Hydrodynamics of stratified epithelium: steady state and linearized dynamics
Yeh, Wei-Ting
2015-01-01
A theoretical model for stratified epithelium is presented. The viscoelastic properties of the tissue is assumed to be dependent on the spatial distribution of proliferative and differentiated cells. Based on this assumption, a hydrodynamic description for tissue dynamics at long-wavelength, long-time limit is developed, and the analysis reveals important insight for the dynamics of an epithelium close to its steady state. When the proliferative cells occupy a thin region close to the basal membrane, the relaxation rate towards the steady state is enhanced by cell division and cell apoptosis. On the other hand, when the region where proliferative cells reside becomes sufficiently thick, a flow induced by cell apoptosis close to the apical surface could enhance small perturbations. This destabilizing mechanism is general for continuous self-renewal multi-layered tissues, it could be related to the origin of certain tissue morphology and developing pattern.
Hydrodynamics of stratified epithelium: Steady state and linearized dynamics
Yeh, Wei-Ting; Chen, Hsuan-Yi
2016-05-01
A theoretical model for stratified epithelium is presented. The viscoelastic properties of the tissue are assumed to be dependent on the spatial distribution of proliferative and differentiated cells. Based on this assumption, a hydrodynamic description of tissue dynamics at the long-wavelength, long-time limit is developed, and the analysis reveals important insights into the dynamics of an epithelium close to its steady state. When the proliferative cells occupy a thin region close to the basal membrane, the relaxation rate towards the steady state is enhanced by cell division and cell apoptosis. On the other hand, when the region where proliferative cells reside becomes sufficiently thick, a flow induced by cell apoptosis close to the apical surface enhances small perturbations. This destabilizing mechanism is general for continuous self-renewal multilayered tissues; it could be related to the origin of certain tissue morphology, tumor growth, and the development pattern.
Fluttering in Stratified Flows
Lam, Try; Vincent, Lionel; Kanso, Eva
2016-11-01
The descent motion of heavy objects under the influence of gravitational and aerodynamic forces is relevant to many branches of engineering and science. Examples range from estimating the behavior of re-entry space vehicles to studying the settlement of marine larvae and its influence on underwater ecology. The behavior of regularly shaped objects freely falling in homogeneous fluids is relatively well understood. For example, the complex interaction of a rigid coin with the surrounding fluid will cause it to either fall steadily, flutter, tumble, or be chaotic. Less is known about the effect of density stratification on the descent behavior. Here, we experimentally investigate the descent of discs in both pure water and in a linearly salt-stratified fluids where the density is varied from 1.0 to 1.14 of that of water where the Brunt-Vaisala frequency is 1.7 rad/sec and the Froude number Fr robots for space exploration and underwater missions.
Continuous Dependence on the Density for Stratified Steady Water Waves
Chen, Robin Ming; Walsh, Samuel
2016-02-01
There are two distinct regimes commonly used to model traveling waves in stratified water: continuous stratification, where the density is smooth throughout the fluid, and layer-wise continuous stratification, where the fluid consists of multiple immiscible strata. The former is the more physically accurate description, but the latter is frequently more amenable to analysis and computation. By the conservation of mass, the density is constant along the streamlines of the flow; the stratification can therefore be specified by prescribing the value of the density on each streamline. We call this the streamline density function. Our main result states that, for every smoothly stratified periodic traveling wave in a certain small-amplitude regime, there is an L ∞ neighborhood of its streamline density function such that, for any piecewise smooth streamline density function in that neighborhood, there is a corresponding traveling wave solution. Moreover, the mapping from streamline density function to wave is Lipschitz continuous in a certain function space framework. As this neighborhood includes piecewise smooth densities with arbitrarily many jump discontinues, this theorem provides a rigorous justification for the ubiquitous practice of approximating a smoothly stratified wave by a layered one. We also discuss some applications of this result to the study of the qualitative features of such waves.
Stability of stratified two-phase flows in inclined channels
Barmak, Ilya; Ullmann, Amos; Brauner, Neima
2016-01-01
Linear stability of stratified gas-liquid and liquid-liquid plane-parallel flows in inclined channels is studied with respect to all wavenumber perturbations. The main objective is to predict parameter regions in which stable stratified configuration in inclined channels exists. Up to three distinct base states with different holdups exist in inclined flows, so that the stability analysis has to be carried out for each branch separately. Special attention is paid to the multiple solution regions to reveal the feasibility of non-unique stable stratified configurations in inclined channels. The stability boundaries of each branch of steady state solutions are presented on the flow pattern map and are accompanied by critical wavenumbers and spatial profiles of the most unstable perturbations. Instabilities of different nature are visualized by streamlines of the neutrally stable perturbed flows, consisting of the critical perturbation superimposed on the base flow. The present analysis confirms the existence of ...
Topographic Effects on Stratified Flows
2003-09-30
Gabersek, S., Gohm, A., Mayr, R., Mobbs, S., Nance, L. B., Vergeiner, I. Vergeiner, J. and Whiteman, C. D. 2003. GAP flow measurements during the...Darby, L. S., Durran, D. R., Gabersek, S., Gohm, A., Mayr, R., Mobbs, S., Nance, L. B., Vergeiner, I. Vergeiner, J. and Whiteman, C. D. 2003. GAP ... flow measurements during the Mesoscale Alpine Programme. Met. and Atm. Phys. (in press, refereed) Eastwood, C. D., Armi, L. and Lasheras, J. C. 2003
Stably Stratified Flow in a Shallow Valley
Mahrt, L.
2017-01-01
Stratified nocturnal flow above and within a small valley of approximately 12-m depth and a few hundred metres width is examined as a case study, based on a network of 20 sonic anemometers and a central 20-m tower with eight levels of sonic anemometers. Several regimes of stratified flow over gentle topography are conceptually defined for organizing the data analysis and comparing with the existing literature. In our case study, a marginal cold pool forms within the shallow valley in the early evening but yields to larger ambient wind speeds after a few hours, corresponding to stratified terrain-following flow where the flow outside the valley descends to the valley floor. The terrain-following flow lasts about 10 h and then undergoes transition to an intermittent marginal cold pool towards the end of the night when the larger-scale flow collapses. During this 10-h period, the stratified terrain-following flow is characterized by a three-layer structure, consisting of a thin surface boundary layer of a few metres depth on the valley floor, a deeper boundary layer corresponding to the larger-scale flow, and an intermediate transition layer with significant wind-directional shear and possible advection of lee turbulence that is generated even for the gentle topography of our study. The flow in the valley is often modulated by oscillations with a typical period of 10 min. Cold events with smaller turbulent intensity and duration of tens of minutes move through the observational domain throughout the terrain-following period. One of these events is examined in detail.
Stability of stratified two-phase flows in inclined channels
Barmak, I.; Gelfgat, A. Yu.; Ullmann, A.; Brauner, N.
2016-08-01
Linear stability of the stratified gas-liquid and liquid-liquid plane-parallel flows in the inclined channels is studied with respect to all wavenumber perturbations. The main objective is to predict the parameter regions in which the stable stratified configuration in inclined channels exists. Up to three distinct base states with different holdups exist in the inclined flows, so that the stability analysis has to be carried out for each branch separately. Special attention is paid to the multiple solution regions to reveal the feasibility of the non-unique stable stratified configurations in inclined channels. The stability boundaries of each branch of the steady state solutions are presented on the flow pattern map and are accompanied by the critical wavenumbers and the spatial profiles of the most unstable perturbations. Instabilities of different nature are visualized by the streamlines of the neutrally stable perturbed flows, consisting of the critical perturbation superimposed on the base flow. The present analysis confirms the existence of two stable stratified flow configurations in a region of low flow rates in the countercurrent liquid-liquid flows. These configurations become unstable with respect to the shear mode of instability. It was revealed that in slightly upward inclined flows the lower and middle solutions for the holdup are stable in the part of the triple solution region, while the upper solution is always unstable. In the case of downward flows, in the triple solution region, none of the solutions are stable with respect to the short-wave perturbations. These flows are stable only in the single solution region at low flow rates of the heavy phase, and the long-wave perturbations are the most unstable ones.
Elastic instability in stratified core annular flow.
Bonhomme, Oriane; Morozov, Alexander; Leng, Jacques; Colin, Annie
2011-06-01
We study experimentally the interfacial instability between a layer of dilute polymer solution and water flowing in a thin capillary. The use of microfluidic devices allows us to observe and quantify in great detail the features of the flow. At low velocities, the flow takes the form of a straight jet, while at high velocities, steady or advected wavy jets are produced. We demonstrate that the transition between these flow regimes is purely elastic--it is caused by the viscoelasticity of the polymer solution only. The linear stability analysis of the flow in the short-wave approximation supplemented with a kinematic criterion captures quantitatively the flow diagram. Surprisingly, unstable flows are observed for strong velocities, whereas convected flows are observed for low velocities. We demonstrate that this instability can be used to measure the rheological properties of dilute polymer solutions that are difficult to assess otherwise.
Elastic instability in stratified core annular flow
Bonhomme, Oriane; Leng, Jacques; Colin, Annie
2010-01-01
We study experimentally the interfacial instability between a layer of dilute polymer solution and water flowing in a thin capillary. The use of microfluidic devices allows us to observe and quantify in great detail the features of the flow. At low velocities, the flow takes the form of a straight jet, while at high velocities, steady or advected wavy jets are produced. We demonstrate that the transition between these flow regimes is purely elastic -- it is caused by viscoelasticity of the polymer solution only. The linear stability analysis of the flow in the short-wave approximation captures quantitatively the flow diagram. Surprisingly, unstable flows are observed for strong velocities, whereas convected flows are observed for low velocities. We demonstrate that this instability can be used to measure rheological properties of dilute polymer solutions that are difficult to assess otherwise.
Steady and unsteady transonic flow
Seegmiller, H. L.; Marvin, J. G.; Levy, L. L., Jr.
1978-01-01
An investigation of the transonic flow over a circular arc airfoil was conducted to obtain basic information for turbulence modeling of shock-induced separated flows and to verify numerical computer codes which are being developed to simulate such flows. The investigation included the employment of a laser velocimeter to obtain data concerning the mean velocity, the shear stress, and the turbulent kinetic energy profiles in the flowfield downstream of the airfoil midchord where the flow features are more complex. Depending on the free-stream Mach number, the flowfield developed was either steady with shock-wave-induced separation extending from the foot of the shock wave to beyond the trailing edge or unsteady with a periodic motion also undergoing shock-induced separation. The experimental data were compared with the results of numerical simulations in which a computer code was employed that solved the time-dependent Reynolds' averaged compressible Navier-Stokes equations.
Topological Structures in Rotating Stratified Flows
Redondo, J. M.; Carrillo, A.; Perez, E.
2003-04-01
Detailled 2D Particle traking and PIV visualizations performed on a series of large scale laboratory experiments at the Coriolis Platform of the SINTEF in Trondheim have revealed several resonances which scale on the Strouhal, the Rossby and the Richardson numbers. More than 100 experiments spanned a wide range of Rossby Deformation Radii and the topological structures (Parabolic /Eliptic /Hyperbolic) of the quasi-balanced stratified-rotating flows were studied when stirring (akin to coastal mixing) occured at a side of the tank. The strong asymetry favored by the total vorticity produces a wealth of mixing patterns.
Weakly nonlinear simulation of planar stratified flows
King, Michael R. [Department of Chemical Engineering, University of Notre Dame, Notre Dame, Indiana 46556 (United States); McCready, Mark J. [Department of Chemical Engineering, University of Notre Dame, Notre Dame, Indiana 46556 (United States)
2000-01-01
The interfacial behavior of two-fluid, planar flows is studied by numerical integration of weakly-nonlinear amplitude equations derived via eigenfunction expansion of the governing equations. This study extends the range of classic Stuart-Landau theories by the inclusion of a spectrum of modes allowing all possible quadratic and cubic interactions. Results are obtained for four cases where linear and Stuart-Landau theories do not give a complete description; gas-liquid and oil-water pressure driven flow, matched-density liquid-liquid Couette flow, and the region of gas-liquid flow near resonance that switches from supercritical to subcritical. It is found that integration of amplitude equations gives better qualitative and quantitative agreement with experiments than Stuart-Landau theory. Further, the distinctively different behaviors of these systems can be understood in terms of the spectrum of nonlinear coefficients. In gas-liquid channel flow a low wave number wave is destabilized through quadratic interaction with the mean flow mode. For liquid-liquid Poiseuille flow, a low wave number wave is destabilized through cubic interactions with higher modes. For depth and viscosity ratios where liquid-liquid Couette flow is unstable to long waves and for which the growth rates are not too large, simulation results predict that the waves grow to a statistically steady state where there is no preferred wave number. Stabilization is provided by an apparently self-similar cascade of energy to higher modes that are linearly stable, explaining why no visible waves occur in experiments done in this region. While Stuart-Landau theory provides no prediction of wave amplitude above criticality for subcritical cases, simulations show that wave saturation at small amplitude is possible and suggests that subcritical predictions may not mean that steady waves do not exist. (c) 2000 American Institute of Physics.
Simulation and study of stratified flows around finite bodies
Gushchin, V. A.; Matyushin, P. V.
2016-06-01
The flows past a sphere and a square cylinder of diameter d moving horizontally at the velocity U in a linearly density-stratified viscous incompressible fluid are studied. The flows are described by the Navier-Stokes equations in the Boussinesq approximation. Variations in the spatial vortex structure of the flows are analyzed in detail in a wide range of dimensionless parameters (such as the Reynolds number Re = Ud/ ν and the internal Froude number Fr = U/( Nd), where ν is the kinematic viscosity and N is the buoyancy frequency) by applying mathematical simulation (on supercomputers of Joint Supercomputer Center of the Russian Academy of Sciences) and three-dimensional flow visualization. At 0.005 < Fr < 100, the classification of flow regimes for the sphere (for 1 < Re < 500) and for the cylinder (for 1 < Re < 200) is improved. At Fr = 0 (i.e., at U = 0), the problem of diffusion-induced flow past a sphere leading to the formation of horizontal density layers near the sphere's upper and lower poles is considered. At Fr = 0.1 and Re = 50, the formation of a steady flow past a square cylinder with wavy hanging density layers in the wake is studied in detail.
Experiments on the transition from stratified to slug flow in multiphase pipe flow
Kristiansen, Olav
2004-12-01
Severe slugging is reported from some field operations, where an increase in the production rate leads to a transition from steady stratified flow to slug flow in the pipeline. The slugs can be longer than anticipated for hydrodynamic slugging and the flow transients can then be a limitation for the production capacity. The objective was to perform a study on the flow pattern transition from stratified to slug flow. A particular point of interest was the possible occurrence of metastable flow and large initial slugs at elevated pressures. New data have been acquired in an experimental investigation of the transition from stratified to slug flow in horizontal and near-horizontal pipes at atmospheric and pressurised conditions. The experiments were performed with two-phase gas liquid and three-phase gas-liquid-liquid flows. Two flow facilities were used the NTNU Multiphase Flow Laboratory (short flow loop) and the SINTEF Multi-phase Flow Laboratory (long flow loop). Hold-up and pressure drop were measured, and flow patterns were determined visually and by evaluation of hold-up time traces. The following parameters were varied: 1) Inlet flow condition by variation of inlet pipe inclination. 2) System pressure (gas density). 3) Test section inclination (horizontal and near-horizontal). 4) Water cut. 5) Gas and liquid flow rates. 6) Pipe length. Slug flow or stratified flow was introduced upstream to promote either early or delayed transition to slug flow in the test section. A time series analysis was performed on the hold-up time traces, and average and distribution slug characteristics are reported, e.g. slug frequency, bubble propagation velocity, slug fraction, slug length, and growth rate. The results have been compared with steady state model predictions. The work consists of the following parts. 1) An initial study was performed at atmospheric air-water conditions in a short pipe. 2) Experiments at atmospheric and elevated pressures were performed in the medium
A study of stratified gas-liquid pipe flow
Johnson, George W.
2005-07-01
This work includes both theoretical modelling and experimental observations which are relevant to the design of gas condensate transport lines. Multicomponent hydrocarbon gas mixtures are transported in pipes over long distances and at various inclinations. Under certain circumstances, the heavier hydrocarbon components and/or water vapour condense to form one or more liquid phases. Near the desired capacity, the liquid condensate and water is efficiently transported in the form of a stratified flow with a droplet field. During operating conditions however, the flow rate may be reduced allowing liquid accumulation which can create serious operational problems due to large amounts of excess liquid being expelled into the receiving facilities during production ramp-up or even in steady production in severe cases. In particular, liquid tends to accumulate in upward inclined sections due to insufficient drag on the liquid from the gas. To optimize the transport of gas condensates, a pipe diameters should be carefully chosen to account for varying flow rates and pressure levels which are determined through the knowledge of the multiphase flow present. It is desirable to have a reliable numerical simulation tool to predict liquid accumulation for various flow rates, pipe diameters and pressure levels which is not presently accounted for by industrial flow codes. A critical feature of the simulation code would include the ability to predict the transition from small liquid accumulation at high flow rates to large liquid accumulation at low flow rates. A semi-intermittent flow regime of roll waves alternating with a partly backward flowing liquid film has been observed experimentally to occur for a range of gas flow rates. Most of the liquid is transported in the roll waves. The roll wave regime is not well understood and requires fundamental modelling and experimental research. The lack of reliable models for this regime leads to inaccurate prediction of the onset of
Turbulent Mixing in Stably Stratified Flows
2008-03-01
Liege Colloquium on Ocean Hydrodynamics, volume 46, page 19889898. Elsevier, 1987. R. M. Kerr. Higher-order derivative correlations and the alignment of...19th International Liege Colloquium on Ocean Hydrodynamics, volume 46, pages 3-9. Elsevier, 1988. P. Meunier and G. Spedding. Stratified propelled
Steady laminar flow of fractal fluids
Balankin, Alexander S.; Mena, Baltasar; Susarrey, Orlando; Samayoa, Didier
2017-02-01
We study laminar flow of a fractal fluid in a cylindrical tube. A flow of the fractal fluid is mapped into a homogeneous flow in a fractional dimensional space with metric induced by the fractal topology. The equations of motion for an incompressible Stokes flow of the Newtonian fractal fluid are derived. It is found that the radial distribution for the velocity in a steady Poiseuille flow of a fractal fluid is governed by the fractal metric of the flow, whereas the pressure distribution along the flow direction depends on the fractal topology of flow, as well as on the fractal metric. The radial distribution of the fractal fluid velocity in a steady Couette flow between two concentric cylinders is also derived.
Steady laminar flow of fractal fluids
Balankin, Alexander S., E-mail: abalankin@ipn.mx [Grupo Mecánica Fractal, ESIME, Instituto Politécnico Nacional, México D.F., 07738 (Mexico); Mena, Baltasar [Laboratorio de Ingeniería y Procesos Costeros, Instituto de Ingeniería, Universidad Nacional Autónoma de México, Sisal, Yucatán, 97355 (Mexico); Susarrey, Orlando; Samayoa, Didier [Grupo Mecánica Fractal, ESIME, Instituto Politécnico Nacional, México D.F., 07738 (Mexico)
2017-02-12
We study laminar flow of a fractal fluid in a cylindrical tube. A flow of the fractal fluid is mapped into a homogeneous flow in a fractional dimensional space with metric induced by the fractal topology. The equations of motion for an incompressible Stokes flow of the Newtonian fractal fluid are derived. It is found that the radial distribution for the velocity in a steady Poiseuille flow of a fractal fluid is governed by the fractal metric of the flow, whereas the pressure distribution along the flow direction depends on the fractal topology of flow, as well as on the fractal metric. The radial distribution of the fractal fluid velocity in a steady Couette flow between two concentric cylinders is also derived. - Highlights: • Equations of Stokes flow of Newtonian fractal fluid are derived. • Pressure distribution in the Newtonian fractal fluid is derived. • Velocity distribution in Poiseuille flow of fractal fluid is found. • Velocity distribution in a steady Couette flow is established.
Plane Stratified Flow in a Room Ventilated by Displacement Ventilation
Nielsen, Peter Vilhelm; Nickel, J.; Baron, D. J. G.
2004-01-01
The air movement in the occupied zone of a room ventilated by displacement ventilation exists as a stratified flow along the floor. This flow can be radial or plane according to the number of wall-mounted diffusers and the room geometry. The paper addresses the situations where plane flow...
Numerical Simulation on Stratified Flow over an Isolated Mountain Ridge
LI Ling; Shigeo Kimura
2007-01-01
The characteristics of stratified flow over an isolated mountain ridge have been investigated numerically. The two-dimensional model equations, based on the time-dependent Reynolds averaged NavierStokes equations, are solved numerically using an implicit time integration in a fitted body grid arrangement to simulate stratified flow over an isolated ideally bell-shaped mountain. The simulation results are in good agreement with the existing corresponding analytical and approximate solutions. It is shown that for atmospheric conditions where non-hydrostatic effects become dominant, the model is able to reproduce typical flow features. The dispersion characteristics of gaseous pollutants in the stratified flow have also been studied. The dispersion patterns for two typical atmospheric conditions are compared. The results show that the presence of a gravity wave causes vertical stratification of the pollutant concentration and affects the diffusive characteristics of the pollutants.
Stability of stratified two-phase flows in horizontal channels
Barmak, Ilya; Ullmann, Amos; Brauner, Neima; Vitoshkin, Helen
2016-01-01
Linear stability of stratified two-phase flows in horizontal channels to arbitrary wavenumber disturbances is studied. The problem is reduced to Orr-Sommerfeld equations for the stream function disturbances, defined in each sublayer and coupled via boundary conditions that account also for possible interface deformation and capillary forces. Applying the Chebyshev collocation method, the equations and interface boundary conditions are reduced to the generalized eigenvalue problems solved by standard means of numerical linear algebra for the entire spectrum of eigenvalues and the associated eigenvectors. Some additional conclusions concerning the instability nature are derived from the most unstable perturbation patterns. The results are summarized in the form of stability maps showing the operational conditions at which a stratified-smooth flow pattern is stable. It is found that for gas-liquid and liquid-liquid systems the stratified flow with smooth interface is stable only in confined zone of relatively lo...
Reconstruction of stratified steady water waves from pressure readings on the ocean bed
Chen, Robin Ming
2015-01-01
Consider a two-dimensional stratified solitary wave propagating through a body of water that is bounded below by an impermeable ocean bed. In this work, we study how such a wave can be reconstructed from data consisting of the wave speed, upstream and downstream density profile, and the trace of the pressure on the bed. First, we prove that this data uniquely determines the wave, both in the (real) analytic and Sobolev regimes. Second, for waves that consist of multiple layers of constant density immiscible fluids, we provide an exact formula describing each of the interfaces in terms of the data. Finally, for continuously stratified fluids, we detail a reconstruction scheme based on approximation by layer-wise constant density flows.
Linear Inviscid Damping for Couette Flow in Stratified Fluid
Yang, Jincheng
2016-01-01
We study the inviscid damping of Coutte flow with an exponentially stratified density. The optimal decay rates of the velocity field and density are obtained for general perturbations with minimal regularity. For Boussinesq approximation model, the decay rates we get are consistent with the previous results in the literature. We also study the decay rates for the full equations of stratified fluids, which were not studied before. For both models, the decay rates depend on the Richardson number in a very similar way. Besides, we also study the inviscid damping of perturbations due to the exponential stratification when there is no shear.
Rarefaction wave in relativistic steady magnetohydrodynamic flows
Sapountzis, Konstantinos, E-mail: ksapountzis@phys.uoa.gr; Vlahakis, Nektarios, E-mail: vlahakis@phys.uoa.gr [Faculty of Physics, University of Athens, 15784 Zografos, Athens (Greece)
2014-07-15
We construct and analyze a model of the relativistic steady-state magnetohydrodynamic rarefaction that is induced when a planar symmetric flow (with one ignorable Cartesian coordinate) propagates under a steep drop of the external pressure profile. Using the method of self-similarity, we derive a system of ordinary differential equations that describe the flow dynamics. In the specific limit of an initially homogeneous flow, we also provide analytical results and accurate scaling laws. We consider that limit as a generalization of the previous Newtonian and hydrodynamic solutions already present in the literature. The model includes magnetic field and bulk flow speed having all components, whose role is explored with a parametric study.
Elementary stratified flows with stability at low Richardson number
Barros, Ricardo [Mathematics Applications Consortium for Science and Industry (MACSI), Department of Mathematics and Statistics, University of Limerick, Limerick (Ireland); Choi, Wooyoung [Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey 07102-1982 (United States)
2014-12-15
We revisit the stability analysis for three classical configurations of multiple fluid layers proposed by Goldstein [“On the stability of superposed streams of fluids of different densities,” Proc. R. Soc. A. 132, 524 (1931)], Taylor [“Effect of variation in density on the stability of superposed streams of fluid,” Proc. R. Soc. A 132, 499 (1931)], and Holmboe [“On the behaviour of symmetric waves in stratified shear layers,” Geophys. Publ. 24, 67 (1962)] as simple prototypes to understand stability characteristics of stratified shear flows with sharp density transitions. When such flows are confined in a finite domain, it is shown that a large shear across the layers that is often considered a source of instability plays a stabilizing role. Presented are simple analytical criteria for stability of these low Richardson number flows.
Stability of stratified two-phase flows in horizontal channels
Barmak, I.; Gelfgat, A.; Vitoshkin, H.; Ullmann, A.; Brauner, N.
2016-04-01
Linear stability of stratified two-phase flows in horizontal channels to arbitrary wavenumber disturbances is studied. The problem is reduced to Orr-Sommerfeld equations for the stream function disturbances, defined in each sublayer and coupled via boundary conditions that account also for possible interface deformation and capillary forces. Applying the Chebyshev collocation method, the equations and interface boundary conditions are reduced to the generalized eigenvalue problems solved by standard means of numerical linear algebra for the entire spectrum of eigenvalues and the associated eigenvectors. Some additional conclusions concerning the instability nature are derived from the most unstable perturbation patterns. The results are summarized in the form of stability maps showing the operational conditions at which a stratified-smooth flow pattern is stable. It is found that for gas-liquid and liquid-liquid systems, the stratified flow with a smooth interface is stable only in confined zone of relatively low flow rates, which is in agreement with experiments, but is not predicted by long-wave analysis. Depending on the flow conditions, the critical perturbations can originate mainly at the interface (so-called "interfacial modes of instability") or in the bulk of one of the phases (i.e., "shear modes"). The present analysis revealed that there is no definite correlation between the type of instability and the perturbation wavelength.
Stability of steam-water countercurrent stratified flow
Lee, S C
1985-10-01
Two flow instabilities which limit the normal condensation processes in countercurrent stratified steam-water flow have been identified experimentally: flooding and condensation-induced waterhammer. In order to initiate condensation-induced waterhammer in nearly horizontal or moderately-inclined steam/subcooled-water flow, two conditions, the appearance of a wavy interface and complete condensation of the incoming steam, are necessary. Analyses of these conditions are performed on a basis of flow stability and heat transfer considerations. Flooding data for several inclinations and channel heights are collected. Effects of condensation, inclination angle and channel height on the flooding characteristics are discussed. An envelope theory for the onset of flooding in inclined stratified flow is developed, which agrees well with the experimental data. Some empirical information on basic flow parameters, such as mean film thickness and interfacial friction factor required for this theory are measured. The previous viewpoints on flooding appear not to conflict with the present experimental data in nearly horizontal flow but the flooding phenomena in nearly vertical flow appear to be more complicated than those described by these viewpoints because of liquid droplet entrainment.
The Universal Aspect Ratio of Vortices in Rotating Stratifi?ed Flows: Experiments and Observations
Aubert, Oriane; Gal, Patrice Le; Marcus, Philip S
2012-01-01
We validate a new law for the aspect ratio $\\alpha = H/L$ of vortices in a rotating, stratified flow, where $H$ and $L$ are the vertical half-height and horizontal length scale of the vortices. The aspect ratio depends not only on the Coriolis parameter f and buoyancy (or Brunt-Vaisala) frequency $\\bar{N}$ of the background flow, but also on the buoyancy frequency $N_c$ within the vortex and on the Rossby number $Ro$ of the vortex such that $\\alpha = f \\sqrt{[Ro (1 + Ro)/(N_c^2- \\bar{N}^2)]}$. This law for $\\alpha$ is obeyed precisely by the exact equilibrium solution of the inviscid Boussinesq equations that we show to be a useful model of our laboratory vortices. The law is valid for both cyclones and anticyclones. Our anticyclones are generated by injecting fluid into a rotating tank filled with linearly-stratified salt water. The vortices are far from the top and bottom boundaries of the tank, so there is no Ekman circulation. In one set of experiments, the vortices viscously decay, but as they do, they c...
Visualization periodic flows in a continuously stratified fluid.
Bardakov, R.; Vasiliev, A.
2012-04-01
To visualize the flow pattern of viscous continuously stratified fluid both experimental and computational methods were developed. Computational procedures were based on exact solutions of set of the fundamental equations. Solutions of the problems of flows producing by periodically oscillating disk (linear and torsion oscillations) were visualized with a high resolutions to distinguish small-scale the singular components on the background of strong internal waves. Numerical algorithm of visualization allows to represent both the scalar and vector fields, such as velocity, density, pressure, vorticity, stream function. The size of the source, buoyancy and oscillation frequency, kinematic viscosity of the medium effects were traced in 2D an 3D posing problems. Precision schlieren instrument was used to visualize the flow pattern produced by linear and torsion oscillations of strip and disk in a continuously stratified fluid. Uniform stratification was created by the continuous displacement method. The buoyancy period ranged from 7.5 to 14 s. In the experiments disks with diameters from 9 to 30 cm and a thickness of 1 mm to 10 mm were used. Different schlieren methods that are conventional vertical slit - Foucault knife, vertical slit - filament (Maksoutov's method) and horizontal slit - horizontal grating (natural "rainbow" schlieren method) help to produce supplementing flow patterns. Both internal wave beams and fine flow components were visualized in vicinity and far from the source. Intensity of high gradient envelopes increased proportionally the amplitude of the source. In domains of envelopes convergence isolated small scale vortices and extended mushroom like jets were formed. Experiments have shown that in the case of torsion oscillations pattern of currents is more complicated than in case of forced linear oscillations. Comparison with known theoretical model shows that nonlinear interactions between the regular and singular flow components must be taken
Instabilities developed in stratified flows over pronounced obstacles
Varela, J.; Araújo, M.; Bove, I.; Cabeza, C.; Usera, G.; Martí, Arturo C.; Montagne, R.; Sarasúa, L. G.
2007-12-01
In the present work we study numerical and experimentally the flow of a two-layer stratified fluid over a topographic obstacle. The problem reflects a wide number of oceanographic and meteorological situations, where the stratification plays an important role. We identify the different instabilities developed by studying the pycnocline deformation due to a pronounced obstacle. The numerical simulations were made using the model caffa3D.MB which works with a numerical model of Navier-Stokes equations with finite volume elements in curvilinear meshes. The experimental results are contrasted with numerical simulations. Linear stability analysis predictions are checked with particle image velocimetry (PIV) measurements.
Interfacial instabilities in a stratified flow of two superposed fluids
Schaflinger, Uwe
1994-06-01
Here we shall present a linear stability analysis of a laminar, stratified flow of two superposed fluids which are a clear liquid and a suspension of solid particles. The investigation is based upon the assumption that the concentration remains constant within the suspension layer. Even for moderate flow-rates the base-state results for a shear induced resuspension flow justify the latter assumption. The numerical solutions display the existence of two different branches that contribute to convective instability: long and short waves which coexist in a certain range of parameters. Also, a range exists where the flow is absolutely unstable. That means a convectively unstable resuspension flow can be only observed for Reynolds numbers larger than a lower, critical Reynolds number but still smaller than a second critical Reynolds number. For flow rates which give rise to a Reynolds number larger than the second critical Reynolds number, the flow is absolutely unstable. In some cases, however, there exists a third bound beyond that the flow is convectively unstable again. Experiments show the same phenomena: for small flow-rates short waves were usually observed but occasionally also the coexistence of short and long waves. These findings are qualitatively in good agreement with the linear stability analysis. Larger flow-rates in the range of the second critical Reynolds number yield strong interfacial waves with wave breaking and detached particles. In this range, the measured flow-parameters, like the resuspension height and the pressure drop are far beyond the theoretical results. Evidently, a further increase of the Reynolds number indicates the transition to a less wavy interface. Finally, the linear stability analysis also predicts interfacial waves in the case of relatively small suspension heights. These results are in accordance with measurements for ripple-type instabilities as they occur under laminar and viscous conditions for a mono-layer of particles.
Chen Xiao-Gang; Guo Zhi-Ping; Song Jin-Bao
2008-01-01
In the present paper,the random interfacial waves in N-layer density-stratified fluids moving at different steady uniform speeds are researched by using an expansion technique,and the second-order asymptotic solutions of the random displacements of the density interfaces and the associated velocity potentials in N-layer fluid are presented based on the small amplitude wave theory.The obtained results indicate that the wave-wave second-order nonlinear interactions of the wave components and the second-order nonlinear interactions between the waves and currents are described.As expected,the solutions include those derived by Chen(2006)as a special case where the steady uniform currents of the N-layer fluids are taken as zero,and the solutions also reduce to those obtained by Song(2005)for second-order solutions for random interracial waves with steady uniform currents if N=2.
Constitutive relations for steady, dense granular flows
Vescovi, D.; Berzi, D.; di Prisco, C. G.
2011-12-01
In the recent past, the flow of dense granular materials has been the subject of many scientific works; this is due to the large number of natural phenomena involving solid particles flowing at high concentration (e.g., debris flows and landslides). In contrast with the flow of dilute granular media, where the energy is essentially dissipated in binary collisions, the flow of dense granular materials is characterized by multiple, long-lasting and frictional contacts among the particles. The work focuses on the mechanical response of dry granular materials under steady, simple shear conditions. In particular, the goal is to obtain a complete rheology able to describe the material behavior within the entire range of concentrations for which the flow can be considered dense. The total stress is assumed to be the linear sum of a frictional and a kinetic component. The frictional and the kinetic contribution are modeled in the context of the critical state theory [8, 10] and the kinetic theory of dense granular gases [1, 3, 7], respectively. In the critical state theory, the granular material approaches a certain attractor state, independent on the initial arrangement, characterized by the capability of developing unlimited shear strains without any change in the concentration. Given that a disordered granular packing exists only for a range of concentration between the random loose and close packing [11], a form for the concentration dependence of the frictional normal stress that makes the latter vanish at the random loose packing is defined. In the kinetic theory, the particles are assumed to interact through instantaneous, binary and uncorrelated collisions. A new state variable of the problem is introduced, the granular temperature, which accounts for the velocity fluctuations. The model has been extended to account for the decrease in the energy dissipation due to the existence of correlated motion among the particles [5, 6] and to deal with non
Stratified flows with variable density: mathematical modelling and numerical challenges.
Murillo, Javier; Navas-Montilla, Adrian
2017-04-01
Stratified flows appear in a wide variety of fundamental problems in hydrological and geophysical sciences. They may involve from hyperconcentrated floods carrying sediment causing collapse, landslides and debris flows, to suspended material in turbidity currents where turbulence is a key process. Also, in stratified flows variable horizontal density is present. Depending on the case, density varies according to the volumetric concentration of different components or species that can represent transported or suspended materials or soluble substances. Multilayer approaches based on the shallow water equations provide suitable models but are not free from difficulties when moving to the numerical resolution of the governing equations. Considering the variety of temporal and spatial scales, transfer of mass and energy among layers may strongly differ from one case to another. As a consequence, in order to provide accurate solutions, very high order methods of proved quality are demanded. Under these complex scenarios it is necessary to observe that the numerical solution provides the expected order of accuracy but also converges to the physically based solution, which is not an easy task. To this purpose, this work will focus in the use of Energy balanced augmented solvers, in particular, the Augmented Roe Flux ADER scheme. References: J. Murillo , P. García-Navarro, Wave Riemann description of friction terms in unsteady shallow flows: Application to water and mud/debris floods. J. Comput. Phys. 231 (2012) 1963-2001. J. Murillo B. Latorre, P. García-Navarro. A Riemann solver for unsteady computation of 2D shallow flows with variable density. J. Comput. Phys.231 (2012) 4775-4807. A. Navas-Montilla, J. Murillo, Energy balanced numerical schemes with very high order. The Augmented Roe Flux ADER scheme. Application to the shallow water equations, J. Comput. Phys. 290 (2015) 188-218. A. Navas-Montilla, J. Murillo, Asymptotically and exactly energy balanced augmented flux
Mohd Hafizi Mat Yasin
2013-01-01
Full Text Available We present the numerical investigation of the steady mixed convection boundary layer flow over a vertical surface embedded in a thermally stratified porous medium saturated by a nanofluid. The governing partial differential equations are reduced to the ordinary differential equations, using the similarity transformations. The similarity equations are solved numerically for three types of metallic or nonmetallic nanoparticles, namely, copper (Cu, alumina (Al2O3, and titania (TiO2, in a water-based fluid to investigate the effect of the solid volume fraction or nanoparticle volume fraction parameter φ of the nanofluid on the flow and heat transfer characteristics. The skin friction coefficient and the velocity and temperature profiles are presented and discussed.
Turbulence comes in bursts in stably stratified flows
Rorai, C; Pouquet, A
2013-01-01
There is a clear distinction between simple laminar and complex turbulent fluids. But in some cases, as for the nocturnal planetary boundary layer, a stable and well-ordered flow can develop intense and sporadic bursts of turbulent activity which disappear slowly in time. This phenomenon is ill-understood and poorly modeled; and yet, it is central to our understanding of weather and climate dynamics. We present here a simple model which shows that in stably stratified turbulence, the stronger bursts can occur when the flow is expected to be more stable. The bursts are generated by a rapid non-linear amplification of energy stored in waves, and are associated with energetic interchanges between vertical velocity and temperature (or density) fluctuations. Direct numerical simulations on grids of 2048^3 points confirm this somewhat paradoxical result of measurably stronger events for more stable flows, displayed not only in the temperature and vertical velocity derivatives, but also in the amplitude of the field...
Stratified Flow Past a Hill: Dividing Streamline Concept Revisited
Leo, Laura S.; Thompson, Michael Y.; Di Sabatino, Silvana; Fernando, Harindra J. S.
2016-06-01
The Sheppard formula (Q J R Meteorol Soc 82:528-529, 1956) for the dividing streamline height H_s assumes a uniform velocity U_∞ and a constant buoyancy frequency N for the approach flow towards a mountain of height h, and takes the form H_s/h=( {1-F} ) , where F=U_{∞}/Nh. We extend this solution to a logarithmic approach-velocity profile with constant N. An analytical solution is obtained for H_s/h in terms of Lambert-W functions, which also suggests alternative scaling for H_s/h. A `modified' logarithmic velocity profile is proposed for stably stratified atmospheric boundary-layer flows. A field experiment designed to observe H_s is described, which utilized instrumentation from the spring field campaign of the Mountain Terrain Atmospheric Modeling and Observations (MATERHORN) Program. Multiple releases of smoke at F≈ 0.3-0.4 support the new formulation, notwithstanding the limited success of experiments due to logistical constraints. No dividing streamline is discerned for F≈ 10, since, if present, it is too close to the foothill. Flow separation and vortex shedding is observed in this case. The proposed modified logarithmic profile is in reasonable agreement with experimental observations.
Interpretation of the exergy equation for steady-flow processes
Siemons, Roland V.
1986-01-01
We define and discuss the terms in exergy equations, with particular reference to the role of chemical terms in the exergy loss for steady-flow processes. Although there is a chemical contribution to exergy, exergy losses of steady-flow processes may be calculated by using a simple expression for th
Hassanzadeh, Pedram
Large coherent vortices are abundant in geophysical and astrophysical flows. They play significant roles in the Earth's oceans and atmosphere, the atmosphere of gas giants, such as Jupiter, and the protoplanetary disks around forming stars. These vortices are essentially three-dimensional (3D) and baroclinic, and their dynamics are strongly influenced by the rotation and density stratification of their environments. This work focuses on improving our understanding of the physics of 3D baroclinic vortices in rotating and continuously stratified flows using 3D spectral simulations of the Boussinesq equations, as well as simplified mathematical models. The first chapter discusses the big picture and summarizes the results of this work. In Chapter 2, we derive a relationship for the aspect ratio (i.e., vertical half-thickness over horizontal length scale) of steady and slowly-evolving baroclinic vortices in rotating stratified fluids. We show that the aspect ratio is a function of the Brunt-Vaisala frequencies within the vortex and outside the vortex, the Coriolis parameter, and the Rossby number of the vortex. This equation is basically the gradient-wind equation integrated over the vortex, and is significantly different from the previously proposed scaling laws that find the aspect ratio to be only a function of the properties of the background flow, and independent of the dynamics of the vortex. Our relation is valid for cyclones and anticyclones in either the cyclostrophic or geostrophic regimes; it works with vortices in Boussinesq fluids or ideal gases, and non-uniform background density gradient. The relation for the aspect ratio has many consequences for quasi-equilibrium vortices in rotating stratified flows. For example, cyclones must have interiors more stratified than the background flow (i.e., super-stratified), and weak anticyclones must have interiors less stratified than the background (i.e., sub-stratified). In addition, this equation is useful to
Local properties of countercurrent stratified steam-water flow
Kim, H J
1985-10-01
A study of steam condensation in countercurrent stratified flow of steam and subcooled water has been carried out in a rectangular channel/flat plate geometry over a wide range of inclination angles (4/sup 0/-87/sup 0/) at several aspect ratios. Variables were inlet water and steam flow rates, and inlet water temperature. Local condensation rates and pressure gradients were measured, and local condensation heat transfer coefficients and interfacial shear stress were calculated. Contact probe traverses of the surface waves were made, which allowed a statistical analysis of the wave properties. The local condensation Nusselt number was correlated in terms of local water and steam Reynolds or Froude numbers, as well as the liquid Prandtl number. A turbulence-centered model developed by Theofanous, et al. principally for gas absorption in several geometries, was modified. A correlation for the interfacial shear stress and the pressure gradient agreed with measured values. Mean water layer thicknesses were calculated. Interfacial wave parameters, such as the mean water layer thickness, liquid fraction probability distribution, wave amplitude and wave frequency, are analyzed.
Internal and vorticity waves in decaying stratified flows
Matulka, A.; Cano, D.
2009-04-01
Most predictive models fail when forcing at the Rossby deformation Radius is important and a large range of scales have to be taken into account. When mixing of reactants or pollutants has to be accounted, the range of scales spans from hundreds of Kilometers to the Bachelor or Kolmogorov sub milimiter scales. We present some theoretical arguments to describe the flow in terms of the three dimensional vorticity equations, using a lengthscale related to the vorticity (or enstrophy ) transport. Effect of intermittent eddies and non-homogeneity of diffusion are also key issues in the environment because both stratification and rotation body forces are important and cause anisotropy/non-homogeneity. These problems need further theoretical, numerical and observational work and one approach is to try to maximize the relevant geometrical information in order to understand and therefore predict these complex environmental dispersive flows. The importance of the study of turbulence structure and its relevance in diffusion of contaminants in environmental flows is clear when we see the effect of environmental disasters such as the Prestige oil spill or the Chernobil radioactive cloud spread in the atmosphere. A series of Experiments have been performed on a strongly stratified two layer fluid consisting of Brine in the bottom and freshwater above in a 1 square meter tank. The evolution of the vortices after the passage of a grid is video recorded and Particle tracking is applied on small pliolite particles floating at the interface. The combination of internal waves and vertical vorticity produces two separate time scales that may produce resonances. The vorticity is seen to oscilate in a complex way, where the frecuency decreases with time.
Steady internal waves in an exponentially stratified two-layer fluid
Makarenko, Nikolay; Maltseva, Janna; Ivanova, Kseniya
2016-04-01
The problem on internal waves in a weakly stratified two-layered fluid is studied analytically. We suppose that the fluid possess exponential stratification in both the layers, and the fluid density has discontinuity jump at the interface. By that, we take into account the influence of weak continuous stratification outside of sharp pycnocline. The model equation of strongly nonlinear interfacial waves propagating along the pycnocline is considered. This equation extends approximate models [1-3] suggested for a two-layer fluid with one homogeneous layer. The derivation method uses asymptotic analysis of fully nonlinear Euler equations. The perturbation scheme involves the long wave procedure with a pair of the Boussinesq parameters. First of these parameters characterizes small density slope outside of pycnocline and the second one defines small density jump at the interface. Parametric range of solitary wave solutions is characterized, including extreme regimes such as plateau-shape solitary waves. This work was supported by RFBR (grant No 15-01-03942). References [1] N. Makarenko, J. Maltseva. Asymptotic models of internal stationary waves, J. Appl. Mech. Techn. Phys, 2008, 49(4), 646-654. [2] N. Makarenko, J. Maltseva. Phase velocity spectrum of internal waves in a weakly-stratified two-layer fluid, Fluid Dynamics, 2009, 44(2), 278-294. [3] N. Makarenko, J. Maltseva. An analytical model of large amplitude internal solitary waves, Extreme Ocean Waves, 2nd ed. Springer 2015, E.Pelinovsky and C.Kharif (Eds), 191-201.
Steady State of Pedestrian Flow in Bottleneck Experiments
Liao, Weichen; Seyfried, Armin; Chraibi, Mohcine; Drzycimski, Kevin; Zheng, Xiaoping; Zhao, Ying
2015-01-01
Experiments with pedestrians could depend strongly on initial conditions. Comparisons of the results of such experiments require to distinguish carefully between transient state and steady state. In this work, a feasible algorithm - Cumulative Sum Control Chart - is proposed and improved to automatically detect steady states from density and speed time series of bottleneck experiments. The threshold of the detection parameter in the algorithm is calibrated using an autoregressive model. Comparing the detected steady states with previous manually selected ones, the modified algorithm gives more reproducible results. For the applications, three groups of bottleneck experiments are analysed and the steady states are detected. The study about pedestrian flow shows that the difference between the flows in all states and in steady state mainly depends on the ratio of pedestrian number to bottleneck width. When the ratio is higher than a critical value (approximately 115 persons/m), the flow in all states is almost ...
Mixing efficiency of turbulent patches in stably stratified flows
Garanaik, Amrapalli; Venayagamoorthy, Subhas Karan
2016-11-01
A key quantity that is essential for estimating the turbulent diapycnal (irreversible) mixing in stably stratified flow is the mixing efficiency Rf*, which is a measure of the amount of turbulent kinetic energy that is irreversibly converted into background potential energy. In particular, there is an ongoing debate in the oceanographic mixing community regarding the utility of the buoyancy Reynolds number (Reb) , particularly with regard to how mixing efficiency and diapycnal diffusivity vary with Reb . Specifically, is there a universal relationship between the intensity of turbulence and the strength of the stratification that supports an unambiguous description of mixing efficiency based on Reb ? The focus of the present study is to investigate the variability of Rf* by considering oceanic turbulence data obtained from microstructure profiles in conjunction with data from laboratory experiments and DNS. Field data analysis has done by identifying turbulent patches using Thorpe sorting method for potential density. The analysis clearly shows that high mixing efficiencies can persist at high buoyancy Reynolds numbers. This is contradiction to previous studies which predict that mixing efficiency should decrease universally for Reb greater than O (100) . Funded by NSF and ONR.
Free convective flow of a stratified fluid through a porous medium bounded by a vertical plane
H. K. Mondal
1994-01-01
Full Text Available Steady two-dimensional free convection flow of a thermally stratified viscous fluid through a highly porous medium bounded by a vertical plane surface of varying temperature, is considered. Analytical expressions for the velocity, temperature and the rate of heat transfer are obtained by perturbation method. Velocity distribution and rate of heat transfer for different values of parameters are shown in graphs. Velocity distribution is also obtained for certain values of the parameters by integrating the coupled differential equations by Runge-Kutta method and compared with the analytical solution. The chief concern of the paper is to study the effect of equilibrium temperature gradient on the velocity and the rate of heat transfer.
