)
Abdelraheem M. Aly
2016-12-01
Full Text Available The double-diffusive natural convection in an enclosure filled with nanofluid is studied using ISPH method. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. In addition the thermal energy equations include regular diffusion and cross-diffusion terms. In ISPH algorithm, a semi implicit velocity correction procedure is utilized and the pressure is implicitly evaluated by solving pressure Poisson equation. The results are presented with flow configurations, isotherms, concentration and nanoparticle volume fraction contours and average Nusselt and Sherwood numbers for different cases. The results from this investigation are well validated and have favorable comparisons with previously published results. It is found that, among all cases, a good natural convection can be obtained by considering the double diffusive case. An increase in Soret number accompanied by a decrease in Dufour number results in an increase in average Nusselt number and a decrease in average Sherwood number.
Number names and number understanding
DEFF Research Database (Denmark)
Ejersbo, Lisser Rye; Misfeldt, Morten
2014-01-01
This paper concerns the results from the first year of a three-year research project involving the relationship between Danish number names and their corresponding digits in the canonical base 10 system. The project aims to develop a system to help the students’ understanding of the base 10 syste...... the Danish number names are more complicated than in other languages. Keywords: A research project in grade 0 and 1th in a Danish school, Base-10 system, two-digit number names, semiotic, cognitive perspectives....
High Ra, high Pr convection with viscosity gradients
Indian Academy of Sciences (India)
First page Back Continue Last page Overview Graphics. High Ra, high Pr convection with viscosity gradients. Weak upward flow through mesh. Top fluid more viscous. Unstable layer Instability Convection.
Stretched flow of Carreau nanofluid with convective boundary ...
Indian Academy of Sciences (India)
journal of. January 2016 physics pp. 3–17. Stretched flow of Carreau nanofluid with ... fluid over a flat plate subjected to convective surface condition. ... the steady laminar boundary layer flow over a permeable plate with a convective boundary.
Energy Technology Data Exchange (ETDEWEB)
Fernandes, Dolfred Vijay; Lee, Heon Deok; Alapati, Suresh; Suh, Yong Kweon [Dong A Univ., Busan (Korea, Republic of)
2012-12-15
We conducted a numerical study on the onset of electro-convection as well as the complex flow phenomena of dielectric liquid subjected to unipolar autonomous charge injection in the annular gap between two concentric circular cylindrical electrodes. The Nernst Planck equations governing the charge density transport, the Poisson equation for the electric potential and the Navier Stokes equations for the fluid flow are solved numerically using the finite volume method. The developed code is validated by comparing the critical stability parameter values for the onset of electro convection with those obtained from the linear stability analysis. We identify in a parameter space the stable hydrostatic state and the electro convection state. The electro convection is again divided into three regimes: stationary, oscillatory and chaotic. For inner cylinder radius 1.0, i r {>=} we observed an increase in the number of charged plumes and vortex pairs with stability parameter T before the electro convection becomes chaotic. For outer injection, although the onset of electroconvection starts at T higher than the inner injection, the onset of chaotic motion occurs at lower T.
Specialists' meeting on evaluation of decay heat removal by natural convection
Energy Technology Data Exchange (ETDEWEB)
NONE
1993-02-01
Decay heat removal by natural convection (DHRNC) is essential to enhancing the safety of liquid metal fast reactors (LMFRs). Various design concepts related to DHRNC have been proposed and experimental and analytical studies have been carried out in a number of countries. The purpose of this Specialists' Meeting on 'Decay Heat Removal by Natural Convection' organized by the International Working Group on Fast Reactors IAEA, is to exchange information about the state of the art related to methodologies on evaluation of DHRNC features (experimental studies and code developments) and to discuss problems which need to be solved in order to evaluate DHRNC properly and reasonably. The following main topical areas were discussed by delegates: Overview; Experimental studies and code validation; Design study. Two main DHR systems for LMFR are under consideration: (i) direct reactor auxiliary cooling system (DRACS) with immersed DFIX in main vessel, intermediate sodium loop and sodium-air heat exchanger; and (ii) auxiliary cooling system which removes heat from the outside surface of the reactor vessel by natural convection of air (RVACS). The practicality and economic viability of the use of RVACS is possible up to a modular type reactor or a middle size reactor based on current technology. For the large monolithic plant concepts DRACS is preferable. The existing experimental results and the codes show encouraging results so that the decay heat removal by pure natural convection is feasible. Concerning the objective, 'passive safety', the DHR by pure natural convection is essential feature to enhance the reliability of DHR.
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.
Specialists' meeting on evaluation of decay heat removal by natural convection
International Nuclear Information System (INIS)
1993-02-01
Decay heat removal by natural convection (DHRNC) is essential to enhancing the safety of liquid metal fast reactors (LMFRs). Various design concepts related to DHRNC have been proposed and experimental and analytical studies have been carried out in a number of countries. The purpose of this Specialists' Meeting on 'Decay Heat Removal by Natural Convection' organized by the International Working Group on Fast Reactors IAEA, is to exchange information about the state of the art related to methodologies on evaluation of DHRNC features (experimental studies and code developments) and to discuss problems which need to be solved in order to evaluate DHRNC properly and reasonably. The following main topical areas were discussed by delegates: Overview; Experimental studies and code validation; Design study. Two main DHR systems for LMFR are under consideration: (i) direct reactor auxiliary cooling system (DRACS) with immersed DFIX in main vessel, intermediate sodium loop and sodium-air heat exchanger; and (ii) auxiliary cooling system which removes heat from the outside surface of the reactor vessel by natural convection of air (RVACS). The practicality and economic viability of the use of RVACS is possible up to a modular type reactor or a middle size reactor based on current technology. For the large monolithic plant concepts DRACS is preferable. The existing experimental results and the codes show encouraging results so that the decay heat removal by pure natural convection is feasible. Concerning the objective, 'passive safety', the DHR by pure natural convection is essential feature to enhance the reliability of DHR
Active Control of Thermal Convection in a Rectangular Loop by Changing its Spatial Orientation
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.
Determination of drying kinetics and convective heat transfer coefficients of ginger slices
Akpinar, Ebru Kavak; Toraman, Seda
2016-10-01
In the present work, the effects of some parametric values on convective heat transfer coefficients and the thin layer drying process of ginger slices were investigated. Drying was done in the laboratory by using cyclone type convective dryer. The drying air temperature was varied as 40, 50, 60 and 70 °C and the air velocity is 0.8, 1.5 and 3 m/s. All drying experiments had only falling rate period. The drying data were fitted to the twelve mathematical models and performance of these models was investigated by comparing the determination of coefficient ( R 2), reduced Chi-square ( χ 2) and root mean square error between the observed and predicted moisture ratios. The effective moisture diffusivity and activation energy were calculated using an infinite series solution of Fick's diffusion equation. The average effective moisture diffusivity values and activation energy values varied from 2.807 × 10-10 to 6.977 × 10-10 m2/s and 19.313-22.722 kJ/mol over the drying air temperature and velocity range, respectively. Experimental data was used to evaluate the values of constants in Nusselt number expression by using linear regression analysis and consequently, convective heat transfer coefficients were determined in forced convection mode. Convective heat transfer coefficient of ginger slices showed changes in ranges 0.33-2.11 W/m2 °C.
Directory of Open Access Journals (Sweden)
Theodore M. Porter
2012-12-01
Full Text Available The struggle over cure rate measures in nineteenth-century asylums provides an exemplary instance of how, when used for official assessments of institutions, these numbers become sites of contestation. The evasion of goals and corruption of measures tends to make these numbers “funny” in the sense of becoming dis-honest, while the mismatch between boring, technical appearances and cunning backstage manipulations supplies dark humor. The dangers are evident in recent efforts to decentralize the functions of governments and corporations using incen-tives based on quantified targets.
Murty, M Ram
2014-01-01
This book provides an introduction to the topic of transcendental numbers for upper-level undergraduate and graduate students. The text is constructed to support a full course on the subject, including descriptions of both relevant theorems and their applications. While the first part of the book focuses on introducing key concepts, the second part presents more complex material, including applications of Baker’s theorem, Schanuel’s conjecture, and Schneider’s theorem. These later chapters may be of interest to researchers interested in examining the relationship between transcendence and L-functions. Readers of this text should possess basic knowledge of complex analysis and elementary algebraic number theory.
Mixed convection in a lid-driven square cavity with partial slip
International Nuclear Information System (INIS)
Ismael, Muneer A.; Pop, Ioan; Chamkha, Ali J.
2014-01-01
Steady laminar mixed convection inside a lid-driven square cavity filled with water is studied numerically. The lid is due to the movement of the isothermal top and bottom walls which are maintained at T c and T h , respectively, with T h is higher than T c . A partial slip condition was imposed in these two moving walls. The vertical walls of the cavity are kept adiabatic. The appliance of the numerical analysis was USR finite difference method with upwind scheme treatments of the convective terms included in the momentum and energy equations. The studied relevant parameters were: the partial slip parameter S (0-∞); Richardson number Ri (0.01-100) and the direction of the moving walls (λ t = 1, λ b = ±1). The results have showed that there are critical values for the partial slip parameter at which the convection is declined. (authors)
Combined Lorentz force and ultrasound Doppler velocimetry in a vertical convection liquid metal flow
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.
Directory of Open Access Journals (Sweden)
Shestakov Igor A.
2015-01-01
Full Text Available The article shows the results of mathematical modeling of convective heat transfer in the low-temperature storage of liquefied natural gas. Regime of natural convection in an enclosure with different intensity of the heat flux at the external borders are investigated. Was examined two-dimensional nonstationary problem within the model of Navier-Stokes in dimensionless variables “vorticity - stream function - temperature”. Distributions of hydrodynamic parameters and temperatures that characterize the basic regularities of the processes are obtained. Circulating flows are determined and carried out the analysis of vortices formation mechanism and the temperature distribution in solution at conditions of natural convection when the Grashof number (Gr = 106. A significant influence of heat transfer rate on solutions boundary on flow structure and temperature field in LNG storage tanks.
Pattern selection in single-component systems coupling Benard convection and solidification
International Nuclear Information System (INIS)
Davis, S.H.; Mueller, U.; Dietsche, C.
1983-12-01
A horizontal layer is heated from below and cooled from above so that the enclosed single-component liquid is frozen in the upper part of the layer. When the imposed temperature difference is such that the Rayleigh number across the liquid is supercritical, there is Benard convection coupled with the dynamics of the solidification interface. An experiment is presented which shows that the interfacial corrugations that result are two-dimensional when this ''ice'' is thin but hexagonal when the ''ice'' is thick. A weakly-nonlinear convective instability theory is presented which explains this behavior, and isolates the mechanism of the pattern selection. Jump behavior is seen in the liquid-layer thickness at the onset of hexagonal convection. (orig.) [de
Intensive probing of clear air convective fields by radar and instrumented drone aircraft.
Rowland, J. R.
1972-01-01
Clear air convective fields were probed in three summer experiments (1969, 1970, and 1971) on an S-band monopulse tracking radar at Wallops Island, Virginia, and a drone aircraft with a takeoff weight of 5.2 kg, wingspan of 2.5 m, and cruising glide speed of 10.3 m/sec. The drone was flown 23.2 km north of the radar and carried temperature, pressure/altitude, humidity, and vertical and airspeed velocity sensors. Extensive time-space convective field data were obtained by taking a large number of RHI and PPI pictures at short intervals of time. The rapidly changing overall convective field data obtained from the radar could be related to the meteorological information telemetered from the drone at a reasonably low cost by this combined technique.