Flow birefringence of a triblock copolymer in steady shear flow
Osaki, Kunihiro; Takatori, Eiichi
1988-06-20
Because the stress-optical law was estimated not to be valid in triblock copolymer, informations on molecular motion can be obtained by studying the discrepancy from stress-optical law. The relatioship between the stress and birefringence for a triblock copolymer was investigated in steady shear flow. It was verified experimentally the discrepancy from the stress-optical law, change of macroscopic stress deviation coefficient and normal stress deviation coefficient due to shear rate, and the difference of average stress-optical coefficients calculated from the compoments. These features of birefringence proved that the contribution to stress of a polymer segment depended on its position along the chain and was larger as it was closer the center of the chain. This was useful to investigate the relaxation behavior of birefringence after the steplike shear deformation, as well as the motion of polymer chain. (4 figs, 1 tab, 11 refs)
Analysis od Ducted Propellers in Steady Flow
1986-02-01
P - ..-- ~ - ....- . *.* .*-.... *% * . N 1-.- TABLE OF CONTENTS 1. BACKGROUND. 1 2. VISCOUS EFFECTS IN TIP GAP FLOWS . 4 3. LIFTING LINE...the development of PSF and BPSF, for which the reader is referred to the beforementioned publications. 6 *-3- 2. VISCOUS EFFECTS IN TIP GAP FLOWS One...these considerations still apply. The existance of such a boundary layer is certainly due to viscous effects, but the local gap flow will be primarily
Approximating hemodynamics of cerebral aneurysms with steady flow simulations.
Geers, A J; Larrabide, I; Morales, H G; Frangi, A F
2014-01-03
Computational fluid dynamics (CFD) simulations can be employed to gain a better understanding of hemodynamics in cerebral aneurysms and improve diagnosis and treatment. However, introduction of CFD techniques into clinical practice would require faster simulation times. The aim of this study was to evaluate the use of computationally inexpensive steady flow simulations to approximate the aneurysm's wall shear stress (WSS) field. Two experiments were conducted. Experiment 1 compared for two cases the time-averaged (TA), peak systole (PS) and end diastole (ED) WSS field between steady and pulsatile flow simulations. The flow rate waveform imposed at the inlet was varied to account for variations in heart rate, pulsatility index, and TA flow rate. Consistently across all flow rate waveforms, steady flow simulations accurately approximated the TA, but not the PS and ED, WSS field. Following up on experiment 1, experiment 2 tested the result for the TA WSS field in a larger population of 20 cases covering a wide range of aneurysm volumes and shapes. Steady flow simulations approximated the space-averaged WSS with a mean error of 4.3%. WSS fields were locally compared by calculating the absolute error per node of the surface mesh. The coefficient of variation of the root-mean-square error over these nodes was on average 7.1%. In conclusion, steady flow simulations can accurately approximate the TA WSS field of an aneurysm. The fast computation time of 6 min per simulation (on 64 processors) could help facilitate the introduction of CFD into clinical practice.
Steady inviscid three-dimensional flows
Adamczyk, J. J.; Chang, S.-C.
1985-01-01
The present analysis combines some of the theoretical concepts suggested by Hawthorne (1955) with a numerical integration procedure suggested by Martin (1978). The resulting algorithm is for inviscid subsonic flows. Thus, it is restricted to high Reynolds number flows. Chang and Adamczyk (1983) have provided a detailed derivation of the present algorithm along with a discussion of its stability bounds. The present paper represents a summary of this work. The integration of the continuity equation is considered along with an evaluation of the entropy, total temperature, and vorticity field. Attention is given to the shear-flow algorithm construction, and an application to a shear flow in a turning channel. A description of numerical results is also provided. The discussed algorithm represents a new procedure for solving inviscid subsonic three-dimensional rotational flows.
The Universal Aspect Ratio of Vortices in Rotating Stratified Flows: Theory and Simulation
Hassanzadeh, Pedram; Gal, Patrice Le
2012-01-01
We derive a relationship for the vortex aspect ratio $\\alpha$ (vertical half-thickness over horizontal length scale) for steady and slowly evolving vortices in rotating stratified fluids, as a function of the Brunt-Vaisala frequencies within the vortex $N_c$ and in the background fluid outside the vortex $\\bar{N}$, the Coriolis parameter $f$, and the Rossby number $Ro$ of the vortex: $\\alpha^2 = Ro(1+Ro) f^2/(N_c^2-\\bar{N}^2)$. This relation is valid for cyclones and anticyclones in either the cyclostrophic or geostrophic regimes; it works with vortices in Boussinesq fluids or ideal gases, and the background density gradient need not be uniform. Our relation for $\\alpha$ has many consequences for equilibrium vortices in rotating stratified flows. For example, cyclones must have $N_c^2 > \\bar{N}^2$; weak anticyclones (with $|Ro| \\bar{N}^2$. We verify our relation for $\\alpha$ with numerical simulations of the three-dimensional Boussinesq equations for a wide variety of vortices, including: vortices that are i...
Instability criteria for steady flows of a perfect fluid.
Friedlander, Susan; Vishik, Misha M.
1992-07-01
An instability criterion based on the positivity of a Lyapunov-type exponent is used to study the stability of the Euler equations governing the motion of an inviscid incompressible fluid. It is proved that any flow with exponential stretching of the fluid particles is unstable. In the case of an arbitrary axisymmetric steady integrable flow, a sufficient condition for instability is exhibited in terms of the curvature and the geodesic torsion of a stream line and the helicity of the flow.
Transport Phenomena in Stratified Multi-Fluid Flow in the Presence and Absence of Gravity
Chigier, Norman; Humphrey, William
1996-01-01
Experiments are being conducted to study the effects of buoyancy on planar density-stratified shear flows. A wind tunnel generates planar flows separated by an insulating splitter plate, with either flow heated, which emerge from a two-dimensional nozzle. The objective is to isolate and define the effect of gravity and buoyancy on a stratified shear layer. To this end, both stably and unstably stratified layers will be investigated. This paper reports on the results of temperature and velocity measurements across the nozzle exit plane and downstream along the nozzle center plane.
Steady streamwise transpiration control in turbulent pipe flow
Gómez, F; Rudman, M; Sharma, AS; McKeon, BJ
2016-01-01
A study of the the main features of low- and high amplitude steady streamwise wall transpiration applied to pipe flow is presented. The effect of the two transpiration parameters, amplitude and wavenumber, on the flow have been investigated by means of direct numerical simulation at a moderate turbulent Reynolds number. The behaviour of the three identified mechanisms that act in the flow: modification of Reynolds shear stress, steady streaming and generation of non-zero mean streamwise gradients, have been linked to the transpiration parameters. The observed trends have permitted the identification of wall transpiration configurations able to reduce or increase the overall flow rate in -36.1% and 19.3% respectively. A resolvent analysis has been carried out to obtain a description of the reorganization of the flow structures induced by the transpiration.
QIU Xiang
2006-01-01
Turbulence structures and turbulent Counter-Gradient Transport(CGT) properties in the stratified flows with a sharp temperature interface are investigated by experimental measurements using LIF and PIV, by LES and by correlation analysis.
The Lagrangian Deformation Structure of Three-Dimensional Steady Flow
Lester, Daniel R; Borgne, Tanguy Le; de Barros, Felipe P J
2016-01-01
Fluid deformation and strain history are central to wide range of fluid mechanical phenomena ranging from fluid mixing and particle transport to stress development in complex fluids and the formation of Lagrangian coherent structures (LCSs). To understand and model these processes it is necessary to quantify Lagrangian deformation in terms of Eulerian flow properties, currently an open problem. To elucidate this link we develop a Protean (streamline) coordinate transform for steady three-dimensional (3D) flows which renders both the velocity gradient and deformation gradient upper triangular. This frame not only simplifies computation of fluid deformation metrics such as fi?nite-time Lyapunov exponents (FTLEs) and elucidates the deformation structure of the flow, but moreover explicitly recovers kinematic and topological constraints upon deformation such as those related to helicity density and the Poincar\\'{e}-Bendixson theorem. We apply this transform to several classes of steady 3D flow, including helical ...
IRROTATIONAL APPROXIMATION TO STEADY SUPERSONIC FLOW IN TWO SPACE VARIABLES
Liu Chong
2008-01-01
On the assumption that the total variation of the initial data is sufficiently small,we can use the stability results of Dafermos to get the L2 estimate of the difference between the solutions to the isentropic steady Euler system and the potential flow equations with the same initial data.
Reduced order modeling of steady flows subject to aerodynamic constraints
Zimmermann, Ralf; Vendl, Alexander; Goertz, Stefan
2014-01-01
A novel reduced-order modeling method based on proper orthogonal decomposition for predicting steady, turbulent flows subject to aerodynamic constraints is introduced. Model-order reduction is achieved by replacing the governing equations of computational fluid dynamics with a nonlinear weighted ...
Modulated stagnation-point flow and steady streaming
Merchant, Gregory J.; Davis, Stephen H.
1989-01-01
Plane stagnation-point flow is modulated in the free stream so that the velocity components are proportional to K(H) + K cos omega t. Similarity solutions of the Navier-Stokes equations are examined using high-frequency asymptotics for K and K(H) of unit order. Special attention is focused on the steady streaming generated in this flow with strongly non-parallel streamlines.
A criterion for the onset of slugging in horizontal stratified air-water countercurrent flow
Chun, Moon-Hyun; Lee, Byung-Ryung; Kim, Yang-Seok [Korea Advanced Institute of Science and Technology, Taejon (Korea, Republic of)] [and others
1995-09-01
This paper presents an experimental and theoretical investigation of wave height and transition criterion from wavy to slug flow in horizontal air-water countercurrent stratified flow conditions. A theoretical formula for the wave height in a stratified wavy flow regime has been developed using the concept of total energy balance over a wave crest to consider the shear stress acting on the interface of two fluids. From the limiting condition of the formula for the wave height, a necessary criterion for transition from a stratified wavy flow to a slug flow has been derived. A series of experiments have been conducted changing the non-dimensional water depth and the flow rates of air in a horizontal pipe and a duct. Comparisons between the measured data and the predictions of the present theory show that the agreement is within {plus_minus}8%.
Short-wave vortex instability in stratified flow
Bovard, Luke
2014-01-01
In this paper we investigate a new instability of the Lamb-Chaplygin dipole in a stratified fluid. Through numerical linear stability analysis, a secondary peak in the growth rate emerges at vertical scales about an order of magnitude smaller than the buoyancy scale $L_{b}=U/N$ where $U$ is the characteristic velocity and $N$ is the Brunt-V\\"{a}is\\"{a}l\\"{a} frequency. This new instability exhibits a growth rate that is similar to, and even exceeds, that of the zigzag instability, which has the characteristic length of the buoyancy scale. This instability is investigated for a wide range of Reynolds $Re=2000-20000$ and horizontal Froude numbers $F_{h}=0.05-0.2$, where $F_{h}=U/NR$, $Re=UR/\
Simple numerical method for predicting steady compressible flows
Vonlavante, Ernst; Nelson, N. Duane
1986-01-01
A numerical method for solving the isenthalpic form of the governing equations for compressible viscous and inviscid flows was developed. The method was based on the concept of flux vector splitting in its implicit form. The method was tested on several demanding inviscid and viscous configurations. Two different forms of the implicit operator were investigated. The time marching to steady state was accelerated by the implementation of the multigrid procedure. Its various forms very effectively increased the rate of convergence of the present scheme. High quality steady state results were obtained in most of the test cases; these required only short computational times due to the relative efficiency of the basic method.
Sung, Chang Kyung [Korea Electric Power Research Institute, Taejon (Korea, Republic of)
1997-12-31
This paper presents a theoretical approach of the instability criterion from stratified to nonstratified flow in horizontal pipe at cocurrent flow conditions. The new theoretical instability criterion for the stratified and nonstratified flow transition in horizontal pipe has been developed by hyperbolic equations in two-phase flow. Critical flow condition criterion and onset of slugging at cocurrent flow condition correspond to zero and imaginary characteristics which occur when the hyperbolicity of a stratified two-phase flow is broken, respectively. Through comparison between results predicted by the present flow is broken, respectively. Through comparison between results predicted by the present theory and the Kukita et al. [1] experimental data of pipes, it is shown that they are in good agreement with data. 4 refs., 2 figs. (Author)
Mathematical models for two-phase stratified pipe flow
Biberg, Dag
2005-06-01
The simultaneous transport of oil, gas and water in a single multiphase flow pipe line has for economical and practical reasons become common practice in the gas and oil fields operated by the oil industry. The optimal design and safe operation of these pipe lines require reliable estimates of liquid inventory, pressure drop and flow regime. Computer simulations of multiphase pipe flow have thus become an important design tool for field developments. Computer simulations yielding on-line monitoring and look ahead predictions are invaluable in day-to-day field management. Inaccurate predictions may have large consequences. The accuracy and reliability of multiphase pipe flow models are thus important issues. Simulating events in large pipelines or pipeline systems is relatively computer intensive. Pipe-lines carrying e.g. gas and liquefied gas (condensate) may cover distances of several hundred km in which transient phenomena may go on for months. The evaluation times associated with contemporary 3-D CFD models are thus not compatible with field applications. Multiphase flow lines are therefore normally simulated using specially dedicated 1-D models. The closure relations of multiphase pipe flow models are mainly based on lab data. The maximum pipe inner diameter, pressure and temperature in a multiphase pipe flow lab is limited to approximately 0.3 m, 90 bar and 60{sup o}C respectively. The corresponding field values are, however, much higher i.e.: 1 m, 1000 bar and 200{sup o}C respectively. Lab data does thus not cover the actual field conditions. Field predictions are consequently frequently based on model extrapolation. Applying field data or establishing more advanced labs will not solve this problem. It is in fact not practically possible to acquire sufficient data to cover all aspects of multiphase pipe flow. The parameter range involved is simply too large. Liquid levels and pressure drop in three-phase flow are e.g. determined by 13 dimensionless parameters
Steady State Stokes Flow Interpolation for Fluid Control
Bhatacharya, Haimasree; Nielsen, Michael Bang; Bridson, Robert
2012-01-01
Fluid control methods often require surface velocities interpolated throughout the interior of a shape to use the velocity as a feedback force or as a boundary condition. Prior methods for interpolation in computer graphics — velocity extrapolation in the normal direction and potential flow...... — suffer from a common problem. They fail to capture the rotational components of the velocity field, although extrapolation in the normal direction does consider the tangential component. We address this problem by casting the interpolation as a steady state Stokes flow. This type of flow captures...... the rotational components and is suitable for controlling liquid animations where tangential motion is pronounced, such as in a breaking wave...
Mixing and entrainment in hydraulically driven stratified sill flows
Holtegaard Nielsen, Morten; Pratt, Larry; Helfrich, Karl
2004-09-01
The investigation involves the hydraulic behaviour of a dense layer of fluid flowing over an obstacle and subject to entrainment of mass and momentum from a dynamically inactive (but possibly moving) overlying fluid. An approach based on the use of reduced gravity, shallow-water theory with a cross-interface entrainment velocity is compared with numerical simulations based on a model with continuously varying stratification and velocity. The locations of critical flow (hydraulic control) in the continuous model are estimated by observing the direction of propagation of small-amplitude long-wave disturbances introduced into the flow field. Although some of the trends predicted by the shallow-water model are observed in the continuous model, the agreement between the interface profiles and the position of critical flow is quantitatively poor. A reformulation of the equations governing the continuous flow suggests that the reduced gravity model systematically underestimates inertia and overestimates buoyancy. These differences are quantified by shape coefficients that measure the vertical non-uniformities of the density and horizontal velocity that arise, in part, by incomplete mixing of entrained mass and momentum over the lower-layer depth. Under conditions of self-similarity (as in Wood's similarity solution) the shape coefficients are constant and the formulation determines a new criterion for and location of critical flow. This location generally lies upstream of the critical section predicted by the reduced-gravity model. Self-similarity is not observed in the numerically generated flow, but the observed critical section continues to lie upstream of the location predicted by the reduced gravity model. The factors influencing this result are explored.
Multiple steady states in coupled flow tank reactors
Hunt, Katharine L. C.; Kottalam, J.; Hatlee, Michael D.; Ross, John
1992-05-01
Coupling between continuous-flow, stirred tank reactors (CSTR's), each having multiple steady states, can produce new steady states with different concentrations of the chemical species in each of the coupled tanks. In this work, we identify a kinetic potential ψ that governs the deterministic time evolution of coupled tank reactors, when the reaction mechanism permits a single-variable description of the states of the individual tanks; examples include the iodate-arsenous acid reaction, a cubic model suggested by Noyes, and two quintic models. Stable steady states correspond to minima of ψ, and unstable steady states to maxima or saddle points; marginally stable states typically correspond to saddle-node points. We illustrate the variation in ψ due to changes in the rate constant for external material intake (k0) and for exchange between tanks (kx). For fixed k0 values, we analyze the changes in numbers and types of steady states as kx increases from zero. We show that steady states disappear by pairwise coalescence; we also show that new steady states may appear with increasing kx, when the reaction mechanism is sufficiently complex. For fixed initial conditions, the steady state ultimately reached in a mixing experiment may depend on the exchange rate constant as a function of time, kx(t) : Adiabatic mixing is obtained in the limit of slow changes in kx(t) and instantaneous mixing in the limit as kx(t)→∞ while t remains small. Analyses based on the potential ψ predict the outcome of mixing experiments for arbitrary kx(t). We show by explicit counterexamples that a prior theory developed by Noyes does not correctly predict the instability points or the transitions between steady states of coupled tanks, to be expected in mixing experiments. We further show that the outcome of such experiments is not connected to the relative stability of steady states in individual tank reactors. We find that coupling may effectively stabilize the tanks. We provide
Arbitrary axisymmetric steady streaming: Flow, force and propulsion
Spelman, Tamsin A
2015-01-01
A well-developed method to induce mixing on microscopic scales is to exploit flows generated by steady streaming. Steady streaming is a classical fluid dynamics phenomenon whereby a time-periodic forcing in the bulk or along a boundary is enhanced by inertia to induce a non-zero net flow. Building on classical work for simple geometrical forcing and motivated by the complex shape oscillations of elastic capsules and bubbles, we develop the mathematical framework to quantify the steady streaming of a spherical body with arbitrary axisymmetric time-periodic boundary conditions. We compute the flow asymptotically for small-amplitude oscillations of the boundary in the limit where the viscous penetration length scale is much smaller than the body. In that case, the flow has a boundary layer structure and the fluid motion is solved by asymptotic matching. Our results, presented in the case of no-slip boundary conditions and extended to include the motion of vibrating free surfaces, recovers classical work as parti...
Stratified shear flow in an inclined duct: coherent structures and mixing
Lefauve, Adrien; Partridge, Jamie; Dalziel, Stuart; Linden, Paul
2016-11-01
We present laboratory experiments on the exchange flow in an inclined square duct connecting two reservoirs at different densities. This system generates and maintains a stratified shear flow, which can be laminar, wavy or turbulent depending on the density difference and inclination angle. It is believed that the mean dissipation is set by the angle, and that high buoyancy Reynolds numbers (i.e. turbulent intensity) can be maintained, making this system suited for the study of continuously forced stratified turbulence. The talk will focus on the analysis of time-resolved, near-instantaneous 3D velocity and density data obtained by stereo particle image velocimetry (PIV) and laser induced fluorescence (LIF). This data allow for the visualisation of 3D coherent structures as well as turbulent mixing properties, which are key in understanding the dynamics of stratified turbulence. Supported by EPSRC Programme Grant EP/K034529/1 entitled "Mathematical Underpinnings of Stratified Turbulence".
Prediction of Stratified Flow Temperature Profiles in a Fully Insulated Environment
Ahmad S. Awad
2014-07-01
Full Text Available The aim of the study is to present an analytical model to predict the temperature profiles in thermal stratified environment. Thermal stratification is encountered in many situations. The flow of contaminants and hydrocarbons in environment often get stratified. The prediction of temperature profiles and flow characteristics are essential for HVAC applications, environment and energy management. The temperature profiles in the stratified region are successfully obtained, in terms of flow-operating functions. The analytical model agrees well with the published experimental data as well as the related closed-form solutions, which is helpful for HVAC applications. The model will be further developed and incorporated within a numerical model in order to investigate the flow field characteristics and establish correlations for a wide range of parameters.
Interfacial area concentration in steady fully-developed bubbly flow
Hibiki, T. [Kyoto Univ., Research Reactor Institute (Japan); Ishii, M. [Purdue Univ., Lafayette, IN (United States). School of Nuclear Engineering
2001-07-01
A simple equation for the interfacial area concentration under steady fully-developed bubbly flow condition has been derived from the interfacial area transport equation. The derived theoretical equation has been modified to obtain experimentally supported predictive correlation. The obtained interfacial area correlation was validated by 204 data sets measured in air-water bubbly flows under various conditions. These data sets covered extensive flow and loop conditions such as channel geometry (circular or rectangular channel), flow direction (vertical or horizontal flow), superficial gas velocity (0,018 m/s - 4,87 m/s), superficial liquid velocity (0,262 m/s - 6,55 m/s) and interfacial area concentration (25,8 m{sup -1} - 1083 m{sup -1} ). An excellent agreement was obtained between the developed semi-theoretical correlation and data within an average relative deviation of 11,1 %. (author)
Steady shear flow thermodynamics based on a canonical distribution approach.
Taniguchi, Tooru; Morriss, Gary P
2004-11-01
A nonequilibrium steady-state thermodynamics to describe shear flow is developed using a canonical distribution approach. We construct a canonical distribution for shear flow based on the energy in the moving frame using the Lagrangian formalism of the classical mechanics. From this distribution, we derive the Evans-Hanley shear flow thermodynamics, which is characterized by the first law of thermodynamics dE=TdS-Qdgamma relating infinitesimal changes in energy E, entropy S, and shear rate gamma with kinetic temperature T. Our central result is that the coefficient Q is given by Helfand's moment for viscosity. This approach leads to thermodynamic stability conditions for shear flow, one of which is equivalent to the positivity of the correlation function for Q. We show the consistency of this approach with the Kawasaki distribution function for shear flow, from which a response formula for viscosity is derived in the form of a correlation function for the time-derivative of Q. We emphasize the role of the external work required to sustain the steady shear flow in this approach, and show theoretically that the ensemble average of its power W must be non-negative. A nonequilibrium entropy, increasing in time, is introduced, so that the amount of heat based on this entropy is equal to the average of W. Numerical results from nonequilibrium molecular-dynamics simulation of two-dimensional many-particle systems with soft-core interactions are presented which support our interpretation.
Experimental investigation on isothermal stratified flow mixing in a horizontal T-junction
Isaev, Alexander; Kulenovic, Rudi; Laurien, Eckart [Stuttgart Univ. (Germany). Inst. fuer Kernenergetik und Energiesysteme (IKE)
2016-10-15
Turbulent and stratified flows can lead to thermal fatigue in piping systems of nuclear power plants (NPP). Such flows can be investigated in the University of Stuttgart Fluid-Structure-Interaction (FSI) facility with a T-Junction at thermal conditions with temperature differences of up to 255 K and at pressures of maximum 75 bars.
Mixing and entrainment in hydraulically driven stratified sill flows
Nielsen, Morten Holtegaard; Pratt, Larry; Helfrich, Karl
2004-01-01
that the reduced gravity model systematically underestimates inertia and overestimates buoyancy. These differences are quantified by shape coefficients that measure the vertical non-uniformities of the density and horizontal velocity that arise, in part, by incomplete mixing of entrained mass and momentum over...... model. Self-similarity is not observed in the numerically generated flow, but the observed critical section continues to lie upstream of the location predicted by the reduced gravity model. The factors influencing this result are explored.......The investigation involves the hydraulic behaviour of a dense layer of fluid flowing over an obstacle and subject to entrainment of mass and momentum from a dynamically inactive (but possibly moving) overlying fluid. An approach based on the use of reduced gravity, shallow-water theory with a cross...
A dynamic subgrid-scale model for the large eddy simulation of stratified flow
刘宁宇; 陆夕云; 庄礼贤
2000-01-01
A new dynamic subgrid-scale (SGS) model, including subgrid turbulent stress and heat flux models for stratified shear flow is proposed by using Yoshizawa’ s eddy viscosity model as a base model. Based on our calculated results, the dynamic subgrid-scale model developed here is effective for the large eddy simulation (LES) of stratified turbulent channel flows. The new SGS model is then applied to the large eddy simulation of stratified turbulent channel flow under gravity to investigate the coupled shear and buoyancy effects on the near-wall turbulent statistics and the turbulent heat transfer at different Richardson numbers. The critical Richardson number predicted by the present calculation is in good agreement with the value of theoretical analysis.
A dynamic subgrid-scale model for the large eddy simulation of stratified flow
无
2000-01-01
A new dynamic subgrid-scale (SGS) model, including subgrid turbulent stress and heat flux models for stratified shear flow is proposed by using Yoshizawa's eddy viscosity model as a base model. Based on our calculated results, the dynamic subgrid-scale model developed here is effective for the large eddy simulation (LES) of stratified turbulent channel flows. The new SGS model is then applied to the large eddy simulation of stratified turbulent channel flow under gravity to investigate the coupled shear and buoyancy effects on the near-wall turbulent statistics and the turbulent heat transfer at different Richardson numbers. The critical Richardson number predicted by the present calculation is in good agreement with the value of theoretical analysis.
A NONHYDROSTATIC NUMERICAL MODEL FOR DENSITY STRATIFIED FLOW AND ITS APPLICATIONS
无
2008-01-01
A modular numerical model was developed for simulating density-stratified flow in domains with irregular bottom topography. The model was designed for examining interactions between stratified flow and topography, e.g., tidally driven flow over two-dimensional sills or internal solitary waves propagating over a shoaling bed. The model was based on the non-hydrostatic vorticity-stream function equations for a continuously stratified fluid in a rotating frame. A self-adaptive grid was adopted in the vertical coordinate, the Alternative Direction Implicit (ADI) scheme was used for the time marching equations while the Poisson equation for stream-function was solved based on the Successive Over Relaxation (SOR) iteration with the Chebyshev acceleration. The numerical techniques were described and three applications of the model were presented.
ZHONG; Fengquan(仲峰泉); LIU; Nansheng(刘难生); LU; Xiyun(陆夕云); ZHUANG; Lixian(庄礼贤)
2002-01-01
In the present paper, a new dynamic subgrid-scale (SGS) model of turbulent stress and heat flux for stratified shear flow is proposed. Based on our calculated results of stratified channel flow, the dynamic subgrid-scale model developed in this paper is shown to be effective for large eddy simulation (LES) of stratified turbulent shear flows. The new SGS model is then applied to the LES of the stratified turbulent channel flow to investigate the coupled shear and buoyancy effects on the behavior of turbulent statistics, turbulent heat transfer and flow structures at different Richardson numbers.
Stability of stratified flow and slugging in horizontal gas-liquid flow
GU Hanyang; GUO Liejin
2005-01-01
A transient one-dimensional two-fluid model is proposed to investigate numerically the interfacial instability and the onset of slugging for liquid-gas flow in a horizontal duct. In the present model, the effects of surface tension and transverse variations in dynamic pressure are taken into account. The evolution of interfacial disturbances is displayed and compared with the linear viscous KelvinHelmholtz stability analyses. It shows that interfacial wave is more instable due to the non-linear effect. The model predicts well the stability limit of stratified flow in comparison with the experimental data, and also automatically tracks the onset of slugging. The results show that the initiation of hydrodynamic slugging is related to local interfacial instability. Based on the cycle of slugging, a model for slug frequency is presented, which predicts the trends of slug frequencies with gas/liquid flow rate well in comparison with the available data. The effects of physical properties on slugging have been examined. It is found that with the increase in the gas viscosity and liquid density the slugging would be inhibited, whereas, with the increase in liquid viscosity and gas density, the slugging can be promoted.
Steady vortex force theory and slender-wing flow diagnosis
Y.T.Yang; R.K.Zhang; Y.R.An; J.Z.Wu
2007-01-01
The concept vortex force in aerodynamics is sys-tematically examined based on a new steady vortex-force theory (Wu et al., Vorticity and vortex dynamics, Springer, 2006) which expresses the aerodynamic force (and moment) by the volume and boundary integrals of the Lamb vector.In this paper, the underlying physics of this theory is explo-red, including the general role of the Lamb vector in non-linear aerodynamics, its initial formation, and its relevance to the total-pressure non-uniformity. As a typical example, the theory is applied to the flow over a slender delta wing at a large angle of attack. The highly localized flow structures with high Lamb-vector peaks are identified in terms of their net contribution to various constituents of the total aerody-namic force. This vortex-force diagnosis sheds new light on the flow control and configuration optimization.
Steady-state flow properties of amorphous materials
Jadhao, Vikram; O'Connor, Thomas; Robbins, Mark
2015-03-01
Molecular dynamics (MD) simulations are used to investigate the steady-state shear flow curves of a standard glass model: the bidisperse Lennard-Jones system. For a wide range of temperatures in the neighborhood of the glass transition temperature Tg predicted by the mode coupling theory, we compute the steady-state shear stress and viscosity as a function of the shear rate γ ˙. At temperatures near and above Tg, the stress crosses over from linear Newtonian behavior at low rates to power law shear-thinning at high rates. As T decreases below Tg, the stress shows a plateau, becoming nearly rate-independent at low γ ˙. There is a weak increase in stress that is consistent with Eyring theory for activated flow of a solid. We find that when the strain rate is reduced to extremely low values, Newtonian behavior appears once more. Insights gained from these simulations are applied to the computation of flow curves of a well-established boundary lubricant: squalane. In the elastohydrodynamic regime, squalane responds like a glassy solid with an Eyring-like response, but at low rates it has a relatively small Newtonian viscosity. Supported by the Army Research Laboratory under Grant W911NF-12-2-0022.
Multiple nonequilibrium steady states for one-dimensional heat flow.
Zhang, F; Isbister, D J; Evans, D J
2001-08-01
A nonequilibrium molecular dynamics model of heat flow in one-dimensional lattices is shown to have multiple steady states for any fixed heat field strength f(e) ranging from zero to a certain positive value. We demonstrate that, depending on the initial conditions, there are at least two possibilities for the system's evolution: (i) formation of a stable traveling wave (soliton), and (ii) chaotic motion throughout the entire simulation. The percentage of the soliton-generating trajectories is zero for small field strength f(e), but increases sharply to unity over a critical region of the parameter f(e).
Lagrangian chaos in three- dimensional steady buoyancy-driven flows
Contreras, Sebastian; Speetjens, Michel; Clercx, Herman
2016-11-01
Natural convection plays a key role in fluid dynamics owing to its ubiquitous presence in nature and industry. Buoyancy-driven flows are prototypical systems in the study of thermal instabilities and pattern formation. The differentially heated cavity problem has been widely studied for the investigation of buoyancy-induced oscillatory flow. However, far less attention has been devoted to the three-dimensional Lagrangian transport properties in such flows. This study seeks to address this by investigating Lagrangian transport in the steady flow inside a cubic cavity differentially-heated from the side. The theoretical and numerical analysis expands on previously reported similarities between the current flow and lid-driven flows. The Lagrangian dynamics are controlled by the Péclet number (Pe) and the Prandtl number (Pr). Pe controls the behaviour qualitatively in that growing Pe progressively perturbs the integable state (Pe =0), thus paving the way to chaotic dynamics. Pr plays an entirely quantitative role in that Pr1 amplifies and diminishes, respectively, the perturbative effect of non-zero Pe. S.C. acknowledges financial support from Consejo Nacional de Ciencia y Tecnología (CONACYT).
Stratified Flow in a Room with Displacement Ventilation and Wall-Mounted Air Terminal devices
Nielsen, Peter V.
This paper describes experiments with wall-mounted air terminal devices. The stratified flow in the room is analyzed, and the influence of stratification and the influence of room dimensions on the velocity level and on the length scale are proved. The velocity level in the occupied zone can be d...
Hirota, Makoto, E-mail: hirota@dragon.ifs.tohoku.ac.jp [Institute of Fluid Science, Tohoku University, Sendai, Miyagi 980-8577 (Japan); Morrison, Philip J. [Department of Physics and Institute for Fusion Studies, University of Texas at Austin, Austin, TX 78712 (United States)
2016-05-06
Highlights: • New stability criteria of stably stratified shear flow are discovered. • Our criteria substantially improve the Howard–Miles criterion (1961). • Our criteria also generalize Rayleigh's inflection point theorem. • The novel approach we found is also efficient as a numerical approach. - Abstract: Linear stability of inviscid, parallel, and stably stratified shear flow is studied under the assumption of smooth strictly monotonic profiles of shear flow and density, so that the local Richardson number is positive everywhere. The marginally unstable modes are systematically found by solving a one-parameter family of regular Sturm–Liouville problems, which can determine the stability boundaries more efficiently than solving the Taylor–Goldstein equation directly. By arguing for the non-existence of a marginally unstable mode, we derive new sufficient conditions for stability, which generalize the Rayleigh–Fjørtoft criterion for unstratified shear flows.
Doubly stratified mixed convection flow of Maxwell nanofluid with heat generation/absorption
Abbasi, F.M., E-mail: abbasisarkar@gmail.com [Department of Mathematics, Comsats Institute of Information Technology, Islamabad 44000 (Pakistan); Shehzad, S.A. [Department of Mathematics, Comsats Institute of Information Technology, Sahiwal 57000 (Pakistan); Hayat, T. [Department of Mathematics, Quaid-i-Azam University, 45320, Islamabad 44000 (Pakistan); NAAM Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589 (Saudi Arabia); Ahmad, B. [NAAM Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589 (Saudi Arabia)
2016-04-15
Magnetohydrodynamic (MHD) doubly stratified flow of Maxwell nanofluid in presence of mixed convection is analyzed in this article. Effects of thermophoresis, Brownian motion and heat generation/absorption are present. The flow is induced due to linear stretching of sheet. Mathematical formulation is made under boundary layer approach. Expressions of velocity, temperature and nanoparticles concentration are developed. The obtained results are plotted and discussed to examine the variations in temperature and nanoparticles concentration due to different physical parameters. Numerical computations are made to obtain the values of local Nusselt and Sherwood numbers. Impact of sundry parameters on the flow quantities is analyzed graphically. - Highlights: • Double stratified flow of Maxwell nanofluid with mixed convection is modeled. • Thermophoresis and Brownian motion effects are encountered. • Computations are made to obtain the solution expressions. • Numerical values of local Nusselt and Sherwood numbers are computed and examined.
Computation of Steady Incompressible Flows in Unbounded Domains
Gustafsson, Jonathan
2014-01-01
In this study we revisit the problem of computing steady Navier-Stokes flows in two-dimensional unbounded domains. Precise quantitative characterization of such flows in the high-Reynolds number limit remains an open problem of theoretical fluid dynamics. Following a review of key mathematical properties of such solutions related to the slow decay of the velocity field at large distances from the obstacle, we develop and carefully validate a spectrally-accurate computational approach which ensures the correct behavior of the solution at infinity. In the proposed method the numerical solution is defined on the entire unbounded domain without the need to truncate this domain to a finite box with some artificial boundary conditions prescribed at its boundaries. Since our approach relies on the streamfunction-vorticity formulation, the main complication is the presence of a discontinuity in the streamfunction field at infinity which is related to the slow decay of this field. We demonstrate how this difficulty ca...
In vitro heart valve testing: steady versus pulsatile flow.
Black, M M; Hose, D R; Lamb, C J; Lawford, P V; Ralph, S J
1994-03-01
The design of artificial heart valves has traditionally been based on the development of a prototype device which was then subjected to extensive laboratory testing in order to confirm its suitability for clinical use. In the past the in vitro assessment of a valve's performance was based principally on the measurement of parameters such as pressure difference, regurgitation and, more recently, energy losses. Such measurements can be defined as being at the 'macro' level and rarely show any clinically significant differences amongst currently available prostheses. The analytical approach to flow through heart valves has previously been hampered by difficulties experienced in solving the relevant equations of flow particularly in the case of pulsatile conditions. Computational techniques are now available which enable appropriate solutions to be obtained for these problems and consequently provide an opportunity for detailed examination of the 'micro' level of flow disturbances exhibited by the different valves. This present preliminary study is designed to illustrate the use of such an analytical approach to the flow through prosthetic valves. A single topic has been selected for this purpose which is the comparative value of steady versus pulsatile flow testing. A bileaflet valve was chosen for the analysis and a mathematical model of this valve in the aortic position of the Sheffield Pulse Duplicator was created. The theoretical analysis was carried out using a commercially available Computational Fluid Dynamics package, namely, FIDAP, on a SUN MICROSYSTEMS 10-30 workstation.(ABSTRACT TRUNCATED AT 250 WORDS)
Models of steady state cooling flows in elliptical galaxies
Vedder, Peter W.; Trester, Jeffrey J.; Canizares, Claude R.
1988-01-01
A comprehensive set of steady state models for spherically symmetric cooling flows in early-type galaxies is presented. It is found that a reduction of the supernova (SN) rate in ellipticals produces a decrease in the X-ray luminosity of galactic cooling flows and a steepening of the surface brightness profile. The mean X-ray temperature of the cooling flow is not affected noticeably by a change in the SN rate. The external pressure around a galaxy does not markedly change the luminosity of the gas within the galaxy but does change the mean temperature of the gas. The presence of a dark matter halo in a galaxy only changes the mean X-ray temperature slightly. The addition of a distribution of mass sinks which remove material from the general accretion flow reduces L(X) very slightly, flattens the surface brightness profile, and reduces the central surface brightness level to values close to those actually observed. A reduction in the stellar mass-loss rate only slightly reduces the X-ray luminosity of the cooling flow and flattens the surface brightness by a small amount.
Garaud, Pascale; Gagnier, Damien; Verhoeven, Jan
2017-03-01
Shear-induced turbulence could play a significant role in mixing momentum and chemical species in stellar radiation zones, as discussed by Zahn. In this paper we analyze the results of direct numerical simulations of stratified plane Couette flows, in the limit of rapid thermal diffusion, to measure the turbulent viscosity and the turbulent diffusivity of a passive tracer as a function of the local shear and the local stratification. We find that the stability criterion proposed by Zahn, namely that the product of the gradient Richardson number and the Prandtl number must be smaller than a critical values {(J\\Pr )}c for instability, adequately accounts for the transition to turbulence in the flow, with {(J\\Pr )}c≃ 0.007. This result recovers and confirms the prior findings of Prat et al. Zahn’s model for the turbulent diffusivity and viscosity, namely that the mixing coefficient should be proportional to the ratio of the thermal diffusivity to the gradient Richardson number, does not satisfactorily match our numerical data. It fails (as expected) in the limit of large stratification where the Richardson number exceeds the aforementioned threshold for instability, but it also fails in the limit of low stratification where the turbulent eddy scale becomes limited by the computational domain size. We propose a revised model for turbulent mixing by diffusive stratified shear instabilities that properly accounts for both limits, fits our data satisfactorily, and recovers Zahn’s model in the limit of large Reynolds numbers.
Nonlinear dynamics at the interface of two-layer stratified flows over pronounced obstacles
Cabeza, C; Bove, I; Freire, D; Marti, Arturo C; Sarasua, L G; Usera, G; Montagne, R; Araújo, M
2008-01-01
The flow of a two--layer stratified fluid over an abrupt topographic obstacle, simulating relevant situations in oceanographic problems, is investigated numerically and experimentally in a simplified two--dimensional situation. Experimental results and numerical simulations are presented at low Froude numbers in a two-layer stratified flow and for two abrupt obstacles, semi--cylindrical and prismatic. We find four different regimes of the flow immediately past the obstacles: sub-critical (I), internal hydraulic jump (II), Kelvin-Helmholtz at the interface (III) and shedding of billows (IV). The critical condition for delimiting the experiments is obtained using the hydraulic theory. Moreover, the dependence of the critical Froude number on the geometry of the obstacle are investigated. The transition from regime III to regime IV is explained with a theoretical stability analysis. The results from the stability analysis are confirmed with the DPIV measurements. In regime (IV), when the velocity upstream is lar...
Laboratory Studies of the Stratified Rotating Flow Passing over an Isolated Obstacle
高守亭; 平凡
2003-01-01
We study the flow of a density-stratified fluid passing over an isolated obstacle, using towing-tank experiments.Our special concern is the response of the flow with different Froude numbers passing over a three-dimensional obstacle. A series of experiments of the stratified rotating flow passing over an isolated obstacle was carried out with the towering-tank controlled by the similarity laws and dynamic non-dimension parameters. These experiments show that the Froude number is a very important parameter, and the lee wave and the eddy structure appear simultaneously under an appropriate conditions. The effect of rotation on the lee wave is mainly to change wave amplitude, particularly to restrain the development of the lee wave and to promote the formation of an eddy.
Numerical study of thermally stratified flows of a fluid overlying a highly porous material
Antoniadis, Panagiotis D.; Papalexandris, Miltiadis V.
2014-11-01
In this talk we are concerned with thermally stratified flows in domains that contain a macroscopic interface between a highly porous material and a pure-fluid domain. Our study is based on the single-domain approach according to which the same set of governing equations is employed both inside the porous medium and in the pure-fluid domain. Also, the mathematical model that we employ treats the porous skeleton as a rigid solid that is in thermal non-equilibrium with the fluid. First, we present briefly the basic steps of the derivation of the mathematical model. Then, we present and discuss numerical results for both thermally stratified shear flows and natural convection. Our discussion focuses on the role of thermal stratification on the flows of interest and on the effect of thermal non-equilibrium between the solid matrix and the fluid inside the porous medium. This work is supported by the National Fund for Scientific Research (FNRS), Belgium.
Animating streamlines with repeated asymmetric patterns for steady flow visualization
Yeh, Chih-Kuo; Liu, Zhanping; Lee, Tong-Yee
2012-01-01
Animation provides intuitive cueing for revealing essential spatial-temporal features of data in scientific visualization. This paper explores the design of Repeated Asymmetric Patterns (RAPs) in animating evenly-spaced color-mapped streamlines for dense accurate visualization of complex steady flows. We present a smooth cyclic variable-speed RAP animation model that performs velocity (magnitude) integral luminance transition on streamlines. This model is extended with inter-streamline synchronization in luminance varying along the tangential direction to emulate orthogonal advancing waves from a geometry-based flow representation, and then with evenly-spaced hue differing in the orthogonal direction to construct tangential flow streaks. To weave these two mutually dual sets of patterns, we propose an energy-decreasing strategy that adopts an iterative yet efficient procedure for determining the luminance phase and hue of each streamline in HSL color space. We also employ adaptive luminance interleaving in the direction perpendicular to the flow to increase the contrast between streamlines.
Hirota, Makoto; Morrison, Philip J.
2016-05-01
Linear stability of inviscid, parallel, and stably stratified shear flow is studied under the assumption of smooth strictly monotonic profiles of shear flow and density, so that the local Richardson number is positive everywhere. The marginally unstable modes are systematically found by solving a one-parameter family of regular Sturm-Liouville problems, which can determine the stability boundaries more efficiently than solving the Taylor-Goldstein equation directly. By arguing for the non-existence of a marginally unstable mode, we derive new sufficient conditions for stability, which generalize the Rayleigh-Fjørtoft criterion for unstratified shear flows.
Perbandingan Hasil Pemodelan Aliran Satu Dimensi Unsteady Flow dan Steady Flow pada Banjir Kota
Andreas Tigor Oktaga
2016-06-01
Full Text Available One dimensional flow is often used as a flood simulation for the planning capacity of the river. Flood is a type of unsteady non-uniform flow, that can be simulated using HEC-RAS. HEC-RAS software is often used for flood modeling with a one-dimensional flow method. Unsteady flow modeling results in HEC-RAS sometimes refer to error and warning due to unstable analysis program. The stability program among others influenced bend in the river flow, the steep slope of the river bottom, and changes in cross-section shape. Because the flood handling required maximum discharge and maximum flood water level, then a steady flow is often used as an alternative to simulate the flood flow. This study aimed to determine the advantages and disadvantages of modeling unsteady non-uniform and steady non-uniform flow. The research location in the Kanal Banjir Barat, in the Semarang City. Hydraulics modeling uses HEC-RAS 4.1 and for discharge the plan is obtained from the HEC-HMS 3.5. Results of the comparison modeling hydraulics the modeling of steady non-uniform flow has a tendency water level is higher and modeling of unsteady non-uniform flow takes longer to analyze. Results of the comparison the average flood water level maximun is less than 15% (± 0,3 meters, that is 0.27 meters (13.16% for Q50, 0.25 meters (11.56% for Q100, dan 0.16 meters (4.73% for Q200. So the modeling steady non-uniform flow can still be used as a companion version the modeling unsteady non-uniform flow.
Dynamic behaviors of cavitation bubble for the steady cavitating flow
Jun CAI; Xiulan HUAI; Xunfeng LI
2009-01-01
In this paper, by introducing the flow velocity item into the classical Rayleigh-Plesset dynamic equation, a new equation, which does not involve the time term and can describe the motion of cavitation bubble in the steady cavitating flow, has been obtained. By solving the new motion equation using Runge-Kutta fourth order method with adaptive step size control, the dynamic behaviors of cavitation bubble driven by the varying pressure field downstream of a venturi cavitation reactor are numerically simulated. The effects of liquid temperature (corre-sponding to the saturated vapor pressure of liquid), cavitation number and inlet pressure of venturi on radial mo-tion of bubble and pressure pulse due to the radial motion are analyzed and discussed in detail. Some dynamic behaviors of bubble different from those in previous papers are displayed. In addition, the internal relationship between bubble dynamics and process intensification is also discussed. The simulation results reported in this work reveal the variation laws of cavitation intensity with the flow conditions of liquid, and will lay a foundation for the practical application of hydrodynamic cavitation technology.
Finite-amplitude steady waves in plane viscous shear flows
Milinazzo, F. A.; Saffman, P. G.
1985-01-01
Computations of two-dimensional solutions of the Navier-Stokes equations are carried out for finite-amplitude waves on steady unidirectional flow. Several cases are considered. The numerical method employs pseudospectral techniques in the streamwise direction and finite differences on a stretched grid in the transverse direction, with matching to asymptotic solutions when unbounded. Earlier results for Poiseuille flow in a channel are re-obtained, except that attention is drawn to the dependence of the minimum Reynolds number on the physical constraint of constant flux or constant pressure gradient. Attempts to calculate waves in Couette flow by continuation in the velocity of a channel wall fail. The asymptotic suction boundary layer is shown to possess finite-amplitude waves at Reynolds numbers orders of magnitude less than the critical Reynolds number for linear instability. Waves in the Blasius boundary layer and unsteady Rayleigh profile are calculated by employing the artifice of adding a body force to cancel the spatial or temporal growth. The results are verified by comparison with perturbation analysis in the vicinity of the linear-instability critical Reynolds numbers.
Efficient solution of two-dimensional steady separated flows
Napolitano, M.
This work is concerned with the numerical solution of 2D incompressible steady laminar separated flows at moderate-to-high values of Re. The vorticity-stream function Navier-Stokes equations, as well as approximate models based upon the boundary-layer theory, will be considered. The main objective of the paper is to present the development of an efficient approach for solving a class of problems usually referred to as high Re weakly separated flows. A description is given of a block-alternating-direction-implicit method, which applies the approximate factorization scheme of Beam and Warming to the vorticity-stream function equations, using the delta form of the deferred correction procedure of Khosla and Rubin to combine the stability of upwind schemes with the accuracy of central differences. The logical steps which led to the development of a more efficient incremental block-line Gauss-Seidel method and to a simple multigrid strategy particularly suited for this kind of numerical scheme are then outlined. Finally, benchmark-quality solutions for separated flows inside diffusers and channels with smooth as well as sudden expansions are presented.
Numerical simulation of stratified shear flow using a higher order Taylor series expansion method
Iwashige, Kengo; Ikeda, Takashi [Hitachi, Ltd. (Japan)
1995-09-01
A higher order Taylor series expansion method is applied to two-dimensional numerical simulation of stratified shear flow. In the present study, central difference scheme-like method is adopted for an even expansion order, and upwind difference scheme-like method is adopted for an odd order, and the expansion order is variable. To evaluate the effects of expansion order upon the numerical results, a stratified shear flow test in a rectangular channel (Reynolds number = 1.7x10{sup 4}) is carried out, and the numerical velocity and temperature fields are compared with experimental results measured by laser Doppler velocimetry thermocouples. The results confirm that the higher and odd order methods can simulate mean velocity distributions, root-mean-square velocity fluctuations, Reynolds stress, temperature distributions, and root-mean-square temperature fluctuations.