Combined effects of crucible geometry and Marangoni convection on silicon Czochralski crystal growth
Energy Technology Data Exchange (ETDEWEB)
Mokhtari, F. [Unit of Developpement of Silicon Technologie, Algiers (Algeria); Bouabdallah, A.; Zizi, M. [LTSE Laboratory, University of Science and Technology USTHB., Babezzouar, Algiers (Algeria); Hanchi, S. [UER Mecanique/ E.M.P/ B.P, El Bahri/Alger (Algeria); Alemany, A. [Laboratoire EPM, CNRS, Grenoble (France)
2009-08-15
In order to understand the influence of crucible geometry combined with natural convection and Marangoni convection on melt flow pattern, temperature and pressure fields in silicon Czochralski crystal growth process, a set of numerical simulations was conducted. We carry out calculation enable us to determine temperature, pressure and velocity fields in function of Grashof and Marangoni numbers. The essential results show that the hemispherical geometry of crucible seems to be adapted for the growth of a good quality crystal and the pressure field is strongly affected by natural and Marangoni convection and it is more sensitive than temperature. (copyright 2009 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
Mean-field theory of differential rotation in density stratified turbulent convection
Rogachevskii, I.
2018-04-01
A mean-field theory of differential rotation in a density stratified turbulent convection has been developed. This theory is based on the combined effects of the turbulent heat flux and anisotropy of turbulent convection on the Reynolds stress. A coupled system of dynamical budget equations consisting in the equations for the Reynolds stress, the entropy fluctuations and the turbulent heat flux has been solved. To close the system of these equations, the spectral approach, which is valid for large Reynolds and Péclet numbers, has been applied. The adopted model of the background turbulent convection takes into account an increase of the turbulence anisotropy and a decrease of the turbulent correlation time with the rotation rate. This theory yields the radial profile of the differential rotation which is in agreement with that for the solar differential rotation.
Numerical Simulation of Water/Al2O3 Nanofluid Turbulent Convection
Directory of Open Access Journals (Sweden)
Vincenzo Bianco
2010-01-01
Full Text Available Turbulent forced convection flow of a water-Al2O3 nanofluid in a circular tube subjected to a constant and uniform temperature at the wall is numerically analyzed. The two-phase mixture model is employed to simulate the nanofluid convection, taking into account appropriate thermophysical properties. Particles are assumed spherical with a diameter equal to 38 nm. It is found that convective heat transfer coefficient for nanofluids is greater than that of the base liquid. Heat transfer enhancement is increasing with the particle volume concentration and Reynolds number. Comparisons with correlations present in the literature are accomplished and a very good agreement is found with Pak and Cho (1998. As for the friction factor, it shows a good agreement with the classical correlation used for normal fluid, such as Blasius formula.
Simulation of regimes of convection and plume dynamics by the thermal Lattice Boltzmann Method
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.
CONVECTION HEAT TRANSFER IN A CHANNEL OF DIFFERENT CROSS SECTION FILLED WITH POROUS MEDIA
Directory of Open Access Journals (Sweden)
Ahmed A. Mohammad Saleh
2018-05-01
Full Text Available A forced convection heat transfer in ducts (circular, triangular, rectangular cross sections and (1m length with hydraulic diameter (0.1m filled with porous media (glass spheres 12 mm diameter is investigated experimentally at constant heat flux from the wall (1070W/m² with Reynolds number range of (12461-2500. Comparison was made between three ducts for local temperature distribution and local Nusselt number. The experimental results showed the effect of Reynolds number and cross section on the temperature profile and local Nusselt number,also empirical correlations for average Nusselt number and Peclet number were obtained for three ducts.
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.
Convectively driven decadal zonal accelerations in Earth's fluid core
More, Colin; Dumberry, Mathieu
2018-04-01
Azimuthal accelerations of cylindrical surfaces co-axial with the rotation axis have been inferred to exist in Earth's fluid core on the basis of magnetic field observations and changes in the length-of-day. These accelerations have a typical timescale of decades. However, the physical mechanism causing the accelerations is not well understood. Scaling arguments suggest that the leading order torque averaged over cylindrical surfaces should arise from the Lorentz force. Decadal fluctuations in the magnetic field inside the core, driven by convective flows, could then force decadal changes in the Lorentz torque and generate zonal accelerations. We test this hypothesis by constructing a quasi-geostrophic model of magnetoconvection, with thermally driven flows perturbing a steady, imposed background magnetic field. We show that when the Alfvén number in our model is similar to that in Earth's fluid core, temporal fluctuations in the torque balance are dominated by the Lorentz torque, with the latter generating mean zonal accelerations. Our model reproduces both fast, free Alfvén waves and slow, forced accelerations, with ratios of relative strength and relative timescale similar to those inferred for the Earth's core. The temporal changes in the magnetic field which drive the time-varying Lorentz torque are produced by the underlying convective flows, shearing and advecting the magnetic field on a timescale associated with convective eddies. Our results support the hypothesis that temporal changes in the magnetic field deep inside Earth's fluid core drive the observed decadal zonal accelerations of cylindrical surfaces through the Lorentz torque.
The Midlatitude Continental Convective Clouds Experiment (MC3E)
Energy Technology Data Exchange (ETDEWEB)
Jensen, Mark P.; Petersen, Walt A.; Bansemer, Aaron; Bharadwaj, Nitin; Carey, Larry; Cecil, D. J.; Collis, Scott M.; Del Genio, Anthony D.; Dolan, Brenda A.; Gerlach, J.; Giangrande, Scott; Heymsfield, Andrew J.; Heymsfield, Gerald; Kollias, Pavlos; Lang, T. J.; Nesbitt, Steve W.; Neumann, Andrea; Poellot, M. R.; Rutledge, Steven A.; Schwaller, Mathew R.; Tokay, Ali; Williams, C. R.; Wolff, D. B.; Xie, Shaocheng; Zipser, Edward J.
2016-10-18
The Midlatitude Continental Convective Clouds Experiment (MC3E), a field program jointly led by the U.S. Department of Energy’s Atmospheric Radiation Measurement program and the NASA Global Precipitation Measurement (GPM) Mission, was conducted in south-central Oklahoma during April – May 2011. MC3E science objectives were motivated by the need to improve understanding of midlatitude continental convective cloud system lifecycles, microphysics, and GPM precipitation retrieval algorithms. To achieve these objectives a multi-scale surface- and aircraft-based in situ and remote sensing observing strategy was employed. A variety of cloud and precipitation events were sampled during the MC3E, of which results from three deep convective events are highlighted. Vertical structure, air motions, precipitation drop-size distributions and ice properties were retrieved from multi-wavelength radar, profiler, and aircraft observations for an MCS on 11 May. Aircraft observations for another MCS observed on 20 May were used to test agreement between observed radar reflectivities and those calculated with forward-modeled reflectivity and microwave brightness temperatures using in situ particle size distributions and ice water content. Multi-platform observations of a supercell that occurred on 23 May allowed for an integrated analysis of kinematic and microphysical interactions. A core updraft of 25 ms-1 supported growth of hail and large rain drops. Data collected during the MC3E campaign is being used in a number of current and ongoing research projects and is available through the DOE ARM and NASA data archives.
Indian Academy of Sciences (India)
this is a characteristic difference between finite and infinite sets and created an immensely useful branch of mathematics based on this idea which had a great impact on the whole of mathe- matics. For example, the question of what is a number (finite or infinite) is almost a philosophical one. However Cantor's work turned it ...
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.
Education: DNA replication using microscale natural convection.
Priye, Aashish; Hassan, Yassin A; Ugaz, Victor M
2012-12-07
There is a need for innovative educational experiences that unify and reinforce fundamental principles at the interface between the physical, chemical, and life sciences. These experiences empower and excite students by helping them recognize how interdisciplinary knowledge can be applied to develop new products and technologies that benefit society. Microfluidics offers an incredibly versatile tool to address this need. Here we describe our efforts to create innovative hands-on activities that introduce chemical engineering students to molecular biology by challenging them to harness microscale natural convection phenomena to perform DNA replication via the polymerase chain reaction (PCR). Experimentally, we have constructed convective PCR stations incorporating a simple design for loading and mounting cylindrical microfluidic reactors between independently controlled thermal plates. A portable motion analysis microscope enables flow patterns inside the convective reactors to be directly visualized using fluorescent bead tracers. We have also developed a hands-on computational fluid dynamics (CFD) exercise based on modeling microscale thermal convection to identify optimal geometries for DNA replication. A cognitive assessment reveals that these activities strongly impact student learning in a positive way.
Evolution of Excited Convective Cells in Plasmas
DEFF Research Database (Denmark)
Pécseli, Hans; Juul Rasmussen, Jens; Sugai, H.
1984-01-01
Convective cells are excited externally in a fully ionized magnetized plasma and their space-time evolution is investigated by two-dimensional potential measurements. A positive cell is excited externally by control of the end losses in the 'scrape off' layer of a plasma column produced by surface...
Free convection film flows and heat transfer
Shang, Deyi
2010-01-01
Presents development of systematic studies for hydrodynamics and heat and mass transfer in laminar free convection, accelerating film boiling and condensation of Newtonian fluids, and accelerating film flow of non-Newtonian power-law fluids. This book provides a system of analysis models with a developed velocity component method.
Radiative-convective equilibrium model intercomparison project
Wing, Allison A.; Reed, Kevin A.; Satoh, Masaki; Stevens, Bjorn; Bony, Sandrine; Ohno, Tomoki
2018-03-01
RCEMIP, an intercomparison of multiple types of models configured in radiative-convective equilibrium (RCE), is proposed. RCE is an idealization of the climate system in which there is a balance between radiative cooling of the atmosphere and heating by convection. The scientific objectives of RCEMIP are three-fold. First, clouds and climate sensitivity will be investigated in the RCE setting. This includes determining how cloud fraction changes with warming and the role of self-aggregation of convection in climate sensitivity. Second, RCEMIP will quantify the dependence of the degree of convective aggregation and tropical circulation regimes on temperature. Finally, by providing a common baseline, RCEMIP will allow the robustness of the RCE state across the spectrum of models to be assessed, which is essential for interpreting the results found regarding clouds, climate sensitivity, and aggregation, and more generally, determining which features of tropical climate a RCE framework is useful for. A novel aspect and major advantage of RCEMIP is the accessibility of the RCE framework to a variety of models, including cloud-resolving models, general circulation models, global cloud-resolving models, single-column models, and large-eddy simulation models.
Phenomenology of convection-parameterization closure
Directory of Open Access Journals (Sweden)
J.-I. Yano
2013-04-01
Full Text Available Closure is a problem of defining the convective intensity in a given parameterization. In spite of many years of efforts and progress, it is still considered an overall unresolved problem. The present article reviews this problem from phenomenological perspectives. The physical variables that may contribute in defining the convective intensity are listed, and their statistical significances identified by observational data analyses are reviewed. A possibility is discussed for identifying a correct closure hypothesis by performing a linear stability analysis of tropical convectively coupled waves with various different closure hypotheses. Various individual theoretical issues are considered from various different perspectives. The review also emphasizes that the dominant physical factors controlling convection differ between the tropics and extra-tropics, as well as between oceanic and land areas. Both observational as well as theoretical analyses, often focused on the tropics, do not necessarily lead to conclusions consistent with our operational experiences focused on midlatitudes. Though we emphasize the importance of the interplays between these observational, theoretical and operational perspectives, we also face challenges for establishing a solid research framework that is universally applicable. An energy cycle framework is suggested as such a candidate.
Unstable mixed convective transport in groundwater
International Nuclear Information System (INIS)
Schincariol, R.A.; Schwartz, F.W.