A 3D Spectral Anelastic Hydrodynamic Code for Shearing, Stratified Flows
Barranco, J A; Barranco, Joseph A.; Marcus, Philip S.
2005-01-01
We have developed a three-dimensional (3D) spectral hydrodynamic code to study vortex dynamics in rotating, shearing, stratified systems (e.g. the atmosphere of gas giant planets, protoplanetary disks around newly forming protostars). The time-independent background state is stably stratified in the vertical direction and has a unidirectional linear shear flow aligned with one horizontal axis. Superposed on this background state is an unsteady, subsonic flow that is evolved with the Euler equations subject to the anelastic approximation to filter acoustic phenomena. A Fourier-Fourier basis in a set of quasi-Lagrangian coordinates that advect with the background shear is used for spectral expansions in the two horizontal directions. For the vertical direction, two different sets of basis functions have been implemented: (1) Chebyshev polynomials on a truncated, finite domain, and (2) rational Chebyshev functions on an infinite domain. Use of this latter set is equivalent to transforming the infinite domain to ...
Mixed Convection Flow along a Stretching Cylinder in a Thermally Stratified Medium
Swati Mukhopadhyay
2012-01-01
Full Text Available An analysis for the axisymmetric laminar boundary layer mixed convection flow of a viscous and incompressible fluid towards a stretching cylinder immersed in a thermally stratified medium is presented in this paper. Similarity transformation is employed to convert the governing partial differential equations into highly nonlinear ordinary differential equations. Numerical solutions of these equations are obtained by a shooting method. It is found that the heat transfer rate at the surface is lower for flow in a thermally stratified medium compared to that of an unstratified medium. Moreover, both the skin friction coefficient and the heat transfer rate at the surface are larger for a cylinder compared to that for a flat plate.
Experimental study of temperature fluctuations in forced stably stratified turbulent flows
Eidelman, A; Gluzman, Y; Kleeorin, N; Rogachevskii, I
2013-01-01
We study experimentally temperature fluctuations in stably stratified forced turbulence in air flow. In the experiments with an imposed vertical temperature gradient, the turbulence is produced by two oscillating grids located nearby the side walls of the chamber. Particle Image Velocimetry is used to determine the turbulent and mean velocity fields, and a specially designed temperature probe with sensitive thermocouples is employed to measure the temperature field. We found that the ratio [(\\ell_x \
A Model for Predicting Holdup and Pressure Drop in Gas-Liquid Stratified Flow
无
2001-01-01
The time-dependent liquid film thickness and pressure drop were measured by using parallel-wire conductance probes and capacitance differential-preesure transducers. Applying the eddy viscosity theory and an appropriate correlation of interfacial sear stress,a new two-dimensional separated model of holdup and pressure drop of turbulent/turbulent gas-liquid stratified flow was presented. Prediction results agreed well with experimental data.
An immersed interface method for two-dimensional modelling of stratified flow in pipes
Berthelsen, Petter Andreas
2004-01-01
This thesis deals with the construction of a numerical method for solving two-dimensional elliptic interface problems, such as fully developed stratified flow in pipes. Interface problems are characterized by its non-smooth and often discontinuous behaviour along a sharp boundary separating the fluids or other materials. Classical numerical schemes are not suitable for these problems due to the irregular geometry of the interface. Standard finite difference discretization across the interface...
A Model of Turbulent-Laminar Gas-Liquid Stratified Flow
无
2001-01-01
The time-dependent liquid film thickness and pressure drop are measured by using parallel-wire conduc tance probes and capacitance differential-pressure transducer. A mathematical model with iterative procedure to calculate holdup and pressure drop in horizontal and inclined gas-liquid stratified flow is developed. The predictions agree well with over a hundred experimental data in 0.024 and 0.04 m diameter pipelines.
Existence and Stability of Solutions for Steady Flows of Fibre Suspension Flows
Munganga, J. M. W.
2013-03-01
We establish existence, uniqueness, convergence and stability of solutions to the equations of steady flows of fibre suspension flows. The existence of a unique steady solution is proven by using an iterative scheme. One of the restrictions imposed on the data confirms a well known fact proven in Galdi and Reddy (J Non-Newtonian Fluid Mech 83:205-230, 1999), Munganga and Reddy (Math Models Methods Appl Sci 12:1177-1203, 2002) and Munganga et al. (J Non-Newtonian fluid Mech 92:135-150, 2000) that the particle number N p must be less than 35/2. Exact solutions are calculated for Couette and Poiseuille flows. Solutions of Poiseuille flows are shown to be more accurate than those of Couette flow when a time perturbation is considered.
Renouf, M.; Bonamy, D.; Dubois, F.; Alart, P.
2005-10-01
The rheology of two-dimensional steady surface flow of cohesionless cylinders in a rotating drum is investigated through nonsmooth contact dynamics simulations. Profiles of volume fraction, translational and angular velocity, rms velocity, strain rate, and stress tensor are measured at the midpoint along the length of the surface-flowing layer, where the flow is generally considered as steady and homogeneous. Analysis of these data and their interrelations suggest the local inertial number—defined as the ratio between local inertial forces and local confinement forces—to be the relevant dimensionless parameter to describe the transition from the quasistatic part of the packing to the flowing part at the surface of the heap. Variations of the components of the stress tensor as well as the ones of rms velocity as a function of the inertial number are analyzed within both the quasistatic and the flowing phases. Their implications are discussed.
Liu, H. H.
2010-09-15
Optimality principles have been used for investigating physical processes in different areas. This work attempts to apply an optimal principle (that water flow resistance is minimized on global scale) to steady-state unsaturated flow processes. Based on the calculus of variations, we show that under optimal conditions, hydraulic conductivity for steady-state unsaturated flow is proportional to a power function of the magnitude of water flux. This relationship is consistent with an intuitive expectation that for an optimal water flow system, locations where relatively large water fluxes occur should correspond to relatively small resistance (or large conductance). Similar results were also obtained for hydraulic structures in river basins and tree leaves, as reported in other studies. Consistence of this theoretical result with observed fingering-flow behavior in unsaturated soils and an existing model is also demonstrated.
Flow and transport within a coastal aquifer adjacent to a stratified water body
Oz, Imri; Yechieli, Yoseph; Eyal, Shalev; Gavrieli, Ittai; Gvirtzman, Haim
2016-04-01
The existence of a freshwater-saltwater interface and the circulation flow of saltwater beneath the interface is a well-known phenomenon found at coastal aquifers. This flow is a natural phenomenon that occurs due to density differences between fresh groundwater and the saltwater body. The goals of this research are to use analytical, numerical, and physical models in order to examine the configuration of the freshwater-saltwater interface and the density-driven flow patterns within a coastal aquifer adjacent to long-term stratified saltwater bodies (e.g. meromictic lake). Such hydrological systems are unique, as they consist of three different water types: the regional fresh groundwater, and low and high salinity brines forming the upper and lower water layers of the stratified water body, respectively. This research also aims to examine the influence of such stratification on hydrogeological processes within the coastal aquifer. The coastal aquifer adjacent to the Dead Sea, under its possible future meromictic conditions, serves as an ideal example to examine these processes. The results show that adjacent to a stratified saltwater body three interfaces between three different water bodies are formed, and that a complex flow system, controlled by the density differences, is created, where three circulation cells are developed. These results are significantly different from the classic circulation cell that is found adjacent to non-stratified water bodies (lakes or oceans). In order to obtain a more generalized insight into the groundwater behavior adjacent to a stratified water body, we used the numerical model to perform sensitivity analysis. The hydrological system was found be sensitive to three dimensionless parameters: dimensionless density (i.e. the relative density of the three water bodies'); dimensionless thickness (i.e. the ratio between the relative thickness of the upper layer and the whole thickness of the lake); and dimensionless flux. The results
An affordable and accurate conductivity probe for density measurements in stratified flows
Carminati, Marco; Luzzatto-Fegiz, Paolo
2015-11-01
In stratified flow experiments, conductivity (combined with temperature) is often used to measure density. The probes typically used can provide very fine spatial scales, but can be fragile, expensive to replace, and sensitive to environmental noise. A complementary instrument, comprising a low-cost conductivity probe, would prove valuable in a wide range of applications where resolving extremely small spatial scales is not needed. We propose using micro-USB cables as the actual conductivity sensors. By removing the metallic shield from a micro-B connector, 5 gold-plated microelectrodes are exposed and available for 4-wire measurements. These have a cell constant ~550m-1, an intrinsic thermal noise of at most 30pA/Hz1/2, as well as sub-millisecond time response, making them highly suitable for many stratified flow measurements. In addition, we present the design of a custom electronic board (Arduino-based and Matlab-controlled) for simultaneous acquisition from 4 sensors, with resolution (in conductivity, and resulting density) exceeding the performance of typical existing probes. We illustrate the use of our conductivity-measuring system through stratified flow experiments, and describe plans to release simple instructions to construct our complete system for around 200.
Implications of Air Ingress Induced by Density-Difference Driven Stratified Flow
Chang Oh; Eung Soo Kim; Richard Schultz; David Petti; C. P. Liou
2008-06-01
One of the design basis accidents for the Next Generation Nuclear Plant (NGNP), a high temperature gas-cooled reactor, is air ingress subsequent to a pipe break. Following a postulated double-ended guillotine break in the hot duct, and the subsequent depressurization to nearly reactor cavity pressure levels, air present in the reactor cavity will enter the reactor vessel via density-gradient-driven-stratified flow. Because of the significantly higher molecular weight and lower initial temperature of the reactor cavity air-helium mixture, in contrast to the helium in the reactor vessel, the air-helium mixture in the cavity always has a larger density than the helium discharging from the reactor vessel through the break into the reactor cavity. In the later stages of the helium blowdown, the momentum of the helium flow decreases sufficiently for the heavier cavity air-helium mixture to intrude into the reactor vessel lower plenum through the lower portion of the break. Once it has entered, the heavier gas will pool at the bottom of the lower plenum. From there it will move upwards into the core via diffusion and density-gradient effects that stem from heating the air-helium mixture and from the pressure differences between the reactor cavity and the reactor vessel. This scenario (considering density-gradient-driven stratified flow) is considerably different from the heretofore commonly used scenario that attributes movement of air into the reactor vessel and from thence to the core region via diffusion. When density-gradient-driven stratified flow is considered as a contributing phenomena for air ingress into the reactor vessel, the following factors contribute to a much earlier natural circulation-phase in the reactor vessel: (a) density-gradient-driven stratified flow is a much more rapid mechanism (at least one order of magnitude) for moving air into the reactor vessel lower plenum than diffusion, and consequently, (b) the diffusion dominated phase begins with a
Contaminant attenuation by shallow aquifer systems under steady flow
Soltani, S. S.; Cvetkovic, V.
2017-10-01
We present a framework for analyzing advection-dominated solute transport and transformation in aquifer systems of boreal catchments that are typically shallow and rest on crystalline bedrock. A methodology is presented for estimating tracer discharge based on particle trajectories from recharge to discharge locations and computing their first passage times assuming that the flow pattern is approximately steady-state. Transformation processes can be included by solving one-dimensional reactive transport with randomized water travel time as the independent variable; the distribution of the travel times incorporates morphological dispersion (due to catchment geometry/topography) as well as macro-dispersion (due to heterogeneity of underlying hydraulic properties). The implementation of the framework is illustrated for the well characterized coastal catchment of Forsmark (Sweden). We find that macro-dispersion has a notable effect on attenuation even though the morphological dispersion is significantly larger. Preferential flow on the catchment scale is found to be considerable with only 5% of the Eulerian velocities contributing to transport over the simulation period of 375 years. Natural attenuation is illustrated as a simple (linear decay) transformation process. Simulated natural attenuation can be estimated analytically reasonably well by using basic hydrological and structural information, the latter being the pathway length distribution and average aquifer depth to the bedrock.
Interfacial shear stress in stratified flow in a horizontal rectangular duct
Lorencez, C.; Kawaji, M. [Univ. of Toronto (Canada); Murao, Y. [Tokushima Univ. (Japan)] [and others
1995-09-01
Interfacial shear stress has been experimentally examined for both cocurrent and countercurrent stratified wavy flows in a horizontal interfacial shear stress from the measurements were examined and the results have been compared with existing correlations. Some differences were found in the estimated interfacial shear stress from the measurements were examined and the results have been compared with existing correlations. Some differences were found in the estimated interfacial shear stress values at high gas flow rates which could be attributed to the assumptions and procedures involved in each method. The interfacial waves and secondary motions were also found to have significant effects on the accuracy of Reynolds stress and turbulence kinetic energy extrapolation methods.
Jet-mixing of initially-stratified liquid-liquid pipe flows: experiments and numerical simulations
Wright, Stuart; Ibarra-Hernandes, Roberto; Xie, Zhihua; Markides, Christos; Matar, Omar
2016-11-01
Low pipeline velocities lead to stratification and so-called 'phase slip' in horizontal liquid-liquid flows due to differences in liquid densities and viscosities. Stratified flows have no suitable single point for sampling, from which average phase properties (e.g. fractions) can be established. Inline mixing, achieved by static mixers or jets in cross-flow (JICF), is often used to overcome liquid-liquid stratification by establishing unstable two-phase dispersions for sampling. Achieving dispersions in liquid-liquid pipeline flows using JICF is the subject of this experimental and modelling work. The experimental facility involves a matched refractive index liquid-liquid-solid system, featuring an ETFE test section, and experimental liquids which are silicone oil and a 51-wt% glycerol solution. The matching then allows the dispersed fluid phase fractions and velocity fields to be established through advanced optical techniques, namely PLIF (for phase) and PTV or PIV (for velocity fields). CFD codes using the volume of a fluid (VOF) method are then used to demonstrate JICF breakup and dispersion in stratified pipeline flows. A number of simple jet configurations are described and their dispersion effectiveness is compared with the experimental results. Funding from Cameron for Ph.D. studentship (SW) gratefully acknowledged.
Prediction of the bed-load transport by gas-liquid stratified flows in horizontal ducts
Franklin, Erick de Moraes
2016-01-01
Solid particles can be transported as a mobile granular bed, known as bed-load, by pressure-driven flows. A common case in industry is the presence of bed-load in stratified gas-liquid flows in horizontal ducts. In this case, an initially flat granular bed may be unstable, generating ripples and dunes. This three-phase flow, although complex, can be modeled under some simplifying assumptions. This paper presents a model for the estimation of some bed-load characteristics. Based on parameters easily measurable in industry, the model can predict the local bed-load flow rates and the celerity and the wavelength of instabilities appearing on the granular bed.
Large eddy simulation of turbulent statistical and transport properties in stably stratified flows
Xiang QIU; Yong-xiang HUANG; Zhi-ming LU; Yu-lu LIU
2009-01-01
Three dimensional large eddy simulation (LES) is performed in the inves-tigation of stably stratified turbulence with a sharp thermal interface. Main results are focused on the turbulent characteristic scale, statistical properties, transport properties,and temporal and spatial evolution of the scalar field. Results show that the buoyancy scale increases first, and then goes to a certain constant value. The stronger the mean shear, the larger the buoyancy scale. The overturning scale increases with the flow, and the mean shear improves the overturning scale. The flatness factor of temperature de-parts from the Ganssian distribution in a fairly large region, and its statistical properties are clearly different from those of the velocity fluctuations in strong stratified cases. Tur-bulent mixing starts from small scale motions, and then extends to large scale motions.
Lakghomi, B; Lawryshyn, Y; Hofmann, R
2015-01-01
An analytical model and a computational fluid dynamic model of particle removal in dissolved air flotation were developed that included the effects of stratified flow and bubble-particle clustering. The models were applied to study the effect of operating conditions and formation of stratified flow on particle removal. Both modeling approaches demonstrated that the presence of stratified flow enhanced particle removal in the tank. A higher air fraction was shown to be needed at higher loading rates to achieve the same removal efficiency. The model predictions showed that an optimum bubble size was present that increased with an increase in particle size.
Garaud, P; Verhoeven, J
2016-01-01
Shear-induced turbulence could play a significant role in mixing momentum and chemical species in stellar radiation zones, as discussed by Zahn (1974). In this paper we analyze the results of direct numerical simulations of stratified plane Couette flows, in the limit of rapid thermal diffusion, to measure the turbulent diffusivity and turbulent viscosity as a function of the local shear and the local stratification. We find that the stability criterion proposed by Zahn (1974), namely that the product of the gradient Richardson number and the Prandtl number must be smaller than a critical values $(J\\Pr)_c$ for instability, adequately accounts for the transition to turbulence in the flow, with $(J\\Pr)_c \\simeq 0.007$. This result recovers and confirms the prior findings of Prat et al. (2016). Zahn's model for the turbulent diffusivity and viscosity (Zahn 1992), namely that the mixing coefficient should be proportional to the ratio of the thermal diffusivity to the gradient Richardson number, does not satisfact...
On the Orientation of Turbulent Structures in Stably Stratified Shear Flows
Jacobitz, Frank; Moreau, Adam; Aguirre, Joylene
2016-11-01
The orientation of turbulent structures in stably stratified shear flows are investigated using the results of a series of direct numerical simulations. The Richardson number is varied from Ri = 0 , corresponding to unstratified shear flow, to Ri = 1 , corresponding to strongly stratified shear flow. The evolution of the turbulent kinetic energy changes from growth for small Richardson numbers to decay for strong stratification. The orientation of turbulent structures in the flows is determined by the three-dimensional two-point autocorrelation coefficient of velocity magnitude, vorticity magnitude, and fluctuating density. An ellipsoid is fitted to the surface given by a constant autocorrelation coefficient value and the major and minor axes are used to determine the inclination angle of turbulent structures in the plane of shear. The inclination angle is observed to be fairly unaffected by the choice of the autocorrelation coefficient value. In was found that the inclination angle decreases with increasing Richardson number. The structure of the turbulent motion, as characterized by the inclination angle, is therefore directly related to the eventual evolution of the turbulence, as described by the growth or decay rate of the turbulent kinetic energy.
A model for steady flows of magma-volatile mixtures
Belan, Marco
2012-01-01
A general one-dimensional model for the steady adiabatic motion of liquid-volatile mixtures in vertical ducts with varying cross-section is presented. The liquid contains a dissolved part of the volatile and is assumed to be incompressible and in thermomechanical equilibrium with a perfect gas phase, which is generated by the exsolution of the same volatile. An inverse problem approach is used -- the pressure along the duct is set as an input datum, and the other physical quantities are obtained as output. This fluid-dynamic model is intended as an approximate description of magma-volatile mixture flows of interest to geophysics and planetary sciences. It is implemented as a symbolic code, where each line stands for an analytic expression, whether algebraic or differential, which is managed by the software kernel independently of the numerical value of each variable. The code is versatile and user-friendly and permits to check the consequences of different hypotheses even through its early steps. Only the las...
Zilitinkevich, S. S.; Elperin, T.; Kleeorin, N.; Rogachevskii, I.; Esau, I.
2013-03-01
Here we advance the physical background of the energy- and flux-budget turbulence closures based on the budget equations for the turbulent kinetic and potential energies and turbulent fluxes of momentum and buoyancy, and a new relaxation equation for the turbulent dissipation time scale. The closure is designed for stratified geophysical flows from neutral to very stable and accounts for the Earth's rotation. In accordance with modern experimental evidence, the closure implies the maintaining of turbulence by the velocity shear at any gradient Richardson number Ri, and distinguishes between the two principally different regimes: "strong turbulence" at {Ri ≪ 1} typical of boundary-layer flows and characterized by the practically constant turbulent Prandtl number Pr T; and "weak turbulence" at Ri > 1 typical of the free atmosphere or deep ocean, where Pr T asymptotically linearly increases with increasing Ri (which implies very strong suppression of the heat transfer compared to the momentum transfer). For use in different applications, the closure is formulated at different levels of complexity, from the local algebraic model relevant to the steady-state regime of turbulence to a hierarchy of non-local closures including simpler down-gradient models, presented in terms of the eddy viscosity and eddy conductivity, and a general non-gradient model based on prognostic equations for all the basic parameters of turbulence including turbulent fluxes.
Testing of RANS Turbulence Models for Stratified Flows Based on DNS Data
Venayagamoorthy, S. K.; Koseff, J. R.; Ferziger, J. H.; Shih, L. H.
2003-01-01
In most geophysical flows, turbulence occurs at the smallest scales and one of the two most important additional physical phenomena to account for is strati cation (the other being rotation). In this paper, the main objective is to investigate proposed changes to RANS turbulence models which include the effects of stratifi- cation more explicitly. These proposed changes were developed using a DNS database on strati ed and sheared homogenous turbulence developed by Shih et al. (2000) and are described more fully in Ferziger et al. (2003). The data generated by Shih, et al. (2000) (hereinafter referred to as SKFR) are used to study the parameters in the k- model as a function of the turbulent Froude number, Frk. A modified version of the standard k- model based on the local turbulent Froude number is proposed. The proposed model is applied to a stratified open channel flow, a test case that differs significantly from the flows from which the modified parameters were derived. The turbulence modeling and results are discussed in the next two sections followed by suggestions for future work.
Study of steady and unsteady wet steam condensing flows in a turbine stage
巫志华; 李亮; 丰镇平
2007-01-01
Objective To develop the numerical method for the steady and unsteady wet steam condensing flow in turbine stage. Methods An Eulerian/Eulerian numerical model is used to describe the spontaneous condensation flow in the steam turbine. For the steady condensing flow computations, the mixing plane model was used. For the unsteady condensing flow computations, the sliding mesh method was used to simulate the rotor-stator interactions. Results The numerical results showed the obvious differences between non-con...
Rapaka, Narsimha R.; Sarkar, Sutanu
2016-10-01
A sharp-interface Immersed Boundary Method (IBM) is developed to simulate density-stratified turbulent flows in complex geometry using a Cartesian grid. The basic numerical scheme corresponds to a central second-order finite difference method, third-order Runge-Kutta integration in time for the advective terms and an alternating direction implicit (ADI) scheme for the viscous and diffusive terms. The solver developed here allows for both direct numerical simulation (DNS) and large eddy simulation (LES) approaches. Methods to enhance the mass conservation and numerical stability of the solver to simulate high Reynolds number flows are discussed. Convergence with second-order accuracy is demonstrated in flow past a cylinder. The solver is validated against past laboratory and numerical results in flow past a sphere, and in channel flow with and without stratification. Since topographically generated internal waves are believed to result in a substantial fraction of turbulent mixing in the ocean, we are motivated to examine oscillating tidal flow over a triangular obstacle to assess the ability of this computational model to represent nonlinear internal waves and turbulence. Results in laboratory-scale (order of few meters) simulations show that the wave energy flux, mean flow properties and turbulent kinetic energy agree well with our previous results obtained using a body-fitted grid (BFG). The deviation of IBM results from BFG results is found to increase with increasing nonlinearity in the wave field that is associated with either increasing steepness of the topography relative to the internal wave propagation angle or with the amplitude of the oscillatory forcing. LES is performed on a large scale ridge, of the order of few kilometers in length, that has the same geometrical shape and same non-dimensional values for the governing flow and environmental parameters as the laboratory-scale topography, but significantly larger Reynolds number. A non-linear drag law
Kim, J.K.; Sung, J.Y. [Seoul National University Graduate School, Seoul (Korea); Chang, J.K.; Yoo, J.Y.; Min, B.G. [Seoul National University, Seoul (Korea)
1999-12-01
Hemodynamic performance of a polyurethane heart valve prosthesis was evaluated in comparison with that of Bjork-Shiley Monostrut mechanical valve in steady flow representing the systolic peak flow phase. Pressure losses through the valves were obtained from the streamwise pressure distributions downstream of the valves. Unsteady and turbulent flow field distal to the heart valve prostheses were investigated using PIV(Particle Image Velocimetry) which can measure the full-field velocity instantaneously and noninvasively. By examining the velocity and Reynolds shear stress fields downstream of the polyurethane heart valve, it is known that there is a large recirculation region near the valve and high shear stress regions exist at the interface between strong axial jet flows along the wall and vortical flows in the central area. The possibilities of vascular complications, such as the thrombus formation and red blood cell damage, could be predicted from the overall view of the velocity and stress fields. (author). 22 refs., 9 figs., 1 tab.
Tsamopoulos, John; Fraggedakis, Dimitris; Dimakopoulos, Yiannis
2015-11-01
We study the flow of two immiscible, Newtonian fluids in a periodically constricted tube driven by a constant pressure gradient. Our Volume-of-Fluid algorithm is used to solve the governing equations. First the code is validated by comparing its predictions to previously reported results for stratified and pulsing flow. Then it is used to capture accurately all the significant topological changes that take place. Initially, the fluids have a core-annular arrangement, which is found to either remain the same or change to a different arrangement depending on the fluid properties, the pressure driving the flow or the flow geometry. The flow-patterns that appear are the core-annular, segmented, churn, spray and segregated flow. The predicted scalings near pinching of the core fluid concur with similarity predictions and earlier numerical results (Cohen et al. (1999)). Flow-pattern maps are constructed in terms of the Reynolds and Weber numbers. Our results provide deeper insights in the mechanism of the pattern transitions and are in agreement with previous studies on core-annular flow (Kouris & Tsamopoulos (2001 & 2002)), segmented flow (Lac & Sherwood (2009)) and churn flow (Bai et al. (1992)). GSRT of Greece through the program ``Excellence'' (Grant No. 1918, entitled ``FilCoMicrA'').
An experimental investigation of stratified two-phase pipe flow at small inclinations
Espedal, Mikal
1998-12-31
The prediction of stratified flow is important for several industrial applications. Stratified flow experiments were carefully performed in order to investigate the performance of a typical model which uses wall friction factors based on single phase pipe flow as described above. The test facility has a 18.5 m long and 60 mm i.d. (L/D=300) acrylic test section which can be inclined between -10 {sup o} and +10 {sup o}. The liquid holdup was measured by using fast closing valves and the pressure gradients by using three differential pressure transducers. Interfacial waves were measured by thin wire conductance probes mounted in a plane perpendicular to the main flow. The experiments were performed using water and air at atmospheric pressure. The selected test section inclinations were between -3 {sup o} and +0.5 {sup o} to the horizontal plane. A large number of experiments were performed for different combinations of air and water flow rates and the rates were limited to avoid slug flow and stratified flow with liquid droplets. The pressure gradient and the liquid holdup were measured. In addition the wave probes were used to find the wave heights and the wave power spectra. The results show that the predicted pressure gradient using the standard models is approximately 30% lower than the measured value when large amplitude waves are present. When the flow is driven by the interfacial force the test section inclination has minor influence on the deviation between predicted and measured pressure gradients. Similar trends are apparent in data from the literature, although they seem to have gone unnoticed. For several data sets large spread in the predictions are observed when the model described above was used. Gas wall shear stress experiments indicate that the main cause of the deviation between measured and predicted pressure gradient and holdup resides in the modelling of the liquid wall friction term. Measurements of the liquid wall shear stress distribution
Self-regulation of mean flows in strongly stratified sheared turbulence
Salehipour, Hesam; Caulfield, Colm-Cille; Peltier, W. Richard
2016-11-01
We investigate the near-equilibrium state of shear-driven stratified turbulence generated by the breaking of Holmboe wave instability (HWI) and Kelvin-Helmholtz instability (KHI). We discuss DNS analyses associated with HWI under various initial conditions. We analyze the time-dependent distribution of the gradient Richardson number, Rig (z , t) associated with the horizontally-averaged velocity and density fields. We demonstrate that unlike the KHI-induced turbulence, the fully turbulent flow that is generated by HWI is robustly characterized by its high probability of Rig 0 . 2 - 0 . 25 , independent of the strength of the initial stratification and furthermore that the turbulence evolves in a 'near-equilibrium' state. The KHI-induced turbulence may become grossly 'out of equilibrium', however, and therefore decays rapidly when the initial value at the interface, Rig (0 , 0) , is closer to the critical value of 1/4; otherwise as Rig (0 , 0) -> 0 the KHI-induced turbulence is close to a state of equilibrium and hence is much more long-lived. We conjecture that stratified shear turbulence tends to adjust to a state of 'near-equilibrium' with horizontally-averaged flows characterized by a high probability of Rig <= 1 / 4 , and hence sustained turbulence over relatively long times.
Kozitsyna, M. V.; Trufanova, N. M.
2017-01-01
Today the process of coextrusion is the most technological in the cable production with cross-linked polyethylene, composed of two or more layers of polymeric insulation. Since the covering technology is a simultaneous imposition of all necessary layers (two semiconducting shields on the insulation and conductor and one - on insulation), the main focus of this study is the analysis of significance of various factors influence on stratified flows characteristics. This paper has considered the flow of two abnormally viscous liquids in the cable head. The problem has been solved through a three-dimensional statement by applying the finite element method in the Ansys software package. The influence has been estimated by varying the rheological properties of materials to create all necessary layers thickness.
Nonlinear waves in stratified Taylor--Couette flow. Part 1. Layer formation
Leclercq, Colin; Augier, Pierre; Caulfield, Colm-Cille P; Dalziel, Stuart B; Linden, Paul F
2016-01-01
This paper is the first part of a two-fold study of mixing, i.e. the formation of layers and upwelling of buoyancy, in axially stratified Taylor--Couette flow, with fixed outer cylinder. Using linear analysis and direct numerical simulation, we show the critical role played by non-axisymmetric instability modes, despite the fact that the flow is centrifugally unstable in the sense of Rayleigh's criterion. Interactions between helical modes of opposite handedness leads to the formation of nonlinear coherent structures: (mixed)-ribbons and (mixed)-cross-spirals. These give birth to complex density interface patterns, seemingly appearing and disappearing periodically as the coherent structure slowly rotates around the annulus. These coherent structures seem to be responsible for the formation of layers reported in a recent experiment by Oglethorpe et al. (2013). We distinguish `dynamic layering', instantaneous, localized and caused by the vortical motions, from `static layering' corresponding to the formation of...
Flow Field Induced Steady Alignment of Oxidized Multi-walled Carbon Nanotubes
Ai Zhong XU; Ming Shu YANG; Qiang WU; Xiao Ming HU; Lei JIANG
2005-01-01
The steady ordered micro-ribbons of oxidized multi-walled carbon nanotubes (MWNTs)were obtained through micro-aperture PTFE membrane by vacuum filtration. After treatment by mixture of concentrated nitric acid and sulfuric acid, the surface functional groups modified MWNTs can be easily dispersed to form a homogeneous suspension. It is found that the steady micro-ribbons existed in the films obtained by vacuum filtration of the suspension. The filtration formed steady flow field and induced steady alignment of oxidized MWNTs. The chemical treatment of MWNTs forming strong interaction between MWNTs is necessity to keep steady of the micro-ribbons microstructure.
E. J. Suarez-Dominguez
2016-12-01
Full Text Available Production of heavy crude oil in Mexico, and worldwide, is increasing which has led to the application of different methods to reduce viscosity or to enhance transport through stratified flow to continue using the existing infrastructures. In this context, injecting a viscosity improver that does not mix completely with the crude, establishes a liquid-liquid stratified flow. On the basis of a parallel plates model, comparing the increase of flow that occurs in the one-phase case which assumes a complete mixture between the crude and the viscosity improver against another stratified liquid-liquid (no mixing between the oil and compared improver; it was found that in both cases there is a flow increase for the same pressure drop with a maximum for the case in which the flow improver is between the plates and the crude.
Chang, Chih-Hao; Liou, Meng-Sing
2007-07-01
In this paper, we propose a new approach to compute compressible multifluid equations. Firstly, a single-pressure compressible multifluid model based on the stratified flow model is proposed. The stratified flow model, which defines different fluids in separated regions, is shown to be amenable to the finite volume method. We can apply the conservation law to each subregion and obtain a set of balance equations . Secondly, the AUSM + scheme, which is originally designed for the compressible gas flow, is extended to solve compressible liquid flows. By introducing additional dissipation terms into the numerical flux, the new scheme, called AUSM +-up, can be applied to both liquid and gas flows. Thirdly, the contribution to the numerical flux due to interactions between different phases is taken into account and solved by the exact Riemann solver. We will show that the proposed approach yields an accurate and robust method for computing compressible multiphase flows involving discontinuities, such as shock waves and fluid interfaces. Several one-dimensional test problems are used to demonstrate the capability of our method, including the Ransom's water faucet problem and the air-water shock tube problem. Finally, several two dimensional problems will show the capability to capture enormous details and complicated wave patterns in flows having large disparities in the fluid density and velocities, such as interactions between water shock wave and air bubble, between air shock wave and water column(s), and underwater explosion. However, conservative form is lost in these balance equations when considering each individual phase; in fact, the interactions that exist simultaneously in both phases manifest themselves as nonconservative terms.
Long ring waves in a stratified fluid over a shear flow
Khusnutdinova, K R
2014-01-01
Oceanic waves registered by satellite observations often have curvilinear fronts and propagate over various currents. In this paper, we study long linear and weakly-nonlinear ring waves in a stratified fluid in the presence of a depth-dependent horizontal shear flow. It is shown that despite the clashing geometries of the waves and the shear flow, there exists a linear modal decomposition (different from the known decomposition in Cartesian geometry), which can be used to describe distortion of the wavefronts of surface and internal waves, and systematically derive a 2+1 - dimensional cylindrical Korteweg - de Vries - type equation for the amplitudes of the waves. The general theory is applied to the case of the waves in a two-layer fluid with a piecewise - constant shear flow, with an emphasis on the effect of the shear flow on the geometry of the wavefronts. The distortion of the wavefronts is described by the singular solution (envelope of the general solution) of the nonlinear first-order differential equ...
On the lifetime of a pancake anticyclone in a rotating stratified flow
Facchini, Giulio; Le Bars, Michael
2016-11-01
We present an experimental study of the time evolution of an isolated anticyclonic pancake vortex in a laboratory rotating stratified flow. Motivations come from the variety of compact anticyclones observed to form and persist for a strikingly long lifetime in geophysical and astrophysical settings combining rotation and stratification. We generate anticyclones by injecting a small amount of isodense fluid at the center of a rotating tank filled with salty water linearly stratified in density. Our two control parameters are the Coriolis parameter f and the Brunt-Väisälä frequency N. We observe that anticyclones always slowly decay by viscous diffusion, spreading mainly in the horizontal direction irrespective of the initial aspect ratio. This behavior is correctly explained by a linear analytical model in the limit of small Rossby and Ekman numbers, where density and velocity equations reduce to a single equation for the pressure. Direct numerical simulations further confirm the theoretical predictions. Notably, they show that the azimuthal shear stress generates secondary circulations, which advect the density anomaly: this mechanism is responsible for the slow time evolution, rather than the classical viscous dissipation of the azimuthal kinetic energy.
Sand Dunes in Steady Flow at Low Froude Numbers: Dune Height Evolution and Flow Resistance
Niemann, S. L.; Fredsøe, Jørgen; Jacobsen, Niels Gjøl
2011-01-01
The development of sand dunes in an erodible bed exposed to flowing water is considered using a numerical flow model. The bed is initially given a small perturbation, which is followed in the time domain. Examples are given where a sinusoidal perturbation reaches the fully developed steady...... equilibrium shape. The flow modeling is based on a k-ω turbulence closure. The sediment transport is assumed to be bed-load only, with an avalanche-like movement on the steep dune front. The model is also found capable of predicting the growth in wavelength if the initially prescribed wavelength...... is sufficiently short. Results of the dune development are presented for different initial wavelengths. It is demonstrated that an equilibrium shape is developed for a range of wavelength-depth ratios as long as this ratio is sufficiently small....
Law of the wall in an unstably stratified turbulent channel flow
Scagliarini, Andrea; Gylfason, Ármann; Toschi, Federico
2015-01-01
We perform direct numerical simulations of an unstably stratified turbulent channel flow to address the effects of buoyancy on the boundary layer dynamics and mean field quantities. We systematically span a range of parameters in the space of friction Reynolds number ($Re_{\\tau}$) and Rayleigh number ($Ra$). Our focus is on deviations from the logarithmic law of the wall due to buoyant motion. The effects of convection in the relevant ranges are discussed providing measurements of mean profiles of velocity, temperature and Reynolds stresses as well as of the friction coefficient. A phenomenological model is proposed and shown to capture the observed deviations of the velocity profile in the log-law region from the non-convective case.
AN EFFICIENT CODE TO COMPUTE NONPARALLEL STEADY FLOWS AND THEIR LINEAR-STABILITY
DIJKSTRA, HA; MOLEMAKER, MJ; VANDERPLOEG, A; BOTTA, EFF
1995-01-01
A simple, fast and efficient algorithm to compute steady non-parallel flows and their linear stability in parameter space is described. The pseudo-arclength continuation method is used to trace branches of steady states as one of the parameters is varied. To determine the linear stability of each st
Exact solutions for steady flows of second-grade fluids
ZHANG Dao-xiang; FENG Su-xiao; LU Zhi-ming; LIU Yu-lu
2009-01-01
This paper aims to investigate exact solutions for a second-grade fluid flow with the inverse method.By assuming the relation between the vorticity field and the streamfunction,the exact solutions of the motion of plane second-grade fluids are investigated and obtained.The solutions obtained include simple Couette flows,slit jet flows and uniform flows over a series of distributed obstacles.
The stability of stratified spatially periodic shear flows at low Péclet number
Garaud, Pascale, E-mail: pgaraud@ucsc.edu [Department of Applied Mathematics and Statistics, Baskin School of Engineering, University of California at Santa Cruz, 1156 High Street, Santa Cruz, California 95064 (United States); Gallet, Basile [Service de Physique de l’Etat Condensé, DSM/IRAMIS, CNRS UMR 3680, CEA Saclay, 91191 Gif-sur-Yvette cedex (France); Bischoff, Tobias [Division of Geological and Planetary Sciences, California Institute of Technology, Mail Code 170-25, 1200 E. California Blvd., Pasadena, California 91125 (United States)
2015-08-15
This work addresses the question of the stability of stratified, spatially periodic shear flows at low Péclet number but high Reynolds number. This little-studied limit is motivated by astrophysical systems, where the Prandtl number is often very small. Furthermore, it can be studied using a reduced set of “low-Péclet-number equations” proposed by Lignières [“The small-Péclet-number approximation in stellar radiative zones,” Astron. Astrophys. 348, 933–939 (1999)]. Through a linear stability analysis, we first determine the conditions for instability to infinitesimal perturbations. We formally extend Squire’s theorem to the low-Péclet-number equations, which shows that the first unstable mode is always two-dimensional. We then perform an energy stability analysis of the low-Péclet-number equations and prove that for a given value of the Reynolds number, above a critical strength of the stratification, any smooth periodic shear flow is stable to perturbations of arbitrary amplitude. In that parameter regime, the flow can only be laminar and turbulent mixing does not take place. Finding that the conditions for linear and energy stability are different, we thus identify a region in parameter space where finite-amplitude instabilities could exist. Using direct numerical simulations, we indeed find that the system is subject to such finite-amplitude instabilities. We determine numerically how far into the linearly stable region of parameter space turbulence can be sustained.
Transition to turbulence in stratified shear flow: experiments in an inclined square duct
Meyer, Colin; Linden, Paul
2013-11-01
We describe laboratory experiments of countercurrent stratified shear flow in an inclined square duct. To achieve this, a long water tank was partitioned into regions of higher and lower density saltwater that are connected by an inclined square duct. The flow regime was characterized to be turbulent, intermittent, Holmboe or laminar as a function of the duct inclination, θ, and the density difference, Δρ , between the two reservoirs. The density difference and duct angle were systematically varied and a phase plane of flow regime was developed. The transition between the interrmittent regime and turbulence was experimentally determined to occur at θΔρ ~= 20 [degrees kg m-3]. This critical combination of parameters fits into the buoyancy-compensated Reynolds number scaling proposed by Brethouwer et al. (J. Fluid Mech., 2007). The turbulent interfacial thickness was found to be a function of the inclination angle, which can be predicted using the buoyancy lengthscale from Waite and Bartello (J. Fluid Mech., 2004) and others. Furthermore, we measured the density profiles at multiple points along the duct, and using these profiles, we modeled the entrainment at the interface. Support provided by the Winston Churchill Foundation of the United States.
X. Gong
2014-06-01
Full Text Available A bell-shape vertical profile of chlorophyll a (Chl a concentration, conventionally referred as Subsurface Chlorophyll Maximum (SCM phenomenon, has frequently been observed in stratified oceans and lakes. This profile is assumed to be a general Gaussian distribution in this study. By substituting the general Gaussian function into ecosystem dynamical equations, the steady-state solutions for SCM characteristics (i.e. SCM layer depth, thickness, and intensity in various scenarios are derived. These solutions indicate that: (1 The maximum in Chl a concentrations occurs at or below the depth with the maximum in growth rates of phytoplankton locating at the transition from nutrient limitation to light limitation, and the depth of SCM layer deepens logarithmically with an increase in surface light intensity; (2 The shape of SCM layer (thickness and intensity is mainly influenced by nutrient supply, but independence of surface light intensity; (3 The intensity of SCM layer is proportional to the diffusive flux of nutrient from below, getting stronger as a result of this layer being shrank by a higher light attenuation coefficient or a larger sinking velocity of phytoplankton. The analytical solutions can be useful to estimate environmental parameters difficultly obtained from on-site observations.
Well balancing of the SWE schemes for moving-water steady flows
Caleffi, Valerio; Valiani, Alessandro
2017-08-01
In this work, the exact reproduction of a moving-water steady flow via the numerical solution of the one-dimensional shallow water equations is studied. A new scheme based on a modified version of the HLLEM approximate Riemann solver (Dumbser and Balsara (2016) [18]) that exactly preserves the total head and the discharge in the simulation of smooth steady flows and that correctly dissipates mechanical energy in the presence of hydraulic jumps is presented. This model is compared with a selected set of schemes from the literature, including models that exactly preserve quiescent flows and models that exactly preserve moving-water steady flows. The comparison highlights the strengths and weaknesses of the different approaches. In particular, the results show that the increase in accuracy in the steady state reproduction is counterbalanced by a reduced robustness and numerical efficiency of the models. Some solutions to reduce these drawbacks, at the cost of increased algorithm complexity, are presented.
Characteristics of reservoir density flow in stratified water environment%分层环境中水库密度流运动特性研究
任实; 张小峰; 陆俊卿
2013-01-01
A flume experiment for the motion of reservoir density current in steady temperature stratified environment was used. Through different tests, simulated the density flow movement under the conditions of different temperature stratification, and analyzed the effects of stratified strength and outlet condition on density flow movement. The density flow movement characteristics under different reservoir operation modes were researched on the basis of model simulation. The research results can provide reference for the management about the water quality of the reservoir and aquatic environment, also can give reference for the early warning plan of reservoir emergency.%该文采用水槽试验对稳定温度分层水库的密度流运动进行了模拟.通过不同的试验方案,模拟了不同温度分层条件下密度流运动形态,分析了水体分层强度和出口条件对密度流运动的影响,并在此基础上,对不同水库运行方式下密度流运动特征进行了模拟研究.该文研究结果为水库水质、水生环境管理与调度以及水库应急预警方案的制定提供了参考.
Computational issues of solving the 1D steady gradually varied flow equation
Artichowicz, Wojciech; Szymkiewicz, Romuald
2014-01-01
In this paper a problem of multiple solutions of steady gradually varied flow equation in the form of the ordinary differential energy equation is discussed from the viewpoint of its numerical solution. Using the Lipschitz theorem dealing with the uniqueness of solution of an initial value problem for the ordinary differential equation it was shown that the steady gradually varied flow equation can have more than one solution. This fact implies that the nonlinear algebraic equation approximat...
On the existence of two-dimensional nonlinear steady states in plane Couette flow
Rincon, Francois
2007-01-01
The problem of two-dimensional steady nonlinear dynamics in plane Couette flow is revisited using homotopy from either plane Poiseuille flow or from plane Couette flow perturbed by a small symmetry-preserving identity operator. Our results show that it is not possible to obtain the nonlinear plane Couette flow solutions reported by Cherhabili and Ehrenstein [Eur. J. Mech. B/Fluids, 14, 667 (1995)] using their Poiseuille-Couette homotopy. We also demonstrate that the steady solutions obtained by Mehta and Healey [Phys. Fluids, 17, 4108 (2005)] for small symmetry-preserving perturbations are influenced by an artefact of the modified system of equations used in their paper. However, using a modified version of their model does not help to find plane Couette flow solution in the limit of vanishing symmetry-preserving perturbations either. The issue of the existence of two-dimensional nonlinear steady states in plane Couette flow remains unsettled.
DONG Yu-hong; LU Xi-yun; ZHUANG Li-xian
2004-01-01
Thermally-stratified shear turbulent channel flow with temperature oscillation on the bottom wall of the channel was investigated with the Large Eddy Simulation (LES) approach coupled with dynamic Sub-Grid-Scale (SGS) models. The effect of temperature oscillation on the turbulent channel flow behavior was examined. The phase-averaged velocities and temperature, and flow structures at different Richardson numbers and periods of the oscillation was analyzed.
CFD Code Validation against Stratified Air-Water Flow Experimental Data
F. Terzuoli
2008-01-01
Full Text Available Pressurized thermal shock (PTS modelling has been identified as one of the most important industrial needs related to nuclear reactor safety. A severe PTS scenario limiting the reactor pressure vessel (RPV lifetime is the cold water emergency core cooling (ECC injection into the cold leg during a loss of coolant accident (LOCA. Since it represents a big challenge for numerical simulations, this scenario was selected within the European Platform for Nuclear Reactor Simulations (NURESIM Integrated Project as a reference two-phase problem for computational fluid dynamics (CFDs code validation. This paper presents a CFD analysis of a stratified air-water flow experimental investigation performed at the Institut de Mécanique des Fluides de Toulouse in 1985, which shares some common physical features with the ECC injection in PWR cold leg. Numerical simulations have been carried out with two commercial codes (Fluent and Ansys CFX, and a research code (NEPTUNE CFD. The aim of this work, carried out at the University of Pisa within the NURESIM IP, is to validate the free surface flow model implemented in the codes against experimental data, and to perform code-to-code benchmarking. Obtained results suggest the relevance of three-dimensional effects and stress the importance of a suitable interface drag modelling.
Interfacial friction factors for air-water co-current stratified flow in inclined channels
Choi, Ki Yong; No, Hee Cheon [Korea Advanced Institute of Science and Technology, Taejon (Korea, Republic of)
1997-12-31
The interfacial shear stress is experimentally investigated for co-current air-water stratified flow in inclined rectangular channels having a length of 1854mm, width of 120 mm and height of 40mm at almost atmospheric pressure. Experiments are carried out in several inclinations from 0 deg up to 10 deg. The local film thickness and the wave height are measured at three locations, i.e., L/H = 8,23, and 40. According to the inclination angle, the experimental data are categorized into two groups; nearly horizontal data group (0 deg {<=} {theta} {<=} 0.7 deg), and inclined channel data group (0.7 deg {<=} {theta} {<=} 10 deg ). Experimental observations for nearly horizontal data group show that the flow is not fully developed due to the water level gradient and the hydraulic jump within the channel. For the inclined channel data group, a dimensionless wave height, {Delta}h/h, is empirically correlated in terms of Re{sub G} and h/H. A modified root-mean-square wave height is proposed to consider the effects of the interfacial and wave propagation velocities. It is found that an equivalent roughness has a linear relationship with the modified root-mean-square wave height and its relationship is independent of the inclination. 10 refs., 6 figs., 1 tab. (Author)
Nonlinear waves in stratified Taylor--Couette flow. Part 2. Buoyancy flux
Leclercq, Colin; Caulfield, Colm-Cille P; Dalziel, Stuart B; Linden, Paul F
2016-01-01
This paper is the second part of a two-fold study of mixing, i.e. the formation of layers and upwelling of buoyancy, in axially stratified Taylor--Couette flow, with fixed outer cylinder. In a first paper, we showed that the dynamics of the flow was dominated by coherent structures made of a superposition of nonlinear waves. (Mixed)-ribbons and (mixed)-cross-spirals are generated by interactions between a pair of linearly unstable helical modes of opposite `handedness', and appear to be responsible for the formation of well-mixed layers and sharp density interfaces. In this paper, we show that these structures are also fully accountable for the upwards buoyancy flux in the simulations. The mechanism by which this occurs is a positive coupling between the density and vertical velocity components of the most energetic waves. This coupling is primarily caused by diffusion of density at low Schmidt number Sc, but can also be a nonlinear effect at larger Sc. Turbulence was found to contribute negatively to the buo...
Coherent structures and enstrophy dynamics in highly stratified flow past a sphere at Re = 3700
Chongsiripinyo, Karu; Pal, Anikesh; Sarkar, Sutanu
2016-11-01
Vortex dynamics of flow past a sphere in a linearly stratified environment is investigated. Simulations are carried out for a flow with Reynolds number of 3700 and for several Froude numbers (Fr) ranging as low as 0.025. Isosurface of Q criterion is used to identify vortical structures whose cross-section and orientation are found to be affected by buoyancy. At low Fr = 0 . 025 , pancake eddies and surfboard-like inclined structures emerge in the near wake and have a regular streamwise spacing that is associated with the frequency of vortex shedding from the sphere. Similar to turbulent kinetic energy, the enstrophy in the near wake decreases with decreasing Fr (increasing stratification) until a minimum at Fr = 0 . 5 but the trend reverses in the low- Fr regime. Vortex stretching by fluctuating and mean strain are both responsible for enhancing vorticity with relatively small contribution from the baroclinic term. Decreasing Fr to O (1) values tends to suppress vortex stretching. Upon further reduction of Fr below 0.25, the vortex stretching term takes large values near the sphere.
Non-Steady Oscillatory Flow in Coarse Granular Materials
Andersen, O. H.; Gent, M. R. A. van; Meer, J. W. van der;
1992-01-01
Stationary and oscillatory flow through coarse granular materials have been investigated experimentally at Delft Hydraulics in their oscillating water tunnel with the objective of determining the coefficients of the extended Forchheimer equation. Cylinders, spheres and different types of rock hav...
Simulations of Steady Cavitating Flow in a Small Francis Turbine
Ahmed Laouari
2016-01-01
Full Text Available The turbulent flow through a small horizontal Francis turbine is solved by means of Ansys-CFX at different operating points, with the determination of the hydrodynamic performance and the best efficiency point. The flow structures at different regimes reveal a large flow eddy in the runner and a swirl in the draft tube. The use of the mixture model for the cavity/liquid two-phase flow allowed studying the influence of cavitation on the hydrodynamic performance and revealed cavitation pockets near the trailing edge of the runner and a cavitation vortex rope in the draft tube. By maintaining a constant dimensionless head and a distributor vane opening while gradually increasing the cavitation number, the output power and efficiency reached a critical point and then had begun to stabilize. The cavitation number corresponding to the safety margin of cavitation is also predicted for this hydraulic turbine.
The Finiteness of vortices in steady incompressible viscous fluid flow
Kalita, Jiten C; Panda, Swapnendu
2016-01-01
In this work, we provide two novel approaches to show that incompressible fluid flow in a finite domain contains at most a finite number vortices. We use a recently developed geometric theory of incompressible viscous flows along with an existing mathematical analysis concept to establish the finiteness. We also offer a second proof of finiteness by roping in the Kolmogorov's length scale criterion in conjunction with the notion of diametric disks.
Predictions of Bedforms in Steady, Tidal and Oscillatory Flows
Gallagher, E. L.
2016-02-01
Bedforms are ubiquitous in unconsolidated sediments. They range in size from small orbital ripples (l 5-50 cm) to megaripples (l 1-5 m) to large dunes (l 10-100 m). Bedforms are important because they affect sediment transport, flow energy dissipation, and larger-scale hydro- and morpho-dynamics. Bedforms in different environments (eg, deserts, rivers and oceans) are thought to be dynamically similar, therefore modeling approaches from one environment can be used to predicted features in another (Gallagher 2011). Here, a self-organization model is used to simulate the formation and development of bedforms in the combined flows of the surf zone, tidal inlets and river mouths. Sediment flux is determined from combined wave and current flows using different formulations, but, interestingly, the transport formulation has little effect on model results. Random bed irregularities, either imposed or resulting from small variations in the flow representing turbulence, are seeds for bedform development. Feedback between the bed and the flow in the form of a shadow zone downstream of a bedform and increasing flow velocity with elevation over bedform crests alter the transport such that organized bedforms emerge. The model has been used to predict surf zone megaripples and bedforms in tidal inlets and river mouths. Many bedform models (e.g., Hulscher et al. 1996, Nielsen 1981, Clifton 1976, Wiberg and Harris 1994), predict specific bedform characteristics for a given flow condition. However, many observations report multiple scales existing simultaneously. A recent study by Lefevbre et al (2013) found that the boundary layer thickness and resulting bedform-induced roughness was different for single and multiple bedform fields. The present model predicts multiple bedform scales. In this study, predictions of different time and length scales of bedform evolution and roughness, as a function of flow magnitude, direction and variability are being examined.
On the One-Dimensional Steady and Unsteady Porous Flow Equation
Andersen, O. H.; Burcharth, H. F.
1995-01-01
Porous flow in coarse granular media is discussed theoretically with special concern given to the variation of the flow resistance with the porosity. For steady state flow, the Navier-Stokes equation is applied as a basis for the derivations. A turbulent flow equation is suggested. Alternative...... derivations based on dimensional analysis and a pipe analogy, respectively, are discussed. For non-steady state flow, the derivations are based on a cylinder/sphere analogy leading to a virtual mass coefficient. For the fully turbulent flow regime, existing experimental data values of the quadratic flow...... resistance coefficients are presented. Moreover, a simple formula for estimation of the turbulent flow coefficient is given. Virtual mass coefficients based on existing data are presented, however, no definite conclusions can be given due to the scarce data available....
Sharma, A.; Leo, L. S.; Thompson, M. Y.; Di Sabatino, S.; Fernando, H. J.; Zhong, Q.; Wang, H.
2015-12-01
It is well known that, when a stably stratified flow with approach velocity U and buoyancy frequency N flows over an obstacle of height h, the low-level flow goes around the object while the rest flows over it for low F = U / N h. The streamline that separates the two types of flow is the dividing streamline, and the prediction of its height Hs is of great practical interest. Sheppard (1956) provided the analytical solution Hs = h (1 - F) and, because of its practical utility, the formula continues to be largely employed, notwithstanding the criticism it has attracted because of certain underlying assumptions, viz., 1) the crude approximation of constant N and uniform approach velocity U, which is unrealistic for atmospheric flows; 2) the incorrect assumption of a complete balance between kinetic and potential energy at the mountain summit, which neglects the energy contributions of the perturbation pressure field as well as viscous dissipation adjacent to the hill surface. In this study, the first limitation is addressed by considering a logarithmic approach velocity profile but with constant N. A modified logarithmic velocity profile for stably stratified flows is proposed, and an analytical solution is obtained for Hs in terms of Lambert-W functions. Results are tested against smoke visualization experiments and related field measurements made during the Mountain Terrain Atmospheric Modeling and Observations (MATERHORN) Program. Some of the assumptions and perceived violations of them are tested using laboratory experiments conducted in a stratified water channel.
Steady hydromagnetic Couette flow in a rotating system with non ...
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energy equation and numerical values of rate of heat transfer at both plates are ... It may be noted that MHD Couette flow may be generated into two ways and .... Equations (5), (6), (10) and (11) with the use of (12), in non-dimensional form, ...
Hydraulic flow through a channel contraction: multiple steady states
Akers, B.; Bokhove, O.
2008-01-01
We have investigated shallow water flows through a channel with a contraction by experimental and theoretical means. The horizontal channel consists of a sluice gate and an upstream channel of constant width $b_0$ ending in a linear contraction of minimum width $b_c$. Experimentally, we observe upst
Hydraulic flow through a contraction: multiple steady states
Akers, B.; Bokhove, O.
2007-01-01
We consider shallow water flows through a channel with a contraction by experimental and theoretical means. The horizontal channel consists of a sluice gate and an upstream channel of constant width $b_0$ ending in a linear contraction of minimum width $b_c$. Experimentally, we observe upstream stea
Stability of 3D Gaussian vortices in rotating stratified Boussinesq flows: Linear analysis
Mahdinia, Mani; Jiang, Chung-Hsiang
2016-01-01
The linear stability of three-dimensional (3D) vortices in rotating, stratified flows has been studied by analyzing the non-hydrostatic inviscid Boussinesq equations. We have focused on a widely-used model of geophysical and astrophysical vortices, which assumes an axisymmetric Gaussian structure for pressure anomalies in the horizontal and vertical directions. For a range of Rossby number ($-0.5 < Ro < 0.5$) and Burger number ($0.02 < Bu < 2.3$) relevant to observed long-lived vortices, the growth rate and spatial structure of the most unstable eigenmodes have been numerically calculated and presented as a function of $Ro-Bu$. We have found neutrally-stable vortices only over a small region of the $Ro-Bu$ parameter space: cyclones with $Ro \\sim 0.02-0.05$ and $Bu \\sim 0.85-0.95$. However, we have also found that anticyclones in general have slower growth rates compared to cyclones. In particular, growth rate of the most unstable eigenmode for anticyclones in a large region of the parameter space ...
Mixed convection flow with non-uniform heat source/sink in a doubly stratified magnetonanofluid
Mehmood, K.; Hussain, S.; Sagheer, M.
2016-06-01
In this study, we explore the unsteady flow of viscous nanofluid driven by an inclined stretching sheet. The novelty of the present study is to account for the effect of a non-uniform heat source/sink in a thermally and solutally stratified magnetonanofluid. Governing system of nonlinear partial differential equations is converted into a system of nonlinear ordinary differential equations. Solution of the transformed system is obtained using RK4 method with shooting technique. It is observed that increase in the values of thermal and mass stratification parameter reduce the velocity profile and increase in the values of variable thermal conductivity parameter and non-uniform heat source/sink parameters enhance the temperature distribution. Moreover, skin friction coefficient, Nusselt number and Sherwood number are discussed. Obtained results are displayed both graphically and in tabular form to illustrate the effect of different parameters on the velocity, temperature and concentration profiles. Numerical results are compared with previous published results and found to be in good agreement for special cases of the emerging parameters.
Gedeon, M.; Mallants, D.
2012-04-01
Radionuclide concentration predictions in aquifers play an important role in estimating impact of planned surface disposal of radioactive waste in Belgium, developed by the Belgian Agency for Radioactive Waste and Enriched Fissile Materials (ONDRAF), who also coordinates and leads the corresponding research. Long-term concentration predictions are based on a steady-state flow solution obtained by a cascade of multi-scale models from the catchment to the detailed (site) scale performed in MODFLOW. To test the concept and accuracy of the groundwater flow solution and conservativeness of the concentration predictions obtained therewith, a transient model, considered more realistic, was set up in a sub-domain of the intermediate scale steady-state model. Besides the modelling domain reduction, the transient model was and exact copy of the steady-state model, having the infiltration as the only time-varying parameter. The transient model was run for a twenty-year period, whereas the results were compared to the steady-state results based on infiltration value and observations averaged over the same period. The comparison of the steady-state and transient flow solutions includes the analyses of the goodness of fit, the parameter sensitivities, relative importance of the individual observations and one-percent sensitivity maps. The steady-state and transient flow solutions were subsequently translated into a site-scale transport model, used to predict the radionuclide concentrations in a hypothetical well in the aquifers. The translation of the flow solutions between the models of distinct scales was performed using the Local grid refinement method available in MODFLOW. In the site-scale models, MT3DMS transport simulations were performed to obtain respective concentration predictions in a hypothetical well, situated at 70 meters from the disposal tumuli. The equilibrium concentrations based on a constant source flux achieved using a steady-state solution were then
Efficient numerical solution of steady free-surface Navier-Stokes flow
Brummelen, E.H. van; Raven, H.C.; Koren, B.
2001-01-01
Numerical solution of flows that are partially bounded by a freely moving boundary is of great importance in practical applications such as ship hydrodynamics. The usual method for solving steady viscous free-surface flow subject to gravitation is alternating time integration of the kinematic cond
Factors influencing flow steadiness in laminar boundary layer shock interactions
Tumuklu, Ozgur; Levin, Deborah A.; Gimelshein, Sergey F.; Austin, Joanna M.
2016-11-01
The Direct Simulation Monte Carlo method has been used to model laminar shock wave boundary interactions of hypersonic flow over a 30/55-deg double-wedge and "tick-shaped" model configurations studied in the Hypervelocity Expansion Tube facility and T-ADFA free-piston shock tunnel, respectively. The impact of thermochemical effects on these interactions by changing the chemical composition from nitrogen to air as well as argon for a stagnation enthalpy of 8.0 MJ/kg flow are investigated using the 2-D wedge model. The simulations are found to reproduce many of the classic features related to Edney Type V strong shock interactions that include the attached, oblique shock formed over the first wedge, the detached bow shock from the second wedge, the separation zone, and the separation and reattachment shocks that cause complex features such as the triple point for both cases. However, results of a reacting air flow case indicate that the size of the separation length, and the movement of the triple point toward to the leading edge is much less than the nitrogen case.
Xu, Qin
1987-01-01
The existence of steady, nonlinear circulations in a flow susceptible to conditionally symmetric instability is studied, treating the latent heating as an energy source which is implicitly related to the motion field. The viscous nonlinear circulations of symmetrical instability are briefly discussed, and an existence theorem for steady, nonlinear symmetric circulations with bounded rates of latent heat release is given. The uniqueness and stability of these circulations are discussed, and some physical interpretations are given.
A p-version finite element method for steady incompressible fluid flow and convective heat transfer
Winterscheidt, Daniel L.
1993-01-01
A new p-version finite element formulation for steady, incompressible fluid flow and convective heat transfer problems is presented. The steady-state residual equations are obtained by considering a limiting case of the least-squares formulation for the transient problem. The method circumvents the Babuska-Brezzi condition, permitting the use of equal-order interpolation for velocity and pressure, without requiring the use of arbitrary parameters. Numerical results are presented to demonstrate the accuracy and generality of the method.
Rubinato, Matteo; Martins, Ricardo; Kesserwani, Georges; Leandro, Jorge; Djordjević, Slobodan; Shucksmith, James
2017-09-01
The linkage between sewer pipe flow and floodplain flow is recognised to induce an important source of uncertainty within two-dimensional (2D) urban flood models. This uncertainty is often attributed to the use of empirical hydraulic formulae (the one-dimensional (1D) weir and orifice steady flow equations) to achieve data-connectivity at the linking interface, which require the determination of discharge coefficients. Because of the paucity of high resolution localised data for this type of flows, the current understanding and quantification of a suitable range for those discharge coefficients is somewhat lacking. To fulfil this gap, this work presents the results acquired from an instrumented physical model designed to study the interaction between a pipe network flow and a floodplain flow. The full range of sewer-to-surface and surface-to-sewer flow conditions at the exchange zone are experimentally analysed in both steady and unsteady flow regimes. Steady state measured discharges are first analysed considering the relationship between the energy heads from the sewer flow and the floodplain flow; these results show that existing weir and orifice formulae are valid for describing the flow exchange for the present physical model, and yield new calibrated discharge coefficients for each of the flow conditions. The measured exchange discharges are also integrated (as a source term) within a 2D numerical flood model (a finite volume solver to the 2D Shallow Water Equations (SWE)), which is shown to reproduce the observed coefficients. This calibrated numerical model is then used to simulate a series of unsteady flow tests reproduced within the experimental facility. Results show that the numerical model overestimated the values of mean surcharge flow rate. This suggests the occurrence of additional head losses in unsteady conditions which are not currently accounted for within flood models calibrated in steady flow conditions.
Study of steady and unsteady wet steam condensing flows in a turbine stage
无
2007-01-01
Objective To develop the numerical method for the steady and unsteady wet steam condensing flow in turbine stage. Methods An Eulerian/Eulerian numerical model is used to describe the spontaneous condensation flow in the steam turbine. For the steady condensing flow computations, the mixing plane model was used. For the unsteady condensing flow computations, the sliding mesh method was used to simulate the rotor-stator interactions. Results The numerical results showed the obvious differences between non-condensing and condensing flows. The results also showed the unsteadiness effect due to rotor-stator interactions had a deep influence on the formation and growth process of water droplets. Conclusion The numerical methods presented in this paper are valid for the condensing flow in the turbine stage.
Yin, W.-L.
1984-04-01
It is shown that, in the case of non-zero charge density, the class of steady, plane, incompressible, aligned-fluid magnetofluiddynamic flows contains no rotational motions. Therefore, this class of flows is exhausted by the irrotational solutions of Kingston and Power.
Steady-state magnetohydrodynamic flow around an unmagnetized conducting sphere
Romanelli, N.; Gómez, D.; Bertucci, C. [Group of Astrophysical Flows, Instituto de Astronomía y Física del Espacio, Buenos Aires (Argentina); Delva, M., E-mail: nromanelli@iafe.uba.ar, E-mail: Magda.Delva@oeaw.ac.at [Space Research Institute, Graz (Austria)
2014-07-01
The noncollisional interaction between conducting obstacles and magnetized plasma winds can be found in different scenarios, from the interaction occurring between regions inside galaxy clusters to the interaction between the solar wind and Mars, Venus, and active comets, or even the interaction between Titan and the Saturnian magnetospheric flow. These objects generate, through several current systems, perturbations in the streaming magnetic field leading to its draping around the obstacle's effective conducting surface. Recent observational results suggest that several properties associated with magnetic field draping, such as the location of the polarity reversal layer of the induced magnetotail, are affected by variations in the conditions of the streaming magnetic field. To improve our understanding of these phenomena, we perform a characterization of several magnetic field draping signatures by analytically solving an ideal problem in which a perfectly conducting magnetized plasma (with frozen-in magnetic field conditions) flows around a spherical body for various orientations of the streaming magnetic field. In particular, we compute the shift of the inverse polarity reversal layer as the orientation of the background magnetic field is changed.
A steady-state solver and stability calculator for nonlinear internal wave flows
Viner, Kevin C.; Epifanio, Craig C.; Doyle, James D.
2013-10-01
A steady solver and stability calculator is presented for the problem of nonlinear internal gravity waves forced by topography. Steady-state solutions are obtained using Newton's method, as applied to a finite-difference discretization in terrain-following coordinates. The iteration is initialized using a boundary-inflation scheme, in which the nonlinearity of the flow is gradually increased over the first few Newton steps. The resulting method is shown to be robust over the full range of nonhydrostatic and rotating parameter space. Examples are given for both nonhydrostatic and rotating flows, as well as flows with realistic upstream shear and static stability profiles. With a modest extension, the solver also allows for a linear stability analysis of the steady-state wave fields. Unstable modes are computed using a shifted-inverse method, combined with a parameter-space search over a set of realistic target values. An example is given showing resonant instability in a nonhydrostatic mountain wave.
Chang Ho Oh; Eung Soo Kim; Hee Cheon No; Nam Zin Cho
2008-12-01
The US Department of Energy is performing research and development (R&D) that focuses on key phenomena that are important during challenging scenarios that may occur in the Next Generation Nuclear Plant (NGNP) Program / GEN-IV Very High Temperature Reactor (VHTR). Phenomena identification and ranking studies (PIRT) to date have identified the air ingress event, following on the heels of a VHTR depressurization, as very important (Schultz et al., 2006). Consequently, the development of advanced air ingress-related models and verification and validation (V&V) are very high priority for the NGNP program. Following a loss of coolant and system depressurization, air will enter the core through the break. Air ingress leads to oxidation of the in-core graphite structure and fuel. The oxidation will accelerate heat-up of the bottom reflector and the reactor core and will cause the release of fission products eventually. The potential collapse of the bottom reflector because of burn-off and the release of CO lead to serious safety problems. For estimation of the proper safety margin we need experimental data and tools, including accurate multi-dimensional thermal-hydraulic and reactor physics models, a burn-off model, and a fracture model. We also need to develop effective strategies to mitigate the effects of oxidation. The results from this research will provide crucial inputs to the INL NGNP/VHTR Methods R&D project. This project is focused on (a) analytical and experimental study of air ingress caused by density-driven, stratified, countercurrent flow, (b) advanced graphite oxidation experiments, (c) experimental study of burn-off in the bottom reflector, (d) structural tests of the burnt-off bottom reflector, (e) implementation of advanced models developed during the previous tasks into the GAMMA code, (f) full air ingress and oxidation mitigation analyses, (g) development of core neutronic models, (h) coupling of the core neutronic and thermal hydraulic models, and (i
Longitudinal Hydraulic Resistance Parameters of Cryocooler and Stirling Regenerators in Steady Flow
Clearman, W. M.; Ghiaasiaan, S. M.; Cha, J. S.; Kirkconnell, C. S.; Desai, P. V.
2008-03-01
The results of an ongoing research program aimed at the measurement and correlation of anisotropic hydrodynamic parameters of widely-used cryocooler regenerator fillers are presented. The hydrodynamic parameters associated with steady, longitudinal flow are addressed in this paper. An experimental apparatus consisting of a cylindrical test section packed with regenerator fillers is used for the measurement of axial permeability and Forchheimer coefficients, with pure helium as the working fluid. The regenerator fillers that are tested include stainless steel 325 and 400-mesh screens with 69.69% porosity, stainless steel 400-mesh sintered mesh filler with 61.65% porosity, stainless steel foam metal with 55.47% porosity, and micro machined nickel disks with 26.8% porosity. The test section is subjected to a steady flow of helium at one end, and is open to the atmosphere at the other end. The instrumentation includes pressure transducers and a high-precision flow meter. For each filler material, the pressures at inlet to the regenerator are measured under steady flow conditions over a wide range of flow rates and a CFD assisted methodology is then used for the analysis and interpretation of the measured data. The viscous and inertial resistance parameter values, and the corresponding permeability and inertial coefficients, obtained using CFD are then compared with the corresponding values that are separately measured under steady-periodic flow conditions.
Investigations of Reduced Equations for Rotating, Stratified and Non-hydrostatic Flows
Nieves, David J.
boundary conditions. These results imply that any horizontal thermal variation along the boundaries that varies on the scale of the convection has no leading order influence on the interior convection, thus providing insight into geophysical and astrophysical flows where stress-free mechanical boundary conditions are often assumed. The final study presented here contrasts the previous investigations. It presents an investigation of rapidly rotating and stably stratified turbulence where the stratification strength is varied from weak (large Froude number) to strong (small Froude number). The investigation is set in the context of the asymptotically reduced model which efficiently retains anisotropic inertia-gravity waves with order-one frequencies and highlights a regime of wave-eddy interactions. Numerical simulations of the reduced model are performed where energy is injected by a stochastic forcing of vertical velocity. The simulations reveal two regimes: one characterized by the presence of well-formed, persistent and thin turbulent layers of locally-weakened stratification: the other characterized by the absence of layers at large Froude numbers. Both regimes are characterized by a large-scale barotropic dipole in a sea of small-scale turbulence. When the Reynolds number is not too large a direct cascade of barotropic kinetic energy is observed and leads to an equilibration of total energy. We examine net energy exchanges that occur through vortex stretching and vertical buoyancy flux and diagnose the horizontal scales active in these exchanges. We find that baroclinic motions inject energy directly to the largest scales of the barotropic mode governed by the two-dimensional vorticity equation, and implies that the large-scale barotropic dipole is not the end result of an inverse cascade within the two-dimensional barotropic mode. An additional yet brief look into the linear vortical and wave modes is considered.
Jilian Wu
2013-01-01
Full Text Available We discuss several stabilized finite element methods, which are penalty, regular, multiscale enrichment, and local Gauss integration method, for the steady incompressible flow problem with damping based on the lowest equal-order finite element space pair. Then we give the numerical comparisons between them in three numerical examples which show that the local Gauss integration method has good stability, efficiency, and accuracy properties and it is better than the others for the steady incompressible flow problem with damping on the whole. However, to our surprise, the regular method spends less CPU-time and has better accuracy properties by using Crout solver.
Evaluation of analytic solutions for steady interface flow where the aquifer extends below the sea
Bakker, Mark; Miller, Anthony D.; Morgan, Leanne K.; Werner, Adrian D.
2017-08-01
A computational approach is presented for steady Dupuit interface flow where the aquifer extends below the sea. A detailed approach is outlined to determine the head at the coastline so that the solution below the leaky seabed may be combined with any type of steady Dupuit interface flow in the aquifer below the land. The method allows for any inland boundary condition including specified head and specified flux; cases of freshwater lenses caused by infiltration are also considered. The approach is implemented in a Python script and a Jupyter Notebook.
Dynamic fluid connectivity during steady-state multiphase flow in a sandstone
Reynolds, Catriona A.; Menke, Hannah; Andrew, Matthew; Blunt, Martin J.; Krevor, Samuel
2017-08-01
The current conceptual picture of steady-state multiphase Darcy flow in porous media is that the fluid phases organize into separate flow pathways with stable interfaces. Here we demonstrate a previously unobserved type of steady-state flow behavior, which we term “dynamic connectivity,” using fast pore-scale X-ray imaging. We image the flow of N2 and brine through a permeable sandstone at subsurface reservoir conditions, and low capillary numbers, and at constant fluid saturation. At any instant, the network of pores filled with the nonwetting phase is not necessarily connected. Flow occurs along pathways that periodically reconnect, like cars controlled by traffic lights. This behavior is consistent with an energy balance, where some of the energy of the injected fluids is sporadically converted to create new interfaces.
Laser Doppler anemometry measurements of steady flow through two bi-leaflet prosthetic heart valves
Ovandir Bazan
2013-12-01
Full Text Available INTRODUCTION: In vitro hydrodynamic characterization of prosthetic heart valves provides important information regarding their operation, especially if performed by noninvasive techniques of anemometry. Once velocity profiles for each valve are provided, it is possible to compare them in terms of hydrodynamic performance. In this first experimental study using laser doppler anemometry with mechanical valves, the simulations were performed at a steady flow workbench. OBJECTIVE: To compare unidimensional velocity profiles at the central plane of two bi-leaflet aortic prosthesis from St. Jude (AGN 21 - 751 and 21 AJ - 501 models exposed to a steady flow regime, on four distinct sections, three downstream and one upstream. METHODS: To provide similar conditions for the flow through each prosthesis by a steady flow workbench (water, flow rate of 17L/min. and, for the same sections and sweeps, to obtain the velocity profiles of each heart valve by unidimensional measurements. RESULTS: It was found that higher velocities correspond to the prosthesis with smaller inner diameter and instabilities of flow are larger as the section of interest is closer to the valve. Regions of recirculation, stagnation of flow, low pressure, and flow peak velocities were also found. CONCLUSIONS: Considering the hydrodynamic aspect and for every section measured, it could be concluded that the prosthesis model AGN 21 - 751 (RegentTM is superior to the 21 AJ - 501 model (Master Series. Based on the results, future studies can choose to focus on specific regions of the these valves.
无
2009-01-01
On the numerical simulation of active scalar,a new explicit algebraic expression on active scalar flux was derived based on Wikstrm,Wallin and Johansson model (aWWJ model). Reynolds stress algebraic expressions were added by a term to account for the buoyancy effect. The new explicit Reynolds stress and active scalar flux model was then established. Governing equations of this model were solved by finite volume method with unstructured grids. The thermal shear stratified cylinder wake flow was computed by this new model. The computational results are in good agreement with laboratorial measurements. This work is the development on modeling of explicit algebraic Reynolds stress and scalar flux,and is also a further modification of the aWWJ model for complex situations such as a shear stratified flow.
Oscillatory and Steady Flows in the Annular Fluid Layer inside a Rotating Cylinder
Veronika Dyakova
2016-01-01
Full Text Available The dynamics of a low-viscosity fluid inside a rapidly rotating horizontal cylinder were experimentally studied. In the rotating frame, the force of gravity induces azimuthal fluid oscillations at a frequency equal to the velocity of the cylinder’s rotation. This flow is responsible for a series of phenomena, such as the onset of centrifugal instability in the Stokes layer and the growth of the relief at the interface between the fluid and the granular medium inside the rotating cylinder. The phase inhomogeneity of the oscillatory fluid flow in the viscous boundary layers near the rigid wall and the free surface generates the azimuthal steady streaming. We studied the relative contribution of the viscous boundary layers in the generation of the steady streaming. It is revealed that the velocity of the steady streaming can be calculated using the velocity of the oscillatory fluid motion.
Ivana Stiperski
2017-01-01
Full Text Available In this article, we present an overview of the HyIV-CNRS-SecORo (Hydralab IV-CNRS-Secondary Orography and Rotors Experiments laboratory experiments carried out in the CNRM (Centre National de Recherches Météorologiques large stratified water flume. The experiments were designed to systematically study the influence of double obstacles on stably stratified flow. The experimental set-up consists of a two-layer flow in the water tank, with a lower neutral and an upper stable layer separated by a sharp density discontinuity. This type of layering over terrain is known to be conducive to a variety of possible responses in the atmosphere, from hydraulic jumps to lee waves and highly turbulent rotors. In each experiment, obstacles were towed through the tank at a constant speed. The towing speed and the size of the tank allowed high Reynolds-number flow similar to the atmosphere. Here, we present the experimental design, together with an overview of laboratory experiments conducted and their results. We develop a regime diagram for flow over single and double obstacles and examine the parameter space where the secondary obstacle has the largest influence on the flow. Trapped lee waves, rotors, hydraulic jumps, lee-wave interference and flushing of the valley atmosphere are successfully reproduced in the stratified water tank. Obstacle height and ridge separation distance are shown to control lee-wave interference. Results, however, differ partially from previous findings on the flow over double ridges reported in the literature due to the presence of nonlinearities and possible differences in the boundary layer structure. The secondary obstacle also influences the transition between different flow regimes and makes trapped lee waves possible for higher Froude numbers than expected for an isolated obstacle.
Computational issues of solving the 1D steady gradually varied flow equation
Artichowicz Wojciech
2014-09-01
Full Text Available In this paper a problem of multiple solutions of steady gradually varied flow equation in the form of the ordinary differential energy equation is discussed from the viewpoint of its numerical solution. Using the Lipschitz theorem dealing with the uniqueness of solution of an initial value problem for the ordinary differential equation it was shown that the steady gradually varied flow equation can have more than one solution. This fact implies that the nonlinear algebraic equation approximating the ordinary differential energy equation, which additionally coincides with the wellknown standard step method usually applied for computing of the flow profile, can have variable number of roots. Consequently, more than one alternative solution corresponding to the same initial condition can be provided. Using this property it is possible to compute the water flow profile passing through the critical stage.
DIPAK SARMA
2012-12-01
Full Text Available A steady two dimensional MHD convective flow of an incompressible viscous and electrically conducting fluid past a continuously moving porous vertical plate with Soret and Dufour effects is analyzed. A magnetic field of uniform strength is assumed to be applied transversely to the direction of the main flow. The solutions for thevelocity field, temperature and concentrations are performed for a wide range of the governing flow parameters viz the Soret number, Prandtl number, Schmidt number, Grashof number for heat transfer, Dufour number, Solutal Grashof number and Hartmann number. The effects of these flow parameters on the velocity, temperature, concentration, skin friction coefficient and Sherwood number are discussed graphically.
Hassager, Ole; Mortensen, Kell; Bach, Anders
2012-01-01
We use small-angle neutron scattering to measure the molecular stretching in polystyrene melts undergoing steady elongational flow at large stretch rates. The radius of gyration of the central segment of a partly deuterated polystyrene molecule is, in the stretching direction, increasing with the...
Out-of-equilibrium energy flow and steady state configurations in AdS/CFT
Megias, Eugenio
2015-01-01
We study out-of-equilibrium energy flow in a strongly coupled system by using the AdS/CFT correspondence. In particular, we describe the appearance of a steady state connecting two asymptotic equilibrium systems. We obtain results within the linear response regime.
ON THE ASYMPTOTIC BEHAVIOUR OF THE STEADY SUPERSONIC FLOWS AT INFINITY
ZHANG YONGQIAN
2005-01-01
This paper studies the asymptotic behaviour of steady supersonic flow past a piecewise smooth corner or bend. Under the hypothese that both vertex angle and the total variation of tangent along the boundary are small, it is shown that the solution can be obtained by a modified Glimm scheme, and that the asymptotic behaviour of the solution is determined by the velocity of incoming flow and the limit of the tangent of the boundary at infinity.
Amy, L. A.; Peakall, J.; Talling, P. J.
2005-08-01
Vertical stratification of particle concentration is a common if not ubiquitous feature of submarine particulate gravity flows. To investigate the control of stratification on current behaviour, analogue stratified flows were studied using laboratory experiments. Stratified density currents were generated by releasing two-layer glycerol solutions into a tank of water. Flows were sustained for periods of tens of seconds and their velocity and concentration measured. In a set of experiments the strength of the initial density and viscosity stratification was increased by progressively varying the lower-layer concentration, CL. Two types of current were observed indicating two regimes of behaviour. Currents with a faster-moving high-concentration basal region that outran the upper layer were produced if CL < 75%. Above this critical value of CL, currents were formed with a relatively slow, high-concentration base that lagged behind the flow front. The observed transition in behaviour is interpreted to indicate a change from inertia- to viscosity-dominated flow with increasing concentration. The reduction in lower-layer velocity at high concentrations is explained by enhanced drag at low Reynolds numbers. Results show that vertical stratification produces longitudinal stratification in the currents. Furthermore, different vertical and temporal velocity and concentration profiles characterise the observed flow types. Implications for the deposit character of particle-laden currents are discussed and illustrated using examples from ancient turbidite systems.
Computational Fluid Dynamics model of stratified atmospheric boundary-layer flow
Koblitz, Tilman; Bechmann, Andreas; Sogachev, Andrey;
2015-01-01
For wind resource assessment, the wind industry is increasingly relying on computational fluid dynamics models of the neutrally stratified surface-layer. So far, physical processes that are important to the whole atmospheric boundary-layer, such as the Coriolis effect, buoyancy forces and heat...
Convective dispersion during steady flow in the conducting airways of the human lung.
Fresconi, Frank E; Prasad, Ajay K
2008-02-01
The adverse health effects of inhaled particulate matter from the environment depend on its dispersion, transport, and deposition in the human airways. Similarly, precise targeting of deposition sites by pulmonary drug delivery systems also relies on characterizing the dispersion and transport of therapeutic aerosols in the respiratory tract. A variety of mechanisms may contribute to convective dispersion in the lung; simple axial streaming, augmented dispersion, and steady streaming are investigated in this effort. Flow visualization of a bolus during inhalation and exhalation, and dispersion measurements were conducted during steady flow in a three-generational, anatomically accurate in vitro model of the conducting airways to support this goal. Control variables included Reynolds number, flow direction, generation, and branch. Experiments illustrate transport patterns in the lumen cross section and map their relation to dispersion metrics. These results indicate that simple axial streaming, rather than augmented dispersion, is the dominant steady convective dispersion mechanism in symmetric Weibel generations 7-13 during normal respiration. Experimental evidence supports the branching nature of the airways as a possible contributor to steady streaming in the lung.
Effects of governing parameters on steady-state inter-wrapper flow in an LMFBR
Moriya, Shoichi [Central Research Inst. of Electric Power Industry, Abiko, Chiba (Japan). Abiko Research Lab
2001-04-01
Hydraulic experiments were performed using a 1/8th scale rectangular model, based on a Japanese demonstration fast breeder reactor design, in order to study fundamental characteristics of interwrapper flows occurring under steady state conditions in an LMFBR. The steady state interwrapper flow of which direction was downward in the center region and upward in the peripheral region of a core barrel was observed because of the radial static pressure gradient in the upper part of the core barrel, produced by a core blockage effect resulting from an above core structure with a perforated skirt. Thermal stratification phenomena were moreover observed in the interwrapper region, created by the hot steady state interwrapper flow from an upper plenum and the cold leakage flow through the separated plate of the core barrel. The thermal interface was generated in higher part of the core barrel when the core blockage effect was smaller and Richardson number and the leakage flow rate ratio were larger. Significant temperature fluctuations occurred in the peripheral region of the core barrel, when the difference between the interface elevations in the center and peripheral regions of the core barrel was enough large. (author)
On the Kaolinite Floc Size at the Steady State of Flocculation in a Turbulent Flow.
Zhu, Zhongfan; Wang, Hongrui; Yu, Jingshan; Dou, Jie
2016-01-01
The flocculation of cohesive fine-grained sediment plays an important role in the transport characteristics of pollutants and nutrients absorbed on the surface of sediment in estuarine and coastal waters through the complex processes of sediment transport, deposition, resuspension and consolidation. Many laboratory experiments have been carried out to investigate the influence of different flow shear conditions on the floc size at the steady state of flocculation in the shear flow. Most of these experiments reported that the floc size decreases with increasing shear stresses and used a power law to express this dependence. In this study, we performed a Couette-flow experiment to measure the size of the kaolinite floc through sampling observation and an image analysis system at the steady state of flocculation under six flow shear conditions. The results show that the negative correlation of the floc size on the flow shear occurs only at high shear conditions, whereas at low shear conditions, the floc size increases with increasing turbulent shear stresses regardless of electrolyte conditions. Increasing electrolyte conditions and the initial particle concentration could lead to a larger steady-state floc size.
On the Kaolinite Floc Size at the Steady State of Flocculation in a Turbulent Flow.
Zhongfan Zhu
Full Text Available The flocculation of cohesive fine-grained sediment plays an important role in the transport characteristics of pollutants and nutrients absorbed on the surface of sediment in estuarine and coastal waters through the complex processes of sediment transport, deposition, resuspension and consolidation. Many laboratory experiments have been carried out to investigate the influence of different flow shear conditions on the floc size at the steady state of flocculation in the shear flow. Most of these experiments reported that the floc size decreases with increasing shear stresses and used a power law to express this dependence. In this study, we performed a Couette-flow experiment to measure the size of the kaolinite floc through sampling observation and an image analysis system at the steady state of flocculation under six flow shear conditions. The results show that the negative correlation of the floc size on the flow shear occurs only at high shear conditions, whereas at low shear conditions, the floc size increases with increasing turbulent shear stresses regardless of electrolyte conditions. Increasing electrolyte conditions and the initial particle concentration could lead to a larger steady-state floc size.
Three dimensional steady and unsteady asymmetric flow past wings of arbitrary planforms
Kandil, O. A.; Atta, E. H.; Nayfeh, A. H.
1978-01-01
The nonlinear discrete vortex method is extended to treat the problem of asymmetric flows past a wing with leading edge separation, including steady and unsteady flows. The problem is formulated in terms of a body fixed frame of reference and the nonlinear-discrete vortex method is modified accordingly. Although the method is general, only examples of flows past delta wings are presented due to the availability of experimental data as well as approximate theories. Comparison of results with experimental results for a delta wing undergoing a steady rolling motion at zero angle of attack demonstrate the superiority of the present method over existing approximate theories in obtaining highly accurate loads. Numerical results for yawed wings at large angles of attack are also presented. In all cases, total load coefficients, pressure distributions, and shapes of the free vortex sheets are shown.
THE STEADY/PULSATILE FLOW AND MACROMOLECULAR TRANSPORT IN T-BIFURCATION BLOOD VESSELS
李丁; 温功碧
2003-01-01
A numerical analysis of the steady and pulsatile, macromolecular( such as lowdensity lipopotein ( LDL ), Albumin ) transport in T-bifurcation was proposed. Theinfluence of Reynolds number and mass flow ratio etc. parameters on the velocity field andmass transport were calculated. The computational results predict that the blood flow factorsaffect the macromolecular distribution and the transport across the wall, it shows thathemodynamic play an important role in the process of atherosclerosis . The LDL and Albuminconcentration on the wall varies most greatly in flow bifurcation area where the wall shearstress varies greatly at the branching vessel and the atherosclerosis often appears there.
Hodographic study of non-Newtonian MHD aligned steady plane fluid flows
P. V. Nguyen
1990-01-01
Full Text Available A study is made of non-Newtonian HHD aligned steady plane fluid flows to find exact solutions for various flow configurations. The equations of motion have been transformed to the hodograph plane. A Legendre-transform function is used to recast the equations in the hodograph plane in terms of this transform function. Solutions for various flow configurations are obtained. Applications are investigated for the fluids of finite and infinite electrical conductivity bringing out the similarities and contrasts in the solutions of these types of fluids.
Vesicle Dynamics in a Confined Poiseuille Flow: From Steady-State to Chaos
Aouane, Othmane; Benyoussef, Abdelilah; Wagner, Christian; Misbah, Chaouqi
2014-01-01
Red blood cells (RBCs) are the major component of blood and the flow of blood is dictated by that of RBCs. We employ vesicles, which consist of closed bilayer membranes enclosing a fluid, as a model system to study the behavior of RBCs under a confined Poiseuille flow. We extensively explore two main parameters: i) the degree of confinement of vesicles within the channel, and ii) the flow strength. Rich and complex dynamics for vesicles are revealed ranging from steady-state shapes (in the form of parachute and slipper) to chaotic dynamics of shape. Chaos occurs through a cascade of multiple periodic oscillations of the vesicle shape. We summarize our results in a phase diagram in the parameter plane (degree of confinement, flow strength). This finding highlights the level of complexity of a flowing vesicle in the small Reynolds number where the flow is laminar in the absence of vesicles and can be rendered turbulent due to elasticity of vesicles.
Turbulent fluxes of entropy and internal energy in temperature stratified flows
Rogachevskii, Igor
2015-01-01
We derive equations for the mean entropy and the mean internal energy in the low-Mach-number temperature stratified turbulence (i.e., for turbulent convection or stably stratified turbulence), and show that turbulent flux of entropy is given by ${\\bf F}_s=\\overline{\\rho} \\, \\overline{{\\bf u} s}$, where $\\overline{\\rho}$ is the mean fluid density, $s$ are fluctuations of entropy and overbars denote averaging over an ensemble of turbulent velocity field, ${\\bf u}$. We demonstrate that the turbulent flux of entropy is different from the turbulent convective flux, ${\\bf F}_c=\\overline{T} \\, \\overline{\\rho} \\, \\overline{{\\bf u} s}$, of the fluid internal energy, where $\\overline{T}$ is the mean fluid temperature. This turbulent convective flux is well-known in the astrophysical and geophysical literature, and it cannot be used as a turbulent flux in the equation for the mean entropy. This result is exact for low-Mach-number temperature stratified turbulence and is independent of the model used. We also derive equa...
M A Hye; M M Rahman; L Nowsher Ali; S Afrin
2013-01-01
... steady solutions with two- and four-vortex solutions are obtained by the Newton-Raphson iteration method. Then, in order to investigate the non-linear behavior of the unsteady solutions, time evolution calculations as well as power spectrum of the solutions are obtained, and it is found that the steady-state flow turns into periodic flow through ...
2008-01-01
Theoretical relations that predict the transition from a stratified pattern to a slug pattern,including a onedimensional wave model that contains less empiricism than the commonly used Taitel-Dukler model,and the ideal model for stratified flow for the gas-liquid flow in horizontal pipes are presented.Superficial velocities of each phase,as the onset of slugging occurs,were predicted,and theoretical analysis was conducted on the stratified to slug flow regime transition.The friction,existing between the fluid and pipe wall,and on the interface of two phases,was especially taken into account.A theoretical model was applied to an experiment about air-oil two-phase flow in a 50 mm horizontal pipe.The effect of pipe diameter on the transition was also studied.The results show that this approach gives a reasonable prediction over the whole range of flow rates,and better agreement has been achieved between predicted and measured critical parameters.
The steady expiratory pressure-flow relation in a model pulmonary bifurcation.
Collins, J M; Shapiro, A H; Kimmel, E; Kamm, R D
1993-08-01
Experiments were conducted over a range of Reynolds numbers from 50 to 8000 to study the pressure-flow relationship for a single bifurcation in a multi-generation model during steady expiratory flow. Using the energy equation, the measured static pressure drop was decomposed into separate components due to fluid acceleration and viscous energy dissipation. The frictional pressure drop was found to closely approximate that for an equivalent length of curved tube with the same curvature ratio as in the model bifurcation. The sensitivity of these results to changes in airway cross-sectional shape, non-planar configuration, and flow regime (laminar-turbulent) was investigated. In separate experiments using dye visualization and hot-wire anemometry, a transition to turbulent flow was observed at Reynolds numbers between 1000 and 1500. Transition had very little effect on the pressure-flow relation.
Steady internal flow and aerodynamic loads analysis of shuttle thermal protection system
Petley, D. H.; Alexander, W., Jr.; Ivey, G. W., Jr.; Kerr, P. A.
1984-01-01
An analytical model for calculation of ascent steady state tile loading was developed and validated with wind tunnel data. The analytical model is described and results are given. Results are given for loading due to shocks and skin friction. The analysis included calculation of internal flow (porous media flow and channel flow) to obtain pressures and integration of the pressures to obtain forces and moments on an insulation tile. A heat transfer program was modified by using analogies between heat transfer and fluid flow so that it could be used for internal flow calculation. The type of insulation tile considered was undensified reusable surface insulation (RSI) without gap fillers, and the location studied was the lower surface of the orbiter. Force and moment results are reported for parameter variations on surface pressure distribution, gap sizes, insulation permeability, and tile thickness.
Noninvasive estimation of 2-D pressure gradients in steady flow using ultrasound
Olesen, Jacob Bjerring; Traberg, Marie Sand; Pihl, Michael Johannes;
2014-01-01
A noninvasive method for estimating 2-D pressure gradients from ultrasound vector velocity data is presented. It relies on vector velocity fields acquired using the transverse oscillation method during steady flow conditions. The pressure gradients are calculated from the velocity fields using...... of -7% for the axial component and -8% for the lateral component. The relative standard deviation of the estimator is 5% (axial component) and 30% (lateral component) when studying the pressure gradient across the constriction using 3 velocity frames per pressure estimate. The study shows that 2-D...... phantom. The geometry of the model is determined from magnetic resonance imaging. The presented study is conducted assuming steady flow using velocity data acquired at 18 frames per second. The proposed method shows pressure gradients at the constricted region from -8 kPa/m to 9 kPa/m, with a maximum bias...
Comparison of Steady-State SVC Models in Load Flow Calculations
Chen, Peiyuan; Chen, Zhe; Bak-Jensen, Birgitte
2008-01-01
This paper compares in a load flow calculation three existing steady-state models of static var compensator (SVC), i.e. the generator-fixed susceptance model, the total susceptance model and the firing angle model. The comparison is made in terms of the voltage at the SVC regulated bus, equivalent...... SVC susceptance at the fundamental frequency and the load flow convergence rate both when SVC is operating within and on the limits. The latter two models give inaccurate results of the equivalent SVC susceptance as compared to the generator model due to the assumption of constant voltage when the SVC...... is operating within the limits. This may underestimate or overestimate the SVC regulating capability. Two modified models are proposed to improve the SVC regulated voltage according to its steady-state characteristic. The simulation results of the two modified models show the improved accuracy...
Velocity-vorticity formulation of three-dimensional, steady, viscous, incompressible flows
Meir, A.J. [Auburn Univ., AL (United States)
1994-12-31
In this work we discuss some aspects of the velocity-vorticity formulation of three-dimensional, steady, viscous, incompressible flows. We describe reasonable boundary conditions that should be imposed on the vorticity and a compatibility condition that the vorticity must satisfy. This formulation may give rise to efficient numerical algorithms for approximating solutions of the Stokes problem, which in turn yields an iterative method for approximating solutions of the Navier-Stokes equations.
Group classification of steady two-dimensional boundary-layer stagnation-point flow equations
Nadjafikhah, Mehdi; Hejazi, Seyed Reza
2010-01-01
Lie symmetry group method is applied to study the boundary-layer equations for two-dimensional steady flow of an incompressible, viscous fluid near a stagnation point at a heated stretching sheet placed in a porous medium equation. The symmetry group and its optimal system are given, and group invariant solutions associated to the symmetries are obtained. Finally the structure of the Lie algebra symmetries is determined.
Heat Transfer on Steady MHD rotating flow through porous medium in a parallel plate channel
Dr. G. Prabhakara Rao,
2015-04-01
Full Text Available We discussed the combined effects of radiative heat transfer and a transverse magnetic field on steady rotating flow of an electrically conducting optically thin fluid through a porous medium in a parallel plate channel and non-uniform temperatures at the walls. The analytical solutions are obtained from coupled nonlinear partial differential equations for the problem. The computational results are discussed quantitatively with the aid of the dimensionless parameters entering in the solution.