1990-01-01
This study is an experimental investigation of variable density groundwater flow in homogeneous and lenticular porous media. A solution of 500 mg/l Rhodamine WT dye served as the carrier for various concentrations of solute (NaCl) introduced into a two-dimensional flow tank at concentrations ranging from 1000 to 100,000 mg/l. At the scale of the experiments, mass transport depends upon both forced and free convection. In addition, density differences as low as 0.008 g/cm 3 (1000 mg/l NaCl) between a plume of dense water and ambient groundwater in homogeneous medium produces gravitational instabilities at realistic groundwater velocities. These instabilities are manifest by lobe-shaped protuberances that formed first along the bottom edge of the plume and later within the plume. As the density difference increases to 0.0015 g/cm 3 (2000 mg/l NaCl), 0.0037 g/cm 3 (5000 mg/l NaCl) or higher, this unstable mixing due to convective dispersion significantly alters the spreading process, resulting in a large degree of vertical spreading of the plume. In a lenticular medium the combination of convective dispersion and nonuniform flow due to heterogeneities results in relatively large dispersion. Scale considerations indicate that convective dispersion may provide an important component of mixing at the field scale. (Author) (30 refs., 12 figs., 3 tabs.)
Solar Hot Water Heating by Natural Convection.
Noble, Richard D.
1983-01-01
Presents an undergraduate laboratory experiment in which a solar collector is used to heat water for domestic use. The working fluid is moved by natural convection so no pumps are required. Experimental apparatus is simple in design and operation so that data can be collected quickly and easily. (Author/JN)
A 'backward' free-convective boundary layer
Kuiken, H.K.
1981-01-01
In this paper the cooling of a low-heat-resistance sheet that moves downwards is considered. The free-convective velocities are assumed to be much larger than the velocity of the sheet. As a result the motion of the fluid is mainly towards the point where the sheet enters the system and a ‘backward’
Convection in Slab and Spheroidal Geometries
Porter, David H.; Woodward, Paul R.; Jacobs, Michael L.
2000-01-01
Three-dimensional numerical simulations of compressible turbulent thermally driven convection, in both slab and spheroidal geometries, are reviewed and analyzed in terms of velocity spectra and mixing-length theory. The same ideal gas model is used in both geometries, and resulting flows are compared. The piecewise-parabolic method (PPM), with either thermal conductivity or photospheric boundary conditions, is used to solve the fluid equations of motion. Fluid motions in both geometries exhibit a Kolmogorov-like k(sup -5/3) range in their velocity spectra. The longest wavelength modes are energetically dominant in both geometries, typically leading to one convection cell dominating the flow. In spheroidal geometry, a dipolar flow dominates the largest scale convective motions. Downflows are intensely turbulent and up drafts are relatively laminar in both geometries. In slab geometry, correlations between temperature and velocity fluctuations, which lead to the enthalpy flux, are fairly independent of depth. In spheroidal geometry this same correlation increases linearly with radius over the inner 70 percent by radius, in which the local pressure scale heights are a sizable fraction of the radius. The effects from the impenetrable boundary conditions in the slab geometry models are confused with the effects from non-local convection. In spheroidal geometry nonlocal effects, due to coherent plumes, are seen as far as several pressure scale heights from the lower boundary and are clearly distinguishable from boundary effects.
Preserving Symmetry in Convection-Diffusion Schemes
Verstappen, R.W.C.P.; Veldman, A.E.P.; Drikakis, D.; Geurts, B.J.
2002-01-01
We propose to perform turbulent flow simulations in such manner that the difference operators do have the same symmetry properties as the corresponding differential operators. That is, the convective operator is represented by a skew-symmetric difference operator and the diffusive operator is
Theories for convection in stellar atmospheres
International Nuclear Information System (INIS)
Nordlund, Aa.
1976-02-01
A discussion of the fundamental differences between laboratory convection in a stellar atmosphere is presented. The shortcomings of laterally homogeneous model atmospheres are analysed, and the extent to which these shortcoming are avoided in the two-component representation is discussed. Finally a qualitative discussion on the scaling properties of stellar granulation is presented. (Auth.)
Energy Technology Data Exchange (ETDEWEB)
Rauf, A., E-mail: raufamar@ciitsahiwal.edu.pk [Department of Mathematics, Comsats Institute of Information Technology, Sahiwal 57000 (Pakistan); Siddiq, M.K. [Centre for Advanced Studies in Pure and Applied Mathematics, Department of Mathematics, Bahauddin Zakariya University, Multan 63000 (Pakistan); Abbasi, F.M. [Department of Mathematics, Comsats Institute of Information Technology, Islamabad 44000 (Pakistan); Meraj, M.A. [Department of Mathematics, Comsats Institute of Information Technology, Sahiwal 57000 (Pakistan); Ashraf, M. [Centre for Advanced Studies in Pure and Applied Mathematics, Department of Mathematics, Bahauddin Zakariya University, Multan 63000 (Pakistan); Shehzad, S.A. [Department of Mathematics, Comsats Institute of Information Technology, Sahiwal 57000 (Pakistan)
2016-10-15
The present work deals with the steady laminar three-dimensional mixed convective magnetohydrodynamic (MHD) boundary layer flow of Casson nanofluid over a bidirectional stretching surface. A uniform magnetic field is applied normal to the flow direction. Similarity variables are implemented to convert the non-linear partial differential equations into ordinary ones. Convective boundary conditions are utilized at surface of the sheet. A numerical technique of Runge–Kutta–Fehlberg (RFK45) is used to obtain the results of velocity, temperature and concentration fields. The physical dimensionless parameters are discussed through tables and graphs. - Highlights: • Mixed convective boundary layer flow of Casson nanofluid is taken into account. • Impact of magnetic field is examined. • Convective heat and mass conditions are imposed. • Numerical solutions are presented and discussed.
Testing particle filters on convective scale dynamics
Haslehner, Mylene; Craig, George. C.; Janjic, Tijana
2014-05-01
Particle filters have been developed in recent years to deal with highly nonlinear dynamics and non Gaussian error statistics that also characterize data assimilation on convective scales. In this work we explore the use of the efficient particle filter (P.v. Leeuwen, 2011) for convective scale data assimilation application. The method is tested in idealized setting, on two stochastic models. The models were designed to reproduce some of the properties of convection, for example the rapid development and decay of convective clouds. The first model is a simple one-dimensional, discrete state birth-death model of clouds (Craig and Würsch, 2012). For this model, the efficient particle filter that includes nudging the variables shows significant improvement compared to Ensemble Kalman Filter and Sequential Importance Resampling (SIR) particle filter. The success of the combination of nudging and resampling, measured as RMS error with respect to the 'true state', is proportional to the nudging intensity. Significantly, even a very weak nudging intensity brings notable improvement over SIR. The second model is a modified version of a stochastic shallow water model (Würsch and Craig 2013), which contains more realistic dynamical characteristics of convective scale phenomena. Using the efficient particle filter and different combination of observations of the three field variables (wind, water 'height' and rain) allows the particle filter to be evaluated in comparison to a regime where only nudging is used. Sensitivity to the properties of the model error covariance is also considered. Finally, criteria are identified under which the efficient particle filter outperforms nudging alone. References: Craig, G. C. and M. Würsch, 2012: The impact of localization and observation averaging for convective-scale data assimilation in a simple stochastic model. Q. J. R. Meteorol. Soc.,139, 515-523. Van Leeuwen, P. J., 2011: Efficient non-linear data assimilation in geophysical
Entropy Generation in Natural Convection Under an Evanescent Magnetic Field
International Nuclear Information System (INIS)
Magherbi, Mourad; El Jery, Atef; Ben Brahim, Ammar
2009-01-01
We numerically study the effect of an externally-evanescent magnetic field on total entropy generation in conducting and non-reactive fluid enclosed in a square cavity. The horizontal walls of the enclosure are assumed to be insulated while the vertical walls are kept isothermal. A control volume finite element method is used to solve the conservation equations at Prandtl number of 0.71. The values of relaxation time of the magnetic field are chosen, so that the Lorentz force acts only in the transient state of entropy generation in natural convection. The total entropy generation was calculated for fixed value of irreversibility distribution ratio, different relaxation time varying from 0 to 1/5 and Grashof number equal to 10 5
International symposium on transient convective heat transfer: book of abstracts
International Nuclear Information System (INIS)
1996-01-01
The international symposium on convective heat transfer was held on 19-23 August 1996, in Cesme, Izmir, Turkey. The spesialists discussed forced convection, heat exchangers, free convection and multiphase media and phase change at the meeting. Almost 53 papers were presented in the meeting
Natural Convection Heat Transfer in Concentric Horizontal Annuli Containing a Saturated Porous Medi
Directory of Open Access Journals (Sweden)
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.
A model for near-wall dynamics in turbulent Rayleigh Bénard convection
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.
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
Turbulent forced convection of nanofluids downstream an abrupt expansion
Kimouche, Abdelali; Mataoui, Amina
2018-03-01
Turbulent forced convection of Nanofluids through an axisymmetric abrupt expansion is investigated numerically in the present study. The governing equations are solved by ANYS 14.0 CFD code based on the finite volume method by implementing the thermo-physical properties of each nanofluid. All results are analyzed through the evolutions of skin friction coefficient and Nusselt number. For each nanofluid, the effect of both volume fraction and Reynolds number on this type of flow configuration, are examined. An increase on average Nusselt number with the volume fraction and Reynolds number, are highlighted and correlated. Two relationships are proposed. The first one, determines the average Nusselt number versus Reynolds number, volume fraction and the ratio of densities of the solid particles to that of the base fluid ( \\overline{Nu}=f(\\operatorname{Re},φ, ρ_s/ρ_f) ). The second one varies according Reynolds number, volume fraction and the conductivities ratio of solid particle to that of the base fluid ( \\overline{Nu}=f(\\operatorname{Re},φ, k_s/k_f) ).
Uncertainty associated with convective wet removal of entrained aerosols in a global climate model
Directory of Open Access Journals (Sweden)
B. Croft
2012-11-01
Full Text Available The uncertainties associated with the wet removal of aerosols entrained above convective cloud bases are investigated in a global aerosol-climate model (ECHAM5-HAM under a set of limiting assumptions for the wet removal of the entrained aerosols. The limiting assumptions for the wet removal of entrained aerosols are negligible scavenging and vigorous scavenging (either through activation, with size-dependent impaction scavenging, or with the prescribed fractions of the standard model. To facilitate this process-based study, an explicit representation of cloud-droplet-borne and ice-crystal-borne aerosol mass and number, for the purpose of wet removal, is introduced into the ECHAM5-HAM model. This replaces and is compared with the prescribed cloud-droplet-borne and ice-crystal-borne aerosol fraction scavenging scheme of the standard model.
A 20% to 35% uncertainty in simulated global, annual mean aerosol mass burdens and optical depth (AOD is attributed to different assumptions for the wet removal of aerosols entrained above convective cloud bases. Assumptions about the removal of aerosols entrained above convective cloud bases control modeled upper tropospheric aerosol concentrations by as much as one order of magnitude.
Simulated aerosols entrained above convective cloud bases contribute 20% to 50% of modeled global, annual mean aerosol mass convective wet deposition (about 5% to 10% of the total dry and wet deposition, depending on the aerosol species, when including wet scavenging of those entrained aerosols (either by activation, size-dependent impaction, or with the prescribed fraction scheme. Among the simulations, the prescribed fraction and size-dependent impaction schemes yield the largest global, annual mean aerosol mass convective wet deposition (by about two-fold. However, the prescribed fraction scheme has more vigorous convective mixed-phase wet removal (by two to five-fold relative to the size-dependent impaction
Uncertainty associated with convective wet removal of entrained aerosols in a global climate model
Croft, B.; Pierce, J. R.; Martin, R. V.; Hoose, C.; Lohmann, U.
2012-11-01
The uncertainties associated with the wet removal of aerosols entrained above convective cloud bases are investigated in a global aerosol-climate model (ECHAM5-HAM) under a set of limiting assumptions for the wet removal of the entrained aerosols. The limiting assumptions for the wet removal of entrained aerosols are negligible scavenging and vigorous scavenging (either through activation, with size-dependent impaction scavenging, or with the prescribed fractions of the standard model). To facilitate this process-based study, an explicit representation of cloud-droplet-borne and ice-crystal-borne aerosol mass and number, for the purpose of wet removal, is introduced into the ECHAM5-HAM model. This replaces and is compared with the prescribed cloud-droplet-borne and ice-crystal-borne aerosol fraction scavenging scheme of the standard model. A 20% to 35% uncertainty in simulated global, annual mean aerosol mass burdens and optical depth (AOD) is attributed to different assumptions for the wet removal of aerosols entrained above convective cloud bases. Assumptions about the removal of aerosols entrained above convective cloud bases control modeled upper tropospheric aerosol concentrations by as much as one order of magnitude. Simulated aerosols entrained above convective cloud bases contribute 20% to 50% of modeled global, annual mean aerosol mass convective wet deposition (about 5% to 10% of the total dry and wet deposition), depending on the aerosol species, when including wet scavenging of those entrained aerosols (either by activation, size-dependent impaction, or with the prescribed fraction scheme). Among the simulations, the prescribed fraction and size-dependent impaction schemes yield the largest global, annual mean aerosol mass convective wet deposition (by about two-fold). However, the prescribed fraction scheme has more vigorous convective mixed-phase wet removal (by two to five-fold relative to the size-dependent impaction scheme) since nearly all
Is convective precipitation increasing? The case of Catalonia
Llasat, M. C.; Marcos, R.; Turco, M.
2012-04-01
A recent work (Turco and Llasat, 2011) has been performed to analyse the trends of the ETCCDI (Expert Team on Climate Change Detection and Indices) precipitation indices in Catalonia (NE Iberian Peninsula) from 1951 to 2003, calculated from a interpolated dataset of daily precipitation, namely SPAIN02, regular at 0.2° horizontal resolution. This work has showed that no general trends at a regional scale have been observed, considering the annual and the seasonal regional values, and only the consecutive dry days index (CDD) at annual scale shows a locally coherent spatial trend pattern. Simultaneously, Llasat et al (2009, 2010) have showed an important increase of flash-flood events in the same region. Although aspects related with vulnerability, exposure and changes in uses of soil have been found as the main responsible of this increase, a major knowledge on the evolution of high rainfall events is mandatory. Heavy precipitation is usually associated to convective precipitation and therefore the analysis of the latter is a good indicator of it. Particularly, in Catalonia, funding was raised to define a parameter, designated as β, related with the greater or lesser convective character of the precipitation (Llasat, 2001). This parameter estimates the contribution of convective precipitation to total precipitation using 1-min or 5-min rainfall intensities usually estimated by rain gauges and it can be also analysed by means of the meteorological radar (Llasat et al, 2007). Its monthly distribution shows a maximum in August, followed by September, which are the months with the major number of flash-floods in Catalonia. This parameter also allows distinguishing between different kinds of precipitation events taking into account the degree of convective contribution. The main problem is the lack of long rainfall rate series that allow analysing trends in convective precipitation. The second one is related with its heterogeneous spatial and temporal distribution. To
A continuous and prognostic convection scheme based on buoyancy, PCMT
Guérémy, Jean-François; Piriou, Jean-Marcel
2016-04-01
A new and consistent convection scheme (PCMT: Prognostic Condensates Microphysics and Transport), providing a continuous and prognostic treatment of this atmospheric process, is described. The main concept ensuring the consistency of the whole system is the buoyancy, key element of any vertical motion. The buoyancy constitutes the forcing term of the convective vertical velocity, which is then used to define the triggering condition, the mass flux, and the rates of entrainment-detrainment. The buoyancy is also used in its vertically integrated form (CAPE) to determine the closure condition. The continuous treatment of convection, from dry thermals to deep precipitating convection, is achieved with the help of a continuous formulation of the entrainment-detrainment rates (depending on the convective vertical velocity) and of the CAPE relaxation time (depending on the convective over-turning time). The convective tendencies are directly expressed in terms of condensation and transport. Finally, the convective vertical velocity and condensates are fully prognostic, the latter being treated using the same microphysics scheme as for the resolved condensates but considering the convective environment. A Single Column Model (SCM) validation of this scheme is shown, allowing detailed comparisons with observed and explicitly simulated data. Four cases covering the convective spectrum are considered: over ocean, sensitivity to environmental moisture (S. Derbyshire) non precipitating shallow convection to deep precipitating convection, trade wind shallow convection (BOMEX) and strato-cumulus (FIRE), together with an entire continental diurnal cycle of convection (ARM). The emphasis is put on the characteristics of the scheme which enable a continuous treatment of convection. Then, a 3D LAM validation is presented considering an AMMA case with both observations and a CRM simulation using the same initial and lateral conditions as for the parameterized one. Finally, global
Oscillatory convection in low aspect ratio Czochralski melts
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.
The Mechanism of First Raindrops Formation in Deep Convective Clouds
Energy Technology Data Exchange (ETDEWEB)
Khain, Alexander; Prabha, Thara; Benmoshe, Nir; Pandithurai, G.; Ovchinnikov, Mikhail
2013-08-22
The formation of first raindrops in deep convective clouds is investigated. A combination of observational data analysis and 2-D and 3-D numerical bin microphysical simulations of deep convective clouds suggests that the first raindrops form at the top of undiluted or slightly diluted cores. It is shown that droplet size distributions in these regions are wider and contain more large droplets than in diluted volumes. The results of the study indicate that the initial raindrop formation is determined by the basic microphysical processes within ascending adiabatic volumes. It allows one to predict the height of the formation of first raindrops considering the processes of nucleation, diffusion growth and collisions. The results obtained in the study explain observational results reported by Freud and Rosenfeld (2012) according to which the height of first raindrop formation depends linearly on the droplet number concentration at cloud base. The results also explain why a simple adiabatic parcel model can reproduce this dependence. The present study provides a physical basis for retrieval algorithms of cloud microphysical properties and aerosol properties using satellites proposed by Rosenfeld et al. ( 2012). The study indicates that the role of mixing and entrainment in the formation of the first raindrops is not of crucial importance. It is also shown that low variability of effective and mean volume radii along horizontal traverses, as regularly observed by in situ measurements, can be simulated by high-resolution cloud models, in which mixing is parameterized by a traditional 1.5 order turbulence closure scheme.
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.
Numerical study of natural melt convection in cylindrical cavity with hot walls and cold bottom sink
Directory of Open Access Journals (Sweden)
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.
The Fractional Step Method Applied to Simulations of Natural Convective Flows
Westra, Douglas G.; Heinrich, Juan C.; Saxon, Jeff (Technical Monitor)
2002-01-01
This paper describes research done to apply the Fractional Step Method to finite-element simulations of natural convective flows in pure liquids, permeable media, and in a directionally solidified metal alloy casting. The Fractional Step Method has been applied commonly to high Reynold's number flow simulations, but is less common for low Reynold's number flows, such as natural convection in liquids and in permeable media. The Fractional Step Method offers increased speed and reduced memory requirements by allowing non-coupled solution of the pressure and the velocity components. The Fractional Step Method has particular benefits for predicting flows in a directionally solidified alloy, since other methods presently employed are not very efficient. Previously, the most suitable method for predicting flows in a directionally solidified binary alloy was the penalty method. The penalty method requires direct matrix solvers, due to the penalty term. The Fractional Step Method allows iterative solution of the finite element stiffness matrices, thereby allowing more efficient solution of the matrices. The Fractional Step Method also lends itself to parallel processing, since the velocity component stiffness matrices can be built and solved independently of each other. The finite-element simulations of a directionally solidified casting are used to predict macrosegregation in directionally solidified castings. In particular, the finite-element simulations predict the existence of 'channels' within the processing mushy zone and subsequently 'freckles' within the fully processed solid, which are known to result from macrosegregation, or what is often referred to as thermo-solutal convection. These freckles cause material property non-uniformities in directionally solidified castings; therefore many of these castings are scrapped. The phenomenon of natural convection in an alloy under-going directional solidification, or thermo-solutal convection, will be explained. The
International Nuclear Information System (INIS)
Zhang, Xuan; Zikanov, Oleg
2017-01-01
Highlights: • 2D convection flow develops with internal heating and strong axial magnetic field. • Poloidal magnetic field suppresses turbulence at high Hartmann number. • Flow structure is dominated by large-scale counter-rotation vortices. • Effective heat transfer is maintained by surviving convection structures. - Abstract: We explore the effect of poloidal magnetic field on the thermal convection flow in a toroidal duct of a generic liquid metal blanket. Non-uniform strong heating (the Grashof number up to 10 11 ) arising from the interaction of high-speed neutrons with the liquid breeder, and strong magnetic field (the Hartmann number up to 10 4 ) corresponding to the realistic reactor conditions are considered. The study continues our earlier work , where the problem was solved for a purely toroidal magnetic field and the convection was found to result in two-dimensional turbulence and strong mixing within the duct. Here, we find that the poloidal component of the magnetic field suppresses turbulence, reduces the flow's kinetic energy and high-amplitude temperature fluctuations, and, at high values of Hartmann number, leads to a steady-state flow. At the same time, the intense mixing by the surviving convection structures remains able to maintain effective heat transfer between the liquid metal and the walls.
Guervilly, C.; Cardin, P.
2017-12-01
Convection is the main heat transport process in the liquid cores of planets. The convective flows are thought to be turbulent and constrained by rotation (corresponding to high Reynolds numbers Re and low Rossby numbers Ro). Under these conditions, and in the absence of magnetic fields, the convective flows can produce coherent Reynolds stresses that drive persistent large-scale zonal flows. The formation of large-scale flows has crucial implications for the thermal evolution of planets and the generation of large-scale magnetic fields. In this work, we explore this problem with numerical simulations using a quasi-geostrophic approximation to model convective and zonal flows at Re 104 and Ro 10-4 for Prandtl numbers relevant for liquid metals (Pr 0.1). The formation of intense multiple zonal jets strongly affects the convective heat transport, leading to the formation of a mean temperature staircase. We also study the generation of magnetic fields by the quasi-geostrophic flows at low magnetic Prandtl numbers.
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
Behaviors and transitions along the path to magnetostrophic convection
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.
Convective equilibrium and mixing-length theory for stellarator reactors
International Nuclear Information System (INIS)
Ho, D.D.M.; Kulsrud, R.M.
1985-09-01
In high β stellarator and tokamak reactors, the plasma pressure gradient in some regions of the plasma may exceed the critical pressure gradient set by ballooning instabilities. In these regions, convective cells break out to enhance the transport. As a result, the pressure gradient can rise only slightly above the critical gradient and the plasma is in another state of equilibrium - ''convective equilibrium'' - in these regions. Although the convective transport cannot be calculated precisely, it is shown that the density and temperature profiles in the convective region can still be estimated. A simple mixing-length theory, similar to that used for convection in stellar interiors, is introduced in this paper to provide a qualitative description of the convective cells and to show that the convective transport is highly efficient. A numerical example for obtaining the density and temperature profiles in a stellarator reactor is given
Friedson, A. James; Gonzales, Erica J.