Spectral Analysis and Computation of Effective Diffusivities for Steady Random Flows
2016-04-28
W. Demmel. Applied Numerical Linear Algebra . SIAM, 1997. [14] E. Di Lorenzo, D. Mountain, H. P. Batchelder, N. Bond, and E. E. Hofmann. Advances in...Such methods have been extended to steady flows where particles diffuse according to linear collisions [42], solute transport in porous media [8...2 is the Laplacian, ε > 0, d is the system dimension, and we denote by 0 the null element on all linear spaces in question. Moreover, ξ·ζ = ξ
Zhang, Wei; Markfort, Corey; Porté-Agel, Fernando
2014-05-01
Turbulent boundary-layer flows over complex topography have been extensively studied in the atmospheric sciences and wind engineering communities. The upwind turbulence level, the atmospheric thermal stability and the shape of the topography as well as surface characteristics play important roles in turbulent transport of momentum and scalar fluxes. However, to the best of our knowledge, atmospheric thermal stability has rarely been taken into account in laboratory simulations, particularly in wind-tunnel experiments. Extension of such studies in thermally-stratified wind tunnels will substantially advance our understanding of thermal stability effects on the physics of flow over complex topography. Additionally, high-resolution experimental data can be used for development of new parameterization of surface fluxes and validation of numerical models such as Large-Eddy Simulation (LES). A series of experiments of neutral and thermally-stratified boundary-layer flows over a wall-mounted 2-D block were conducted at the Saint Anthony Falls Laboratory boundary-layer wind tunnel. The 2-D block, with a width to height ratio of 2:1, occupied the lowest 25% of the turbulent boundary layer. Stable and convective boundary layers were simulated by independently controlling the temperature of air flow, the test section floor, and the wall-mounted block surfaces. Measurements using high-resolution Particle Image Velocimetry (PIV), x-wire/cold-wire anemometry, thermal-couples and surface heat flux sensors were made to quantify the turbulent properties and surface fluxes in distinct macroscopic flow regions, including the separation/recirculation zones, evolving shear layer and the asymptotic far wake. Emphasis will be put on addressing thermal stability effects on the spatial distribution of turbulent kinetic energy (TKE) and turbulent fluxes of momentum and scalar from the near to far wake region. Terms of the TKE budget equation are also inferred from measurements and
Chu, In Cheol; Yu, Seon Oh; Chun, Moon Hyun [Korea Advanced Institute of Science and Technology, Taejon (Korea, Republic of); Kim, Byong Sup; Kim, Yang Seok; Kim, In Hwan; Lee, Sang Won [Korea Electric Power Research Institute, Taejon (Korea, Republic of)
1998-12-31
An interfacial condensation heat transfer phenomenon in a steam/water countercurrent stratified flow in a nearly horizontal pipe has been experimentally investigated. The present study has been focused on the measurement of the temperature and velocity distributions within the water layer. In particular, the water layer thickness used in the present work is large enough so that the turbulent mixing is limited and the thermal stratification is established. As a result, the thermal resistance of the water layer to the condensation heat transfer is increased significantly. An empirical correlation of the interfacial condensation heat transfer has been developed. The present correlation agrees with the data within {+-} 15%. 5 refs., 6 figs. (Author)
Numerical Investigation of Submarine Hydrodynamics and Flow Field in Steady Turn
曹留帅; 朱军; 万文彬
2016-01-01
This paper presents numerical simulations of viscous flow past a submarine model in steady turn by solving the Reynolds-Averaged Navier-Stokes Equations (RANSE) for incompressible, steady flows. The rotating coordinate system was adopted to deal with the rotation problem. The Coriolis force and centrifugal force due to the computation in a body-fixed rotating frame of reference were treated explicitly and added to momentum equations as source terms. Furthermore, velocities of entrances were coded to give the correct magnitude and direction needed. Two turbulence closure models (TCMs), the RNG k-εmodel with wall functions and curvature correction and the Shear Stress Transport (SST) k-ωmodel without the use of wall functions, but with curvature correction and low-Re correction were introduced, respectively. Take DARPA SUBOFF model as the test case, a series of drift angle varying between 0° and 16° at a Reynolds number of 6.53×106 undergoing rotating arm test simulations were conducted. The computed forces and moment as a function of drift angle during the steady turn are mostly in close agreement with available experimental data. Though the difference between the pressure coefficients around the hull form was observed, they always show the same trend. It was demonstrated that using sufficiently fine grids and advanced turbulence models will lead to accurate prediction of the flow field as well as the forces and moments on the hull.
Numerical investigation of submarine hydrodynamics and flow field in steady turn
Cao, Liu-shuai; Zhu, Jun; Wan, Wen-bin
2016-03-01
This paper presents numerical simulations of viscous flow past a submarine model in steady turn by solving the Reynolds-Averaged Navier-Stokes Equations (RANSE) for incompressible, steady flows. The rotating coordinate system was adopted to deal with the rotation problem. The Coriolis force and centrifugal force due to the computation in a bodyfixed rotating frame of reference were treated explicitly and added to momentum equations as source terms. Furthermore, velocities of entrances were coded to give the correct magnitude and direction needed. Two turbulence closure models (TCMs), the RNG κ - ɛ model with wall functions and curvature correction and the Shear Stress Transport (SST) κ - ω model without the use of wall functions, but with curvature correction and low- Re correction were introduced, respectively. Take DARPA SUBOFF model as the test case, a series of drift angle varying between 0° and 16° at a Reynolds number of 6.53×106 undergoing rotating arm test simulations were conducted. The computed forces and moment as a function of drift angle during the steady turn are mostly in close agreement with available experimental data. Though the difference between the pressure coefficients around the hull form was observed, they always show the same trend. It was demonstrated that using sufficiently fine grids and advanced turbulence models will lead to accurate prediction of the flow field as well as the forces and moments on the hull.
NUMERICAL SIMULATIONS OF HIGHLY NONLINEAR STEADY AND UNSTEADY FREE SURFACE FLOWS
YANG Chi; HUANG Fuxin; WANG Lijue; WAN De-cheng
2011-01-01
A numerical simulation model based on an open source Computational Fluid Dynamics (CFD) package-Open Field Operation and Manipulation (OpenFOAM) has been developed to study highly nonlinear steady and unsteady free surface flows.A two-fluid formulation is used in this model and the free surface is captured using the classical Volume Of Fluid (VOF) method.The incompressible Euler/Navier-Stokes equations are solved using a finite volume method on unstructured polyhedral cells.Both steady and unsteady free surface flows are simulated,which include:(1) a submerged NACA0012 2-D hydrofoil moving at a constant speed,(2) the Wigley hull moving at a constant speed,(3) numerical wave tank,(4) green water overtopping a fixed 2-D deck,(5) green water impact on a fixed 3-D body without or with a vertical wall on the deck.The numerical results obtained have been compared with the experimental measurements and other CFD results,and the agreements are satisfactory.The present numerical model can thus be used to simulate highly nonlinear steady and unsteady free surface flows.
Analysis and modelling of non-steady flow in pipe and channel networks
Jovic, Vinko
2013-01-01
Analysis and Modelling of Non-Steady Flow in Pipe and Channel Networks deals with flows in pipes and channel networks from the standpoints of hydraulics and modelling techniques and methods. These engineering problems occur in the course of the design and construction of hydroenergy plants, water-supply and other systems. In this book, the author presents his experience in solving these problems from the early 1970s to the present day. During this period new methods of solving hydraulic problems have evolved, due to the development of computers and numerical methods. This book
On the accuracy of Whitham's method. [for steady ideal gas flow past cones
Zahalak, G. I.; Myers, M. K.
1974-01-01
The steady flow of an ideal gas past a conical body is studied by the method of matched asymptotic expansions and by Whitham's method in order to assess the accuracy of the latter. It is found that while Whitham's method does not yield a correct asymptotic representation of the perturbation field to second order in regions where the flow ahead of the Mach cone of the apex is disturbed, it does correctly predict the changes of the second-order perturbation quantities across a shock (the first-order shock strength). The results of the analysis are illustrated by a special case of a flat, rectangular plate at incidence.
Yamamoto, Takahisa; MITACHI, Koshi; Suzuki, Takashi
2005-01-01
The Molten Salt Reactor (MSR) is a thermal neutron reactor with graphite moderation and operates on the thorium-uranium fuel cycle. The feature of the MSR is that fuel salt flows inside the reactor during the nuclear fission reaction. In the previous study, the authors developed numerical model with which to simulate the effects of fuel salt flow on the reactor characteristics. In this study, we apply the model to the steady-state analysis of a small MSR system and estimate the effects of fue...
Lift and drag in three-dimensional steady viscous and compressible flow
Liu, Luoqin; Kang, Linlin; Wu, Jiezhi
2016-01-01
In a recent paper, Liu, Zhu & Wu (2015, J. Fluid Mech. 784: 304; LZW for short) present a far-field theory for the aerodynamic force experienced by a body in a two-dimensional, viscous, compressible and steady flow. In this companion theoretical paper we do the same for three-dimensional flow. By a rigorous fundamental solution method of the linearized Navier-Stokes equations, we not only improve the far-field force formula for incompressible flow originally derived by Goldstein in 1931 and summarized by Milne-Thomson in 1968, both being far from complete, to its perfect final form, but also prove that this final form holds universally true in a wide range of compressible flow, from subsonic to supersonic flows. We call this result the unified force theorem (UF theorem for short) and state it as a theorem, which is exactly the counterpart of the two-dimensional compressible Joukowski-Filon theorem obtained by LZW. Thus, the steady lift and drag are always exactly determined by the values of vector circula...
Salek, M. Mehdi; Martinuzzi, Robert
2012-02-01
Several researchers have observed that the formation, morphology and susceptibility of bacterial biofilms are affected by the local hydrodynamic condition and, in particular, shear stresses acting on the fluid-biofilm interface. A backwards facing step (BFS) experimental model has been widely utilized as an in vitro model to examine and characterize the effect of flow separation and recirculation zones comparable to those present within various medical devices as well as those observed in vivo. The specific geometry of BFS covers a vide range of flow features observed in physiological or environmental conditions. The hypothesis of this study is that the flow behavior and structures can effectively contribute to the transport and attachment of cells and affecting the morphology of adhered colonies as well as suspended structures (i.e. biofilm streamers). Hence, the formation of the recirculation region occurring within a backward facing step (BFS) under steady and pulsatile conditions as well as three-dimensional flow structures arising close to the side walls are investigated to correlate to biofilms behavior. This hypothesis is investigated using a backward facing step incorporated into a flow cell under steady and pulsatile flow regimes to study the growth of methicillin resistant Staphylococcus aureus (MRSA) UC18 as the study microorganism.
Nasibullayev, I S; Krekhov, A P; Kramer, L
2005-01-01
We study the homogeneous and the spatially periodic instabilities in a nematic liquid crystal layer subjected to steady plane {\\em Couette} or {\\em Poiseuille} flow. The initial director orientation is perpendicular to the flow plane. Weak anchoring at the confining plates and the influence of the external {\\em electric} and/or {\\em magnetic} field are taken into account. Approximate expressions for the critical shear rate are presented and compared with semi-analytical solutions in case of Couette flow and numerical solutions of the full set of nematodynamic equations for Poiseuille flow. In particular the dependence of the type of instability and the threshold on the azimuthal and the polar anchoring strength and external fields is analysed.
Inspiratory and expiratory steady flow analysis in a model symmetrically bifurcating airway.
Zhao, Y; Brunskill, C T; Lieber, B B
1997-02-01
Steady inspiratory and expiratory flow in a symmetrically bifurcating airway model was studied numerically using the finite element method (FIDAP). Flows of Reynolds number of 500 and 1000 during inspiration and a flow of Reynolds number of 500 during expiration were analyzed. Since the geometry of the bifurcation model used in this study is exactly the same as the model used in the experimental studies, the computed results were compared to the experimental findings. Results show that most of the important flow features that were observed in the experiment, such as the skewed velocity profiles in the daughter branches during inspiration and velocity peak in the parent tube during expiration, were captured in the numerical simulation. Quantitatively, the computed velocity profiles are in good agreement with the measured profiles. This comparison validates the computational simulations.
Analytical solution of laminar-laminar stratified two-phase flows with curved interfaces
Brauner, N.; Rovinsky, J.; Maron, D.M. [Tel-Aviv Univ. (Israel)
1995-09-01
The present study represents a complete analytical solution for laminar two-phase flows with curved interfaces. The solution of the Navier-Stokes equations for the two-phases in bipolar coordinates provides the `flow monograms` describe the relation between the interface curvature and the insitu flow geometry when given the phases flow rates and viscosity ratios. Energy considerations are employed to construct the `interface monograms`, whereby the characteristic interfacial curvature is determined in terms of the phases insitu holdup, pipe diameter, surface tension, fluids/wall adhesion and gravitation. The two monograms are then combined to construct the system `operational monogram`. The `operational monogram` enables the determination of the interface configuration, the local flow characteristics, such as velocity profiles, wall and interfacial shear stresses distribution as well as the integral characteristics of the two-phase flow: phases insitu holdup and pressure drop.
Steady flows at the top of earth's core derived from geomagnetic field models
Voorhies, Coerte V.
1986-01-01
Select models of the main geomagnetic field and its secular variation are extrapolated to the base of an insulating mantle and used to estimate the adjacent fluid motion of a perfectly conducting outer core. The assumption of steady motion provides formally unique solutions and is tested along with that of no upwelling. The hypothesis of no upwelling is found to be substantially worse than that of steady motion. Although the actual motion is not thought to be steady, the large-scale secular variation at the top of the core can be adequately described by a large-scale, combined toroidal-poloidal circulation which is steady for intervals of at least a decade or two. The derived flows include a bulk westward drift but are complicated by superimposed jets, gyres, and surface divergence indicative of vigorous vertical motion at depth. The circulation pattern and key global properties including rms speed, upwelling, and westward drift are found to be fairly insensitive to variations in modeling parameters.
Modeling of the blood rheology in steady-state shear flows
Apostolidis, Alex J.; Beris, Antony N., E-mail: beris@udel.edu [Department of Chemical and Biomolecular Engineering, University of Delaware, Newark, Delaware 19716 (United States)
2014-05-15
We undertake here a systematic study of the rheology of blood in steady-state shear flows. As blood is a complex fluid, the first question that we try to answer is whether, even in steady-state shear flows, we can model it as a rheologically simple fluid, i.e., we can describe its behavior through a constitutive model that involves only local kinematic quantities. Having answered that question positively, we then probe as to which non-Newtonian model best fits available shear stress vs shear-rate literature data. We show that under physiological conditions blood is typically viscoplastic, i.e., it exhibits a yield stress that acts as a minimum threshold for flow. We further show that the Casson model emerges naturally as the best approximation, at least for low and moderate shear-rates. We then develop systematically a parametric dependence of the rheological parameters entering the Casson model on key physiological quantities, such as the red blood cell volume fraction (hematocrit). For the yield stress, we base our description on its critical, percolation-originated nature. Thus, we first determine onset conditions, i.e., the critical threshold value that the hematocrit has to have in order for yield stress to appear. It is shown that this is a function of the concentration of a key red blood cell binding protein, fibrinogen. Then, we establish a parametric dependence as a function of the fibrinogen and the square of the difference of the hematocrit from its critical onset value. Similarly, we provide an expression for the Casson viscosity, in terms of the hematocrit and the temperature. A successful validation of the proposed formula is performed against additional experimental literature data. The proposed expression is anticipated to be useful not only for steady-state blood flow modeling but also as providing the starting point for transient shear, or more general flow modeling.
Implicit unified gas-kinetic scheme for steady state solutions in all flow regimes
Zhu, Yajun; Zhong, Chengwen; Xu, Kun
2016-06-01
This paper presents an implicit unified gas-kinetic scheme (UGKS) for non-equilibrium steady state flow computation. The UGKS is a direct modeling method for flow simulation in all regimes with the updates of both macroscopic flow variables and microscopic gas distribution function. By solving the macroscopic equations implicitly, a predicted equilibrium state can be obtained first through iterations. With the newly predicted equilibrium state, the evolution equation of the gas distribution function and the corresponding collision term can be discretized in a fully implicit way for fast convergence through iterations as well. The lower-upper symmetric Gauss-Seidel (LU-SGS) factorization method is implemented to solve both macroscopic and microscopic equations, which improves the efficiency of the scheme. Since the UGKS is a direct modeling method and its physical solution depends on the mesh resolution and the local time step, a physical time step needs to be fixed before using an implicit iterative technique with a pseudo-time marching step. Therefore, the physical time step in the current implicit scheme is determined by the same way as that in the explicit UGKS for capturing the physical solution in all flow regimes, but the convergence to a steady state speeds up through the adoption of a numerical time step with large CFL number. Many numerical test cases in different flow regimes from low speed to hypersonic ones, such as the Couette flow, cavity flow, and the flow passing over a cylinder, are computed to validate the current implicit method. The overall efficiency of the implicit UGKS can be improved by one or two orders of magnitude in comparison with the explicit one.
Lam Ghai Lim
2016-07-01
Full Text Available A 360° twisted helical capacitance sensor was developed for holdup measurement in horizontal two-phase stratified flow. Instead of suppressing nonlinear response, the sensor was optimized in such a way that a ‘sine-like’ function was displayed on top of the linear function. This concept of design had been implemented and verified in both software and hardware. A good agreement was achieved between the finite element model of proposed design and the approximation model (pure sinusoidal function, with a maximum difference of ±1.2%. In addition, the design parameters of the sensor were analysed and investigated. It was found that the error in symmetry of the sinusoidal function could be minimized by adjusting the pitch of helix. The experiments of air-water and oil-water stratified flows were carried out and validated the sinusoidal relationship with a maximum difference of ±1.2% and ±1.3% for the range of water holdup from 0.15 to 0.85. The proposed design concept therefore may pose a promising alternative for the optimization of capacitance sensor design.
Effects of Steady Flow on Magnetoacoustic-Gravity Surface Waves: I. The Weak Field Case
Erdélyi, R.; Mather, J. F.
2017-02-01
Magnetoacoustic gravity (MAG) waves have been studied for some time. In this article, we investigate the effect that a shear flow at a tangential discontinuity embedded in a gravitationally stratified and magnetised plasma has on MAG surface waves. The dispersion relation found is algebraically analogous to the relation of the non-flow cases obtained by Miles and Roberts ( Solar Phys. 141, 205, 1992), except for the introduction of a Doppler-shifted frequency for the eigenvalue. This feature, however, introduces rather interesting physics, including the asymmetric presence of forward- and backward-propagating surface waves. We find that increasing the equilibrium flow speed leads to a shift in the permitted regions of propagation for surface waves. For most wave number combinations this leads to the fast mode being completely removed, as well as more limited phase speed regimes for slow-mode propagation. We also find that upon increasing the flow, the phase speeds of the backward propagating waves are increased. Eventually, at high enough flow speeds, the wave's direction of propagation is reversed and is in the positive direction. However, the phase speed of the forward-propagating wave remains mainly the same. For strong enough flows we find that the Kelvin-Helmholtz instability can also occur when the forward- and backward-propagating modes couple.
Loganathan Parasuraman
2015-01-01
Full Text Available An analysis has been carried out to investigate the influence of combined effects of MHD, suction and radiation on forced convection boundary layer flow of a nanofluid over an exponentially stretching sheet, embedded in a thermally stratified medium. The governing boundary layer equations of the problem are formulated and transformed into ordinary differential equations, using a similarity transformation. The resulting ordinary differential equations are solved numerically, by the shooting method. The effects of the governing parameters on the flow and heat transfer characteristics are studied and discussed in detail. Different types of nanoparticles, namely, Cu, Ag, Al2O3 and TiO2, with water as the base fluid, are studied. It is found that the effects of the radiation parameter, volume fraction and suction are same on the temperature profiles, in contrast to the effects of the thermal stratification. Comparisons with previously published works are performed in some special cases, and found to be in good agreement.
Volume of the steady-state space of financial flows in a monetary stock-flow-consistent model
Hazan, Aurélien
2016-01-01
We show that a steady-state stock-flow consistent macroeconomic model can be represented as a Constraint Satisfaction Problem (CSP). The set of solutions is a polytope, which volume depends on the constraints applied and reveals the potential fragility of the economic circuit, with no need to specify the dynamics. Several methods to compute the volume are compared, inspired by operations research methods and the analysis of metabolic networks, both exact and approximate. We also introduce a random transaction matrix, and study the particular case of linear flows with respect to money stocks.
A k-Model for Stably Stratified Nearly Horizontal Turbulent Flows
Kranenburg, C.
1985-01-01
A k-model is formulated that consists of the turbulent kinetic energy equation and an algebraic expression for the mixing length taking into account the influence of stratification. Applicability of the model is restricted to shallow, nearly horizontal flows. For local-equilibrium flows the model re
Constitutive Curve and Velocity Profile in Entangled Polymers during Start-Up of Steady Shear Flow
Hayes, Keesha A.
2010-05-11
Time-dependent shear stress versus shear rate, constitutive curve, and velocity profile measurements are reported in entangled polymer solutions during start-up of steady shear flow. By combining confocal microscopy and particle image velocimetry (PIV), we determine the time-dependent velocity profile in polybutadiene and polystyrene solutions seeded with fluorescent 150 nm silica and 7.5 μm melamine particles. By comparing these profiles with time-dependent constitutive curves obtained from experiment and theory, we explore the connection between transient nonmonotonic regions in the constitutive curve for an entangled polymer and its susceptibility to unstable flow by shear banding [Adams et al. Phys. Rev. Lett. 2009, 102, 067801-4]. Surprisingly, we find that even polymer systems which exhibit transient, nonmonotonic shear stress-shear rate relationships in bulk rheology experiments manifest time-dependent velocity profiles that are decidedly linear and show no evidence of unstable flow. We also report that interfacial slip plays an important role in the steady shear flow behavior of entangled polymers at shear rates above the reciprocal terminal relaxation time but has little, if any, effect on the shape of the velocity profile. © 2010 American Chemical Society.
Fedosov, Dmitry A; Karniadakis, George Em; Caswell, Bruce
2010-04-14
Polymer fluids are modeled with dissipative particle dynamics (DPD) as undiluted bead-spring chains and their solutions. The models are assessed by investigating their steady shear-rate properties. Non-Newtonian viscosity and normal stress coefficients, for shear rates from the lower to the upper Newtonian regimes, are calculated from both plane Couette and plane Poiseuille flows. The latter is realized as reverse Poiseuille flow (RPF) generated from two Poiseuille flows driven by uniform body forces in opposite directions along two-halves of a computational domain. Periodic boundary conditions ensure the RPF wall velocity to be zero without density fluctuations. In overlapping shear-rate regimes the RPF properties are confirmed to be in good agreement with those calculated from plane Couette flow with Lees-Edwards periodic boundary conditions (LECs), the standard virtual rheometer for steady shear-rate properties. The concentration and the temperature dependence of the properties of the model fluids are shown to satisfy the principles of concentration and temperature superposition commonly employed in the empirical correlation of real polymer-fluid properties. The thermodynamic validity of the equation of state is found to be a crucial factor for the achievement of time-temperature superposition. With these models, RPF is demonstrated to be an accurate and convenient virtual rheometer for the acquisition of steady shear-rate rheological properties. It complements, confirms, and extends the results obtained with the standard LEC configuration, and it can be used with the output from other particle-based methods, including molecular dynamics, Brownian dynamics, smooth particle hydrodynamics, and the lattice Boltzmann method.
Lehoucq, Richard B.; Salinger, Andrew G.
1999-08-01
We present an approach for determining the linear stability of steady states of PDEs on massively parallel computers. Linearizing the transient behavior around a steady state leads to a generalized eigenvalue problem. The eigenvalues with largest real part are calculated using Arnoldi's iteration driven by a novel implementation of the Cayley transformation to recast the problem as an ordinary eigenvalue problem. The Cayley transformation requires the solution of a linear system at each Arnoldi iteration, which must be done iteratively for the algorithm to scale with problem size. A representative model problem of 3D incompressible flow and heat transfer in a rotating disk reactor is used to analyze the effect of algorithmic parameters on the performance of the eigenvalue algorithm. Successful calculations of leading eigenvalues for matrix systems of order up to 4 million were performed, identifying the critical Grashof number for a Hopf bifurcation.
Run Li; Jingsheng Zhang; Yumei Yong; Yang Wang; Chao Yang
2015-01-01
This work presents a numerical investigation on steady internal, external and surface flows of a liquid sphere im-mersed in a simple shear flow at low and intermediate Reynolds numbers. The control volume formulation is adopted to solve the governing equations of two-phase flow in a 3-D spherical coordinate system. Numerical re-sults show that the streamlines for Re=0 are closed Jeffery orbits on the surface of the liquid sphere, and also closed curves outside and inside the liquid sphere. However, the streamlines have intricate and non-closed struc-tures for Re≠0. The flow structure is dependent on the values of Reynolds number and interior-to-exterior vis-cosity ratio.
Lakshminarayana, B.; Ho, Y.; Basson, A.
1993-01-01
The objective of this research is to simulate steady and unsteady viscous flows, including rotor/stator interaction and tip clearance effects in turbomachinery. The numerical formulation for steady flow developed here includes an efficient grid generation scheme, particularly suited to computational grids for the analysis of turbulent turbomachinery flows and tip clearance flows, and a semi-implicit, pressure-based computational fluid dynamics scheme that directly includes artificial dissipation, and is applicable to both viscous and inviscid flows. The values of these artificial dissipation is optimized to achieve accuracy and convergency in the solution. The numerical model is used to investigate the structure of tip clearance flows in a turbine nozzle. The structure of leakage flow is captured accurately, including blade-to-blade variation of all three velocity components, pitch and yaw angles, losses and blade static pressures in the tip clearance region. The simulation also includes evaluation of such quantities of leakage mass flow, vortex strength, losses, dominant leakage flow regions and the spanwise extent affected by the leakage flow. It is demonstrated, through optimization of grid size and artificial dissipation, that the tip clearance flow field can be captured accurately. The above numerical formulation was modified to incorporate time accurate solutions. An inner loop iteration scheme is used at each time step to account for the non-linear effects. The computation of unsteady flow through a flat plate cascade subjected to a transverse gust reveals that the choice of grid spacing and the amount of artificial dissipation is critical for accurate prediction of unsteady phenomena. The rotor-stator interaction problem is simulated by starting the computation upstream of the stator, and the upstream rotor wake is specified from the experimental data. The results show that the stator potential effects have appreciable influence on the upstream rotor wake
Time-dependent rotating stratified shear flow: exact solution and stability analysis.
Salhi, A; Cambon, C
2007-01-01
A solution of the Euler equations with Boussinesq approximation is derived by considering unbounded flows subjected to spatially uniform density stratification and shear rate that are time dependent [S(t)= partial differentialU3/partial differentialx2]. In addition to vertical stratification with constant strength N(v)2, this base flow includes an additional, horizontal, density gradient characterized by N(h)2(t). The stability of this flow is then analyzed: When the vertical stratification is stabilizing, there is a simple harmonic motion of the horizontal stratification N(h)2(t) and of the shear rate S(t), but this flow is unstable to certain disturbances, which are amplified by a Floquet mechanism. This analysis may involve an additional Coriolis effect with Coriolis parameter f, so that governing dimensionless parameters are a modified Richardson number, R=[S(0)2+N(h)4(0)/N(v)2]1/2, and f(v)=f/N(v), as well as the initial phase of the periodic shear rate. Parametric resonance between the inertia-gravity waves and the oscillating shear is demonstrated from the dispersion relation in the limit R-->0. The parametric instability has connection with both baroclinic and elliptical flow instabilities, but can develop from a very different base flow.
A Computer Method of Steady Non-Uniform Gradually Varied Flow in Open Channel & in River
无
1999-01-01
Most of water flow in open channel or in river belongs to steady non-uniform flow. The surface profiles are caused by changes of channel section. It is very important to analyze its computation. According to the regularity of its surface change, the suitable sectional dimensions of open channel or flood control work can be designed. Commonly, computation of non-uniform flow adopts the traditional methods by hand or by graphic method. The speed and precision of computation are restricted. In this paper, a software to calculate water surface profile is introduced. The software is put forward by using C++ .By means of interpolate method and dialogue between user and computer, we can calculate the water surface profile much more quickly and exactly.
Steady shocks around black holes produced by sub-keplerian flows with negative energy
Molteni, D; Teresi, V
2006-01-01
We discuss a special case of formation of axisymmetric shocks in the accretion flow of ideal gas onto a Schwarzschild black hole: when the total energy of the flow is negative. The result of our analysis enlarges the parameter space for which these steady shocks are exhibited in the accretion of gas rotating around relativistic stellar objects. Since keplerian disks have negative total energy, we guess that, in this energy range, the production of the shock phenomenon might be easier than in the case of positive energy. So our outcome reinforces the view that sub-keplerian flows of matter may significantly affect the physics of the high energy radiation emission from black hole candidates. We give a simple procedure to obtain analytically the position of the shocks. The comparison of the analytical results with the data of 1D and 2D axisymmetric numerical simulations confirms that the shocks form and are stable.
Steady flow of a non-Newtonian fluid through a contraction
Gatski, T. B.; Lumley, J. L.
1978-01-01
A steady-state analysis is conducted to examine the basic flow structure of a non-Newtonian fluid in a domain including an inflow region, a contraction region, and an outflow region. A Cartesian grid system is used throughout the entire flow domain, including the contraction region, thus creating an irregular grid cell structure adjacent to the curved boundary. At node points adjacent to the curved boundary symmetry conditions are derived for the different flow variables in order to solve the governing difference equations. Attention is given to the motion and non-Newtonian constitutive equations, the boundary conditions, the numerical modeling of the non-Newtonian equations, the stream function contour lines for the non-Newtonian fluid, the vorticity contour lines for the non-Newtonian fluid, the velocity profile across the contraction, and the shear stress contour lines for the non-Newtonian fluid.
A finite element formulation of Euler equations for the solution of steady transonic flows
Ecer, A.; Akay, H. U.
1982-01-01
The main objective of the considered investigation is related to the development of a relaxation scheme for the analysis of inviscid, rotational, transonic flow problems. To formulate the equations of motion for inviscid flows in a fixed coordinate system, an Eulerian type variational principle is required. The derivation of an Eulerian variational principle which is employed in the finite element formulation is discussed. The presented numerical method describes the mathematical formulation and the application of a numerical process for the direct solution of steady Euler equations. The development of the procedure as an extension of existing potential flow formulations provides the applicability of previous procedures, e.g., proper application of the artificial viscosity for supersonic elements, and the accurate modeling of the shock.
Chigozie Israel-Cookey
2010-09-01
Full Text Available This paper investigates effects of thermal radiation and magnetic field on hydromagnetic Couette flow of a highly viscous fluid with temperature-dependent viscosity and thermal conductivity at constant pressure through a porous channel. The influence of the channel permeability is also assessed. The relevant governing partial differential equations have been transformed to non-linear coupled ordinary differential equations by virtue of the steady nature of the flow and are solved numerically using a marching finite difference scheme to give approximate solutions for the velocity and temperature profiles. We highlight the effects of Nahme numbers, magnetic field, radiation and permeability parameters on both profiles. The results obtained are used to give graphical illustrations of the distribution of the flow variables and are discussed.
Why do inverted-flags flap in a uniform steady flow?
Sader, John; Cossé, Julia; Kim, Daegyoum; Fan, Boyu; Gharib, Morteza
2016-11-01
The dynamics of a cantilevered elastic sheet, with a uniform steady flow impinging on its clamped-end, have been studied widely and provide insight into the stability of flags and biological phenomena. Recent measurements by Kim et al. show that reversing the sheet's orientation, with the flow impinging on its free-edge, dramatically alters its dynamics. In this talk, we use a combination of mathematical theory, scaling analysis and measurement to explore the physical mechanisms driving the observed large-amplitude flapping motion of an inverted-flag. Flapping is found to be periodic predominantly, with a transition to chaos as flow speed increases. These findings have implications to leaf motion and other biological processes, such as the dynamics of individual hairs, because they also can present an inverted-flag configuration. Gordon and Betty Moore Foundation; Ministry of Trade, Industry and Energy, Republic of Korea; Australian Research Council Grants scheme.
Investigations of non-hydrostatic, stably stratified and rapidly rotating flows
Nieves, David; Juilen, Keith; Weiss, Jeffrey B
2016-01-01
We present an investigation of rapidly rotating (small Rossby number $Ro\\ll 1$) and stratified turbulence where the stratification strength is varied from weak (large Froude number $Fr\\gg1$) to strong ($Fr\\ll1$). The investigation is set in the context of a reduced model derived from the Boussinesq equations that efficiently retains anisotropic inertia-gravity waves with order-one frequencies and highlights a regime of wave-eddy interactions. Numerical simulations of the reduced model are performed where energy is injected by a stochastic forcing of vertical velocity, which forces wave modes only. The simulations reveal two regimes characterized by the presence of well-formed, persistent and thin turbulent layers of locally-weakened stratification at small Froude numbers, and by the absence of layers at large Froude numbers. Both regimes are characterized by a large-scale barotropic dipole enclosed by small-scale turbulence. When the Reynolds number is not too large a direct cascade of barotropic kinetic ener...
The calculation of mechanical energy loss for incompressible steady pipe flow of homogeneous fluid
刘士和; 薛娇; 范敏
2013-01-01
The calculation of the mechanical energy loss is one of the fundamental problems in the field of Hydraulics and Enginee- ring Fluid Mechanics. However, for a non-uniform flow the relation between the mechanical energy loss in a volume of fluid and the kinematical and dynamical characteristics of the flow field is not clearly established. In this paper a new mechanical energy equation for the incompressible steady non-uniform pipe flow of homogeneous fluid is derived, which includes the variation of the mean tur- bulent kinetic energy, and the formula for the calculation of the mechanical energy transformation loss for the non-uniform flow bet- ween two cross sections is obtained based on this equation. This formula can be simplified to the Darcy-Weisbach formula for the uniform flow as widely used in Hydraulics. Furthermore, the contributions of the mechanical energy loss relative to the time avera- ged velocity gradient and the dissipation of the turbulent kinetic energy in the turbulent uniform pipe flow are discussed, and the con- tributions of the mechanical energy loss in the viscous sublayer, the buffer layer and the region above the buffer layer for the turbu- lent uniform flow are also analyzed.
Car-following theory of steady-state traffic flow using time-to-collision
Sheng JIN; Zhi-yi HUANG; Peng-fei TAO; Dian-hai WANG
2011-01-01
The conventional car-following theory is based on the assumption that vehicles will travel along the center line of lanes.However,according to the field survey data,in complex traffic conditions,a lateral separation between the leader and the follower frequently occurs.Accordingly,by taking lateral separation into account,we redefined the equation of time-to-collision (TTC) using visual angle information.Based on the stimulus-response framework,TTC was introduced into the basic General Motors (GM) model as a stimulus,and a non-lane-based car-following model of steady-state traffic flow was developed.The property of flow-density relationship was further investigated after integrating the proposed car-following model with different parameters.The results imply that the property of steady-state traffic flow and the capacity of each lane are highly relevant to the microscopic staggered car-following behavior,and the proposed model significantly enhances the practicality of the human driving behavior model.
Modelling of stratified flows in the problem of the morphological behaviour of a sandpit
Parshakova, Ya N.; Lyubimova, T. P.; Ivantsov, A. O.
2016-02-01
The problem of the removal of brines from underwater sand pits is studied. The intensity of the removal of brines from the pits due to the changes in the hydrological regime of the river is calculated in three-dimensional approach. It is found that for the flow rates typical for the summer, the removal of brines collected in underwater pits does not occur. At flow rates typical for the spring, there is a fairly intensive removal of accumulated brines. Numerical experiments have shown that the underwater pits can serve as brines batteries, becoming an additional source of river pollution under certain hydrological conditions.
Papalexandris, Miltiadis V.; Antoniadis, Panagiotis D.
2015-11-01
In this talk we are concerned with thermally stratified flows at the interface between superposed porous and pure-fluid layers. In our study we employ a thermo-mechanical model for the flows of interest that was recently developed by our team. According to this model, both the fluid and the solid matrix are treated as two separate and identifiable continua that are in thermal non-equilibrium with each other. This allows for the derivation of a single set of equations that are simultaneously valid both in the porous and pure-fluid regions. First, we briefly present the basic steps of the derivation of the mathematical model and describe an algorithm for its numerical treatment. Then, we present and discuss numerical results for transient shear flows in the domains of interest, under both stable and unstable thermal stratification. Emphasis is placed on the effects of buoyancy to the evolution of the flow structures at the interface and on the mechanisms that induce thermal non-equilibrium inside the porous medium. This work is supported by the National Fund for Scientific Research (FNRS), Belgium.
Computing 3-D steady supersonic flow via a new Lagrangian approach
Loh, C. Y.; Liou, M.-S.
1993-01-01
The new Lagrangian method introduced by Loh and Hui (1990) is extended for 3-D steady supersonic flow computation. Details of the conservation form, the implementation of the local Riemann solver, and the Godunov and the high resolution TVD schemes are presented. The new approach is robust yet accurate, capable of handling complicated geometry and reactions between discontinuous waves. It keeps all the advantages claimed in the 2-D method of Loh and Hui, e.g., crisp resolution for a slip surface (contact discontinuity) and automatic grid generation along the stream.
Steady-state thermal Herschel-Bulkley flow with Tresca's friction law
Farid Messelmi
2010-04-01
Full Text Available We consider a mathematical model which describes the steady-state flow of a Herschel-Bulkley fluid whose the consistency and the yield limit depend on the temperature and with mixed boundary conditions, including a frictional boundary condition. We derive a weak formulation of the coupled system of motion and energy equations which consists of a variational inequality for the velocity field. We prove the existence of weak solutions. In the asymptotic limit case of a high thermal conductivity, the temperature becomes a constant solving an implicit total energy equation involving the consistency function and the yield limit.
Creep measurements confirm steady flow after stress maximum in extension of branched polymer melts
Javier Alvarez, Nicolas; Román Marín, José Manuel; Huang, Qian;
2013-01-01
We provide conclusive evidence of nonmonotonic mechanical behavior in the extension of long-chain branched polymer melts. While nonmonotonic behavior is known to occur for solids, for the case of polymeric melts, this phenomenon is in direct contrast with current theoretical models. We rule out...... the possibility of the overshoot being an experimental artifact by confirming the existence of steady flow after a maximum in the ratio of stress to strain rate versus strain under both constant stress and constant strain-rate kinematics. This observation indicates the omission of important physics from current...
Steady thermocapillary flows in a two-layer liquid system with flat interfaces
del Arco, E. Crespo; Extremet, G. P.; Sani, R. L.
1993-01-01
Steady thermocapillary convection is studied in a system of two flat, superposed layers of immiscible liquids with two fluid-fluid interfaces in a configuration similar to that of an encapsulated crystal growth. The layers are bounded on the sides by isothermal vertical walls maintained at different constant temperatures. A simplified analytical solution is used initially to explore different potential flow regimes in a parameter space of large dimensionality. Then the coupled Navier-Stokes and heat transfer equations are solved numerically with a finite element method via FIDAP, in a rectangular cavity filled with two immiscible liquids in the absence of a gravitational field.
Stability of Multidimensional Phase Transitions in a Steady van der Waals Flow
Shuyi ZHANG
2008-01-01
In this paper,the author studies the multidimensional stability of subsonic phase transitions in a steady supersonic flow of van der Waals type.The viscosity capillarity criterion (in "Arch.Rat.Mech.Anal.,81(4),1983,301-315") is used to seek physical admissible planar waves.By showing the Lopatinski determinant being non-zero,it is proved that subsonic phase transitions are uniformly stable in the sense of Majda (in "Mem.Amer.Math.Soc.,41(275),1983,1-95") under both one dimensional and multidimensional perturbations.
Ilin, K
2010-01-01
We study the steady streaming between two infinitely long circular cylinders produced by small amplitude transverse vibrations of the inner cylinder about the axis of the outer cylinder. The Vishik-Lyusternik method is employed to construct an asymptotic expansion of the solution of the Navier-Stokes equations in the limit of high-frequency vibrations for Reynolds numbers of order of unity. The effect of the Stokes drift of fluid particles is also studied. It is shown that it is nonzero not only within the boundary layers but also in higher order terms of the expansion of the averaged outer flow.
Mitarai, Namiko; Nakanishi, Hiizu
2002-01-01
Dynamical behavior of steady granular flow is investigated numerically in the inelastic hard sphere limit of the soft sphere model. We find distinctively different limiting behaviors for the two flow regimes, i.e., the collisional flow and the frictional flow. In the collisional flow, the hard sphere limit is straightforward; the number of collisions per particle per unit time converges to a finite value and the total contact time fraction with other particles goes to zero. For the frictional...
The period ratio P_1/P_2 of torsional Alfv\\'en waves with steady flows in spicules
Ebadi, H; Farahani, S Vasheghani
2016-01-01
The aim here is to model the standing torsional oscillations in solar spicules in the presence of density stratification, magnetic field expansion, and steady flows. By implementing cylindrical geometry, the eigenfrequencies, eigenfunctions, and the period ratio P_1/P_2 of these waves is obtained for finite plasma-beta. The shifts created by the steady flow justifies the divergence of the observed period ratio for the first and second periods from the number 2.
Cunningham, A. M., Jr.
1976-01-01
The feasibility of calculating steady mean flow solutions for nonlinear transonic flow over finite wings with a linear theory aerodynamic computer program is studied. The methodology is based on independent solutions for upper and lower surface pressures that are coupled through the external flow fields. Two approaches for coupling the solutions are investigated which include the diaphragm and the edge singularity method. The final method is a combination of both where a line source along the wing leading edge is used to account for blunt nose airfoil effects; and the upper and lower surface flow fields are coupled through a diaphragm in the plane of the wing. An iterative solution is used to arrive at the nonuniform flow solution for both nonlifting and lifting cases. Final results for a swept tapered wing in subcritical flow show that the method converges in three iterations and gives excellent agreement with experiment at alpha = 0 deg and 2 deg. Recommendations are made for development of a procedure for routine application.
Finite volume simulation of 2-D steady square lid driven cavity flow at high reynolds numbers
K. Yapici
2013-12-01
Full Text Available In this work, computer simulation results of steady incompressible flow in a 2-D square lid-driven cavity up to Reynolds number (Re 65000 are presented and compared with those of earlier studies. The governing flow equations are solved by using the finite volume approach. Quadratic upstream interpolation for convective kinematics (QUICK is used for the approximation of the convective terms in the flow equations. In the implementation of QUICK, the deferred correction technique is adopted. A non-uniform staggered grid arrangement of 768x768 is employed to discretize the flow geometry. Algebraic forms of the coupled flow equations are then solved through the iterative SIMPLE (Semi-Implicit Method for Pressure-Linked Equation algorithm. The outlined computational methodology allows one to meet the main objective of this work, which is to address the computational convergence and wiggled flow problems encountered at high Reynolds and Peclet (Pe numbers. Furthermore, after Re > 25000 additional vortexes appear at the bottom left and right corners that have not been observed in earlier studies.
Fabric inlet stratifiers for solar tanks with different volume flow rates
Andersen, Elsa; Furbo, Simon
2006-01-01
in the centre of a glass tank (400 x 400 x 900 mm). The forced volume flow rate is in the range of 6 – 10 l/min, and water enters the stratification pipe from the bottom of the tank. The thermal behaviour of the stratification pipes is investigated for different realistic operation conditions...
Stability of viscosity stratified flows down an incline: Role of miscibility and wall slip
Ghosh, Sukhendu
2016-01-01
The effects of wall velocity slip on the linear stability of a gravity-driven miscible two-fluid flow down an incline are examined. The fluids have the matched density but different viscosity. A smooth viscosity stratification is achieved due to the presence of a thin mixed layer between the fluids. The results show that the presence of slip exhibits a promise for stabilizing the miscible flow system by raising the critical Reynolds number at the onset and decreasing the bandwidth of unstable wave numbers beyond the threshold of the dominant instability. This is different from its role in the case of a single fluid down a slippery substrate where slip destabilizes the flow system at the onset. Though the stability properties are analogous to the same flow system down a rigid substrate, slip is shown to delay the surface mode instability for any viscosity contrast. It has a damping/promoting effect on the overlap modes (which exist due to the overlap of critical layer of dominant disturbance with the mixed lay...
Finch, Colton G.; Pine, William E.; Yackulic, Charles B.; Dodrill, Michael J.; Yard, Michael D.; Gerig, Brandon S.; Coggins,, Lewis G.; Korman, Josh
2016-01-01
The Colorado River below Glen Canyon Dam, Arizona, is part of an adaptive management programme which optimizes dam operations to improve various resources in the downstream ecosystem within Grand Canyon. Understanding how populations of federally endangered humpback chub Gila cypha respond to these dam operations is a high priority. Here, we test hypotheses concerning temporal variation in juvenile humpback chub apparent survival rates and abundance by comparing estimates between hydropeaking and steady discharge regimes over a 3-year period (July 2009–July 2012). The most supported model ignored flow type (steady vs hydropeaking) and estimated a declining trend in daily apparent survival rate across years (99.90%, 99.79% and 99.67% for 2009, 2010 and 2011, respectively). Corresponding abundance of juvenile humpback chub increased temporally; open population model estimates ranged from 615 to 2802 individuals/km, and closed model estimates ranged from 94 to 1515 individuals/km. These changes in apparent survival and abundance may reflect broader trends, or simply represent inter-annual variation. Important findings include (i) juvenile humpback chub are currently surviving and recruiting in the mainstem Colorado River with increasing abundance; (ii) apparent survival does not benefit from steady fall discharges from Glen Canyon Dam; and (iii) direct assessment of demographic parameters for juvenile endangered fish are possible and can rapidly inform management actions in regulated rivers.
Stability of viscosity stratified flows down an incline: Role of miscibility and wall slip
Ghosh, Sukhendu; Usha, R.
2016-10-01
The effects of wall velocity slip on the linear stability of a gravity-driven miscible two-fluid flow down an incline are examined. The fluids have the matched density but different viscosity. A smooth viscosity stratification is achieved due to the presence of a thin mixed layer between the fluids. The results show that the presence of slip exhibits a promise for stabilizing the miscible flow system by raising the critical Reynolds number at the onset and decreasing the bandwidth of unstable wave numbers beyond the threshold of the dominant instability. This is different from its role in the case of a single fluid down a slippery substrate where slip destabilizes the flow system at the onset. Though the stability properties are analogous to the same flow system down a rigid substrate, slip is shown to delay the surface mode instability for any viscosity contrast. It has a damping/promoting effect on the overlap modes (which exist due to the overlap of critical layer of dominant disturbance with the mixed layer) when the mixed layer is away/close from/to the slippery inclined wall. The trend of slip effect is influenced by the location of the mixed layer, the location of more viscous fluid, and the mass diffusivity of the two fluids. The stabilizing characteristics of slip can be favourably used to suppress the non-linear breakdown which may happen due to the coexistence of the unstable modes in a flow over a substrate with no slip. The results of the present study suggest that it is desirable to design a slippery surface with appropriate slip sensitivity in order to meet a particular need for a specific application.
Schvidler, M.; Karasaki, K.
2011-06-15
In previous papers (Shvidler and Karasaki, 1999, 2001, 2005, and 2008) we presented and analyzed an approach for finding the general forms of exactly averaged equations of flow and transport in porous media. We studied systems of basic equations for steady flow with sources in unbounded domains with stochastically homogeneous conductivity fields. A brief analysis of exactly averaged equations of nonsteady flow and nonreactive solute transport was also presented. At the core of this approach is the existence of appropriate random Green's functions. For example, we showed that in the case of a 3-dimensional unbounded domain the existence of appropriate random Green's functions is sufficient for finding the exact nonlocal averaged equations for flow velocity using the operator with a unique kernel-vector. Examination of random fields with global symmetry (isotropy, transversal isotropy and orthotropy) makes it possible to describe significantly different types of averaged equations with nonlocal unique operators. It is evident that the existence of random Green's functions for physical linear processes is equivalent to assuming the existence of some linear random operators for appropriate stochastic equations. If we restricted ourselves to this assumption only, as we have done in this paper, we can study the processes in any dimensional bounded or unbounded fields and in addition, cases in which the random fields of conductivity and porosity are stochastically nonhomogeneous, nonglobally symmetrical, etc.. It is clear that examining more general cases involves significant difficulty and constricts the analysis of structural types for the processes being studied. Nevertheless, we show that we obtain the essential information regarding averaged equations for steady and transient flow, as well as for solute transport.