2017-11-01
We explore the conditions under which ordinary and double-diffusive thermal convection may be inhibited by water condensation in the hydrogen atmospheres of the ice giants and examine the consequences. The saturation of vapor in the condensation layer induces a vertical gradient in the mean molecular weight that stabilizes the layer against convective instability when the abundance of vapor exceeds a critical value. In this instance, the layer temperature gradient can become superadiabatic and heat must be transported vertically by another mechanism. On Uranus and Neptune, water is inferred to be sufficiently abundant for inhibition of ordinary convection to take place in their respective condensation zones. We find that suppression of double-diffusive convection is sensitive to the ratio of the sedimentation time scale of the condensates to the buoyancy period in the condensation layer. In the limit of rapid sedimentation, the layer is found to be stable to diffusive convection. In the opposite limit, diffusive convection can occur. However, if the fluid remains saturated, then layered convection is generally suppressed and the motion is restricted in form to weak, homogeneous, oscillatory turbulence. This form of diffusive convection is a relatively inefficient mechanism for transporting heat, characterized by low Nusselt numbers. When both ordinary and layered convection are suppressed, the condensation zone acts effectively as a thermal insulator, with the heat flux transported across it only slightly greater than the small value that can be supported by radiative diffusion. This may allow a large superadiabatic temperature gradient to develop in the layer over time. Once the layer has formed, however, it is vulnerable to persistent erosion by entrainment of fluid into the overlying convective envelope of the cooling planet, potentially leading to its collapse. We discuss the implications of our results for thermal evolution models of the ice giants, for
Energy Technology Data Exchange (ETDEWEB)
Khan, Masood; Malik, Rabia, E-mail: rabiamalik.qau@gmail.com; Munir, Asif [Department of Mathematics, Quaid-i-Azam University, Islamabad 44000 (Pakistan)
2015-08-15
In this article, the mixed convective heat transfer to Sisko fluid over a radially stretching surface in the presence of convective boundary conditions is investigated. The viscous dissipation and thermal radiation effects are also taken into account. The suitable transformations are applied to convert the governing partial differential equations into a set of nonlinear coupled ordinary differential equations. The analytical solution of the governing problem is obtained by using the homotopy analysis method (HAM). Additionally, these analytical results are compared with the numerical results obtained by the shooting technique. The obtained results for the velocity and temperature are analyzed graphically for several physical parameters for the assisting and opposing flows. It is found that the effect of buoyancy parameter is more prominent in case of the assisting flow as compared to the opposing flow. Further, in tabular form the numerical values are given for the local skin friction coefficient and local Nusselt number. A remarkable agreement is noticed by comparing the present results with the results reported in the literature as a special case.
International Nuclear Information System (INIS)
Khan, Masood; Malik, Rabia; Munir, Asif
2015-01-01
In this article, the mixed convective heat transfer to Sisko fluid over a radially stretching surface in the presence of convective boundary conditions is investigated. The viscous dissipation and thermal radiation effects are also taken into account. The suitable transformations are applied to convert the governing partial differential equations into a set of nonlinear coupled ordinary differential equations. The analytical solution of the governing problem is obtained by using the homotopy analysis method (HAM). Additionally, these analytical results are compared with the numerical results obtained by the shooting technique. The obtained results for the velocity and temperature are analyzed graphically for several physical parameters for the assisting and opposing flows. It is found that the effect of buoyancy parameter is more prominent in case of the assisting flow as compared to the opposing flow. Further, in tabular form the numerical values are given for the local skin friction coefficient and local Nusselt number. A remarkable agreement is noticed by comparing the present results with the results reported in the literature as a special case
Moisture Vertical Structure, Deep Convective Organization, and Convective Transition in the Amazon
Schiro, K. A.; Neelin, J. D.
2017-12-01
Constraining precipitation processes in climate models with observations is crucial to accurately simulating current climate and reducing uncertainties in future projections. Results from the Green Ocean Amazon (GOAmazon) field campaign (2014-2015) provide evidence that deep convection is strongly controlled by the availability of moisture in the free troposphere over the Amazon, much like over tropical oceans. Entraining plume buoyancy calculations confirm that CWV is a good proxy for the conditional instability of the environment, yet differences in convective onset as a function of CWV exist over land and ocean, as well as seasonally and diurnally over land. This is largely due to variability in the contribution of lower tropospheric humidity to the total column moisture. Boundary layer moisture shows a strong relationship to the onset during the day, which largely disappears during nighttime. Using S-Band radar, these transition statistics are examined separately for unorganized and mesoscale-organized convection, which exhibit sharp increases in probability of occurrence with increasing moisture throughout the column, particularly in the lower free troposphere. Retrievals of vertical velocity from a radar wind profiler indicate updraft velocity and mass flux increasing with height through the lower troposphere. A deep-inflow mixing scheme motivated by this — corresponding to deep inflow of environmental air into a plume that grows with height — provides a weighting of boundary layer and free tropospheric air that yields buoyancies consistent with the observed onset of deep convection across seasons and times of day, across land and ocean sites, and for all convection types. This provides a substantial improvement relative to more traditional constant mixing assumptions, and a dramatic improvement relative to no mixing. Furthermore, it provides relationships that are as strong or stronger for mesoscale-organized convection as for unorganized convection.
Freche, John C; Schum, Eugene F
1951-01-01
Blade-to-coolant convective heat-transfer coefficients were obtained on a forced-convection water-cooled single-stage turbine over a large laminar flow range and over a portion of the transition range between laminar and turbulent flow. The convective coefficients were correlated by the general relation for forced-convection heat transfer with laminar flow. Natural-convection heat transfer was negligible for this turbine over the Grashof number range investigated. Comparison of turbine data with stationary tube data for the laminar flow of heated liquids showed good agreement. Calculated average midspan blade temperatures using theoretical gas-to-blade coefficients and blade-to-coolant coefficients from stationary-tube data resulted in close agreement with experimental data.
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.
Activity-related characteristics of the convective envelopes in evolving low-mass stars
International Nuclear Information System (INIS)
Rucinski, S.M.; Vandenberg, D.A.; Victoria Univ., Canada)
1986-01-01
Convective envelope structures have been computed for the post-main-sequence evolutionary phases of 0.7-1.6 solar mass model stars having initial mass-fraction abundances of helium and heavier elements equal to Y = 0.25 and Z = 0.0169 (solar), respectively. Two types of quantities as a function of the basic stellar parameters have been studied. The first of these is relevant to the theory of stellar dynamos and includes estimates of the convective turnover time, various dynamo number parameters, and the maximum nonthermal energy which is available for the dynamo action. The other is related to the expected sizes of inhomogeneities on the stellar surfaces and comprises the determination of the depth of the convective zone, the pressure scale height at the outer edge of the convective region, and the thicknesses of the shells where the superadiabatic gradient is large and where the opacity is within 10 percent of its maximum. All of the above properties, which are fully discussed, are extensively tabulated and their variations as a function of evolutionary state are conveniently displayed in a number of contour plots to facilitate comparisons with observations. 29 references
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
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.
Planform structure and heat transfer in turbulent free convection over horizontal surfaces
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.
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
The amplitude of the deep solar convection and the origin of the solar supergranulation
Rast, Mark
2017-11-01
Recent observations and models have raised questions about our understanding of the dynamics of the deep solar convection. In particular, the amplitude of low wavenumber convective motions appears to be too high in both local area radiative magnetohydrodynamic and global spherical shell magnetohydrodynamic simulations. In global simulations this results in weaker than needed rotational constraints and consequent non solar-like differential rotation profiles. In deep local area simulations it yields strong horizontal flows in the photosphere on scales much larger than the observed supergranulation. We have undertaken numerical studies that suggest that solution to this problem is closely related to the long standing question of the origin of the solar supergranulation. Two possibilities have emerged. One suggests that small scale photospherically driven motions dominate convecive transport even at depth, descending through a very nearly adiabatic interior (more more nearly adiabatic than current convection models achieve). Convection of this form can meet Rossby number constraints set by global scale motions and implies that the solar supergranulation is the largest buoyantly driven scale of motion in the Sun. The other possibility is that large scale convection driven deeep in the Sun dynamically couples to the near surface shear layer, perhaps as its origin. In this case supergranulation would be the largest non-coupled convective mode, or only weakly coupled and thus potentially explaining the observed excess power in the prograde direction. Recent helioseismic results lend some support to this. We examind both of these possibilities using carefully designed numerical experiments, and weigh thier plausibilities in light of recent observations.
Mixed convection around calandria tubes in a ¼ scale CANDU-6 moderator circulation tank
Energy Technology Data Exchange (ETDEWEB)
Atkins, M.D.; Rossouw, D.J.; Boer, M. [Nuclear Science Division, School of Mechanical and Aeronautical Engineering, University of the Witwatersrand, Johannesburg (South Africa); Kim, T., E-mail: tong.kim@wits.ac.za [Nuclear Science Division, School of Mechanical and Aeronautical Engineering, University of the Witwatersrand, Johannesburg (South Africa); Rhee, B.W.; Kim, H.T. [Severe Accident and PHWR Safety Research Division, Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2017-05-15
Highlights: • A secondary jet is formed at a stagnation region and is directed towards the center of the MCT. • The secondary jet undergoes the significant dissipation and mixing due to calandria tubes (CTs). • Its cooling effectiveness is reduced on the CTs in the bottom of the MCT. • With forced convection dominance, peak heat transfer is on the upper CT surface. • With natural convection dominance, peak heat transfer is on the lower CT surface. - Abstract: This study experimentally characterizes mixed convection around calandria tubes (CTs) in a ¼ scale CANDU-6 moderator circulation tank (MCT) that uses air as the working fluid. In a full scale CANDU-6 reactor that undergoes a postulated dual failure with a loss-of-coolant accident without the emergency core cooling system available, mixed convection heat transfer occurs around the CTs. The cooling effectiveness of the moderator is diminished as an emergency heat sink if overheating eventually leads to film boiling. To prevent the onset of film boiling, local sub-cooling margins of the moderator needs to be maintained or else the critical heat flux should be increased. Circulating the moderator which interacts with the overheated CTs increases the heat transfer into the moderator which may suppress film boiling. The present experimental results demonstrate that the cooling effectiveness of the circulating moderator, in particular the secondary jet, is attenuated substantially as it is convected away from the inner wall towards the center of the MCT. The momentum of the secondary jet is diffused through the CTs. At a low jet Reynolds number, the secondary jet becomes ineffective so that some overheated CTs positioned in the other half of the MCT are cooled only by natural convection.
Research of heat transfer of staggered horizontal bundles of finned tubes at free air convection
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.
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
Mamgain, Ashu; Rajagopal, E. N.; Mitra, A. K.; Webster, S.
2018-03-01
There are increasing efforts towards the prediction of high-impact weather systems and understanding of related dynamical and physical processes. High-resolution numerical model simulations can be used directly to model the impact at fine-scale details. Improvement in forecast accuracy can help in disaster management planning and execution. National Centre for Medium Range Weather Forecasting (NCMRWF) has implemented high-resolution regional unified modeling system with explicit convection embedded within coarser resolution global model with parameterized convection. The models configurations are based on UK Met Office unified seamless modeling system. Recent land use/land cover data (2012-2013) obtained from Indian Space Research Organisation (ISRO) are also used in model simulations. Results based on short-range forecast of both the global and regional models over India for a month indicate that convection-permitting simulations by the high-resolution regional model is able to reduce the dry bias over southern parts of West Coast and monsoon trough zone with more intense rainfall mainly towards northern parts of monsoon trough zone. Regional model with explicit convection has significantly improved the phase of the diurnal cycle of rainfall as compared to the global model. Results from two monsoon depression cases during study period show substantial improvement in details of rainfall pattern. Many categories in rainfall defined for operational forecast purposes by Indian forecasters are also well represented in case of convection-permitting high-resolution simulations. For the statistics of number of days within a range of rain categories between `No-Rain' and `Heavy Rain', the regional model is outperforming the global model in all the ranges. In the very heavy and extremely heavy categories, the regional simulations show overestimation of rainfall days. Global model with parameterized convection have tendency to overestimate the light rainfall days and
Thermal Rayleigh-Marangoni convection in a three-layer liquid-metal-battery model
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.