Zilitinkevich, S S; Kleeorin, N; Rogachevskii, I; Esau, I
2011-01-01
In this paper we advance physical background of the EFB turbulence closure and present its comprehensive description. It is based on four budget equations for the second moments: turbulent kinetic and potential energies (TKE and TPE) and vertical turbulent fluxes of momentum and buoyancy; a new relaxation equation for the turbulent dissipation time-scale; and advanced concept of the inter-component exchange of TKE. The EFB closure is designed for stratified, rotating geophysical flows from neutral to very stable. In accordance to modern experimental evidence, it grants maintaining turbulence by the velocity shear at any gradient Richardson number Ri, and distinguishes between the two principally different regimes: "strong turbulence" at Ri 1 typical of the free atmosphere or deep ocean, where Pr_T asymptotically linearly increases with increasing Ri that implies strong suppressing of the heat transfer compared to momentum transfer. For use in different applications, the EFB turbulence closure is formulated a...
Ababou, R.
1991-08-01
This report develops a broad review and assessment of quantitative modeling approaches and data requirements for large-scale subsurface flow in radioactive waste geologic repository. The data review includes discussions of controlled field experiments, existing contamination sites, and site-specific hydrogeologic conditions at Yucca Mountain. Local-scale constitutive models for the unsaturated hydrodynamic properties of geologic media are analyzed, with particular emphasis on the effect of structural characteristics of the medium. The report further reviews and analyzes large-scale hydrogeologic spatial variability from aquifer data, unsaturated soil data, and fracture network data gathered from the literature. Finally, various modeling strategies toward large-scale flow simulations are assessed, including direct high-resolution simulation, and coarse-scale simulation based on auxiliary hydrodynamic models such as single equivalent continuum and dual-porosity continuum. The roles of anisotropy, fracturing, and broad-band spatial variability are emphasized. 252 refs.
Restricted Equilibrium and the Energy Cascade in Rotating and Stratified Flows
Herbert, Corentin; Marino, Raffaele
2014-01-01
Most of the turbulent flows appearing in nature (e.g. geophysical and astrophysical flows) are subjected to strong rotation and stratification. These effects break the symmetries of classical, homogenous isotropic turbulence. In doing so, they introduce a natural decomposition of phase space in terms of wave modes and potential vorticity modes. The appearance of a new time scale associated to the propagation of waves, in addition to the eddy turnover time, increases the complexity of the energy transfers between the various scales; nonlinearly interacting waves may dominate at some scales while balanced motion may prevail at others. In the end, it is difficult to predict \\emph{a priori} if the energy cascades downscale as in homogeneous isotropic turbulence, upscale as expected from balanced dynamics, or follows yet another phenomenology. In this paper, we suggest a theoretical approach based on equilibrium statistical mechanics for the ideal system, inspired from the restricted partition function formalism i...
Sid, Samir; Terrapon, Vincent; Dubief, Yves
2015-11-01
Results of direct numerical simulation of turbulent channel flows under unstable stratification are reported. Two Reynolds number are considered: Reτ = 180 , 395 and the Rayleigh number ranges between Ra = [106 -109 ] . The Prandtl number is set to 1. The channel is periodic in both streamwise and spanwise directions and non-slip/isothermal boundary conditions are imposed at the walls. The temperature difference between the walls is set so that the stratification is unstable and the coupling between temperature and momentum is achieved using the Boussinesq approximation. The dependency of the typical large scale convective structures on both Reynolds and Rayleigh numbers are investigated through cross flow sectional statistics and instantaneous flow field visualizations. Moreover, the effects of the natural convection on the coherent structures associated to the cycle of wall-bounded turbulence (Jimenez, et al. JFM 1999), namely velocity streaks and streamwise vortices, are examined. Finally, macroscopic quantities such as friction coefficient and Nusselt number are reported as a function of the Rayleigh number and are compared for both Reynolds numbers. The Belgian Team acknowledges computational resources from CÉCI (F.R.S.-FNRS grant No.2.5020.11) and the PRACE infrastructure. YD acknowledges the support of NSF and DOE under grant NSF/DOE 1258697.
A new Lagrangian method for three-dimensional steady supersonic flows
Loh, Ching-Yuen; Liou, Meng-Sing
1993-01-01
In this report, the new Lagrangian method introduced by Loh and Hui is extended for three-dimensional, steady supersonic flow computation. The derivation of the conservation form and the solution of the local Riemann solver using the Godunov and the high-resolution TVD (total variation diminished) scheme is presented. This new approach is accurate and robust, capable of handling complicated geometry and interactions between discontinuous waves. Test problems show that the extended Lagrangian method retains all the advantages of the two-dimensional method (e.g., crisp resolution of a slip-surface (contact discontinuity) and automatic grid generation). In this report, we also suggest a novel three dimensional Riemann problem in which interesting and intricate flow features are present.
Three-dimensional collapse and steady flow in thick-walled flexible tubes
Marzo, A.; Luo, X. Y.; Bertram, C. D.
2005-08-01
Three-dimensional collapse of and steady flow through finite-length elastic tubes are studied numerically. The Navier-Stokes equations coupled with large, nonlinear deformation of the elastic wall are solved by using the finite-element software, FIDAP. Three-dimensional solid elements are used for the elastic wall, allowing us to specify any wall thickness required. Plane-strain results for the cross-sectional shape of thinner-walled tubes are validated by comparison with published numerical data. Three-dimensional results for flow through finite-thickness tubes are in excellent agreement with published numerical results based on thin-shell elements, and are used to show the effects of varying wall thickness. Finally, the computational predictions are compared with experimental pressure area relationships for thick-walled tubes. The simulations confirm a previously neglected experimental finding, that the Young wavespeed can be lower between buckling and osculation for thick tubes than for thinner ones.
Koroglu, Batikan; Mehl, Marco; Armstrong, Michael R.; Crowhurst, Jonathan C.; Weisz, David G.; Zaug, Joseph M.; Dai, Zurong; Radousky, Harry B.; Chernov, Alex; Ramon, Erick; Stavrou, Elissaios; Knight, Kim; Fabris, Andrea L.; Cappelli, Mark A.; Rose, Timothy P.
2017-09-01
We present the development of a steady state plasma flow reactor to investigate gas phase physical and chemical processes that occur at high temperature (1000 reactor consists of a glass tube that is attached to an inductively coupled argon plasma generator via an adaptor (ring flow injector). We have modeled the system using computational fluid dynamics simulations that are bounded by measured temperatures. In situ line-of-sight optical emission and absorption spectroscopy have been used to determine the structures and concentrations of molecules formed during rapid cooling of reactants after they pass through the plasma. Emission spectroscopy also enables us to determine the temperatures at which these dynamic processes occur. A sample collection probe inserted from the open end of the reactor is used to collect condensed materials and analyze them ex situ using electron microscopy. The preliminary results of two separate investigations involving the condensation of metal oxides and chemical kinetics of high-temperature gas reactions are discussed.
Algebraic approach to non-integrability of Bajer-Moffattʼs steady Stokes flow
Nishiyama, Takahiro
2014-12-01
Non-integrability of the streamline system of equations for a steady Stokes flow, which Bajer and Moffatt introduced by the name of stretch-twist-fold flow, is discussed by an algebraic method without assuming its closeness to an integrable system. In the author's previous paper, the non-existence of a real meromorphic first integral of the streamline system was proved on the basis of Ziglin's theory and the differential Galois theory, where a parameter was assumed not to belong to a set of exceptional values. In this paper, this assumption is proved to be removable by making further use of some results from the differential Galois theory. The road to this result is explained in the form of a recipe in order to make clear how the differential Galois theory is applied.
Boujo, Edouard
2014-01-01
A variational technique is used to derive analytical expressions for the sensitivity of several geometric indicators of flow separation to steady actuation. Considering the boundary layer flow above a wall-mounted bump, the six following representative quantities are considered: the locations of the separation point and reattachment point connected by the separatrix, the separation angles at these stagnation points, the backflow area and the recirculation area. For each geometric quantity, linear sensitivity analysis allows us to identify regions which are the most sensitive to volume forcing and wall blowing/suction. Validations against full non-linear Navier-Stokes calculations show excellent agreement for small-amplitude control for all considered indicators. With very resemblant sensitivity maps, the reattachment point, the backflow and recirculation areas are seen to be easily manipulated. In contrast, the upstream separation point and the separatrix angles are seen to remain extremely robust with respec...
The effect of viscosity on steady transonic flow with a nodal solution topology
Owocki, Stanley P.; Zank, Gary P.
1991-01-01
The effect of viscosity on a steady, transonic flow for which the inviscid limit has a nodal solution topology near the critical point is investigated. For the accelerating case, viscous solutions tend to repel each other, so that a very delicate choice of initial conditions is required to prevent them from diverging. Only the two critical solutions extend to arbitrarily large distances into both the subsonic and supersonic flows. For the decelerating case, the solutions tend to attract, and so an entire two-parameter family of solutions now extends over large distances. The general effect of viscosity on the solution degeneracy of a nodal topology is thus to reduce or limit it for the accelerating case and to enhance it for the decelerating case. The astrophysical implications of these findings are addressed.
Steady streaming: A key mixing mechanism in low-Reynolds-number acinar flows
Kumar, Haribalan; Tawhai, Merryn H.; Hoffman, Eric A.; Lin, Ching-Long
2011-01-01
Study of mixing is important in understanding transport of submicron sized particles in the acinar region of the lung. In this article, we investigate transport in view of advective mixing utilizing Lagrangian particle tracking techniques: tracer advection, stretch rate and dispersion analysis. The phenomenon of steady streaming in an oscillatory flow is found to hold the key to the origin of kinematic mixing in the alveolus, the alveolar mouth and the alveolated duct. This mechanism provides the common route to folding of material lines and surfaces in any region of the acinar flow, and has no bearing on whether the geometry is expanding or if flow separates within the cavity or not. All analyses consistently indicate a significant decrease in mixing with decreasing Reynolds number (Re). For a given Re, dispersion is found to increase with degree of alveolation, indicating that geometry effects are important. These effects of Re and geometry can also be explained by the streaming mechanism. Based on flow conditions and resultant convective mixing measures, we conclude that significant convective mixing in the duct and within an alveolus could originate only in the first few generations of the acinar tree as a result of nonzero inertia, flow asymmetry, and large Keulegan–Carpenter (KC) number. PMID:21580803
A numerical study of steady flow through a curved tube with wavy walls
Prince, Chekema; Gu, Mingyao; Peterson, Sean
2011-11-01
Flow through curved tubes has been studied for nearly a century owing to the practical industrial applications and general academic interest. More recently, interest in curved tubes has resurfaced due to the ubiquity of curvature in the vasculature and the resulting need to accurately model arterial vessels. Previous studies have focused primarily on circular cross sections and the roles of the Dean number and curvature ratio on the flow physics. In this study we examine the effect of wavy walls, that is, axially aligned ribs extending the length of the tube, on steady flow through mildly and finite curved tubes using computational fluid dynamics. Analytical work on the subject has been limited to low Dean numbers and small bump heights, thus we primarily focus on the impact of higher Dean number with large protrusions on the flow physics. The results are compared with those in circular cross section tubes at the same Dean number. Particular attention is paid to flow characteristics of interest in the vasculature, such as wall shear stress, that have been shown to stimulate biochemical pathways that trigger cell growth.
Two-lane traffic-flow model with an exact steady-state solution.
Kanai, Masahiro
2010-12-01
We propose a stochastic cellular-automaton model for two-lane traffic flow based on the misanthrope process in one dimension. The misanthrope process is a stochastic process allowing for an exact steady-state solution; hence, we have an exact flow-density diagram for two-lane traffic. In addition, we introduce two parameters that indicate, respectively, driver's driving-lane preference and passing-lane priority. Due to the additional parameters, the model shows a deviation of the density ratio for driving-lane use and a biased lane efficiency in flow. Then, a mean-field approach explicitly describes the asymmetric flow by the hop rates, the driving-lane preference, and the passing-lane priority. Meanwhile, the simulation results are in good agreement with an observational data, and we thus estimate these parameters. We conclude that the proposed model successfully produces two-lane traffic flow particularly with the driving-lane preference and the passing-lane priority.
Experiments on a Steady Low Reynolds Number Airfoil in a Shear Flow
Olson, David; Naguib, Ahmed; Koochesfahani, Manoochehr
2016-11-01
The aerodynamics of steady airfoils in uniform flow have received considerably more attention than that of an airfoil operating in a non-uniform flow. Inviscid theory by Tsien (1943) shows that an airfoil experiences a decrease in the zero lift angle of attack for a shear flow with uniform clockwise vorticity. The current work utilizes a shaped honeycomb technique to create a velocity profile with a large region of uniform shear in a water tunnel. Direct force measurements are implemented and validated using experiments on a circular cylinder and NACA 0012 in a uniform cross-flow. Results for a NACA 0012 airfoil with a chord Reynolds number of 1.2 ×104 in a non-uniform approach flow are compared to concurrent CFD calculations (presented in a companion talk) showing an increase in the zero lift angle of attack; in contradiction with inviscid theory. The effect of shear on the mean lift coefficient over a wide range of angles of attack is also explored. This work was supported by AFOSR Award Number FA9550-15-1-0224.
On the pressure and stress singularities induced by steady flows of incompressible viscous fluids
G.B.Sinclair; X.Chi; T.I-P.Shih
2009-01-01
Design for structural integrity requires an appreciation of where stress singularities can occur in structural configurations. While there is a rich literature devoted to the identification of such singular behavior in solid mechanics, to date there has been relatively little explicit identification of stress singularities caused by fluid flows. In this study, stress and pressure singularities induced by steady flows of viscous incompressible fluids are asymptotically identified. This is done by taking advantage of an earlier result that the Navier-Stokes equations are locally governed by Stokes flow in angular corners. Findings for power singularities are confirmed by developing and using an analogy with solid mechanics. This analogy also facilitates the identification of flow-induced log singularities. Both types of singularity are further confirmed for two global configurations by applying convergence-divergence checks to numerical results. Even though these flow-induced stress singularities are analogous to singularities in solid mechanics, they nonetheless render a number of structural configurations singular that were not previously appreciated as such from identifications within solid mechanics alone.
Shiqian Nie
2017-01-01
Full Text Available The fractional advection-diffusion equation (fADE model is a new approach to describe the vertical distribution of suspended sediment concentration in steady turbulent flow. However, the advantages and parameter definition of the fADE model in describing the sediment suspension distribution are still unclear. To address this knowledge gap, this study first reviews seven models, including the fADE model, for the vertical distribution of suspended sediment concentration in steady turbulent flow. The fADE model, among others, describes both Fickian and non-Fickian diffusive characteristics of suspended sediment, while the other six models assume that the vertical diffusion of suspended sediment follows Fick’s first law. Second, this study explores the sensitivity of the fractional index of the fADE model to the variation of particle sizes and sediment settling velocities, based on experimental data collected from the literatures. Finally, empirical formulas are developed to relate the fractional derivative order to particle size and sediment settling velocity. These formulas offer river engineers a substitutive way to estimate the fractional derivative order in the fADE model.
Steady-State Flows in Two-Fluid Models of NSTX and DIII-D Plasmas
Ferraro, N. M.; Jardin, S. C.; Chen, J.
2009-05-01
Accurate axisymmetric steady-states of a comprehensive two-fluid model are calculated for plasmas in diverted NSTX and DIII-D geometries using the M3D-C^1 code [1]. It is found that gyroviscosity may have a significant effect on the flows in steady-state when a localized density source is present. The model implemented in M3D-C^1 self-consistently includes the effects of flows, anisotropic viscosity, anisotropic thermal conductivity, and resistivity. Results for ohmically driven plasmas are presented. New capabilities of M3D-C^1 allow the three-dimensional linear stability of axisymmetric equilibria to be calculated; these capabilities and preliminary stability results are discussed. Also discussed are recent and future extensions to M3D-C^1, including heuristic bootstrap current models, coupling to a physics-based transport model, and nonlinear non-axisymmetric capability. 3pt[1] S. C. Jardin, J. Breslau, N. Ferraro, J. Comput. Phys, 226 (2007) 2146
Naftz, David L.; Carling, Gregory T.; Angeroth, Cory; Freeman, Michael; Rowland, Ryan; Pazmiño, Eddy
2014-01-01
Density stratification in saline and hypersaline water bodies from throughout the world can have large impacts on the internal cycling and loading of salinity, nutrients, and trace elements. High temporal resolution hydroacoustic and physical/chemical data were collected at two sites in Great Salt Lake (GSL), a saline lake in the western USA, to understand how density stratification may influence salinity and mercury (Hg) distributions. The first study site was in a causeway breach where saline water from GSL exchanges with less saline water from a flow restricted bay. Near-surface-specific conductance values measured in water at the breach displayed a good relationship with both flow and wind direction. No diurnal variations in the concentration of dissolved (total and MeHg loadings was observed during periods of elevated salinity. The second study site was located on the bottom of GSL where movement of a high-salinity water layer, referred to as the deep brine layer (DBL), is restricted to a naturally occurring 1.5-km-wide “spillway” structure. During selected time periods in April/May, 2012, wind-induced flow reversals in a railroad causeway breach, separating Gunnison and Gilbert Bays, were coupled with high-velocity flow pulses (up to 55 cm/s) in the DBL at the spillway site. These flow pulses were likely driven by a pressure response of highly saline water from Gunnison Bay flowing into the north basin of Gilbert Bay. Short-term flow reversal events measured at the railroad causeway breach have the ability to move measurable amounts of salt and Hg from Gunnison Bay into the DBL. Future disturbance to the steady state conditions currently imposed by the railroad causeway infrastructure could result in changes to the existing chemical balance between Gunnison and Gilbert Bays. Monitoring instruments were installed at six additional sites in the DBL during October 2012 to assess impacts from any future modifications to the railroad causeway.
Kuntoro, Hadiyan Yusuf; Indarto,
2015-01-01
In the chemical, petroleum and nuclear industries, pipelines are often used to transport fluids from one process site to another one. The understanding of the fluids behavior inside the pipelines is the most important consideration for the engineers and scientists. From the previous studies, there are several two-phase flow patterns in horizontal pipe. One of them is stratified flow pattern, which is characterized by the liquid flowing along the bottom of the pipe and the gas moving above it cocurrently. Another flow patterns are slug and plug flow patterns. This kind of flow triggers the damage in pipelines, such as corrosion, abrasion, and blasting pipe. Therefore, slug and plug flow patterns are undesirable in pipelines, and the flow is maintained at the stratified flow condition for safety reason. In this paper, the analytical-based study on the experiment of the stratified flow pattern in a 26 mm i.d. horizontal pipe is presented. The experiment is performed to develop a high quality database of the stra...
R. Mantovani
2002-01-01
Full Text Available This paper presents the analysis of symmetric circulations of a rotating baroclinic flow, forced by a steady thermal wind and dissipated by Laplacian friction. The analysis is performed with numerical time-integration. Symmetric flows, vertically bound by horizontal walls and subject to either periodic or vertical wall lateral boundary conditions, are investigated in the region of parameter-space where unstable small amplitude modes evolve into stable stationary nonlinear solutions. The distribution of solutions in parameter-space is analysed up to the threshold of chaotic behaviour and the physical nature of the nonlinear interaction operating on the finite amplitude unstable modes is investigated. In particular, analysis of time-dependent energy-conversions allows understanding of the physical mechanisms operating from the initial phase of linear instability to the finite amplitude stable state. Vertical shear of the basic flow is shown to play a direct role in injecting energy into symmetric flow since the stage of linear growth. Dissipation proves essential not only in limiting the energy of linearly unstable modes, but also in selecting their dominant space-scales in the finite amplitude stage.
Thermal Performance of a Large Low Flow Solar Heating System with a Highly Thermally Stratified Tank
Furbo, Simon; Vejen, Niels Kristian; Shah, Louise Jivan
2005-01-01
are facing west. The collector tilt is 15° from horizontal for all collectors. Both the east-facing and the west-facing collectors have their own solar collector loop, circulation pump, external heat exchanger and control system. The external heat exchangers are used to transfer the heat from the solar...... collector fluid to the domestic water. The domestic water is pumped from the bottom of the hot-water tank to the heat exchanger and back to the hot-water tank through stratification inlet pipes. The return flow from the DHW circulation pipe also enters the tank through stratification inlet pipes. The tank...... performance and for the excellent utilization of the solar radiation is the high hot-water consumption and the good system design making use of external heat exchangers and stratification inlet pipes....
Tasawar Hayat
Full Text Available This paper investigates the unsteady MHD flow of viscous fluid between two parallel rotating disks. Fluid fills the porous space. Energy equation has been constructed by taking Joule heating, thermal stratification and radiation effects into consideration. We convert system of partial differential equations into system of highly nonlinear ordinary differential equations after employing the suitable transformations. Convergent series solutions are obtained. Behavior of different involved parameters on velocity and temperature profiles is examined graphically. Numerical values of skin friction coefficient and Nusselt number are computed and inspected. It is found that tangential velocity profile is increasing function of rotational parameter. Fluid temperature reduces for increasing values of thermal stratification parameter. At upper disk heat transfer rate enhances for larger values of Eckert and Prandtl numbers.
Hayat, Tasawar; Qayyum, Sumaira; Imtiaz, Maria; Alsaedi, Ahmed
2016-01-01
This paper investigates the unsteady MHD flow of viscous fluid between two parallel rotating disks. Fluid fills the porous space. Energy equation has been constructed by taking Joule heating, thermal stratification and radiation effects into consideration. We convert system of partial differential equations into system of highly nonlinear ordinary differential equations after employing the suitable transformations. Convergent series solutions are obtained. Behavior of different involved parameters on velocity and temperature profiles is examined graphically. Numerical values of skin friction coefficient and Nusselt number are computed and inspected. It is found that tangential velocity profile is increasing function of rotational parameter. Fluid temperature reduces for increasing values of thermal stratification parameter. At upper disk heat transfer rate enhances for larger values of Eckert and Prandtl numbers.
Turbulence energetics in stably stratified geophysical flows: strong and weak mixing regimes
Zilitinkevich, S S; Kleeorin, N; Rogachevskii, I; Esau, I; Mauritsen, T; Miles, M W
2008-01-01
Traditionally, turbulence energetics is characterized by turbulent kinetic energy (TKE) and modelled using solely the TKE budget equation. In stable stratification, TKE is generated by the velocity shear and expended through viscous dissipation and work against buoyancy forces. The effect of stratification is characterized by the ratio of the buoyancy gradient to squared shear, called Richardson number, Ri. It is widely believed that at Ri exceeding a critical value, Ric, local shear cannot maintain turbulence, and the flow becomes laminar. We revise this concept by extending the energy analysis to turbulent potential and total energies (TPE and TTE = TKE + TPE), consider their budget equations, and conclude that TTE is a conservative parameter maintained by shear in any stratification. Hence there is no "energetics Ric", in contrast to the hydrodynamic-instability threshold, Ric-instability, whose typical values vary from 0.25 to 1. We demonstrate that this interval, 0.25>1, clarify principal difference betw...
Upscaling of Two-Phase Immiscible Flows in Communicating Stratified Reservoirs
Zhang, Xuan; Shapiro, Alexander; Stenby, Erling Halfdan
2011-01-01
forces and gravity may be neglected. The method is discussed on the example of its basic application: waterflooding in petroleum reservoirs. We apply asymptotic analysis to a system of two-dimensional (2D) mass conservation equations for incompressible fluids. For high anisotropy ratios, the pressure...... gradient in vertical direction may be set zero, which is the only assumption of our derivation. In this way, the 2D Buckley–Leverett problem may be reduced to a one-dimensional problem for a system of quasi-linear hyperbolic equations, of a number equal to the number of layers in the reservoir....... They are solved numerically, based on an upstream finite difference algorithm. Self-similarity of the solution makes it possible to compute pseudofractional flow functions depending on the average saturation. The computer partial differential equation solver COMSOL is used for comparison of the complete 2D...
Cha, Jeesung Jeff
microporous structures. This is particularly troubling with regards to the regenerator, where friction and thermal non-equilibrium between the fluid and the structure play crucial roles. Little attention has been paid to this issue primarily because of the difficulty of experimental measurements. Multi-dimensional modeling of a regenerator is very complex and requires knowledge about the anisotropic hydrodynamic parameters in various components, in particular the regenerator. In view of the above, this investigation was aimed at: (a) experimental measurement and correlation of the steady and periodic flow directional Darcy permeability and Forchheimer's inertial hydrodynamic parameters for some widely-used regenerator fillers; (b) system-level parametric CFD-based analyses of entire PTC systems; and (c) a preliminary CFD-based assessment of the effect of direct and linear scale-down of current Inertance Tube Pulse Tube Cryocooler (ITPTCs) on their thermal performance. Modular experimental apparatuses were designed and built for the measurement of pressure drops across five different and widely-used regenerator fillers, under steady-state and steady periodic flow conditions. Separate test sections were used so that the pressure drops in axial and lateral directions could be measured. The fillers that were investigated included 325 mesh stainless steel screens, 400 mesh stainless steel screens, sintered 400 mesh stainless steel screens, stainless steel metal foam, and stacked nickel micro-machined disks. The parametric effects that were addressed in the experiments included the porosity in the range of 26.8% to 69.2%, and frequency in the range of 5 Hz to 60 Hz for the periodic flow tests. A CFDassisted method was developed, which allowed for obtaining the directional permeability and Forchheimer coefficients from the experimental data in a rigorous manner and without any arbitrary assumption. Using the Fluent code, parametric CID analyses were performed in which entire ITPTC
Steady film flow over 2D topography with air inclusion formed inside the trench
Tsamopoulos, John; Varchanis, Stylianos; Dimakopoulos, Yannis
2016-11-01
Liquid film flow along an inclined, solid substrate featuring periodic rectangular trenches may either completely wet the trench floor (Wenzel state) or pin on the entrance and exit corners of the trench (Cassie state) or assume any other configuration in between these two extremes. In the intermediate cases a second gas-liquid interface inside the trench is formed, which adheres to the walls of the trench forming two three-phase contact lines, and encloses a different amount of air under different physical conditions. The Galerkin finite element method is used to solve the Navier-Stokes equations in a physical domain, which is adaptively re-meshed. Multiple steady solutions, connected by turning points and transcritical bifurcations as well as isolated solution branches, are revealed by pseudo arc-length continuation. Two possible cases of a single air inclusion inside the trench are examined. The penetration of the liquid inside the trench is enhanced primarily by increasing either the wettability of the substrate or the capillarity or by decreasing the flow rate. Flow hysteresis may occur when the liquid does not penetrate deep enough inside the trench leading to different flow patterns. The interplay of inertia, viscous, gravity and capillary forces along with substrate wettability determines the volume of the air encapsulated in the trench and the extent of free surface deformation. GSRT of Greece via the program "Excellence" and the LIMMAT foundation.
Experimental investigations of the steady flow through an idealized model of a femoral artery bypass
Giurgea Corina
2014-03-01
Full Text Available The present paper presents the steps taken by the authors in the first stage of an experimental program within a larger national research project whose objective is to characterize the flow through a femoral artery bypass with a view to finding solutions for its optimization. The objective of the stage is to investigate by means of the PIV method the stationary flow through a bypass model with an idealized geometry. A bypass assembly which reunites the idealized geometry models of the proximal and distal anastomoses, and which respects the lengths of a femoral artery bypass was constructed on the basis of data for a real patient provided by medical investigations. With the aim of testing the model and the established experimental set-up with regard to their suitability for the assessment of the velocity field associated to the steady flow through the bypass, three zones that can restore the whole distal anastomosis were PIV investigated. The measurements were taken in the conditions of maintained inflow at the bypass entry of 0.9 l / min (Re = 600. The article presents comparatively the flow spectra and the velocity fields for each zone obtained in two situations: with the femoral artery completely occluded and completely open.
Measurements of steady flow through a bileaflet mechanical heart valve using stereoscopic PIV.
Hutchison, Chris; Sullivan, Pierre; Ethier, C Ross
2011-03-01
Computational modeling of bileaflet mechanical heart valve (BiMHV) flow requires experimentally validated datasets and improved knowledge of BiMHV fluid mechanics. In this study, flow was studied downstream of a model BiMHV in an axisymmetric aortic sinus using stereoscopic particle image velocimetry. The inlet flow was steady and the Reynolds number based on the aortic diameter was 7600. Results showed the out-of-plane velocity was of similar magnitude as the transverse velocity. Although additional studies are needed for confirmation, analysis of the out-of-plane velocity showed the possible presence of a four-cell streamwise vortex structure in the mean velocity field. Spatial data for all six Reynolds stress components were obtained. Reynolds normal stress profiles revealed similarities between the central jet and free jets. These findings are important to BiMHV flow modeling, though clinical relevance is limited due to the idealized conditions chosen. To this end, the dataset is publicly available for CFD validation purposes.
Lift on a Steady Airfoil in Low Reynolds Number Shear Flow
Hammer, Patrick; Visbal, Miguel; Naguib, Ahmed; Koochesfahani, Manoochehr
2016-11-01
Current understanding of airfoil aerodynamics is primarily based on a uniform freestream velocity approaching the airfoil, without consideration for possible presence of shear in the approach flow. Inviscid theory by Tsien (1943) shows that a symmetric airfoil at zero angle of attack experiences positive lift, i.e. a shift in the zero-lift angle of attack, in the presence of positive mean shear in the approach flow. In the current work, 2D computations are conducted on a steady NACA 0012 airfoil at a chord Reynolds number of Re = 12,000, at zero angle of attack. A uniform shear profile (i.e. a linear velocity variation) is used for the approach flow by modifying the FDL3DI Navier-Stokes solver (Visbal and Gaitonde, 1999). Interestingly, opposite to the inviscid prediction of Tsien (1943), the results for the airfoil at zero angle of attack show that the average lift is negative in the shear flow. The magnitude of this lift grows as the shear rate increases. Additional results are presented regarding the physics underlying the shear effect on lift. A companion experimental study is also given in a separate presentation. This work was supported by AFOSR Award Number FA9550-15-1-0224.
Vallee, Christophe
2012-08-22
Stratified two-phase flows were investigated at different test facilities with horizontal test sections in order to provide an experimental database for the development and validation of computational fluid dynamics (CFD) codes. These channels were designed with rectangular cross-sections to enable optimal observation conditions for the application of optical measurement techniques. Consequently, the local flow structure was visualised with a high-speed video camera, delivering data with highresolution in space and time as needed for CFD code validation. Generic investigations were performed at atmospheric pressure and room temperature in two air/water channels made of acrylic glass. Divers preliminary experiments were conducted with various measuring systems in a test section mounted between two separators. The second test facility, the Horizontal Air/Water Channel (HAWAC), is dedicated to co-current flow investigations. The hydraulic jump as the quasi-stationary discontinuous transition between super- and subcritical flow was studied in this closed channel. Moreover, the instable wave growth leading to slug flow was investigated from the test section inlet. For quantitative analysis of the optical measurements, an algorithm was developed to recognise the stratified interface in the camera frames, allowing statistical treatments for comparison with CFD calculation results. The third test apparatus was installed in the pressure chamber of the TOPFLOW test facility in order to be operated at reactor typical conditions under pressure equilibrium with the vessel atmosphere. The test section representing a flat model of the hot leg of the German Konvoi pressurised water reactor (PWR) scaled at 1:3 is equipped with large glass side walls in the region of the elbow and of the steam generator inlet chamber to allow visual observations. The experiments were conducted with air and water at room temperature and maximum pressures of 3 bar as well as with steam and water at
Flow and flow-induced vibration of a square array of cylinders in steady currents
Zhao, Ming [School of Computing, Engineering and Mathematics, University of Western Sydney, Locked Bag 1797, Penrith, NSW 2751 (Australia); Cheng, Liang; An, Hongwei; Tong, Feifei, E-mail: m.zhao@uws.edu.au [School of Civil, Environmental and Mining Engineering, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009 (Australia)
2015-08-15
Flow and flow-induced vibration of a square array of cylinders are investigated by two-dimensional numerical simulations. Flow past 36 cylinders in an inline arranged square array and 33 cylinders in a staggered arranged square array is firstly simulated, for Re = 100 and the spacing ratios of L/D = 1.5, 2, 3, 4, 5. Only one vortex street is observed in the wake of the cylinder array when the spacing ratio is 1.5 in the inline arrangement and 1.5 and 2 in the staggered arrangement, indicating that the critical spacing ratio for the single-vortex street mode in the staggered arrangement is higher than that in the inline arrangement. The vortex shedding from the cylinders is suppressed at L/D = 3 for both inline and staggered arrangements. Vortex shedding from each individual cylinder is observed when L/D = 4. Flow-induced vibration of 36 cylinders in an inline square arrangement is studied for a constant Reynolds number of 100, two spacing ratios of 2 and 5, a constant mass ratio of 2.5 and a wide range of reduced velocities. It is found that for a spacing ratio of 2, the vibration of the cylinders in the four downstream columns does not start until the reduced velocity exceeds 4.5. The vibration of the cylinders progresses downstream with increasing reduced velocity. For a spacing ratio of 5, the vibrations of the cylinders in the most upstream column are similar to that of a single cylinder. The vibration amplitudes of the downstream cylinders peak at higher reduced velocities than that of a single cylinder. The maximum possible response amplitudes occur at the most downstream cylinders. (paper)
Capponi, A.; James, M. R.; Lane, S. J.
2016-02-01
The canonical Strombolian paradigm of a gas slug ascending and bursting in a homogeneous low-viscosity magma cannot explain the complex details in eruptive dynamics recently revealed by field measurements and textural and geochemical analyses. Evidence points to the existence of high-viscosity magma at the top of the conduit of Strombolian-type volcanoes, acting as a plug. Here, new experiments detail the range of flow configurations that develop during the ascent and burst of a slug through rheologically stratified magma within a conduit. End-member scenarios of a tube fully filled with either high- or low-viscosity liquid bracket three main flow configurations: (1) a plug sufficiently large to fully accommodate an ascending gas slug; (2) A plug that can accommodate the intrusion of low-viscosity liquid driven by the gas expansion, but not all the slug volume, so the slug bursts with the nose in the plug whilst the base is still in the low-viscosity liquid; (3) Gas expansion is sufficient to drive the intrusion of low-viscosity liquid through the plug, with the slug bursting in the low-viscosity layer emplaced dynamically above the plug. We show that the same flow configurations are viable at volcanic-scale through a new experimentally-validated 1D model and 3D computational fluid dynamic simulations. Applied to Stromboli, our results demonstrate that the key parameters controlling the transition between each configuration are gas volume, plug thickness and plug viscosity. The flow processes identified include effective dynamic narrowing and widening of the conduit, instabilities within the falling magma film, transient partial and complete blockage of the conduit, and slug disruption. These complexities influence eruption dynamics and vigour, promoting magma mingling and resulting in pulsatory release of gas.
Biswas, Dipankar; Casey, David M; Crowder, Douglas C; Steinman, David A; Yun, Yang H; Loth, Francis
2016-07-01
Blood is a complex fluid that, among other things, has been established to behave as a shear thinning, non-Newtonian fluid when exposed to low shear rates (SR). Many hemodynamic investigations use a Newtonian fluid to represent blood when the flow field of study has relatively high SR (>200 s-1). Shear thinning fluids have been shown to exhibit differences in transition to turbulence (TT) compared to that of Newtonian fluids. Incorrect prediction of the transition point in a simulation could result in erroneous hemodynamic force predictions. The goal of the present study was to compare velocity profiles near TT of whole blood and Newtonian blood analogs in a straight rigid pipe with a diameter 6.35 mm under steady flow conditions. Rheology was measured for six samples of whole porcine blood and three samples of a Newtonian fluid, and the results show blood acts as a shear thinning non-Newtonian fluid. Measurements also revealed that blood viscosity at SR = 200 s-1 is significantly larger than at SR = 1000 s-1 (13.8%, p velocity profiles for blood and Newtonian samples at different flow rates to produce Reynolds numbers (Re) ranging from 1000 to 3300 (based on viscosity at SR = 1000 s-1). Two mathematically defined methods, based on the velocity profile shape change and turbulent kinetic energy (TKE), were used to detect TT. Results show similar parabolic velocity profiles for both blood and the Newtonian fluid for Re velocity profiles for larger Re. The Newtonian fluid had blunt-like velocity profiles starting at Re = 2403 ± 8 which indicated transition. In contrast, blood did not show this velocity profile change until Re = 2871 ± 104. The Newtonian fluid had large velocity fluctuations (root mean square (RMS) > 20%) with a maximum TKE near the pipe center at Re = 2316 ± 34 which indicated transition. In contrast, blood results showed the maximum TKE at Re = 2806 ± 109. Overall, the critical Re was
Deformation mechanism of leukocyte adhering to vascular surface under steady shear flow
LIU; Xiaoheng; WANG; Xiong; YIN; Hongmei; CHEN; Huaiqing
2004-01-01
The adhesion of leukocytes to vascular surface is an important biomedical problem and has drawn extensive attention. In this study, we propose a compound drop model to simulate a leukocyte with a nucleus adhering to the surface of blood vessel under steady shear flow. A two-dimensional computational fluid dynamics (CFD) is conducted to determine the local distribution of pressure on the surface of the adherent model cell. By introducing the parameter of deformation index (DI), we investigate the deformation of the leukocyte and its nucleus under controlled conditions. Our numerical results show that: (i) the leukocyte is capable of deformation under external exposed flow field. The deformation index increases with initial contact angle and Reynolds number of external exposed flow. (ii) The nucleus deforms with the cell, and the deformation index of the leukocyte is greater than that of the nucleus. The leukocyte is more deformable while the nucleus is more capable of resisting external shear flow. (iii) The leukocyte and the nucleus are not able to deform infinitely with the increase of Reynolds number because the deformation index reaches a maximum. (iv) Pressure distribution confirms that there exists a region downstream of the cell, which produces high pressure to retard continuous deformation and provide a positive lift force on the cell. Meanwhile, we have measured the deformation of human leukocytes exposed to shear flow by using a flow chamber system. We found that the numerical results are well consistent with those of experiment. We conclude that the nucleus with high viscosity plays a particular role in leukocyte deformation.
刘士和; 薛娇
2016-01-01
The mechanical energy loss and the wall resistance are very important in practical engineering. These problems are investigated through theoretical analysis and numerical simulation in this paper. The results are as follows. (1) A new mechanical energy equation for the total flow is obtained, and a general formula for the calculation of the mechanical energy loss is proposed. (2) The general relationship between the wall resistance and the mechanical energy loss for the steady channel flow is obtained, the simplified form of which for the steady uniform channel flow is in consistent with the formula used in Hydraulics deduced byπ theorem and dimensional analysis. (3) The steady channel flow over a backward facing step with a small expansion ratio is numerica- lly simulated, and the mechanical energy loss, the wall resistance as well as the relationship between the wall resistance and the mechanical energy loss are calculated and analyzed.
A new approach to calibrate steady groundwater flow models with time series of head observations
Obergfell, C.; Bakker, M.; Maas, C.
2012-04-01
We developed a new method to calibrate aquifer parameters of steady-state well field models using measured time series of head fluctuations. Our method is an alternative to standard pumping tests and is based on time series analysis using parametric impulse response functions. First, the pumping influence is isolated from the overall groundwater fluctuation observed at monitoring wells around the well field, and response functions are determined for each individual well. Time series parameters are optimized using a quasi-Newton algorithm. For one monitoring well, time series model parameters are also optimized by means of SCEM-UA, a Markov Chain Monte Carlo algorithm, as a control on the validity of the parameters obtained by the faster quasi-Newton method. Subsequently, the drawdown corresponding to an average yearly pumping rate is calculated from the response functions determined by time series analysis. The drawdown values estimated with acceptable confidence intervals are used as calibration targets of a steady groundwater flow model. A case study is presented of the drinking water supply well field of Waalwijk (Netherlands). In this case study, a uniform aquifer transmissivity is optimized together with the conductance of ditches in the vicinity of the well field. Groundwater recharge or boundary heads do not have to be entered, which eliminates two import sources of uncertainty. The method constitutes a cost-efficient alternative to pumping tests and allows the determination of pumping influences without changes in well field operation.
Steady Stagnation Point Flow and Heat Transfer Over a Shrinking Sheet with Induced Magnetic Field
Aniruddha Sinha
2014-01-01
Full Text Available The problem of the steady magnetohydrodynamic (MHD stagnation-point flow of an incompressible, viscous and electrically conducting fluid over a shrinking sheet is studied. The effects of an induced magnetic field and thermal radiation are taken into account. Velocity and thermal slip conditions have also been incorporated in the study. The nonlinear partial differential equations are transformed into ordinary differential equations via the similarity transformation. The transformed boundary layer equations are solved numerically using Newton’s linearization method. Computational results for the variation in velocity, temperature, skin-friction co-efficient and Nusselt number are presented graphically and in tabular form. Study reveals that the surface velocity gradient and heat transfer are enhanced by decreasing magnetic parameter.
Dissipation on Steady MHD Marangoni Convection Flow over a Flat Surface with Suction and Injection
S. Mohammed Ibrahim
2013-01-01
Full Text Available The combined effects of radiation and mass transfer on a steady MHD two-dimensional Marangoni convection flow over a flat surface in presence of Joule heating and viscous dissipation under influence of suction and injection is studied numerically. The general governing partial differential equations are transformed into a set of nonlinear ordinary differential equations by using unique similarity transformation. Numerical solutions of the similarity equations are obtained using the Runge-Kutta method along with shooting technique. The effects of governing parameters on velocity, temperature, and concentration as well as interface velocity, the surface temperature gradient, and the surface concentration gradient were presented in graphical and tabular forms. Comparisons with previously published work are performed and the results are found to be in excellent agreement.
Steady nanofluid flow between parallel plates considering thermophoresis and Brownian effects
M. Sheikholeslami
2016-10-01
Full Text Available In this article, heat and mass transfer behavior of steady nanofluid flow between parallel plates in the presence of uniform magnetic field is studied. The important effect of Brownian motion and thermophoresis has been included in the model of nanofluid. The governing equations are solved via the Differential Transformation Method. The validity of this method was verified by comparison of previous work which is done for viscous fluid. The analysis is carried out for different parameters namely: viscosity parameter, Magnetic parameter, thermophoretic parameter and Brownian parameter. Results reveal that skin friction coefficient enhances with rise of viscosity and Magnetic parameters. Also it can be found that Nusselt number augments with an increase of viscosity parameters but it decreases with augment of Magnetic parameter, thermophoretic parameter and Brownian parameter.
Brooks, Lynette E.; Masbruch, Melissa D.; Sweetkind, Donald S.; Buto, Susan G.
2014-01-01
This report describes the construction, calibration, evaluation, and results of a steady-state numerical groundwater flow model of the Great Basin carbonate and alluvial aquifer system that was developed as part of the U.S. Geological Survey National Water Census Initiative to evaluate the nation’s groundwater availability. The study area spans 110,000 square miles across five states. The numerical model uses MODFLOW-2005, and incorporates and tests complex hydrogeologic and hydrologic elements of a conceptual understanding of an interconnected groundwater system throughout the region, including mountains, basins, consolidated rocks, and basin fill. The level of discretization in this model has not been previously available throughout the study area.
Frozen reaction fronts in steady flows: a burning-invariant-manifold perspective
Mahoney, John R; Boyer, Carleen; Solomon, Tom; Mitchell, Kevin A
2015-01-01
The dynamics of fronts, such as chemical reaction fronts, propagating in two-dimensional fluid flows can be remarkably rich and varied. For time-invariant flows, the front dynamics may simplify, settling in to a steady state in which the reacted domain is static, and the front appears "frozen". Our central result is that these frozen fronts in the two-dimensional fluid are composed of segments of burning invariant manifolds---invariant manifolds of front-element dynamics in $xy\\theta$-space, where $\\theta$ is the front orientation. Burning invariant manifolds (BIMs) have been identified previously as important local barriers to front propagation in fluid flows. The relevance of BIMs for frozen fronts rests in their ability, under appropriate conditions, to form global barriers, separating reacted domains from nonreacted domains for all time. The second main result of this paper is an understanding of bifurcations that lead from a nonfrozen state to a frozen state, as well as bifurcations that change the topol...
Comparison of tricuspid and bicuspid aortic valve hemodynamics under steady flow conditions
Seaman, Clara; Ward, James; Sucosky, Philippe
2011-11-01
The bicuspid aortic valve (BAV), a congenital valvular defect consisting of two leaflets instead of three, is associated with a high prevalence of calcific aortic valve disease (CAVD). CAVD also develops in the normal tricuspid aortic valve (TAV) but its progression in the BAV is more severe and rapid. Although hemodynamic abnormalities are increasingly considered potential pathogenic contributor, the native BAV hemodynamics remain largely unknown. Therefore, this study aims at comparing experimentally the hemodynamic environments in TAV and BAV anatomies. Particle-image velocimetry was used to characterize the flow downstream of a native TAV and a model BAV mounted in a left-heart simulator and subjected to three steady flow rates characterizing different phases of the cardiac cycle. While the TAV developed a jet aligned along the valve axis, the BAV was shown to develop a skewed systolic jet with skewness decreasing with increasing flow rate. Measurement of the transvalvular pressure revealed a valvular resistance up to 50% larger in the BAV than in the TAV. The increase in velocity between the TAV and BAV leads to an increase in shear stress downstream of the valve. This study reveals strong hemodynamic abnormalities in the BAV, which may contribute to CAVD pathogenesis.
BASANT K JHA; BABATUNDE AINA
2016-08-01
This work reports an analytical solution for fully developed mixed convection flow of viscous,incompressible, electrically conducting fluid in vertical concentric annuli under the influence of a transverse magnetic field, where the outer surface of inner cylinder is heated sinusoidally and the inner surface of outercylinder is kept at a constant temperature. The analysis is carried out for fully developed parallel flow and steady-periodic regime. The governing dimensionless momentum and energy equations are separated into steadyand periodic parts and solved analytically. Closed form solutions are expressed in terms of modified Bessel function of first and second kind. The influence of each governing parameters such as magnetic field parameter,Prandtl number and the dimensionless frequency of heating on flow formation and thermal behaviour are discussed with the aid of graphs. During the course of investigation, it is found that the oscillation amplitude of the friction factor is maximized at a resonance frequency near the surface of the concentric annuli where there is periodic heating. Furthermore, increasing transverse magnetic field decreases the oscillation amplitude of the friction factor.
Development of high-lift laminar wing using steady active flow control
Clayton, Patrick J.
Fuel costs represent a large fraction of aircraft operating costs. Increased aircraft fuel efficiency is thus desirable. Laminar airfoils have the advantage of reduced cruise drag and increased fuel efficiency. Unfortunately, they cannot perform adequately during high-lift situations (i.e. takeoff and landing) due to low stall angles and low maximum lift caused by flow separation. Active flow control has shown the ability to prevent or mitigate separation effects, and increase maximum lift. This fact makes AFC technology a fitting solution for improving high-lift systems and reducing the need for slats and flap elements. This study focused on experimentally investigating the effects of steady active flow control from three slots, located at 1%, 10%, and 80% chord, respectively, over a laminar airfoil with 45 degree deflected flap. A 30-inch-span airfoil model was designed, fabricated, and then tested in the Bill James 2.5'x3' Wind Tunnel at Iowa State University. Pressure data were collected along the mid-span of the airfoil, and lift and drag were calculated. Five test cases with varying injection locations and varying Cμ were chosen: baseline, blown flap, leading edge blowing, equal blowing, and unequal blowing. Of these cases, unequal blowing achieved the greatest lift enhancement over the baseline. All cases were able to increase lift; however, gains were less than anticipated.
Chauchat, J.; Revil-Baudard, T.; Hurther, D.
2014-12-01
Sheet flow is believed to be a major process for morphological evolution of natural systems. An important research effort has been dedicated to laboratory and numerical studies of sheet flow regime that have allowed to make some progress in the understanding of the underlying physical processes. Recent advances made in high resolution measurement techniques allows to give new insights into the small scale physical processes. In this contribution, a novel uniform and steady sheet flow dataset based on an Acoustic Concentration and Velocity Profiler (ACVP) is presented. Profile of colocated velocities (streamwise and wall-normal) and sediment concentration has been measured at high-resolution (3 mm ; 78 Hz for the velocities and 4.9 Hz for the concentration). The measured profiles extend over the whole water column, from the free surface down to the fixed bed and an ensemble averaging over eleven realisations of the same experimental conditions has been used to obtain mean profiles of streamwise velocity, concentration, sediment flux and turbulent shear stress. The present experiment corresponds to a Shields number of θ=0.44 and a suspension number of ws/u*=1.1 corresponding to the lower limit of the no-suspension sheet flow regime. The analysis of the mixing length profile allows to identify two layers, a dilute suspension layer dominated by turbulence and a dense moving bed layer dominated by granular interactions. Our measurements show that the Von Karman parameter is reduced by a factor of more than two and that the Schmidt number is almost constant with a mean value of σs=0.44. Frictional and collisional interactions are encountered in the bed layer. Frictional interactions dominate close to the fixed bed interface whereas collisional interactions seems to control the flow at the transition between the dense and dilute layers. The relevancy of different constitutive laws for two-phase flow models are discussed.
Signal processing and statistical descriptive reanalysis of steady state chute-flow experiments
truong, hoan; eckert, nicolas; keylock, chris; naaim, mohamed; bellot, hervé
2014-05-01
An accurate knowledge of snow rheology is needed for the mitigation against avalanche hazard. Indeed snow avalanches have a significant impact on the livelihoods and economies of alpine communities. To do so, 60 small-scale in-situ flow experiments were performed with various slopes, temperatures and flow depths. The investigation of these data previously seemed to show the dense flow of dry snow may be composed of two layers; a sheared basal layer made of single snow grains and a less sheared upper layer made of large aggregates. These outcomes were mainly based on the mean velocity profile of the flow and on interpretation in terms of rheological behavior of granular materials and snow microstructure [Pierre G. Rognon et al., 2007]. Here, the main objective remains the same, but the rheological and physical viewpoints are put aside to extract as much information contained in the data as possible various using signal processing methods and descriptive statistics methods as the maximum overlap discrete wavelet transform (MODWT), transfer entropy (TE) and maximum cross-correlation (MCC). Specifically, we aim at the improving the velocity estimations as function of the depth particularly the velocity fluctuations around the mean profile to better document the behavior of dense dry snow flows during a steady and uniform chute regime. The data are composed of pairs of voltage signals (right and left), which makes that the velocity is known indirectly only. The MCC method is classically used to determine the time lag between both signals. Previously, the MCC method that showed the mean velocity profile may be fitted by a simple bilinear function [Pierre G. Rognon et al., 2007], but no interesting temporal dynamics could be highlighted. Hence, a new process method was developed to provide velocity series with much better temporal resolution. The process is mainly made of a MODWT-based denoising method and the choice of window size for correlation. The results prove to be
Balluch, M.
1991-03-01
Recent developments concerning spherically symmetric (1D-) numerical models of protostellar evolution show that steady protostellar accretion flows (resp. their shockfronts) may be unstable at least in the very early (Tscharnuter 1987a) and late stages (Balluch 1988) of accretion. A global, linear stability analysis of the structure of steady protostellar accretion flows with a shock discontinuity (Balluch 1990) is therefore presented to investigate such flows by different methods. Thereby three characteristic wave types, the radiation-, radiation diffusion- and acoustic modes were found. In the `ideal case' of a perfect gas law and constant opacity, the shockfront appears to be oscillatory unstable due to critical cooling as long as the mass flux rate is larger than a critical one of Mṡcrit = 10-6 Msun yr-1. In the `real case' with more realistic constitutive relations, an additional vibrational instability occurs due to the κ-mechanism in the outer layers of the core. This is shown to be the case in the whole range of core masses between 0.01 and 1 Msun, mass flow rates between 10-3 and 10-7 Msun yr-1 and different outer boundary conditions (corresponding to different states of the surrounding interstellar cloud). Analysing the first, outer protostellar cores before they get dynamically unstable due to H2-dissociation in their interiors, similar instabilities as mentioned above were found. Now the unstable κ-behaviour is due to dust instead of the deep ionisation zone as in the case of second, inner cores. According to the linear analysis, the instabilities should first appear in the velocity and the radiation flux in the settling zone. In the case of first, outer cores, these variations should be accompanied by an oscillation of the radiation flux in the region upstream from the shock up to r = 1014 cm. Sooner or later, the shockfront should oscillate in both cases too. These results are finally compared with the characteristics of the accretion shock
STUDY AND APPLICATION OF STEADY FLOW AND UNSTEADY FLOW MATHEMATICAL MODEL FOR CHANNEL NETWORKS
无
2007-01-01
Based on the Preissmann implicit scheme for the one-dimensional Saint-Venant equation, the mathematical model for one-dimensional river networks and canal networks was developed and the key issues on the model were expatiated particularly in this article. This model applies the method of three-steps solution for channel-junction-channel to simulate the river networks, and the Gauss elimination method was used to calculate the sparse matrix. This model was applied to simulate the tree-type irrigation canal networks, complex looped channel networks and the Lower Columbia Slough networks. The results of water level and discharge agree with the data from the Adlul and field data. The model is proved to be robust for simulating unsteady flows in river networks with various degrees of complex structure. The calculated results show that this model is useful for engineering applications in complicated river networks. Future research was recommended to focus on setting up ecological numerical model of water quality in river networks and canal networks.
Kuntoro, Hadiyan Yusuf, E-mail: hadiyan.y.kuntoro@mail.ugm.ac.id; Majid, Akmal Irfan; Deendarlianto, E-mail: deendarlianto@ugm.ac.id [Center for Energy Studies, Gadjah Mada University, Sekip K-1A Kampus UGM, Yogyakarta 55281 (Indonesia); Department of Mechanical and Industrial Engineering, Faculty of Engineering, Gadjah Mada University, Jalan Grafika 2, Yogyakarta 55281 (Indonesia); Hudaya, Akhmad Zidni; Dinaryanto, Okto [Department of Mechanical and Industrial Engineering, Faculty of Engineering, Gadjah Mada University, Jalan Grafika 2, Yogyakarta 55281 (Indonesia)
2016-06-03
Due to the importance of the two-phase flow researches for the industrial safety analysis, many researchers developed various methods and techniques to study the two-phase flow phenomena on the industrial cases, such as in the chemical, petroleum and nuclear industries cases. One of the developing methods and techniques is image processing technique. This technique is widely used in the two-phase flow researches due to the non-intrusive capability to process a lot of visualization data which are contain many complexities. Moreover, this technique allows to capture direct-visual information data of the flow which are difficult to be captured by other methods and techniques. The main objective of this paper is to present an improved algorithm of image processing technique from the preceding algorithm for the stratified flow cases. The present algorithm can measure the film thickness (h{sub L}) of stratified flow as well as the geometrical properties of the interfacial waves with lower processing time and random-access memory (RAM) usage than the preceding algorithm. Also, the measurement results are aimed to develop a high quality database of stratified flow which is scanty. In the present work, the measurement results had a satisfactory agreement with the previous works.
Kuntoro, Hadiyan Yusuf; Hudaya, Akhmad Zidni; Dinaryanto, Okto; Majid, Akmal Irfan; Deendarlianto
2016-06-01
Due to the importance of the two-phase flow researches for the industrial safety analysis, many researchers developed various methods and techniques to study the two-phase flow phenomena on the industrial cases, such as in the chemical, petroleum and nuclear industries cases. One of the developing methods and techniques is image processing technique. This technique is widely used in the two-phase flow researches due to the non-intrusive capability to process a lot of visualization data which are contain many complexities. Moreover, this technique allows to capture direct-visual information data of the flow which are difficult to be captured by other methods and techniques. The main objective of this paper is to present an improved algorithm of image processing technique from the preceding algorithm for the stratified flow cases. The present algorithm can measure the film thickness (hL) of stratified flow as well as the geometrical properties of the interfacial waves with lower processing time and random-access memory (RAM) usage than the preceding algorithm. Also, the measurement results are aimed to develop a high quality database of stratified flow which is scanty. In the present work, the measurement results had a satisfactory agreement with the previous works.
Erpelding, Marion; Sinha, Santanu; Tallakstad, Ken Tore; Hansen, Alex; Flekkøy, Eirik Grude; Måløy, Knut Jørgen
2013-11-01
It is well known that the transient behavior during drainage or imbibition in multiphase flow in porous media strongly depends on the history and initial condition of the system. However, when the steady-state regime is reached and both drainage and imbibition take place at the pore level, the influence of the evolution history and initial preparation is an open question. Here, we present an extensive experimental and numerical work investigating the history dependence of simultaneous steady-state two-phase flow through porous media. Our experimental system consists of a Hele-Shaw cell filled with glass beads which we model numerically by a network of disordered pores transporting two immiscible fluids. From measurements of global pressure evolution, histograms of saturation, and cluster-size distributions, we find that when both phases are flowing through the porous medium, the steady state does not depend on the initial preparation of the system or on the way it has been reached.
Lee, Jeffrey M.
1999-01-01
This study establishes a consistent set of differential equations for use in describing the steady secondary flows generated by periodic compression and expansion of an ideal gas in pulse tubes. Also considered is heat transfer between the gas and the tube wall of finite thickness. A small-amplitude series expansion solution in the inverse Strouhal number is proposed for the two-dimensional axisymmetric mass, momentum and energy equations. The anelastic approach applies when shock and acoustic energies are small compared with the energy needed to compress and expand the gas. An analytic solution to the ordered series is obtained in the strong temperature limit where the zeroth-order temperature is constant. The solution shows steady velocities increase linearly for small Valensi number and can be of order I for large Valensi number. A conversion of steady work flow to heat flow occurs whenever temperature, velocity or phase angle gradients are present. Steady enthalpy flow is reduced by heat transfer and is scaled by the Prandtl times Valensi numbers. Particle velocities from a smoke-wire experiment were compared with predictions for the basic and orifice pulse tube configurations. The theory accurately predicted the observed steady streaming.
de Castro, Marcelo Souza; Rodriguez, Oscar Mauricio Hernandez
2016-06-01
The study of the hydrodynamic stability of flow patterns is important in the design of equipment and pipelines for multiphase flows. The maintenance of a particular flow pattern becomes important in many applications, e.g., stratified flow pattern in heavy oil production avoiding the formation of emulsions because of the separation of phases and annular flow pattern in heat exchangers which increases the heat transfer coefficient. Flow maps are drawn to orientate engineers which flow pattern is present in a pipeline, for example. The ways how these flow maps are drawn have changed from totally experimental work, to phenomenological models, and then to stability analysis theories. In this work an experimental liquid-liquid flow map, with water and viscous oil as work fluids, drawn via subjective approach with high speed camera was used to compare to approaches of the same theory: the interfacial-tension-force model. This theory was used to drawn the wavy stratified flow pattern transition boundary. This paper presents a comparison between the two approaches of the interfacial-tension-force model for transition boundaries of liquid-liquid flow patterns: (i) solving the wave equation for the wave speed and using average values for wave number and wave speed; and (ii) solving the same equation for the wave number and then using a correlation for the wave speed. The results show that the second approach presents better results.
Parameter scaling toward high-energy density in a quasi-steady flow Z-pinch
Hughes, M. C.; Shumlak, U.; Nelson, B. A.; Golingo, R. P.; Claveau, E. L.; Doty, S. A.; Forbes, E. G.; Kim, B.; Ross, M. P.
2016-10-01
Sheared axial flows are utilized by the ZaP Flow Z-Pinch Experiment to stabilize MHD instabilities. The pinches formed are 50 cm long with radii ranging from 0.3 to 1.0 cm. The plasma is generated in a coaxial acceleration region, similar to a Marshall gun, which provides a steady supply of plasma for approximately 100 us. The power to the plasma is partially decoupled between the acceleration and pinch assembly regions through the use of separate power supplies. Adiabatic scaling of the Bennett relation gives targets for future devices to reach high-energy density conditions or fusion reactors. The applicability of an adiabatic assumption is explored and work is done experimentally to clarify the plasma compression process, which may be more generally polytropic. The device is capable of a much larger parameter space than previous machine iterations, allowing flexibility in the initial conditions of the compression process to preserve stability. This work is supported by DoE FES and NNSA.
Numerical study of steady turbulent flow through bifurcated nozzles in continuous casting
Najjar, Fady M.; Thomas, Brian G.; Hershey, Donald E.
1995-08-01
Bifurcated nozzles are used in continuous casting of molten steel, where they influence the quality of the cast steel slabs. The present study performs two-dimensional (2-D) and three-dimensional (3-D) simulations of steady turbulent (K- ɛ) flow in bifurcated nozzles, using a finite-element (FIDAP) model, which has been verified previously with water model experiments. The effects of nozzle design and casting process operating variables on the jet characteristics exiting the nozzle are investigated. The nozzle design parameters studied include the shape, angle, height, width, and thickness of the ports and the bottom geometry. The process operating practices include inlet velocity profile and angle as well as port curvature caused by erosion or inclusion buildup. Results show that the jet angle is controlled mainly by the port angle but is steeper with larger port area and thinner walls. The degree of swirl is increased by larger or rounder ports. The effective port area, where there is no recirculation, is increased by smaller or curved ports. Flow asymmetry is more severe with skewed or angled inlet conditions or unequal port sizes. Turbulence levels in the jet are higher with higher casting speed and smaller ports.
Comparison between RHD simulation of supercritical accretion flows and steady model with outflows
Jiao, Cheng-Liang; Takeuchi, Shun; Ohsuga, Ken
2015-01-01
We apply our two-dimensional (2D), radially self-similar steady-state accretion flow model to the analysis of hydrodynamic simulation results of supercritical accretion flows. Self-similarity is checked and the input parameters for the model calculation, such as advective factor and heat capacity ratio, are obtained from time-averaged simulation data. Solutions of the model are then calculated and compared with the simulation results. We find that in the converged region of the simulation, excluding the part too close to the black hole, the radial distribution of azimuthal velocity $v_\\phi$, density $\\rho$ and pressure $p$ basically follows the self-similar assumptions, i.e. they are roughly proportional to $r^{-0.5}$, $r^{-n}$, and $r^{-(n+1)}$, respectively, where $n\\sim0.85$ for the mass injection rate of $1000L_\\mathrm{E}/c^2$, and $n\\sim0.74$ for $3000L_\\mathrm{E}/c^2$. The distribution of $v_r$ and $v_\\theta$ agrees less with self-similarity, possibly due to convective motions in the $r\\theta$ plane. Th...
Kuntoro, Hadiyan Yusuf; Dinaryanto, Okto; Deendarlianto,; Indarto,
2015-01-01
Experimental series of stratified gas-liquid two-phase flows had been carried out in a 26 mm i.d. transparent acrylic horizontal pipe. The study was aimed to determine the interfacial wave characteristics of the flow and to develop a high quality database of it. The longitudinal section of the pipe was used as the reference section of image recording. Air and water were used as the test fluids, flowing co-currently inside the pipe. The flow behavior was recorded by using a high-speed video camera around 5 m in axial distance from the inlet pipe to ensure the fully-developed stratified gas-liquid two-phase flow. To correct the refraction due to the acrylic pipe, a correction box was employed in the visualization test section. The group of stratified smooth and wavy two-phase flows were successfully recorded and classified on the basis of the visualization study from 24 couples of test condition of superficial water and air velocities. Digital image processing technique was then used to perform quantitative ana...
Pathapati, Subbu-Srikanth; Sansalone, John J
2011-07-01
Computational fluid dynamics (CFD) is emerging as a model for resolving the fate of particulate matter (PM) by unit operations subject to rainfall-runoff loadings. However, compared to steady flow CFD models, there are greater computational requirements for unsteady hydrodynamics and PM loading models. Therefore this study examines if integrating a stepwise steady flow CFD model can reproduce PM separation by common unit operations loaded by unsteady flow and PM loadings, thereby reducing computational effort. Utilizing monitored unit operation data from unsteady events as a metric, this study compares the two CFD modeling approaches for a hydrodynamic separator (HS), a primary clarifier (PC) tank, and a volumetric clarifying filtration system (VCF). Results indicate that while unsteady CFD models reproduce PM separation of each unit operation, stepwise steady CFD models result in significant deviation for HS and PC models as compared to monitored data; overestimating the physical size requirements of each unit required to reproduce monitored PM separation results. In contrast, the stepwise steady flow approach reproduces PM separation by the VCF, a combined gravitational sedimentation and media filtration unit operation that provides attenuation of turbulent energy and flow velocity.
Numerical Studies of Two-Fluid Axisymmetric Steady-States with Flow in Ohmic NSTX-like Plasmas
Ferraro, Nathaniel; Jardin, Stephen
2008-11-01
Axisymmetric steady-states of the resistive two-fluid equations, including flow and gyroviscosity, are obtained by evolving these nonlinear equations from an initial ideal MHD equilibrium using the code M3D-C^1 [1], which has now been extended to toroidal geometry. Steady-states for high-β, inductively driven discharges in diverted NSTX geometries are studied. Excellent agreement with theoretical predictions of cross-surface Pfirsch-Schlüter flows in the axisymmetric steady-states is found. The dependence of flow velocities with resistivity is explored. It is found that in the two-fluid model, the statistical steady-state may be a fixed point, a limit cycle, or chaotic, depending on the parameters. Two-fluid terms lead to a preferred direction of toroidal rotation. The inclusion of gyroviscosity is observed to alter the character of the steady-state. The three-dimensional linear stability of simple equilibria in this two-fluid model are also explored using M3D-C^1 [2]. [1] N. Ferraro, S. Jardin. Phys. Plasmas 13:092101 (2006). [2] S. Jardin, N. Ferraro, J. Breslau, J. Chen, and M. Chance. Initial results for linear 3D Toroidal Two-Fluid stability using M3D-C1. APS DPP Conference, Dallas, TX (2008).
Khodarahmi, Iman; Shakeri, Mostafa; Sharp, M; Amini, Amir A
2010-01-01
Pressure gradient across a Gaussian-shaped 87% area stenosis phantom was estimated by solving the pressure Poisson equation (PPE) for a steady flow mimicking the blood flow through the human iliac artery. The velocity field needed to solve the pressure equation was obtained using particle image velocimetry (PIV). A steady flow rate of 46.9 ml/s was used, which corresponds to a Reynolds number of 188 and 595 at the inlet and stenosis throat, respectively (in the range of mean Reynolds number encountered in-vivo). In addition, computational fluid dynamics (CFD) simulation of the same flow was performed. Pressure drops across the stenosis predicted by PPE/PIV and CFD were compared with those measured by a pressure catheter transducer. RMS errors relative to the measurements were 17% and 10% for PPE/PIV and CFD, respectively.
Chang H. Oh; Eung S. Kim; Hee C. NO; Nam Z. Cho
2011-01-01
The U.S. Department of Energy is performing research and development that focuses on key phenomena that are important during challenging scenarios that may occur in the Next Generation Nuclear Plant (NGNP)/Generation IV very high temperature reactor (VHTR). Phenomena Identification and Ranking studies to date have identified the air ingress event, following on the heels of a VHTR depressurization, as very important. Consequently, the development of advanced air ingress-related models and verification & validation are of very high priority for the NGNP Project. Following a loss of coolant and system depressurization incident, air ingress will occur through the break, leading to oxidation of the in-core graphite structure and fuel. This study indicates that depending on the location and the size of the pipe break, the air ingress phenomena are different. In an effort to estimate the proper safety margin, experimental data and tools, including accurate multidimensional thermal-hydraulic and reactor physics models, a burn-off model, and a fracture model are required. It will also require effective strategies to mitigate the effects of oxidation, eventually. This 3-year project (FY 2008–FY 2010) is focused on various issues related to the VHTR air-ingress accident, including (a) analytical and experimental study of air ingress caused by density-driven, stratified, countercurrent flow, (b) advanced graphite oxidation experiments, (c) experimental study of burn-off in the core bottom structures, (d) structural tests of the oxidized core bottom structures, (e) implementation of advanced models developed during the previous tasks into the GAMMA code, (f) full air ingress and oxidation mitigation analyses, (g) development of core neutronic models, (h) coupling of the core neutronic and thermal hydraulic models, and (i) verification and validation of the coupled models.
Nasibullayev, I Sh; Tarasov, O S; Krekhov, A P; Kramer, L
2005-11-01
We study the homogeneous and the spatially periodic instabilities in a nematic liquid crystal layer subjected to steady plane Couette or Poiseuille flow. The initial director orientation is perpendicular to the flow plane. Weak anchoring at the confining plates and the influence of the external electric and/or magnetic field are taken into account. Approximate expressions for the critical shear rate are presented and compared with semianalytical solutions in case of Couette flow and numerical solutions of the full set of nematodynamic equations for Poiseuille flow. In particular the dependence of the type of instability and the threshold on the azimuthal and the polar anchoring strength and external fields is analyzed.
Schaffrath, A.; Kruessenberg, A.K.; Weiss, F.P.; Beyer, M.; Carl, H.; Prasser, H.M.; Schuster, J.; Schuetz, P.; Tamme, M.; Zimmermann, W. [Forschungszentrum Rossendorf e.V. (FZR) (Germany). Inst. fuer Sicherheitsforschung; Hicken, E.F. [Forschungszentrum Juelich (Germany). Inst. fuer Sicherheitsforschung und Reaktortechnik
2001-08-01
The Forschungszentrum Rossendorf (FZR) e. V. is constructing a new large-scale test facility, TOPFLOW, for thermalhydraulic single effect tests. The acronym stands for transient two phase flow test facility. It will mainly be used for the investigation of generic and applied steady state and transient two phase flow phenomena and the development and validation of models of computational fluid dynamic (CFD) codes. (orig.)
Chen, Lingen; Kan, Xuxian; Sun, Fengrui; Wu, Feng [College of Naval Architecture and Power, Naval University of Engineering, Wuhan 430033 (China)
2013-07-01
The operation of a universal steady flow endoreversible refrigeration cycle model consisting of a constant thermal-capacity heating branch, two constant thermal-capacity cooling branches and two adiabatic branches is viewed as a production process with exergy as its output. The finite time exergoeconomic performance optimization of the refrigeration cycle is investigated by taking profit rate optimization criterion as the objective. The relations between the profit rate and the temperature ratio of working fluid, between the COP (coefficient of performance) and the temperature ratio of working fluid, as well as the optimal relation between profit rate and the COP of the cycle are derived. The focus of this paper is to search the compromised optimization between economics (profit rate) and the utilization factor (COP) for endoreversible refrigeration cycles, by searching the optimum COP at maximum profit, which is termed as the finite-time exergoeconomic performance bound. Moreover, performance analysis and optimization of the model are carried out in order to investigate the effect of cycle process on the performance of the cycles using numerical example. The results obtained herein include the performance characteristics of endoreversible Carnot, Diesel, Otto, Atkinson, Dual and Brayton refrigeration cycles.
Non-Newtonian steady shear flow characteristics of waxy crude oil
黄树新; 陈鑫; 鲁传敬; 侯磊; 范毓润
2008-01-01
The experimental research on the non-Newtonian flow characteristic of a waxy crude oil was conducted through a rotational parallel-plates rheometer system.The test temperature is about 6.5 ℃ higher than its gel point.The shear stress and viscosity of the waxy crude oil show sophisticate non-Newtonian characteristics in the shear rate of 10-4-102 s-1,in which the shear stress can be divided into three parts qualitatively,i.e.stress-up region,leveling-off region,and stress-up region.This indicates that there is a yielding process in shearing for the waxy crude oil at the experimental temperature,which is similar to the yield phenomenon in thixotropy-loop test discussed by CHANG and BOGER.Furthermore,the steady shear experiment after the pre-shear process shows that the stress leveling-off region at low shear rate disappears for the waxy crude oil and the stress curve becomes a monotonic climbing one,which demonstrates that the internal structure property presenting through yielding stress at low shear rate can be changed by shearing.The experimental results also show that the internal structure of waxy crude oil presenting at low shear rate has no influence on the shear viscosity obtained at the shear rate higher than 0.1 s-1.The generalized Newtonian model is adopted to describe the shear-thinning viscosity property of the waxy crude oil at high shear rate.
Lingen Chen, Xuxian Kan, Fengrui Sun, Feng Wu
2013-01-01
Full Text Available The operation of a universal steady flow endoreversible refrigeration cycle model consisting of a constant thermal-capacity heating branch, two constant thermal-capacity cooling branches and two adiabatic branches is viewed as a production process with exergy as its output. The finite time exergoeconomic performance optimization of the refrigeration cycle is investigated by taking profit rate optimization criterion as the objective. The relations between the profit rate and the temperature ratio of working fluid, between the COP (coefficient of performance and the temperature ratio of working fluid, as well as the optimal relation between profit rate and the COP of the cycle are derived. The focus of this paper is to search the compromised optimization between economics (profit rate and the utilization factor (COP for endoreversible refrigeration cycles, by searching the optimum COP at maximum profit, which is termed as the finite-time exergoeconomic performance bound. Moreover, performance analysis and optimization of the model are carried out in order to investigate the effect of cycle process on the performance of the cycles using numerical example. The results obtained herein include the performance characteristics of endoreversible Carnot, Diesel, Otto, Atkinson, Dual and Brayton refrigeration cycles.
Front propagation in steady cellular flows: A large-deviation approach
Tzella, Alexandra; Vanneste, Jacques
2012-11-01
We examine the speed of propagation of chemical fronts modelled by the Fisher-Kolmogorov-Petrovskii-Piskunov nonlinearity in steady cellular flows. A number of predictions have been previously derived assuming small molecular diffusivity (large Péclet number) and either very slow (small Damköhler number) or very fast (large Damköhler number) chemical reactions. Here, we employ the theory of large deviations to obtain a family of eigenvalue problems from whose solution the front speed is inferred. The matched-asymptotics solution of these eigenvalue problems in the limit of large Péclet number provides approximations for the front speed for a wide range of Damköhler numbers. Two distinguished regimes are identified; in both regimes the front speed is given by a non-trivial function of the Péclet and Damköhler numbers which we determine. Earlier results, characterised by power-law dependences on these numbers, are recovered as limiting cases. The theoretical results are illustrated by a number of numerical simulations. The authors acknowledge support from EPSRC grant EP/I028072/1.
Faiez, Reza; Rezaei, Yazdan
2016-12-01
In this paper, steady-oscillatory transition of the convective flow in a Czochralski (Cz) growth system was numerically studied. In this configuration, rapid variations in density across narrow region of the flow in the vicinity of the crystallization front leads to an unstable stratification of the flow in this region. Time-dependent, finite volume method calculation of the momentum and heat transport equations shows that an instability mechanism, giving rise to the formation of cold plumes beneath the phase boundary, might be associated with an irreversible change in the convexity of the front. Dynamics of the crystallization front was found to be correlated with the periodic oscillation of the flow. It was shown that the interface inversion process occurs at a critical Reynolds number significantly (˜25%) lower than that predicted by the steady-state Cz-oxide model analysis. Consistently, the time-averaged maximum value of stream function was found to be larger than its corresponding steady-state value. This indicates that the mechanism behind the oscillatory transition of the flow has a positive feedback on the intensity of forced convection flow. These numerical results were attributed to the baroclinic instability mechanism characterized by oscillations of a cold plume appearing at the crystal periphery and descending along the symmetry axis. The time period of oscillations was found to be considerably (30-40%) decreases and, simultaneously, the inclination angle of isopycnals increases (˜48%) at a critical rotation rate of the crystal for which the interface inversion occurs.
无
2009-01-01
The steady-state dendritic growth from the undercooled binary alloy melt with the far field flow is considered. By neglecting the interface energy, interface kinetics and buoyancy effects in the system, we obtaine the steady-state solution for the case of the large Schmidt number, in terms of the multiple variable expansion method. The changes of the temperature and concentration fields, the morphology of the interface, the normalization parameter and the Peclet number of the system induced by uniform external flow are derived. The results show that, compared with the system of dendritic growth from undercooled pure melt, the convective flow in the system of growth from undercooled binary alloy has stronger effects on the morphology of the interface. Nevertheless, the shape of the interface still remains nearly a paraboloid.
CHEN MingWen; WANG ZiDong; XU JianJun
2009-01-01
The steady-state dendritic growth from the undercooled binary alloy melt with the far field flow is considered.By neglecting the interface energy,interface kinetics and buoyancy effects in the system,we obtaine the steady-state solution for the case of the large Schmidt number,in terms of the multiple variable expansion method.The changes of thtemperature and concentration fields,the morphology of the interface,the normalization parameter and the Peclet number of the system induced by uniform external flow are derived.The results show that,compared with the system of dendritic growth from undercooled pure melt,the convective flow in the system of growth from undercooled binary alloy has stronger effects on the morphology of the interface.Nevertheless,the shape of the interface still remains nearly a paraboloid.
Saeed Dinarvand
2012-01-01
Full Text Available The steady three-dimensional flow of condensation or spraying on inclined spinning disk is studied analytically. The governing nonlinear equations and their associated boundary conditions are transformed into the system of nonlinear ordinary differential equations. The series solution of the problem is obtained by utilizing the homotopy perturbation method (HPM. The velocity and temperature profiles are shown and the influence of Prandtl number on the heat transfer and Nusselt number is discussed in detail. The validity of our solutions is verified by the numerical results. Unlike free surface flows on an incline, this through flow is highly affected by the spray rate and the rotation of the disk.
Pantellini, Filippo; Griton, Léa
2016-10-01
The spatial structure of a steady state plasma flow is shaped by the standing modes with local phase velocity exactly opposite to the flow velocity. The general procedure of finding the wave vectors of all possible standing MHD modes in any given point of a stationary flow requires numerically solving an algebraic equation. We present the graphical procedure (already mentioned by some authors in the 1960's) along with the exact solution for the Alfvén mode and approximate analytic solutions for both fast and slow modes. The technique can be used to identify MHD modes in space and laboratory plasmas as well as in numerical simulations.
Chang H. Oh; Eung S. Kim
2009-12-01
The Idaho National Laboratory (INL), under the auspices of the U.S. Department of Energy, is performing research and development that focuses on key phenomena important during potential scenarios that may occur in the Next Generation Nuclear Plant (NGNP)/Gen-IV very high temperature reactor (VHTR). Phenomena Identification and Ranking Studies to date have identified that an air ingress event following on the heels of a VHTR depressurization is a very important incident. Consequently, the development of advanced air ingress-related models and verification and validation data are a very high priority for the NGNP Project. Following a loss of coolant and system depressurization incident, air will enter the core through the break, leading to oxidation of the in-core graphite structure and fuel. If this accident occurs, the oxidation will accelerate heat-up of the bottom reflector and the reactor core and will eventually cause the release of fission products. The potential collapse of the core bottom structures causing the release of CO and fission products is one of the concerns. Therefore, experimental validation with the analytical model and computational fluid dynamic (CFD) model developed in this study is very important. Estimating the proper safety margin will require experimental data and tools, including accurate multidimensional thermal-hydraulic and reactor physics models, a burn-off model, and a fracture model. It will also require effective strategies to mitigate the effects of oxidation. The results from this research will provide crucial inputs to the INL NGNP/VHTR Methods Research and Development project. The second year of this three-year project (FY-08 to FY-10) was focused on (a) the analytical, CFD, and experimental study of air ingress caused by density-driven, stratified, countercurrent flow; (b) advanced graphite oxidation experiments and modeling; (c) experimental study of burn-off in the core bottom structures, (d) implementation of advanced
Mitarai, Namiko; Nakanishi, Hiizu
2003-02-01
Dynamical behavior of steady granular flow is investigated numerically in the inelastic hard-sphere limit of the soft-sphere model. We find distinctively different limiting behaviors for the two flow regimes, i.e., the collisional flow and the frictional flow. In the collisional flow, the hard-sphere limit is straightforward; the number of collisions per particle per unit time converges to a finite value and the total contact time fraction with other particles goes to zero. For the frictional flow, however, we demonstrate that the collision rate diverges as the power of the particle stiffness so that the time fraction of the multiple contacts remains finite even in the hard-sphere limit, although the contact time fraction for the binary collisions tends to zero.
Küntz, M.; Dyskin, A.; Lavallée, P.
1998-01-01
A steady-state flow method is used to examine micromechanisms of brittle failure in 2D elastic cracked media submitted to uniaxial compressive stress. The steady-state flow experiments were conducted with an incompressible Newtonian fluid in a Hele Shaw cell. Thin linear rubber inclusions were
Om Prakash; Devendra Kumar; Y K Dwivedi
2012-12-01
The paper investigates the effects of heat transfer in MHD flow of viscoelastic stratified fluid in porous medium on a parallel plate channel inclined at an angle . A laminar convection flow for incompressible conducting fluid is considered. It is assumed that the plates are kept at different temperatures which decay with time. The partial differential equations governing the flow are solved by perturbation technique. Expressions for the velocity of fluid and particle phases, temperature field, Nusselt number, skin friction and flow flux are obtained within the channel. The effects of various parameters like stratification factor, magnetic field parameter, Prandtl number on temperature field, heat transfer, skin friction, flow flux, velocity for both the fluid and particle phases are displayed through graphs and discussed numerically.
Behrens, Geoffrey; Agarwal, Ramesh; Moghaddam, Abbas N.; Choi, Eric T.; Amini, Amir A.
2003-11-01
A commercially available numerical flow solver "FLUENT" is employed in simulation of blood flow through vascular stenoses. Fluid properties are set to match those of the blood mimicking fluid used in flow phantom experiments at the Washington University School of Medicine. Computational results are compared for steady flow through axisymmetric and three-dimensional phantoms modeling mild to severe stenonses with the data collected using Phase Contrast Magnetic Resonance Imaging (PC-MRI) technique by colleagues in the CVIA laboratory at Washington University School of Medicine. Computations are also performed for pulsatile flow through vascular stenoses. Comparisons of PC-MRI and FLUENT output data show qualitative agreement in streamline patterns and good quantitative agreement for pressure drop across the stenoses.
Marios S. Valavanides
2016-02-01
Full Text Available Steady-state two-phase flow in porous media is a process whereby a wetting phase displaces a non-wetting phase within a pore network. It is an off-equilibrium stationary process—in the sense that it is maintained in dynamic equilibrium at the expense of energy supplied to the system. The efficiency of the process depends on its spontaneity, measurable by the rate of global entropy production. The latter has been proposed to comprise two components: the rate of mechanical energy dissipation at constant temperature (a thermal entropy component, Q/T, in the continuum mechanics scale and the configurational entropy (a Boltzmann–Gibbs entropy component, klnW, due to the existence of a canonical ensemble of flow configurations, physically admissible to the externally imposed macrostate conditions. Here, we propose an analytical model to account the number of microstates, lnW, in two-phase flows in pore networks. Combinatorial analysis is implemented to evaluate the number of identified microstates per physically admissible internal flow arrangement, compatible with the imposed steady-state flow conditions. Then, Stirling’s approximation is applied to downscale the large factorial numbers. Finally, the number of microstates is estimated by contriving an appropriate mixing scheme over the canonical ensemble of the physically admissible flow configurations. Indicative computations are furnished.
Pasch, James Jay
2017-02-07
A method of resolving a balanced condition that generates control parameters for start-up and steady state operating points and various component and cycle performances for a closed split flow recompression cycle system. The method provides for improved control of a Brayton cycle thermal to electrical power conversion system. The method may also be used for system design, operational simulation and/or parameter prediction.
Shibahara, M.; Fukuda, K.; Liu, Q. S.; Hata, K.
2017-03-01
Steady and transient heat transfer coefficients for water flowing in small tubes with exponentially increasing heat inputs were measured. Platinum tubes with inner diameters of 1.0 and 2.0 mm were used as test tubes, which were mounted vertically in the experimental water loop. In the experiment, the upward flow velocity ranged from 2 to 16 m/s, and the corresponding Reynolds numbers ranged from 4.77 × 103 to 9.16 × 104 at the inlet liquid temperatures ranged from 298 to 343 K. The heat generation rate exponentially increased with the function. The period of the heat generation rate ranged from 24 ms to 17.5 s. Experimental results indicate that steady heat transfer coefficients decreased with the increase in the inner diameter of the small tube. Moreover, the ratio of bulk viscosity to near-wall viscosity of water increased with the rise in surface temperature of the vertical tube. From the experimental data, correlations of steady-state heat transfer for inner diameters of 1.0 and 2.0 mm were obtained. The heat transfer coefficient increased with decreasing the period of the heat generation rate as the flow velocity decreased. Moreover, the Nusselt number under the transient condition was affected by the Fourier number and the Reynolds number.
Shibahara, M.; Fukuda, K.; Liu, Q. S.; Hata, K.
2016-06-01
Steady and transient heat transfer coefficients for water flowing in small tubes with exponentially increasing heat inputs were measured. Platinum tubes with inner diameters of 1.0 and 2.0 mm were used as test tubes, which were mounted vertically in the experimental water loop. In the experiment, the upward flow velocity ranged from 2 to 16 m/s, and the corresponding Reynolds numbers ranged from 4.77 × 103 to 9.16 × 104 at the inlet liquid temperatures ranged from 298 to 343 K. The heat generation rate exponentially increased with the function. The period of the heat generation rate ranged from 24 ms to 17.5 s. Experimental results indicate that steady heat transfer coefficients decreased with the increase in the inner diameter of the small tube. Moreover, the ratio of bulk viscosity to near-wall viscosity of water increased with the rise in surface temperature of the vertical tube. From the experimental data, correlations of steady-state heat transfer for inner diameters of 1.0 and 2.0 mm were obtained. The heat transfer coefficient increased with decreasing the period of the heat generation rate as the flow velocity decreased. Moreover, the Nusselt number under the transient condition was affected by the Fourier number and the Reynolds number.
Zhang, Wei; Markfort, Corey; Porté-Agel, Fernando
2014-11-01
Turbulent flows over complex surface topography have been of great interest in the atmospheric science and wind engineering communities. The geometry of the topography, surface roughness and temperature characteristics as well as the atmospheric thermal stability play important roles in determining momentum and scalar flux distribution. Studies of turbulent flow over simplified topography models, under neutrally stratified boundary-layer conditions, have provided insights into fluid dynamics. However, atmospheric thermal stability has rarely been considered in laboratory experiments, e.g., wind-tunnel experiments. Series of wind-tunnel experiments of thermally-stratified boundary-layer flow over a surface-mounted 2-D block, in a well-controlled boundary-layer wind tunnel, will be presented. Measurements using high-resolution PIV, x-wire/cold-wire anemometry and surface heat flux sensors were conducted to quantify the turbulent flow properties, including the size of the recirculation zone, coherent vortex structures and the subsequent boundary layer recovery. Results will be shown to address thermal stability effects on momentum and scalar flux distribution in the wake, as well as dominant mechanism of turbulent kinetic energy generation and consumption. The authors gratefully acknowledge funding from the Swiss National Foundation (Grant 200021-132122), the National Science Foundation (Grant ATM-0854766) and NASA (Grant NNG06GE256).
Fractal Dimension of Cohesive Sediment Flocs at Steady State under Seven Shear Flow Conditions
Zhongfan Zhu
2015-08-01
Full Text Available The morphological properties of kaolin flocs were investigated in a Couette-flow experiment at the steady state under seven shear flow conditions (shear rates of 5.36, 9.17, 14, 24, 31, 41 and 53 s−1. These properties include a one-dimensional (1-D fractal dimension (D1, a two-dimensional (2-D fractal dimension (D2, a perimeter-based fractal dimension (Dpf and an aspect ratio (AR. They were calculated based on the projected area (A, equivalent size, perimeter (P and length (L of the major axis of the floc determined through sample observation and an image analysis system. The parameter D2, which characterizes the relationship between the projected area and the length of the major axis using a power function, , increased from 1.73 ± 0.03, 1.72 ± 0.03, and 1.75 ± 0.04 in the low shear rate group (G = 5.36, 9.17, and 14 s−1 to 1.92 ± 0.03, 1.82 ± 0.02, 1.85 ± 0.02, and 1.81 ± 0.02 in the high shear rate group (24, 31, 41 and 53 s−1, respectively. The parameter D1 characterizes the relationship between the perimeter and length of the major axis by the function and decreased from 1.52 ± 0.02, 1.48 ± 0.02, 1.55 ± 0.02, and 1.63 ± 0.02 in the low shear group (5.36, 9.17, 14 and 24 s−1 to 1.45 ± 0.02, 1.39 ± 0.02, and 1.39 ± 0.02 in the high shear group (31, 41 and 53 s−1, respectively. The results indicate that with increasing shear rates, the flocs become less elongated and that their boundary lines become tighter and more regular, caused by more breakages and possible restructurings of the flocs. The parameter Dpf, which is related to the perimeter and the projected area through the function , decreased as the shear rate increased almost linearly. The parameter AR, which is the ratio of the length of the major axis and equivalent diameter, decreased from 1.56, 1.59, 1.53 and 1.51 in the low shear rate group to 1.43, 1.47 and 1.48 in the high shear rate group. These changes in Dpf and AR show that the flocs become less
Pathak, M. G.; Helvensteijn, B. P.; Patel, V. C.; Ghiaasiaan, S. M.; Mulcahey, T. I.; Kashani, A.; Feller, J. R.
2014-01-01
The regenerator, typically a microporous structure that is subject to periodic flow of a cryogenic fluid, is a critical component of pulse tube or Stirling cryocoolers, which are widely used for high-demand aerospace and defense applications. In this investigation, experiments were conducted in which steady and oscillatory flows of helium were imposed on ErPr rare-Earth regenerator filler material and mass flow and pressure drop data were recorded under ambient temperature conditions. A computational fluid dynamics (CFD)-assisted method was applied for the analysis and interpretation of the experimental data. The permeability and inertial coefficients that lead to agreement between the experimental data and computational simulations were iteratively obtained. The Darcy permeability and Forchheimer inertial coefficients were obtained and were found to be functions of the system charge pressure, operating frequency, and compressor piston stroke within the studied range of interest. The results also exhibit that the periodic flow hydrodynamic resistance parameters are in general different than steady flow parameters.
Efficient computation of steady, 3D water-wave patterns, application to hovercraft-type flows
M.R. Lewis; B. Koren (Barry)
2002-01-01
textabstractNumerical methods for the computation of stationary free surfaces is the subject of much current research in computational engineering. The present report is directed towards free surfaces in maritime engineering. Of interest here are the long steady waves generated by hovercraft and
Efficient computation of steady, 3D water-wave patterns, application to hovercraft-type flows
Lewis, M.R.; Koren, B.
2002-01-01
Numerical methods for the computation of stationary free surfaces is the subject of much current research in computational engineering. The present report is directed towards free surfaces in maritime engineering. Of interest here are the long steady waves generated by hovercraft and ships, the grav
Takeshi Kitano; S A R Hashmi; Navin Chand
2004-10-01
An experimental study was conducted to observe the effects of parallel-superposed flow condition on viscoelastic properties of LLDPE, Kevlar fibre reinforced LLDPE and hybrid of short glass fibre and Kevlar fibre reinforced LLDPE. Parallel-plate rheometer was employed for these tests. Rheological parameters such as loss modulus (″) and dynamic viscosity (′) do not vary significantly on superposing steady state shear with oscillatory shear in the studied range of experiment at 185°C in un-reinforced LLDPE. Kevlar fibre reinforced LLDPE and Kevlar/glass fibre reinforced LLDPE showed significant changes in the flow behaviour under various sets of superposed conditions. Storage modulus (′), and ″ become highly sensitive to low oscillatory angular frequencies () under superposed conditions. These curves show two different regions with increased value. At low values, parameters ′ and ″ change sharply reaching a certain value, thereafter, changes are moderate with increased . In case of ′ a maxima is observed, position of which, depends upon the value of steady shear rate. Maxima shifts towards higher frequencies with the increased steady shear rate.
A closed-form solution for steady-state coupled phloem/xylem flow using the Lambert-W function.
Hall, A J; Minchin, P E H
2013-12-01
A closed-form solution for steady-state coupled phloem/xylem flow is presented. This incorporates the basic Münch flow model of phloem transport, the cohesion model of xylem flow, and local variation in the xylem water potential and lateral water flow along the transport pathway. Use of the Lambert-W function allows this solution to be obtained under much more general and realistic conditions than has previously been possible. Variation in phloem resistance (i.e. viscosity) with solute concentration, and deviations from the Van't Hoff expression for osmotic potential are included. It is shown that the model predictions match those of the equilibrium solution of a numerical time-dependent model based upon the same mechanistic assumptions. The effect of xylem flow upon phloem flow can readily be calculated, which has not been possible in any previous analytical model. It is also shown how this new analytical solution can handle multiple sources and sinks within a complex architecture, and can describe competition between sinks. The model provides new insights into Münch flow by explicitly including interactions with xylem flow and water potential in the closed-form solution, and is expected to be useful as a component part of larger numerical models of entire plants. © 2013 John Wiley & Sons Ltd.
ZHANG Da-Lin; QIU Sui-Zheng; LIU Chang-Liang; SU Guang-Hui
2008-01-01
The Molten Salt Reactor (MSR),one of the‘Generation Ⅳ'concepts,is a liquid-fuel reactor,which is different from the conventional reactors using solid fissile materials due to the flow effect of fuel salt.The study on its neutronice considering the fuel salt flow,which is the base of the thermal-hydraulic calculation and safety analysis,must be done.In this paper,the theoretical model on neutronics under steady condition for a single-liquid-fueled MSR is conducted and calculated by numerical method.The neutronics model consists of two group neutron diffusion equations for fast and thermal neutron fluxes,and balance equations for six-group delayed neutron precursors considering the flow effect of fuel salt. The spatial discretization of the above models is based on the finite volume method,and the discretization equations are computed by the source iteration method.The distributions of neutron fluxes and the distributions of the delayed neutron precursors in the core are obtained.The numerical calculated results show that,the fuel salt flow has little effect on the distribution of fast and thermal neutron fluxes and the effective multiplication factor;however,it affects the distribution of the delayed neutron precursors significantly,especially the long-lived one.In addition,it could be found that the delayed neutron precursors influence the nentronics slightly under the steady condition.
Fractal Dimension of Cohesive Sediment Flocs at Steady State under Seven Shear Flow Conditions
Zhu, Zhongfan; Yu, Jingshan; Wang, Hongrui; Dou, Jie; Wang, Cheng
2015-08-01
The morphological properties of kaolin flocs were investigated in a Couetteflow experiment at the steady state under seven shear flow conditions (shear rates of 5.36, 9.17, 14, 24, 31, 41 and 53 s-1). These properties include a one-dimensional (1-D) fractal dimension (D1), a two-dimensional (2-D) fractal dimension (D2), a perimeter-based fractal dimension (Dpf) and an aspect ratio (AR). They were calculated based on the projected area (A), equivalent size, perimeter (P) and length (L) of the major axis of the floc determined through sample observation and an image analysis system. The parameter D2, which characterizes the relationship between the projected area and the length of the major axis using a power function, , increased from 1.73 ± 0.03, 1.72 ± 0.03, and 1.75 ± 0.04 in the low shear rate group (G = 5.36, 9.17, and 14 s-1) to 1.92 ± 0.03, 1.82 ± 0.02, 1.85 ± 0.02, and 1.81 ± 0.02 in the high shear rate group (24, 31, 41 and 53 s-1), respectively. The parameter D1 characterizes the relationship between the perimeter and length of the major axis by the function and decreased from 1.52 ± 0.02, 1.48 ± 0.02, 1.55 ± 0.02, and 1.63 ± 0.02 in the low shear group (5.36, 9.17, 14 and 24 s-1) to 1.45 ± 0.02, 1.39 ± 0.02, and 1.39 ± 0.02 in the high shear group (31, 41 and 53 s-1), respectively. The results indicate that with increasing shear rates, the flocs become less elongated and that their boundary lines become tighter and more regular, caused by more breakages and possible restructurings of the flocs. The parameter Dpf, which is related to the perimeter and the projected area through the function , decreased as the shear rate increased approximately linearly. The parameter AR, which is the ratio of the length of the major axis and equivalent diameter, decreased from 1.56, 1.59, 1.53 and 1.51 in the low shear rate group to 1.43, 1.47 and 1.48 in the high shear rate group. These changes in Dpf and AR show that the flocs become less convoluted and
Hossain, Delowar; Samad, Abdus; Alam, Mahmud
2017-06-01
The ion-slip effects on unsteady MHD free convection flow past an infinite vertical porous plate with the effect of temperature stratified porous medium in a rotating system with viscous dissipation and Joule heating has been studied numerically. Introducing a time dependent suction to the plate, a similarity procedure has been adopted by taking a time dependent similarity parameter. The governing differential equations are transformed by introducing usual similarity variables. The resultant equations are solved numerically using Runge-Kutta method along with shooting technique. Resulting non-dimensional velocity and temperature profiles are then presented graphically for different values of the parameters entering into the problem.