Coupling of convection and circulation at various resolutions
Directory of Open Access Journals (Sweden)
Cathy Hohenegger
2015-03-01
Full Text Available A correct representation of the coupling between convection and circulation constitutes a prerequisite for a correct representation of precipitation at all scales. In this study, the coupling between convection and a sea breeze is investigated across three main resolutions: large-eddy resolution where convection is fully explicit, convection-permitting resolution where convection is partly explicit and coarse resolution where convection is parameterised. The considered models are the UCLA-LES, COSMO and ICON. Despite the use of prescribed surface fluxes, comparison of the simulations reveals that typical biases associated with a misrepresentation of convection at convection-permitting and coarser resolutions significantly alter the characteristics of the sea breeze. The coarse-resolution simulations integrated without convective parameterisation and the convection-permitting simulations simulate a too slow propagation of the breeze front as compared to the large-eddy simulations. From the various factors affecting the propagation, a delayed onset and intensification of cold pools primarily explains the differences. This is a direct consequence of a delayed development of convection when the grid spacing is coarsened. Scaling the time the sea breeze reaches the centre of the land patch by the time precipitation exceeds 2 mm day−1, used as a measure for significant evaporation, yields a collapse of the simulations onto a simple linear relationship although subtle differences remain due to the use of different turbulence and microphysical schemes. Turning on the convection scheme significantly disrupts the propagation of the sea breeze due to a misrepresented timing (too early triggering and magnitude (too strong precipitation evaporation in one of the tested convection schemes of the convective processes.
Natural convection in heat-generating fluids
International Nuclear Information System (INIS)
Bol'shov, Leonid A; Kondratenko, Petr S; Strizhov, Valerii F
2001-01-01
Experimental and theoretical studies of convective heat transfer from a heat-generating fluid confined to a closed volume are reviewed. Theoretical results are inferred from analytical estimates based on the relevant conservation laws and the current understanding of the convective heat-transfer processes. Four basic and one asymptotic regime of heat transfer are identified depending on the heat generation rate. Limiting heat-transfer distribution patterns are found for the lower boundary. Heat transfer in a quasi-two-dimensional geometry is analyzed. Quasi-steady-state heat transfer from a cooling-down fluid without internal heat sources is studied separately. Experimental results and theoretical predictions are compared. (reviews of topical problems)
Topology optimisation of natural convection problems
DEFF Research Database (Denmark)
Alexandersen, Joe; Aage, Niels; Andreasen, Casper Schousboe
2014-01-01
This paper demonstrates the application of the density-based topology optimisation approach for the design of heat sinks and micropumps based on natural convection effects. The problems are modelled under the assumptions of steady-state laminar flow using the incompressible Navier-Stokes equations...... coupled to the convection-diffusion equation through the Boussinesq approximation. In order to facilitate topology optimisation, the Brinkman approach is taken to penalise velocities inside the solid domain and the effective thermal conductivity is interpolated in order to accommodate differences...... in thermal conductivity of the solid and fluid phases. The governing equations are discretised using stabilised finite elements and topology optimisation is performed for two different problems using discrete adjoint sensitivity analysis. The study shows that topology optimisation is a viable approach...
Convective instabilities in SN 1987A
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.
Natural convection heat transfer in SIGMA experiment
International Nuclear Information System (INIS)
Lee, Seung Dong; Lee, Gang Hee; Suh, Kune Yull
2004-01-01
A loss-of-coolant accident (LOCA) results in core melt formation and relocation at various locations within the reactor core over a considerable period of time. If there is no effective cooling mechanism, the core debris may heat up and commence natural circulation. The high temperature pool of molten core material will threaten the structural integrity of the reactor vessel. The extent and urgency of this threat depend primarily upon the intensity of the internal heat sources and upon the consequent distribution of the heat fluxes on the vessel walls in contact with the molten core material pools. In such a steady molten pool convection state, the thermal loads against the vessel would be determined by the in-vessel heat transfer distribution involving convective and conductive heat transfer from the decay-heated core material pool to the lower head wall in contact with the core material. In this study, upward and downward heat transfer fraction ratio is focused on
MHD natural convection in open inclined square cavity with a heated circular cylinder
Hosain, Sheikh Anwar; Alim, M. A.; Saha, Satrajit Kumar
2017-06-01
MHD natural convection in open cavity becomes very important in many scientific and engineering problems, because of it's application in the design of electronic devices, solar thermal receivers, uncovered flat plate solar collectors having rows of vertical strips, geothermal reservoirs, etc. Several experiments and numerical investigations have been presented for describing the phenomenon of natural convection in open cavity for two decades. MHD natural convection and fluid flow in a two-dimensional open inclined square cavity with a heated circular cylinder was considered. The opposite wall to the opening side of the cavity was first kept to constant heat flux q, at the same time the surrounding fluid interacting with the aperture was maintained to an ambient temperature T∞. The top and bottom wall was kept to low and high temperature respectively. The fluid with different Prandtl numbers. The properties of the fluid are assumed to be constant. As a result a buoyancy force is created inside the cavity due to temperature difference and natural convection is formed inside the cavity. The Computational Fluid Dynamics (CFD) code are used to discretize the solution domain and represent the numerical result to graphical form.. Triangular meshes are used to obtain the solution of the problem. The streamlines and isotherms are produced, heat transfer parameter Nu are obtained. The results are presented in graphical as well as tabular form. The results show that heat flux decreases for increasing inclination of the cavity and the heat flux is a increasing function of Prandtl number Pr and decreasing function of Hartmann number Ha. It is observed that fluid moves counterclockwise around the cylinder in the cavity. Various recirculations are formed around the cylinder. The almost all isotherm lines are concentrated at the right lower corner of the cavity. The object of this work is to develop a Mathematical model regarding the effect of MHD natural convection flow around
Convection and crystal settling in sills
Gibb, Fergus G. F.; Henderson, C. Michael B.
1992-02-01
It has been advocated that convective and crystal settling processes play significant, and perhaps crucial, roles in magmatic differentiation. The fluid dynamics of magma chambers have been extensively studied in recent years, both theoretically and experimentally, but there is disagreement over the nature and scale of the convection, over its bearing on fractionation and possibly over whether it occurs at all. The differential distribution of modal olivine with height in differentiated alkaline basic sills provides critical evidence to resolve this controversy, at least for small to medium-large magma chambers. Our own and others' published data for such sills show that, irrespective of overall olivine content, modal olivine contents tend to increase in a roughly symmetrical manner inwards from the upper and lower margins of the sill, i.e. the distribution patterns are more often approximately D-shaped rather than the classic S-shape generally ascribed to gravity settling. We concur with the majority of other authors that this is an original feature of the filling process which has survived more or less unchanged since emplacement. We therefore conclude that the magmas have not undergone turbulent convection and that gravity settling has usually played only a minor modifying role since the intrusion of these sills. We offer a possible explanation for the apparent contradiction between fluid dynamical theory and the petrological evidence by suggesting that such sills rarely fill by the rapid injection of a single pulse of magma. Rather, they form from a series of pulses or a continuous pulsed influx over a protracted interval during which marginal cooling severely limits the potential for thermal convection.
Nonlinear Convective Models of RR Lyrae Stars
Feuchtinger, M.; Dorfi, E. A.
The nonlinear behavior of RR Lyrae pulsations is investigated using a state-of-the-art numerical technique solving the full time-dependent system of radiation hydrodynamics. Grey radiative transfer is included by a variable Eddington-factor method and we use the time-dependent turbulent convection model according to Kuhfuss (1986, A&A 160, 116) in the version of Wuchterl (1995, Comp. Phys. Comm. 89, 19). OPAL opacities extended by the Alexander molecule opacities at temperatures below 6000 K and an equation of state according to Wuchterl (1990, A&A 238, 83) close the system. The resulting nonlinear system is discretized on an adaptive mesh developed by Dorfi & Drury (1987, J. Comp. Phys. 69, 175), which is important to provide the necessary spatial resolution in critical regions like ionization zones and shock waves. Additionally, we employ a second order advection scheme, a time centered temporal discretizaton and an artificial tensor viscosity in order to treat discontinuities. We compute fundamental as well first overtone models of RR Lyrae stars for a grid of stellar parameters both with and without convective energy transport in order to give a detailed picture of the pulsation-convection interaction. In order to investigate the influence of the different features of the convection model calculations with and without overshooting, turbulent pressure and turbulent viscosity are performed and compared with each other. A standard Fourier decomposition is used to confront the resulting light and radial velocity variations with recent observations and we show that the well known RR Lyrae phase discrepancy problem (Simon 1985, ApJ 299, 723) can be resolved with these stellar pulsation computations.
Natural convective heat transfer from square cylinder
Energy Technology Data Exchange (ETDEWEB)
Novomestský, Marcel, E-mail: marcel.novomestsky@fstroj.uniza.sk; Smatanová, Helena, E-mail: helena.smatanova@fstroj.uniza.sk; Kapjor, Andrej, E-mail: andrej.kapjor@fstroj.uniza.sk [University of Žilina, Faculty of Mechanical Engineering, Department of Power Engineering, Univerzitná 1, 010 26 Žilina (Slovakia)
2016-06-30
This article is concerned with natural convective heat transfer from square cylinder mounted on a plane adiabatic base, the cylinders having an exposed cylinder surface according to different horizontal angle. The cylinder receives heat from a radiating heater which results in a buoyant flow. There are many industrial applications, including refrigeration, ventilation and the cooling of electrical components, for which the present study may be applicable.
Study of mixed convection in sodium pool
International Nuclear Information System (INIS)
Wang Zhou; Chen Yan
1995-01-01
The mixed convection phenomena in the sodium pool of fast reactor have been studied systematically by the two dimensional modeling method. A generalized concept of circumferential line in the cylindrical coordinates was proposed to overcome the three dimensional effect induced by the pool geometry in an analysis of two dimensional modeling. A method of sub-step in time was developed for solving the turbulent equations. The treatments on the boundary condition for the auxiliary velocity field have been proposed, and the explanation of allowing the flow function method to be used in the flow field in presence of a mass source term was given. As examples of verification, the experiments were conducted with water flow in a rectangular cavity. The results from theoretical analysis were applied to the numerical computation for the mixed convection in the cavity. The mechanism of stratified flow in the cavity was studied. A numerical calculation was carried out for the mixed convection in hot plenum of a typical fast reactor
Modeling mantle convection in the spherical annulus
Hernlund, John W.; Tackley, Paul J.
2008-12-01
Most methods for modeling mantle convection in a two-dimensional (2D) circular annular domain suffer from innate shortcomings in their ability to capture several characteristics of the spherical shell geometry of planetary mantles. While methods such as rescaling the inner and outer radius to reduce anomalous effects in a 2D polar cylindrical coordinate system have been introduced and widely implemented, such fixes may have other drawbacks that adversely affect the outcome of some kinds of mantle convection studies. Here we propose a new approach that we term the "spherical annulus," which is a 2D slice that bisects the spherical shell and is quantitatively formulated at the equator of a spherical polar coordinate system after neglecting terms in the governing equations related to variations in latitude. Spherical scaling is retained in this approximation since the Jacobian function remains proportional to the square of the radius. We present example calculations to show that the behavior of convection in the spherical annulus compares favorably against calculations performed in other 2D annular domains when measured relative to those in a fully three-dimensional (3D) spherical shell.
Thermal convection and nonlinear effects of a superfluid 3He-4He mixture in a porous medium
International Nuclear Information System (INIS)
Chien, L.C.L.
1986-01-01
The convective instability of one-component classical fluids in a porous medium confined between two unbounded slabs was studied. This system behaves like a high Prandtl number bulk fluid. It has boundary conditions similar to the stress-free boundary conditions of bulk one-component classical fluids. Both the amplitude expansion method and the Galerkin method were used to investigate the nonlinear steady convection. Two dimensional rolls are the only stable motion at the onset of convection. Beyond threshold, the steady convection rolls become unstable to formation of cross-roll and zigzag instabilities. Applying the phase-dynamics approach for the zigzag instability, the author obtained the diffusion coefficient D, which can signal the onset of instability. Also investigated was the convective instability of superfluid 3 He- 4 He mixtures in porous media. Assuming no interaction between the average superflow and the porous medium and treating the normal flow in the equation of motion like a classical fluid in a porous medium, it was found that the superfluid mixtures in a porous medium. To investigate the effects of a lateral boundary, the convective instability of classical one-component fluids in porous media inside a box was studied. The zigzag instability does not exist because of the boundary conditions at the side of the box
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.
Wulfmeyer, V.; Branch, O.; Adebabseh, A.; Temimi, M.
2017-12-01
Irrigated plantations and modified terrain can provide a sustainable means of enhancing convective rainfall in arid regions like the United Arab Emirates, or UAE, and can be used to aid ongoing cloud seeding operations through the geographic-localization of seedable cloud formation. The first method, the planting of vast irrigated plantations of hardy desert shrubs, can lead to wind convergence and vertical mixing through increased roughness and modified radiative balances. When upper-air atmospheric instability is present, these phenomena can initiate convection. The second method, increasing the elevation of moderate-sized mountains, is based on the correlation between elevation and the number of summertime convection initiation events observed in the mountains of the UAE and Oman. This augmentation of existing orographic features should therefore increase the likelihood and geographic range of convection initiation events. High-resolution simulations provide a powerful means of assessing the likely impacts of land surface modifications. Previous convection-permitting simulations have yielded some evidential support for these hypotheses, but higher resolutions down to 1 km provide more detail regarding convective processes and land surface representation. Using seasonal simulations with the WRF-NOAHMP land-atmosphere model at a 2.5 km resolution, we identify frequent zones of convergence and atmospheric instability in the UAE and select interesting cases. Using these results, as well as an agricultural feasibility study, we identify optimal plantation positions within the UAE. We then run realistic plantation scenarios for single case studies at 1 km resolution. Using the same cases, we simulate the impact of augmenting mountain elevations on convective processes, with the augmentation being achieved through GIS-based modification of the terrain data. For both methods, we assess the impacts quantitatively and qualitatively, and assess key processes and
Thermal convection in a toroidal duct of a liquid metal blanket. Part II. Effect of axial mean flow
Energy Technology Data Exchange (ETDEWEB)
Zhang, Xuan, E-mail: xuanz@umich.edu; Zikanov, Oleg
2017-03-15
Highlights: • 2D convection flow develops with internal heating and strong axial magnetic field. • The flow is strongly modified by the buoyancy force associated with growing T{sub m}. • Thermal convection is suppressed at high Gr. • High temperature difference between top and bottom walls is expected at high Gr. - Abstract: The work continues the exploration of the effect of thermal convection on flows in toroidal ducts of a liquid metal blanket. This time we consider the effect of the mean flow along the duct and of the associated heat transfer diverting the heat deposited by captured neutrons. Numerical simulations are conducted for a model system with two-dimensional (streamwise-uniform) fully developed flow, purely toroidal magnetic field, and perfectly electrically and thermally insulating walls. Realistically high Grashof (up to 10{sup 11}) and Reynolds (up to 10{sup 6}) numbers are used. It is found that the flow develops thermal convection in the transverse plane at moderate Grashof numbers. At large Grashof numbers, the flow is dominated by the top-bottom asymmetry of the streamwise velocity and stable stratification of temperature, which are caused by the buoyancy force due to the mean temperature growing along the duct. This leads to suppression of thermal convection, weak mixing, and substantial gradients of wall temperature. Further analysis based on more realistic models is suggested.
Local multiplicative Schwarz algorithms for convection-diffusion equations
Cai, Xiao-Chuan; Sarkis, Marcus
1995-01-01
We develop a new class of overlapping Schwarz type algorithms for solving scalar convection-diffusion equations discretized by finite element or finite difference methods. The preconditioners consist of two components, namely, the usual two-level additive Schwarz preconditioner and the sum of some quadratic terms constructed by using products of ordered neighboring subdomain preconditioners. The ordering of the subdomain preconditioners is determined by considering the direction of the flow. We prove that the algorithms are optimal in the sense that the convergence rates are independent of the mesh size, as well as the number of subdomains. We show by numerical examples that the new algorithms are less sensitive to the direction of the flow than either the classical multiplicative Schwarz algorithms, and converge faster than the additive Schwarz algorithms. Thus, the new algorithms are more suitable for fluid flow applications than the classical additive or multiplicative Schwarz algorithms.
Convective instabilities in liquid centrifugation for nuclear wastes separation
Energy Technology Data Exchange (ETDEWEB)
Camassa, R. [Los Alamos National Laboratory, NM (United States)
1995-10-01
The separation of fission products from liquid solutions using centrifugal forces may prove an effective alternative to chemical processing in cases where radioactive materials necessitate minimal mixed-waste products or when allowing access to sophisticated chemical processing is undesirable. This investigation is a part of the effort to establish the feasibility of using liquid centrifugation for nuclear waste separation in the Accelerator Driven Energy Production (ADEP) program. A number of fundatmental issues in liquid centrifugation with radioactive elements need to be addressed in order to validate the approach and provide design criteria for experimental liquid salt (LiF and BeF{sub 2}) centrifuge. The author concentrates on one such issue, the possible onset of convective instabilities which could inhibit separation.
Soluto-capillary convection in micro-encapsulation
International Nuclear Information System (INIS)
Subramanian, P.; Zebib, A.
2005-01-01
Spherical shells used as laser targets in inertial confinement fusion (ICF) experiments are made by micro-encapsulation. In one phase of manufacturing, the spherical shells contain a solvent (fluoro-benzene, FB) and a solute (polystyrene, PAMS) in a water-FB environment. Evaporation of the FB results in the desired hardened plastic hollow spherical shells, 1-2 mm in diameter. Perfect sphericity is demanded for efficient fusion ignition and the observed surface roughness maybe driven by Marangoni instabilities due to surface tension dependence on the FB concentration (buoyant forces are negligible in this micro-scale problem). Here we model this drying process and compute nonlinear, time-dependent, axisymmetric, variable viscosity, infinite Schmidt number soluto-capillary convection in the shells. Comparison with results from linear theory and available experiments are made. (authors)
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
Onset of Vibrational Convection in a Binary Fluid Saturated Non-Darcy Porous Layer Heated from Above
Directory of Open Access Journals (Sweden)
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.
Dynamo action and magnetic buoyancy in convection simulations with vertical shear
Guerrero, G.; Käpylä, P.
2011-10-01
A hypothesis for sunspot formation is the buoyant emergence of magnetic flux tubes created by the strong radial shear at the tachocline. In this scenario, the magnetic field has to exceed a threshold value before it becomes buoyant and emerges through the whole convection zone. In this work we present the results of direct numerical simulations of compressible turbulent convection that include a vertical shear layer. Like the solar tachocline, the shear is located at the interface between convective and stable layers. We follow the evolution of a random seed magnetic field with the aim of study under what conditions it is possible to excite the dynamo instability and whether the dynamo generated magnetic field becomes buoyantly unstable and emerges to the surface as expected in the flux-tube context. We find that shear and convection are able to amplify the initial magnetic field and form large-scale elongated magnetic structures. The magnetic field strength depends on several parameters such as the shear amplitude, the thickness and location of the shear layer, and the magnetic Reynolds number (Rm). Models with deeper and thicker shear layers allow longer storage and are more favorable for generating a mean magnetic field. Models with higher Rm grow faster but saturate at slightly lower levels. Whenever the toroidal magnetic field reaches amplitudes greater a threshold value which is close to the equipartition value, it becomes buoyant and rises into the convection zone where it expands and forms mushroom shape structures. Some events of emergence, i.e., those with the largest amplitudes of the amplified field, are able to reach the very uppermost layers of the domain. These episodes are able to modify the convective pattern forming either broader convection cells or convective eddies elongated in the direction of the field. However, in none of these events the field preserves its initial structure. The back-reaction of the magnetic field on the fluid is also
Directory of Open Access Journals (Sweden)
Shewale Vinod C.
2017-01-01
Full Text Available Spherical cavity receiver of solar concentrator is made up of Cu tubing material having cavity diameter 385 mm to analyze the different heat losses such as conduction, convection and radiation. As the convection loss plays major role in heat loss analysis of cavity receiver, the experimental analysis is carried out to study convective heat loss for the temperature range of 55-75°C at 0°, 15°, 30°, 45°, 60°, and 90° inclination angle of downward facing cavity receiver. The numerical analysis is carried out to study convective heat loss for the low temperature range (55-75°C as well as high temperature range (150-300 °C for no wind condition only. The experimental set-up mainly consists of spherical cavity receiver which is insulated with glass wool insulation to reduce the heat losses from outside surface. The numerical analysis is carried out by using CFD software and the results are compared with the experimental results and found good agreement. The result shows that the convective loss increases with decrease in cavity inclination angle and decreases with decrease in mean cavity receiver temperature. The maximum losses are obtained at 0° inclination angle and the minimum losses are obtained at 90° inclination angle of cavity due to increase in stagnation zone in to the cavity from 0° to 90° inclination. The Nusselt number correlation is developed for the low temperature range 55-75°C based on the experimental data. The analysis is also carried out to study the effect of wind speed and wind direction on convective heat losses. The convective heat losses are studied for two wind speeds (3 m/s and 5 m/s and four wind directions [α is 0° (Side-on wind, 30°, 60°, and 90° (head-on wind]. It is found that the convective heat losses for both wind speed are higher than the losses obtained by no wind test. The highest heat losses are found for wind direction α is 60° with respect to receiver stand and lowest heat losses are found
Adjoint optimization of natural convection problems: differentially heated cavity
Saglietti, Clio; Schlatter, Philipp; Monokrousos, Antonios; Henningson, Dan S.
2017-12-01
Optimization of natural convection-driven flows may provide significant improvements to the performance of cooling devices, but a theoretical investigation of such flows has been rarely done. The present paper illustrates an efficient gradient-based optimization method for analyzing such systems. We consider numerically the natural convection-driven flow in a differentially heated cavity with three Prandtl numbers (Pr=0.15{-}7) at super-critical conditions. All results and implementations were done with the spectral element code Nek5000. The flow is analyzed using linear direct and adjoint computations about a nonlinear base flow, extracting in particular optimal initial conditions using power iteration and the solution of the full adjoint direct eigenproblem. The cost function for both temperature and velocity is based on the kinetic energy and the concept of entransy, which yields a quadratic functional. Results are presented as a function of Prandtl number, time horizons and weights between kinetic energy and entransy. In particular, it is shown that the maximum transient growth is achieved at time horizons on the order of 5 time units for all cases, whereas for larger time horizons the adjoint mode is recovered as optimal initial condition. For smaller time horizons, the influence of the weights leads either to a concentric temperature distribution or to an initial condition pattern that opposes the mean shear and grows according to the Orr mechanism. For specific cases, it could also been shown that the computation of optimal initial conditions leads to a degenerate problem, with a potential loss of symmetry. In these situations, it turns out that any initial condition lying in a specific span of the eigenfunctions will yield exactly the same transient amplification. As a consequence, the power iteration converges very slowly and fails to extract all possible optimal initial conditions. According to the authors' knowledge, this behavior is illustrated here for
Convective Heat Transfer Coefficients of the Human Body under Forced Convection from Ceiling
DEFF Research Database (Denmark)
Kurazumi, Yoshihito; Rezgals, Lauris; Melikov, Arsen Krikor
2014-01-01
The average convective heat transfer coefficient for a seated human body exposed to downward flow from above was determined. Thermal manikin with complex body shape and size of an average Scandinavian female was used. The surface temperature distribution of the manikin’s body was as the skin...... of the convective heat transfer coefficient of the whole body (hc [W/(m2•K)]) was proposed: hc=4.088+6.592V1.715 for a seated naked body at 20ºC and hc=2.874+7.427V1.345 for a seated naked body at 26ºC. Differences in the convective heat transfer coefficient of the whole body in low air velocity range, V
Regimes of Axisymmetric Flow and Scaling Laws in a Rotating Annulus with Local Convective Forcing
Directory of Open Access Journals (Sweden)
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.
NUMERICAL ANALYSIS OF NATURAL CONVECTION IN A PRISMATIC ENCLOSURE
Directory of Open Access Journals (Sweden)
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 in asymmetric triangular enclosures heated from below
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.
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
Scaling the heterogeneously heated convective boundary layer
Van Heerwaarden, C.; Mellado, J.; De Lozar, A.
2013-12-01
We have studied the heterogeneously heated convective boundary layer (CBL) by means of large-eddy simulations (LES) and direct numerical simulations (DNS). What makes our study different from previous studies on this subject are our very long simulations in which the system travels through multiple states and that from there we have derived scaling laws. In our setup, a stratified atmosphere is heated from below by square patches with a high surface buoyancy flux, surrounded by regions with no or little flux. By letting a boundary layer grow in time we let the system evolve from the so-called meso-scale to the micro-scale regime. In the former the heterogeneity is large and strong circulations can develop, while in the latter the heterogeneity is small and does no longer influence the boundary layer structure. Within each simulation we can now observe the formation of a peak in kinetic energy, which represents the 'optimal' heterogeneity size in the meso-scale, and the subsequent decay of the peak and the development towards the transition to the micro-scale. We have created a non-dimensional parameter space that describes all properties of this system. By studying the previously described evolution for different combinations of parameters, we have derived three important conclusions. First, there exists a horizontal length scale of the heterogeneity (L) that is a function of the boundary layer height (h) and the Richardson (Ri) number of the inversion at the top of the boundary layer. This relationship has the form L = h Ri^(3/8). Second, this horizontal length scale L allows for expressing the time evolution, and thus the state of the system, as a ratio of this length scale and the distance between two patches Xp. This ratio thus describes to which extent the circulation fills up the space that exists between two patch centers. The timings of the transition from the meso- to the micro-scale collapse under this scaling for all simulations sharing the same flux
Mixed convection heat transfer from confined tandem square cylinders in a horizontal channel
Huang, Zhu
2013-11-01
This paper presents a numerical study on the two-dimensional laminar mixed convective flow and heat transfer around two identical isothermal square cylinders arranged in tandem and confined in a channel. The spacing between the cylinders is fixed with four widths of the cylinder and the blockage ratio and the Prandtl number are fixed at 0.1 and 0.7 respectively. The mixed convective flow and heat transfer is simulated by high accuracy multidomain pseudospectral method. The Reynolds number (Re) is studied in the range 80 ≤ Re ≤ 150, the Richardson number (Ri) demonstrating the influence of thermal buoyancy ranges from 0 to 1. Numerical results reveal that, with the thermal buoyancy effect, the mixed convective flow sheds vortex behind the cylinders and keeps periodic oscillating. The variations of characteristic quantities related to flow and heat transfer processes, such as the overall drag and lift coefficients and the Nusselt numbers, are presented and discussed. Furthermore, the influence of thermal buoyancy on the fluid flow and heat transfer are discussed and analysed. © 2013 Elsevier Ltd. All rights reserved.
International Nuclear Information System (INIS)
Cho, Jae Seon; Suh, Kune Y.; Chung, Chang Hyun; Park, Rae Joon; Kim, Sang Baik
1999-01-01
Experimental study was performed to investigate the natural convection heat transfer characteristics and the crust formation of the molten metal pool concurrent with forced convective boiling of the overlying coolant. Tests were performed under the condition of the bottom surface heating in the test section and the forced convection of the coolant being injected onto the molten metal pool. The constant temperature and constant heater input power conditions were adopted for the bottom heating. Test results showed that the temperature distribution and crust layer thickness in the metal layer are appreciably affected by the heated bottom surface temperature of the test section, but not much by the coolant injection rate. The relationship between the Nu number and Ra number in the molten metal pool region is determined and compared with the correlations in the literature, and the experiment without coolant boiling. A new correlation on the relationship between the Nu number and Ra number in the molten metal pool with crust formation is developed from the experimental data
Vorticity imbalance and stability in relation to convection
Read, W. L.; Scoggins, J. R.
1977-01-01
A complete synoptic-scale vorticity budget was related to convection storm development in the eastern two-thirds of the United States. The 3-h sounding interval permitted a study of time changes of the vorticity budget in areas of convective storms. Results of analyses revealed significant changes in values of terms in the vorticity equation at different stages of squall line development. Average budgets for all areas of convection indicate systematic imbalance in the terms in the vorticity equation. This imbalance resulted primarily from sub-grid scale processes. Potential instability in the lower troposphere was analyzed in relation to the development of convective activity. Instability was related to areas of convection; however, instability alone was inadequate for forecast purposes. Combinations of stability and terms in the vorticity equation in the form of indices succeeded in depicting areas of convection better than any one item separately.
A Thermodynamically General Theory for Convective Circulations and Vortices
Renno, N. O.
2007-12-01
Convective circulations and vortices are common features of atmospheres that absorb low-entropy-energy at higher temperatures than they reject high-entropy-energy to space. These circulations range from small to planetary-scale and play an important role in the vertical transport of heat, momentum, and tracer species. Thus, the development of theoretical models for convective phenomena is important to our understanding of many basic features of planetary atmospheres. A thermodynamically general theory for convective circulations and vortices is proposed. The theory includes irreversible processes and quantifies the pressure drop between the environment and any point in a convective updraft. The article's main result is that the proposed theory provides an expression for the pressure drop along streamlines or streamtubes that is a generalization of Bernoulli's equation to convective circulations. We speculate that the proposed theory not only explains the intensity, but also shed light on other basic features of convective circulations and vortices.
Thermo-electro-hydrodynamic convection under microgravity: a review
Energy Technology Data Exchange (ETDEWEB)
Mutabazi, Innocent; Yoshikawa, Harunori N; Fogaing, Mireille Tadie; Travnikov, Vadim; Crumeyrolle, Olivier [Laboratoire Ondes et Milieux Complexes, UMR 6294, CNRS-Université du Havre, CS 80450, F-76058 Le Havre Cedex (France); Futterer, Birgit; Egbers, Christoph, E-mail: Innocent.Mutabazi@univ-lehavre.fr [Department of Aerodynamics and Fluid Mechanics, Brandenburg University of Technology Cottbus-Senftenberg, Cottbus (Germany)
2016-12-15
Recent studies on thermo-electro-hydrodynamic (TEHD) convection are reviewed with focus on investigations motivated by the analogy with natural convection. TEHD convection originates in the action of the dielectrophoretic force generated by an alternating electric voltage applied to a dielectric fluid with a temperature gradient. This electrohydrodynamic force is analogous to Archimedean thermal buoyancy and can be regarded as a thermal buoyancy force in electric effective gravity. The review is concerned with TEHD convection in plane, cylindrical, and spherical capacitors under microgravity conditions, where the electric gravity can induce convection without any complexities arising from geometry or the buoyancy force due to the Earth’s gravity. We will highlight the convection in spherical geometry, comparing developed theories and numerical simulations with the GEOFLOW experiments performed on board the International Space Station (ISS). (paper)
Ladino, Luis A.; Korolev, Alexei; Heckman, Ivan; Wolde, Mengistu; Fridlind, Ann M.; Ackerman, Andrew S.
2018-01-01
Over decades, the cloud physics community has debated the nature and role of aerosol particles in ice initiation. The present study shows that the measured concentration of ice crystals in tropical mesoscale convective systems exceeds the concentration of ice nucleating particles (INPs) by several orders of magnitude. The concentration of INPs was assessed from the measured aerosol particles concentration in the size range of 0.5 to 1 µm. The observations from this study suggest that primary ice crystals formed on INPs make only a minor contribution to the total concentration of ice crystals in tropical mesoscale convective systems. This is found by comparing the predicted INP number concentrations with in-situ ice particle number concentrations. The obtained measurements suggest that ice multiplication is the likely explanation for the observed high concentrations of ice crystals in this type of convective system. PMID:29551842
Jana, S.; Chakraborty, R.; Maitra, A.
2017-12-01
Nowcasting of lightning activities during intense convective events using a single electric field monitor (EFM) has been carried out at a tropical location, Kolkata (22.65oN, 88.45oE). Before and at the onset of heavy lightning, certain changes of electric field (EF) can be related to high liquid water content (LWC) and low cloud base height (CBH). The present study discusses the utility of EF observation to show a few aspects of convective events. Large convective cloud showed by high LWC and low CBH can be detected from EF variation which could be a precursor of upcoming convective events. Suitable values of EF gradient can be used as an indicator of impending lightning events. An EF variation of 0.195 kV/m/min can predict lightning within 17.5 km radius with a probability of detection (POD) of 91% and false alarm rate (FAR) of 8% with a lead time of 45 min. The total number of predicted lightning strikes is nearly 9 times less than that measured by the lightning detector. This prediction technique can, therefore, give an estimate of cloud to ground (CG) and intra cloud (IC) lighting occurrences within the surrounding area. This prediction technique involving POD, FAR and lead time information shows a better prediction capability compared to the techniques reported earlier. Thus an EFM can be effectively used for prediction of lightning events at a tropical location.
Sainsbury-Martinez, Felix; Browning, Matthew; Miesch, Mark; Featherstone, Nicholas A.
2018-01-01
Low-Mass stars are typically fully convective, and as such their dynamics may differ significantly from sun-like stars. Here we present a series of 3D anelastic HD and MHD simulations of fully convective stars, designed to investigate how the meridional circulation, the differential rotation, and residual entropy are affected by both varying stellar parameters, such as the luminosity or the rotation rate, and by the presence of a magnetic field. We also investigate, more specifically, a theoretical model in which isorotation contours and residual entropy (σ‧ = σ ‑ σ(r)) are intrinsically linked via the thermal wind equation (as proposed in the Solar context by Balbus in 2009). We have selected our simulation parameters in such as way as to span the transition between Solar-like differential rotation (fast equator + slow poles) and ‘anti-Solar’ differential rotation (slow equator + fast poles), as characterised by the convective Rossby number and △Ω. We illustrate the transition from single-celled to multi-celled MC profiles, and from positive to negative latitudinal entropy gradients. We show that an extrapolation involving both TWB and the σ‧/Ω link provides a reasonable estimate for the interior profile of our fully convective stars. Finally, we also present a selection of MHD simulations which exhibit an almost unsuppressed differential rotation profile, with energy balances remaining dominated by kinetic components.
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
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.