Zeegers, Jos; Ende, van den Dirk; Blom, Cor; Altena, Egbert G.; Beukema, Gerrit J.; Mellema, Jorrit
1995-01-01
A new instrument to carry out complex viscosity measurements in equilibrium and in a steady shear flow has been developed. A small amplitude harmonic excitation is superimposed orthogonally to the steady shear rate component. It is realized by a thin-walled cylinder, which oscillates in the axial di
Talmage, Gita; Walker, John S.; Brown, Samuel H.; Sondergaard, Neal A.
1993-09-01
In homopolar motors and generators, large dc electric currents pass through the sliding electrical contacts between rotating copper disks (rotors) and static copper surfaces shrouding the rotor tips (stators). A liquid metal in the small radial gap between the rotor tip and concentric stator surface can provide a low-resistance, low-drag electrical contact. Since there is a strong magnetic field in the region of the electrical contacts, there are large electromagnetic body forces on the liquid metal. The primary, azimuthal motion consists of simple Couette flow, plus an electromagnetically driven flow with large extremes of the azimuthal velocity near the rotor corners. The secondary flow involves the radial and axial velocity components, is driven by the centrifugal force associated with the primary flow, and is opposed by the electromagnetic body force, so that the circulation varies inversely as the square of the magnetic-field strength. Three flow regimes are identified as the angular velocity Ω of the rotor is increased. For small Ω, the primary flow is decoupled from the secondary flow. As Ω increases, the secondary flow begins to convect the azimuthal-velocity peaks radially outward, which in turn changes the centrifugal force driving the secondary flow. At some critical value of Ω, the flow becomes periodic through the coupling of the primary and secondary flows. The azimuthal-velocity peaks begin to move radially in and out with an accompanying oscillation in the secondary-flow strength.
Numerical Solution of Compressible Steady Flows around the RAE 2822 Airfoil
Kryštůfek, P.; Kozel, K.
2014-03-01
The article presents results of a numerical solution of subsonic, transonic and supersonic flows described by the system of Navier-Stokes equations in 2D laminar compressible flows around the RAE 2822 airfoil. Authors used FVM multistage Runge-Kutta method to numerically solve the flows around the RAE 2822 airfoil.
Lashkar Ara, A., E-mail: Lashkarara@iust.ac.i [Department of Electrical Engineering, Iran University of Science and Technology, Narmak, Tehran, P.O. Box 1684613114 (Iran, Islamic Republic of); Kazemi, A., E-mail: Kazemi@iust.ac.i [Department of Electrical Engineering, Iran University of Science and Technology, Tehran (Iran, Islamic Republic of); Nabavi Niaki, S.A., E-mail: nabavi.niaki@utoronto.c [Department of Electrical and Computer Engineering, University of Toronto, Toronto, ON, M5 S 3G4 (Canada)
2011-02-15
In this paper a hybrid configuration of a FACTS controller called Optimal Unified Power Flow Controller (OUPFC) which is composed of a mechanical phase shifting transformer augmented with a small scale Unified Power Flow Controller (UPFC) is introduced. The steady-state model of OUPFC is developed as a power injection model. This model is used to develop an Optimal Power Flow (OPF) algorithm including OUPFC to find the optimum number, location, and settings of OUPFCs to minimize the total fuel cost and power losses. Simulation results are presented for the IEEE 14-, 30-, and 118-bus systems. The optimization method is numerically solved using Matlab and General Algebraic Modelling System (GAMS) software environments. The results demonstrate the effectiveness of the proposed approach to solve the optimal location and settings of OUPFCs incorporated in OPF problem and improve the power system operation. Furthermore, the ability of OUPFC to optimize the objective functions is compared to that of PST and UPFC.
Zhao, X.
1992-01-01
We show that the 25 November 1978 shock pair was caused by the interaction of a fast steady flow with a slow coronal mass ejection in interplanetary space (ICME). It is suggested that the slow ICME may be disconnected from the sun. In addition, a new method to infer the shock angle and Mach number from the observed upstream plasma beta and the jump ratios of proton density and magnetic flux density across a shock is described.
Rassi, Erik M.; Codd, Sarah L.; Seymour, Joseph D.
2011-01-01
Flow in porous media and the resultant hydrodynamics are important in fields including but not limited to the hydrology, chemical, medical and petroleum industries. The observation and understanding of the hydrodynamics in porous media are critical to the design and optimal utilization of porous media, such as those seen in trickle-bed reactors, medical filters, subsurface flows and carbon sequestration. Magnetic resonance (MR) provides for a non-invasive technique that can probe the hydrodynamics on pore and bulk scale lengths; many previous works have characterized fully saturated porous media, while rapid MR imaging (MRI) methods in particular have previously been applied to partially saturated flows. We present time- and ensemble-averaged MR measurements to observe the effects on a bead pack partially saturated with air under flowing water conditions. The 10 mm internal diameter bead pack was filled with 100 μm borosilicate glass beads. Air was injected into the bead pack as water flowed simultaneously through the sample at 25 ml h-1. The initial partially saturated state was characterized with MRI density maps, free induction decay (FID) experiments, propagators and velocity maps before the water flow rate was increased incrementally from 25 to 500 ml h-1. After the maximum flow rate of 500 ml h-1, the MRI density maps, FID experiments, propagators and velocity maps were repeated and compared to the data taken before the maximum flow rate. This work shows that a partially saturated single-phase flow has global flow dynamics that return to characteristic flow statistics once a steady-state high flow rate has been reached. This high flow rate pushed out a significant amount of the air in the bead pack and caused the return of a preferential flow pattern. Velocity maps indicated that local flow statistics were not the same for the before and after blow out conditions. It has been suggested and shown previously that a flow pattern can return to
Feedback control of unstable steady states of flow past a flat plate using reduced-order estimators
Ahuja, Sunil
2009-01-01
We present an estimator-based control design procedure for flow control, using reduced-order models of the governing equations, linearized about a possibly unstable steady state. The reduced models are obtained using an approximate balanced truncation method that retains the most controllable and observable modes of the system. The original method is valid only for stable linear systems, and we present an extension to unstable linear systems. The dynamics on the unstable subspace are represented by projecting the original equations onto the global unstable eigenmodes, assumed to be small in number. A snapshot-based algorithm is developed, using approximate balanced truncation, for obtaining a reduced-order model of the dynamics on the stable subspace. The proposed algorithm is used to study feedback control of 2-D flow over a flat plate at a low Reynolds number and at large angles of attack, where the natural flow is vortex shedding, though there also exists an unstable steady state. For control design, we de...
Cho, Seong-Mook; Kim, Seon-Hyo; Thomas, Brian G
2014-01-01
... steady steel slab casting. In Part II of this two-part article, the effect of applying a static magnetic field on stabilizing the transient flow is investigated by modeling a double-ruler Electro-Magnetic Braking (EMBr...
Gabriel, Stephan Gerhard
2015-07-01
A stratified counter-current two-phase gas/liquid flow can occur in various technical systems. In the past investigations have mainly been motivated by the possible occurrence of these flows in accident scenarios of nuclear light water-reactors and in numerous applications in process engineering. However, the precise forecast of flow parameters, is still challenging, for instance due to their strong dependency on the geometric boundary conditions. A new approach which uses CFD methods (Computational Fluid Dynamics) promises a better understanding of the flow phenomena and simultaneously a higher scalability of the findings. RANS methods (Reynolds Averaged Navier Stokes) are preferred in order to compute industrial processes and geometries. A very deep understanding of the flow behavior and equation systems based on real physics are necessary preconditions to develop the equation system for a reliable RANS approach with predictive power. Therefore, local highly resolved, experimental data is needed in order to provide and validate the required turbulence and phase interaction models. The central objective of this work is to provide the data needed for the code development for these unsteady, turbulent and three-dimensional flows. Experiments were carried out at the WENKA facility (Water Entrainment Channel Karlsruhe) at the Karlsruhe Institute of Technology (KIT). The work consists of a detailed description of the test-facility including a new bended channel, the measurement techniques and the experimental results. The characterization of the new channel was done by flow maps. A high-speed imaging study gives an impression of the occurring flow regimes, and different flow phenomena like droplet separation. The velocity distributions as well as various turbulence values were investigated by particle image velocimetry (PIV). In the liquid phase fluorescent tracer-particles were used to suppress optical reflections from the phase surface (fluorescent PIV, FPIV
Marios S. Valavanides; Tryfon Daras
2016-01-01
Steady-state two-phase flow in porous media is a process whereby a wetting phase displaces a non-wetting phase within a pore network. It is an off-equilibrium stationary process—in the sense that it is maintained in dynamic equilibrium at the expense of energy supplied to the system. The efficiency of the process depends on its spontaneity, measurable by the rate of global entropy production. The latter has been proposed to comprise two components: the rate of mechanical energy dissipation at...
Numerical Solution of Inviscid Compressible Steady Flows around the RAE 2822 Airfoil
Kryštůfek, P.; Kozel, K.
2015-05-01
The article presents results of a numerical solution of subsonic, transonic and supersonic flows described by the system of Euler equations in 2D compressible flows around the RAE 2822 airfoil. Authors used FVM multistage Runge-Kutta method to numerically solve the flows around the RAE 2822 airfoil. The results are compared with the solution using the software Ansys Fluent 15.0.7.
A dual-phantom system for validation of velocity measurements in stenosis models under steady flow.
Blake, James R; Easson, William J; Hoskins, Peter R
2009-09-01
A dual-phantom system is developed for validation of velocity measurements in stenosis models. Pairs of phantoms with identical geometry and flow conditions are manufactured, one for ultrasound and one for particle image velocimetry (PIV). The PIV model is made from silicone rubber, and a new PIV fluid is made that matches the refractive index of 1.41 of silicone. Dynamic scaling was performed to correct for the increased viscosity of the PIV fluid compared with that of the ultrasound blood mimic. The degree of stenosis in the models pairs agreed to less than 1%. The velocities in the laminar flow region up to the peak velocity location agreed to within 15%, and the difference could be explained by errors in ultrasound velocity estimation. At low flow rates and in mild stenoses, good agreement was observed in the distal flow fields, excepting the maximum velocities. At high flow rates, there was considerable difference in velocities in the poststenosis flow field (maximum centreline differences of 30%), which would seem to represent real differences in hydrodynamic behavior between the two models. Sources of error included: variation of viscosity because of temperature (random error, which could account for differences of up to 7%); ultrasound velocity estimation errors (systematic errors); and geometry effects in each model, particularly because of imperfect connectors and corners (systematic errors, potentially affecting the inlet length and flow stability). The current system is best placed to investigate measurement errors in the laminar flow region rather than the poststenosis turbulent flow region.
Interpolation-based reduced-order modelling for steady transonic flows via manifold learning
Franz, Thomas; Zimmermann, Ralf; Goertz, Stefan
2014-01-01
This paper presents a parametric reduced-order model (ROM) based on manifold learning (ML) for use in steady transonic aerodynamic applications. The main objective of this work is to derive an efficient ROM that exploits the low-dimensional nonlinear solution manifold to ensure an improved...... that has the ability to predict approximate CFD solutions at untried parameter combinations, Isomap is coupled with an interpolation method to capture the variations in parameters like the angle of attack or the Mach number. Furthermore, an approximate local inverse mapping from the reduced...
Analysis on Non-Uniform Flow in Steam Generator During Steady State Natural Circulation Cooling
Susyadi
2007-07-01
Full Text Available Investigation on non uniform flow behavior among U-tube in steam generator during natural circulation cooling has been conducted using RELAP5. The investigation is performed by modeling the steam generator into multi channel models, i.e. 9-tubes model. Two situations are implemented, high pressure and low pressure cases. Using partial model, the calculation simulates situation similar to the natural circulation test performed in LSTF. The imposed boundary conditions are flow rate, quality, pressure of the primary side, feed water temperature, steam generator liquid level, and pressure in the secondary side. Calculation result shows that simulation using model with nine tubes is capable to capture important non-uniform phenomena such as reverse flow, fill-and-dump, and stagnant vertical stratification. As a result of appropriate simulation of non uniform flow, the calculated steam generator outlet flow in the primary loop is stable as observed in the experiments. The results also clearly indicate the importance of simulation of non-uniform flow in predicting both the flow stability and heat transfer between the primary and secondary side. In addition, the history of transient plays important role on the selection of the flow distribution among tubes. © 2007 Atom Indonesia. All rights reserved
Application of Potential Theory to Steady Flow Past Two Cylinders in Tandem Arrangement
Yangyang Gao
2014-01-01
Full Text Available The wake flow patterns associated with flow past a cylinder and a cylinder-pair in tandem configuration are revisited, compared, and evaluated with respect to the streamline patterns generated based on potential flow theory and superposition of various potential flow elements. The wakes, which are vortex shedding in the lee of the cylinder(s, are reproduced by placing pairs of equal but opposite circulation elements in the potential flow field. The strength of the circulation elements determines the size of the vortices produced. The streamline patterns of flow past a pair of unequal cylinders in tandem configuration provide an indirect means to establish the threshold condition for the wake transition from that of a single bluff body to alternating reattachment behavior. This threshold condition is found to be a function of the diameter ratio, d/D (diameters d and D, d≤D , spacing ratio, L/D (centre-to-centre distance, L, to cylinder diameter, D, and equivalent incident flow speed, U. A unique functional relationship f (L/D, d/D, U of this threshold condition is established.
Degani, D.
1984-01-01
A numerical algorithm that is second-order accurate in time has been developed for the conjugated problem of a separated, compressible flow field and a conductive solid body. The full two-dimensional time-dependent Navier-Stokes equations are coupled with the time-dependent energy equation for the solid body and are solved simultaneously. using implicit algorithms. The energy equation for the solid body may include arbitrarily distributed heat sources. The algorithm has been exmined for the case of two-dimensional supersonic compression-corner interaction, with a heat source embedded in the wall in the vicinity of the separation bubble and the attached boundary layer. The effect of the heat source on the flow field is studied for steady and transient cases.
Papaloizou, J C B
2004-01-01
We carry out a general study of the stability of astrophysical flows that appear steady in a uniformly rotating frame. Such a flow might correspond to a stellar pulsation mode or an accretion disk with a free global distortion giving it finite eccentricity. We consider perturbations arbitrarily localized in the neighbourhood of unperturbed fluid streamlines.When conditions do not vary around them, perturbations take the form of oscillatory inertial or gravity modes. However, when conditions do vary so that a circulating fluid element is subject to periodic variations, parametric instability may occur. For nearly circular streamlines, the dense spectra associated with inertial or gravity modes ensure that resonance conditions can always be satisfied when twice the period of circulation round a streamline falls within. We apply our formalism to a differentially rotating disk for which the streamlines are Keplerian ellipses, with free eccentricity up to 0.7, which do not precess in an inertial frame. We show tha...
李林娟; 郑金海; 彭于轩; 张继生; 吴修广
2015-01-01
Horizontal axis tidal turbines have attracted more and more attentions nowadays, because of their convenience and low expense in construction and high efficiency in extracting tidal energy. The present study numerically investigates the flow motion and performance of a horizontal axis tidal turbine with a supporting vertical cylinder under steady current. In the numerical model, the continuous equation and incompressible Reynolds-averaged Navier-Stokes equations are solved, and the volume of fluid method is employed to track free surface motion. The RNG k-εmodel is adopted to calculate turbulence transport while the fractional area/volume obstacle representation method is used to describe turbine characteristics and movement. The effects of installation elevation of tidal turbine and inlet velocity on the water elevation, and current velocity, rotating speed and resultant force on turbine are discussed. Based on the comparison of the numerical results, a better understanding of flow structure around horizontal axis tidal turbine and turbine performance is achieved.
P. D. Williams
2004-01-01
Full Text Available We report on a numerical study of the impact of short, fast inertia-gravity waves on the large-scale, slowly-evolving flow with which they co-exist. A nonlinear quasi-geostrophic numerical model of a stratified shear flow is used to simulate, at reasonably high resolution, the evolution of a large-scale mode which grows due to baroclinic instability and equilibrates at finite amplitude. Ageostrophic inertia-gravity modes are filtered out of the model by construction, but their effects on the balanced flow are incorporated using a simple stochastic parameterization of the potential vorticity anomalies which they induce. The model simulates a rotating, two-layer annulus laboratory experiment, in which we recently observed systematic inertia-gravity wave generation by an evolving, large-scale flow. We find that the impact of the small-amplitude stochastic contribution to the potential vorticity tendency, on the model balanced flow, is generally small, as expected. In certain circumstances, however, the parameterized fast waves can exert a dominant influence. In a flow which is baroclinically-unstable to a range of zonal wavenumbers, and in which there is a close match between the growth rates of the multiple modes, the stochastic waves can strongly affect wavenumber selection. This is illustrated by a flow in which the parameterized fast modes dramatically re-partition the probability-density function for equilibrated large-scale zonal wavenumber. In a second case study, the stochastic perturbations are shown to force spontaneous wavenumber transitions in the large-scale flow, which do not occur in their absence. These phenomena are due to a stochastic resonance effect. They add to the evidence that deterministic parameterizations in general circulation models, of subgrid-scale processes such as gravity wave drag, cannot always adequately capture the full details of the nonlinear interaction.
Metri, Prashant G.; Narayana, Mahesha; Silvestrov, Sergei
2017-01-01
In this paper, we examine the hydromagnetic boundary layer flow and heat transfer characteristics of a laminar nanoliquid film over an unsteady stretching sheet is presented. The highly nonlinear partial differential equations governing flow and heat transport are simplified using similarity transformation. The analytical solutions of the resulting ODEs are obtained for some special case of nano liquid film using hypergeometric power series functions, and from which the analytical solutions of the original problem are presented. The influence of pertinent parameters such as the magnetic parameter, the solid volume fraction of nanoparticles and the type of nanofluid on the flow, heat transfer, Nusselt number and skin friction coefficient is discussed analytically.
Parachute gore shape and flow visualization during transient and steady-state conditions.
Dereng, V. G.
1973-01-01
Single parachute gore segments were tested in an experimental wind tunnel having a unique 'V' splitter plate test section with a glass panel on the near side and a grid of orifices for smoke injection on the back panel. The parachute gore shape and flow patterns were viewed in cross section during the inflation process and also during changing flow conditions as would occur with rapid reduction of payload weight. Observations of flow during inflation revealed a transient internal counterflow and the formation and degeneration of several trailing vortices. Gore shapes observed compared well with those of free flight.
Steadiness of a “water bell” surface to a destruction at a flow around of the thin rods assembly
Slesareva Ekaterina
2015-01-01
Full Text Available The experimental research of hydrodynamic stability of a dome-shaped film liquid at a flow around a thin plate has been carried out. Experiments were carry out with a film in shape a «water bell». The film was formed by a leak-in jet of water width 10 mm on a hard disk with diameter 14.5 mm. The width of a plate ζ changed from 0.05 to 3.5 mm. The plate placed along or across relative to the vector of velocity of a liquid in a film. Experiments have shown, that stability of a film of liquid at a flow around the plate is defined by velocity of water and a thickness of a film δ in front of the rod. It is shown, that for the appointed value of Reynolds number Reδ probably continuous flow at a flow around the plate, if Weber number Weζ less than threshold value. The criterion of steadiness a film of the «water bell» by a surface destruction at a flow around the rod is determined on the transverse size of the rod relative to the vector of velocity of a liquid.
Cimorelli, L.; Cozzolino, L.; D'Aniello, A.; Morlando, F.; Pianese, D.; Singh, V. P.
2016-07-01
In this paper, a new numerical model for the simulation of constituent transport in both steady and unsteady flow conditions is presented. The transport model is a routing procedure in which the advection process is solved by means of the Lagrangian coordinate transformation, while the dispersion process is approximated within each time step by means of the convolution principle, exploiting a multilinear procedure. In order to facilitate the application of the Lagrangian coordinate transformation during unsteady flow conditions, the unsteady velocity field corresponding to the linearized parabolic approximation of the Saint Venant Equations is provided, taking into account appropriate boundary conditions. Finally, classic BOD-DO relationships are embedded into the routing procedure in order to perform water quality applications with reactive constituents. The model is first demonstrated with respect to a numerical water quality model in both steady and unsteady hydraulic conditions, and is then applied to two real-world cases. Because of its characteristics, the proposed model seems suitable for real time forecast of pollutant concentrations when an emergency event occurs, or for water quality management in real rivers.
1984-05-16
Ranque - Hilsch ( vortex tube ) effect." 5. List of Professional Personnel Associated with the Research The recipient of advanced degrees awarded in...SUB. GR. AIRCRAFT ENGINES RANQUE - HILSCH EFFECT i UNSTEADY FLOW ENERGY SEPARATION IN FLOW(KARMAN VORTEX STREET ORGAINIZED REYNOLDS STRESSES 19. ABSTRACT...turbomachinery. Specific objectives are twofold: Task (A). To complete the investigation of the Ranque - Hilsch effect con- ducted under AFOSR Contract
Steady-State Flow-Force Compensation in a Hydraulic Spool Valve
Lugowski, Jan
2013-01-01
A high-speed jet flowing inside of a partially-open hydraulic valve is accompanied by a reaction force, also referred to as flow force. The nature of this force has remained a mystery despite an extensive research effort spanning many decades. The momentum theory on the flow force by Lee and Blackburn (1952) explains the origin of the flow force and offers a design solution to shape the valve spool as a turbine bucket. It provides a model to calculate the compensated flow force as well. This paper shows that the model applies to a different flow case due to incorrect assumptions made. A corrected equation is presented based on a detailed analysis of the static-pressure distribution in the valve cavity as well as on a literature review of pressure loss in diffusers and nozzles. The new equation is based on the compensation taking place upstream of the valve orifice, not downstream as assumed by the momentum theory. The new model can be applied to chamfers or notches on the valve spool without the need to machi...
Sarimurat, Mehmet Nasir
Flow blowing/suction has multiple beneficial effects on the performance of axial flow compressors. In both low speed and high speed compressors a small amount of flow blowing and/or suction can be applied in the region of adverse pressure gradient to control the boundary layer separation and obtain high pressure ratio across the compressor. On the other hand in high speed compressors where a passage shock is present inside the passage, flow blowing/suction can also be used to manage the shock location inside the passage and increase the operating range of the compressor. In the first part of this study, an analytical model based on the integral method for boundary layer with flow blowing in incompressible flows is developed that shows the effect of mass, momentum, velocity magnitude and injection angle of the blowing flow on the behavior of the boundary layer. According to the model the change in the boundary layer momentum thickness across the blowing location is linear function of the momentum of the blowing flow and exponential function of the velocity of the blowing flow. Also if the size of the blowing slot and the velocity of the blown flow are kept constant, when the amount of the blown flow is increased by increasing the blowing angle, there is an "optimum" angle that maximizes the decrease in the momentum thickness across the blowing station. This angle is a function of the velocity ratio and it reaches an asymptotic value of around 40°. The model also shows that the change in the trailing-edge momentum thickness is an exponential function of the change in the momentum thickness across the blowing location. The developed modeled is confirmed for the NACA-65-410 low speed cascade using Computational Fluid Dynamics and a good agreement between the theory and CFD is obtained. In the second part of the thesis a quasi-1D inviscid and compressible flow theory in a converging/diverging flow passage is presented that can predict the amount of flow blowing or
Rehman, Khalil Ur; Malik, M. Y.; Salahuddin, T.; Naseer, M.
2016-07-01
Present work is made to study the effects of double stratified medium on the mixed convection boundary layer flow of Eyring-Powell fluid induced by an inclined stretching cylinder. Flow analysis is conceded in the presence of heat generation/absorption. Temperature and concentration are supposed to be higher than ambient fluid across the surface of cylinder. The arising flow conducting system of partial differential equations is primarily transformed into coupled non-linear ordinary differential equations with the aid of suitable transformations. Numerical solutions of resulting intricate non-linear boundary value problem are computed successfully by utilizing fifth order Runge-Kutta algorithm with shooting technique. The effect logs of physical flow controlling parameters on velocity, temperature and concentration profiles are examined graphically. Further, numerical findings are obtained for two distinct cases namely, zero (plate) and non-zero (cylinder) values of curvature parameter and the behaviour are presented through graphs for skin-friction coefficient, Nusselt number and Sherwood number. The current analysis is validated by developing comparison with previously published work, which sets a benchmark of quality of numerical approach.
Miyoshi, Koji, E-mail: miyoshi.koj@inss.co.jp; Takenaka, Nobuyuki; Ishida, Taisuke; Sugimoto, Katsumi
2017-05-15
Highlights: • Thermal hydraulics phenomena were discussed in a spray pipe of pressurizer. • Temperature fluctuation was investigated in a stratified steam-water two-phase. • Remarkable liquid temperature fluctuations were observed in the liquid layer. • The observed temperature fluctuations were caused by the internal gravity wave. • The temperature fluctuations decreased with increasing dissolved oxygen. - Abstract: Temperature fluctuation phenomena in a stratified steam-water two-phase flow in a horizontal rectangular duct, which simulate a pressurizer spray pipe of a pressurized water reactor, were studied experimentally. Vertical distributions of the temperature and the liquid velocity were measured with water of various dissolved oxygen concentrations. Large liquid temperature fluctuations were observed when the water was deaerated well and dissolved oxygen concentration was around 10 ppb. The large temperature fluctuations were not observed when the oxygen concentration was higher. It was shown that the observed temperature fluctuations were caused by the internal gravity wave since the Richardson numbers were larger than 0.25 and the temperature fluctuation frequencies were around the Brunt-Väisälä frequencies in the present experimental conditions. The temperature fluctuations decreased by the non-condensable gas since the non-condensable gas suppressed the condensation and the temperature difference in the liquid layer was small.
Poul S. Larsen
2011-09-01
To obtain precise and reliable laboratory clearance rate (filtration rate measurements with the ‘flow-through chamber method’ (FTC the design must ensure that only inflow water reaches the bivalve's inhalant aperture and that exit flow is fully mixed. As earlier recommended these prerequisites can be checked by a plot of clearance rate (CR versus increasing through-flow (Fl to reach a plateau, which is the true CR, but we also recommend to plot percent particles cleared versus reciprocal through-flow where the plateau becomes the straight line CR/Fl, and we emphasize that the percent of particles cleared is in itself neither a criterion for valid CR measurement, nor an indicator of appropriate ‘chamber geometry’ as hitherto adapted in many studies. For the ‘steady-state method’ (SS, the design must ensure that inflow water becomes fully mixed with the bivalve's excurrent flow to establish a uniform chamber concentration prevailing at its incurrent flow and at the chamber outlet. These prerequisites can be checked by a plot of CR versus increasing Fl, which should give the true CR at all through-flows. Theoretically, the experimental uncertainty of CR for a given accuracy of concentration measurements depends on the percent reduction in particle concentration (100×P from inlet to outlet of the ideal ‘chamber geomety’. For FTC, it decreases with increasing values of P while for SS it first decreases but then increases again, suggesting the use of an intermediate value of P. In practice, the optimal value of P may depend on the given ‘chamber geometry’. The fundamental differences between the FTC and the SS methods and practical guidelines for their use are pointed out, and new data on CR for the blue mussel, Mytilus edulis, illustrate a design and use of the SS method which may be employed in e.g. long-term growth experiments at constant algal concentrations.
Druzhinin, Oleg; Troitskaya, Yliya; Zilitinkevich, Sergej
2015-04-01
Detailed knowledge of the interaction of surface water waves with the wind flow is of primary importance for correct parameterization of turbulent momentum and heat fluxes which define the energy and momentum transfer between the atmosphere and hydrosphere. The objective of the present study is to investigate the properties of the stably stratified turbulent boundary-layer (BL) air-flow over waved water surface by direct numerical simulation (DNS) at a bulk Reynolds number varying from 15000 to 80000 and the surface-wave slope up to ka = 0.2. The DNS results show that the BL-flow remains in the statistically stationary, turbulent regime if the Reynolds number (ReL) based on the Obukhov length scale and friction velocity is sufficiently large (ReL > 100). In this case, mean velocity and temperature vertical profiles are well predicted by log-linear asymptotic solutions following from the Monin-Obukhov similarity theory provided the velocity and temperature roughness parameters, z0U and z0T, are appropriately prescribed. Both z0U and z0T increase for larger surface-wave slope. DNS results also show that turbulent momentum and heat fluxes and turbulent velocity and temperature fluctuations are increased for larger wave slope (ka) whereas the mean velocity and temperature derivatives remain practically the same for different ka. Thus, we conclude that the source of turbulence enhancement in BL-flow are perturbations induced by the surface wave, and not the shear instability of the bulk flow. On the other hand, if stratification is sufficiently strong, and the surface-wave slope is sufficiently small, the BL-flow over waved surface relaminarizes in the bulk of the domain. However, if the surface-wave slope exceeds a threshold value, the velocity and temperature fluctuations remain finite in the vicinity of the critical-layer level, where the surface-wave phase velocity coincides with the mean flow velocity. We call this new stably-stratified BL-flow regime observed in
Steady state cooling flow models with gas loss for normal elliptical galaxies
Sarazin, Craig L.; Ashe, Gregory A.
1989-01-01
A grid of cooling flow models for the hot gas in normal elliptical galaxies is calculated, including the loss of gas due to inhomogeneous cooling. The loss process is modeled as a distributed sink for the gas with the rate of loss being proportional to the local cooling rate. The cooling flow models with gas loss have smaller sonic radii, smaller inflow rates in their central regions, lower densities, and higher temperatures than homogeneous models. The reduction in the amount of hot gas flowing into the center of the models brings the models into much better agreement with the observed X-ray surface brightness profiles of elliptical galaxies. However, there is a large dispersion in the observed X-ray luminosities of ellipticals, and this cannot be explained by variations in the efficiency of gas loss. The gas-loss models have X-ray surface brightness profiles which are much less centrally peaked than the no-gas-loss models.
Subsonic flow past an oscillating cascade with steady blade loading - Basic formulation
Verdon, J. M.; Caspar, J. R.; Adamczyk, J. J.
1975-01-01
A nonlinear boundary value problem governing the subsonic flow in a single, extended, blade passage region of a high-deflection, two dimensional, oscillating cascade is derived. The blades are assumed to be undergoing identical harmonic motions of small amplitude with constant phase angle between the motion of adjacent blades. An asymptotic perturbation approach is used to determine the velocity potential. This formulation can be used in the numerical determination of unsteady potential and thus the unsteady aerodynamic force and moment under various combinations of cascade and flow parameters.
Koroglu, Batikan; Armstrong, Mike; Cappelli, Mark; Chernov, Alex; Crowhurst, Jonathan; Mehl, Marco; Radousky, Harry; Rose, Timothy; Zaug, Joe
2016-10-01
The high temperature chemistry of rapidly condensing matter is under investigation using a steady state inductively coupled plasma (ICP) flow reactor. The objective is to study chemical processes on cooling time scales similar to that of a low yield nuclear fireball. The reactor has a nested set of gas flow rings that provide flexibility in the control of hydrodynamic conditions and mixing of chemical components. Initial tests were run using two different aqueous solutions (ferric nitrate and uranyl nitrate). Chemical reactants passing through the plasma torch undergo non-linear cooling from 10,000K to 1,000K on time scales of <0.1 to 0.5s depending on flow conditions. Optical spectroscopy measurements were taken at different positions along the flow axis to observe the in situ spatial and temporal evolution of chemical species at different temperatures. The current data offer insights into the changes in oxide chemistry as a function of oxygen fugacity. The time resolved measurements will also serve as a validation target for the development of kinetic models that will be used to describe chemical fractionation during nuclear fireball condensation. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
A numerical study of steady-state two-phase flow in porous media
Knudsen, Henning Arendt
2002-07-01
Two-phase flow in porous media means the simultaneous flow of two phases, say two liquids, e.g., oil and water. This flow is restrained to be within a porous medium. For example sandstone and limestone are typical porous stones that can contain oil and gas in nature. In the extraction of oil from reservoirs, oil is usually displaced by water. So on a large scale we can consider it to be a displacement process. However, on pore scale the ''mix'' and flow processes are complicated. Idealistically, one might consider the search for truth a sufficient motivation for work in this field. Nevertheless, from an economic and technological point of view, enhanced oil recovery is the main motivation for the study of two-phase flow in porous media. Luckily, there are additional systems in real world that falls into this category. One such system is the flow of water and pollutants in aquifers. General knowledge in the field might be beneficial for preserving ground water reserves in the future. In the laboratory one often encounters artificially made porous media. For example glass beads between two glass plates. Therein, one of the phases flowing may be a mixture of glycerol and water. The other phase can be air which then is the non-wetting phase; air does not wet glass. It can also be silicone oil, and in that case the water/glycerol is normally the nonwetting phase. There are other possibilities. In general, laboratory studies are performed on systems on pore scale. The flow properties on the various length scales found in flow systems in nature depend on these properties on pore scale. The so-called upscaling problem concerns how to relate pore scale properties with properties on larger scales. The scope of this thesis is the study of properties on pore scale. The upscaling problem, which is a large research field in itself, is thus outside the scope of this thesis. The results of Paper 3 is an exception since they may infer also to larger scales than
Quasi-steady accelerator operation on the ZAP flow Z-pinch
Hughes, M. C., E-mail: mchugs@uw.edu; Shumlak, U., E-mail: mchugs@uw.edu; Golingo, R. P., E-mail: mchugs@uw.edu; Nelson, B. A., E-mail: mchugs@uw.edu; Ross, M. P., E-mail: mchugs@uw.edu [Aerospace and Energetics Research Program, University of Washington, Seattle, WA 98195 (United States)
2014-12-15
The ZaP Flow Z-Pinch Experiment utilizes sheared flows to stabilize an otherwise unstable equilibrium. The sheared flows are maintained by streaming high velocity plasma parallel to the pinch. Previous operations of the machine show depletion of the accelerator’s neutral gas supply late in the pulse leading to pinch instability. The current distribution in the accelerator exhibits characteristic modes during this operation, which is corroborated by interferometric signals. The decrease in density precipitates a loss of plasma quiescence in the pinch, which occurs on a timescale related to the flow velocity from the plasma source. To abate the depletion, the geometry of the accelerator is altered to increase the neutral gas supply. The design creates a standing deflagration front in the accelerator that persists for the pulse duration. The new operating mode is characterized by the same diagnostics as the previous mode. The lessons learned in the accelerator operations have been applied to the design of a new experiment, ZaP-HD. This work was supported by grants from the Department of Energy and the National Nuclear Security Administration.
Channel roughness in 1D steady uniform flow: Manning or Chézy?
Huthoff, F.; Augustijn, D.
2004-01-01
In river flow applications, consensus on the most appropriate roughness descriptor has yet to be found. A disturbing observation is that the coefficients and formulae of Chézy, Darcy Weisbach, Manning, Strickler and White Colebrook are used rather arbitrarily, and that a widely accepted scientific j
1994-10-10
correction a) Axial velocity contours; L b) Perimetral wall stress Fig 7 Prediction of flow In plane channel rotating in orthogonal mode. Symbols; DNS...layer: anticyclonic in the uipper layer (green line), strong anticyclone in the intermediate layer ( red line), cyclonic in the lower layer (blue). a...mostly to the boundaries, and Red ; 50 so the support wires have little effect on the sphere wake itself. The spheres were towed through a 2.4m 2
On the validity of travel-time based nonlinear bioreactive transport models in steady-state flow.
Sanz-Prat, Alicia; Lu, Chuanhe; Finkel, Michael; Cirpka, Olaf A
2015-01-01
Travel-time based models simplify the description of reactive transport by replacing the spatial coordinates with the groundwater travel time, posing a quasi one-dimensional (1-D) problem and potentially rendering the determination of multidimensional parameter fields unnecessary. While the approach is exact for strictly advective transport in steady-state flow if the reactive properties of the porous medium are uniform, its validity is unclear when local-scale mixing affects the reactive behavior. We compare a two-dimensional (2-D), spatially explicit, bioreactive, advective-dispersive transport model, considered as "virtual truth", with three 1-D travel-time based models which differ in the conceptualization of longitudinal dispersion: (i) neglecting dispersive mixing altogether, (ii) introducing a local-scale longitudinal dispersivity constant in time and space, and (iii) using an effective longitudinal dispersivity that increases linearly with distance. The reactive system considers biodegradation of dissolved organic carbon, which is introduced into a hydraulically heterogeneous domain together with oxygen and nitrate. Aerobic and denitrifying bacteria use the energy of the microbial transformations for growth. We analyze six scenarios differing in the variance of log-hydraulic conductivity and in the inflow boundary conditions (constant versus time-varying concentration). The concentrations of the 1-D models are mapped to the 2-D domain by means of the kinematic (for case i), and mean groundwater age (for cases ii & iii), respectively. The comparison between concentrations of the "virtual truth" and the 1-D approaches indicates extremely good agreement when using an effective, linearly increasing longitudinal dispersivity in the majority of the scenarios, while the other two 1-D approaches reproduce at least the concentration tendencies well. At late times, all 1-D models give valid approximations of two-dimensional transport. We conclude that the
Bortsaikin, S.M.; Levitan, Yu.S.
1977-07-01
An examination is made of steady-state turbulent flow of a conducting liquid in a cylindrical channel in a longitudinal magnetic field. The system of motion equations and energy can be recorded in a convenient integral form by using the Prandtl hypothesis for computing turbulent coefficients with rather simple assumptions about the nature of the velocity gradient. A small parameter in the equations can be easily identified in direct proximity to the channel's wall that makes it possible to find an approximate analytical solution to this problem in this region. 6 references, 1 figure.
Novel Slope Source Term Treatment for Preservation of Quiescent Steady States in Shallow Water Flows
Khawar Rehman
2016-10-01
Full Text Available This paper proposes a robust method for modeling shallow-water flows and near shore tsunami propagation, applicable for both simple and complex geometries with uneven beds. The novel aspect of the model includes the introduction of a new method for slope source terms treatment to preserve quiescent equilibrium over uneven topographies, applicable to both structured and unstructured mesh systems with equal accuracy. Our model is based on the Godunov-type finite volume numerical approximation. Second-order spatial and temporal accuracy is achieved through high resolution gradient reconstruction and the predictor-corrector method, respectively. The approximate Riemann solver of Harten, Lax, and van Leer with contact wave restoration (HLLC is used to compute fluxes. Comparisons of the model’s results with analytical, experimental, and published numerical solutions show that the proposed method is capable of accurately predicting experimental and real-time tsunami propagation/inundation, and dam-break flows over varying topographies.
Assessment of the effect of vessel curvature on Doppler measurements in steady flow.
Balbis, S; Guiot, C; Roatta, S; Arina, R; Todros, T
2004-05-01
Blood vessel curvature is responsible for the appearance of nonaxial velocity components and for minor changes in the pattern of the axial flow. All the velocity components are expected to contribute to the Doppler signal produced by the ultrasound (US) backscattered by the insonated blood cells, the axial velocity, contributing to the actual volumetric blood flow, and the transverse velocity, causing the recirculating vortices. A detailed, separate analysis of the velocity components is, therefore, mandatory to quantify how vessel curvature can affect results and clinical diagnosis. Both experimental in vitro measures and numerical simulations were performed on a curved tube and the Doppler power spectra so obtained were compared. The satisfactorily agreement of the above spectra shows that the nonaxial velocity components are easily detectable with clinical equipment and that their amplitude, as expected, is not negligible and can bias Doppler measurements and resulting clinical diagnosis.
M.S Uddin
2011-01-01
Full Text Available The paper is concerned to find the distribution of the chemically reactant solute in the MHD flow of an electrically conducting viscous incompressible fluid over a stretching surface. The first order chemical reaction and the variable solute distribution along the surface are taken into consideration. The governing partial differential equations along with appropriate boundary conditions for flow field and reactive solute are transformed into a set of non-linear self-similar ordinary differential equations by using scaling group of transformations. An exact analytic solution is obtained for the velocity field. Using this velocity field, we obtain numerical solution for the reactant concentration field. It reveals from the study that the values of concentration profile enhances with the increase of the magnetic field and decreases with increase of Schmidt number as well as the reaction rate parameter. Most importantly, when the solute distribution along the surface increases then the concentration profile decreases.
Ali, M.E. [King Saud University, Riyadh (Saudi Arabia). Mechanical Engineering Department; Magyari, E. [Institute of Building Technology, ETH Zuerich (Switzerland)
2007-01-15
The title problem arises in the terminal stage of a large class of industrial manufacturing processes as polymer extrusion, wire drawing, drawing of plastic sheets, etc. It concerns the transient crossover to the state of rest of the fluid and heat flow which accompanies the steady fabrication process, when the devices are switched off gradually (i.e. when the motion is slowed down and the surface temperature approaches the ambient temperature continuously). The mechanical and thermal characteristics of such an unsteady process are investigated in the boundary layer approximation, assuming a linear variation of the steady stretching velocity with the longitudinal coordinate x and an inverse linear law for its decrease with time during the gradual switch-off process. For the corresponding surface temperature a general power-law variation is admitted. The paper presents the similarity analysis of several specific cases. The cases of basic interest of a constant surface temperature T{sub w} and of a constant surface heat flux q{sub w} are discussed in some detail. In the case T{sub w}=const. an exact solution is reported and the Prandtl number dependence of the corresponding surface heat flux is given for all 0
Pathak, M. G.; Patel, V. C.; Ghiaasiaan, S. M.; Mulcahey, T. I.; Helvensteijn, B. P.; Kashani, A.; Feller, J. R.
2013-12-01
The regenerator, typically a microporous structure that is subject to periodic flow of a cryogenic fluid, is the most critical component of Pulse Tube or Stirling cryocoolers, which are widely used for high-demand defense and aerospace applications. Despite the critical impact of hydrodynamic irreversibilities in the regenerator on the overall cycle efficiency, the impact of the parameters that influence these losses are poorly understood.
Application of Les, Pans and Rans to a Case of Intake Channel Steady Flow Test Bench
Vítek Oldřich
2015-12-01
Full Text Available The paper deals with evaluation of intake channel flow properties (discharge coefficient, tumble and swirl ratio using both 3-D CFD simulation and measurement. Sensitivity of different calculation parameters was tested. The most important ones are mesh parameters and applied turbulence models (considered models: LES, PANS and RANS. Concerning the mesh, the critical parameter is a mesh configuration near a wall - a thickness of mesh boundary layer and an amount of these layers have significant impact on mass flow rate while tumble/swirl ratio is unaffected by that. Based on that, these mesh parameters can be considered as tuning constants for fine-tuning the CFD model. Regarding the mesh cell size, 2 different values were tested (0.6 and 0.3 mm. It was found out that neither mesh is fine enough to perform proper LES. Hence, PANS performance is close to RANS. Concerning the turbulence models, PANS seems to be the best one as it combines advantages of both LES and RANS. Generally speaking, mass flow rate prediction is relatively good while swirl/tumble one is more problematic as only qualitative agreement can be achieved.
A numerical program for steady-state flow of magma-gas mixtures through vertical eruptive conduits
Mastin, Larry G.; Ghiorso, Mark S.
2000-01-01
This report presents a model that calculates flow properties (pressure, vesicularity, and some 35 other parameters) as a function of vertical position within a volcanic conduit during a steady-state eruption. The model idealizes the magma-gas mixture as a single homogeneousfluid and calculates gas exsolution under the assumption of equilibrium conditions. These are the same assumptions on which classic conduit models (e.g. Wilson and Head, 1981) have been based. They are most appropriate when applied to eruptions of rapidly ascending magma (basaltic lava-fountain eruptions, and Plinian or sub-Plinian eruptions of intermediate or silicic magmas) that contains abundant nucleation sites (microlites, for example) for bubble growth.
A. A. SIDDIQUI; A. LAKHTAKIA
2013-01-01
Analytic expressions for speed, flux, microrotation, stress, and couple stress in a micropolar fluid exhibiting a steady, symmetric, and one-dimensional electro-osmotic flow in a uniform cylindrical microcapillary were derived under the constraint of the Debye-H¨uckel approximation, which is applicable when the cross-sectional radius of the microcapillary exceeds the Debye length, provided that the zeta potential is suﬃciently small in magnitude. Since the aciculate particles in a micropolar fluid can rotate without translation, micropolarity affects the fluid speed, fluid flux, and one of the two non-zero components of the stress tensor. The axial speed in a micropolar fluid intensifies when the radius increases. The stress tensor is confined to the region near the wall of the mi-crocapillary, while the couple stress tensor is uniform across the cross-section.
Clearman, W. M.; Cha, J. S.; Ghiaasiaan, S. M.; Kirkconnell, C. S.
2008-03-01
The hydrodynamic parameters associated with steady longitudinal and lateral (radial) flow of helium in several widely-used pulse tube and Stirling cryocooler regenerator fillers were measured and correlated in this investigation. Pressure drops in test sections packed with regenerator fillers were experimentally measured. Computational fluid dynamics (CFD) models of the regenerator test sections and their vicinities were developed and simulations were performed in which the regenerator test sections were modeled as porous media. By iterative repetition of the simulations, the longitudinal and radial permeability and Forchheimer inertial coefficients were determined such that they would lead to agreement between experimental measurements and the simulations. The regenerator fillers included 325 and 400 mesh stainless steel screens, stainless steel metal foam, sintered 400 mesh stainless steel screens, and a stack of micromachined perforated plates. The hydrodynamic response of the regenerator fillers were also correlated as friction factors. The results confirm that the aforementioned regenerator fillers are anisotropic.
Quasi-steady-state model of a counter flow air-to-air heat exchanger with phase change
Rose, Jørgen; Nielsen, Toke Rammer; Kragh, Jesper;
2008-01-01
into account the effects of condensation and frost formation. The model is developed as an Excel spreadsheet, and specific results are compared with laboratory measurements. As an example, the model is used to determine the most energy-efficient control strategy for a specific heat-exchanger under northern......Using mechanical ventilation with highly efficient heat-recovery in northern European or arctic climates is a very efficient way of reducing the energy use for heating in buildings. However, it also presents a series of problems concerning condensation and frost formation in the heat......-exchanger. Developing highly efficient heat-exchangers and strategies to avoid/remove frost formation implies the use of detailed models to predict and evaluate different heat-exchanger designs and strategies. This paper presents a quasi-steady-state model of a counter-flow air-to-air heat-exchanger that takes...
Sharma Pushkar Raj
2009-01-01
Full Text Available Aim of the paper is to investigate effects of ohmic heating and viscous dissipation on steady flow of a viscous incompressible electrically conducting fluid in the presence of uniform transverse magnetic field and variable free stream near a stagnation point on a stretching non-conducting isothermal sheet. The governing equations of continuity, momentum, and energy are transformed into ordinary differential equations and solved numerically using Runge-Kutta fourth order with shooting technique. The velocity and temperature distributions are discussed numerically and presented through graphs. Skin-friction coefficient and the Nusselt number at the sheet are derived, discussed numerically, and their numerical values for various values of physical parameters are compared with earlier results and presented through tables.
Yousefi, Ali R; Eivazlou, Razieh; Razavi, Seyed M A
2016-10-01
The rheological properties of food hydrocolloids are remarkably influenced by the quality of solvent/cosolutes in a food system. In this work, the steady shear flow behavior of sage seed gum (SSG, 0.5% w/w) at the presence of different levels of salts (KCl & MgCl2, 0-100mM) and sugars (sucrose, lactose & glucose, 0-6% w/w) was studied. It was found that the rheological properties of SSG were affected by the type of sugars and salts and their concentrations as well. Synergistic interaction was observed between SSG and sugars which enhanced the viscosity of gum solutions, while salts addition diminished the viscosity. SSG solutions exhibited a shear thinning behavior at all conditions tested. Various time-independent rheological models were used to fit the shear stress-shear rate data, although the Herschel-Bulkley (R(2)=0.994-0.999) and Sisko (R(2)=0.995-0.999) models showed the best results to describe the flow behavior of SSG. In the presence of salts, the yield stress (τ0), consistency coefficient (k), and flow behavior index (n) values decreased. The k and τ0 values enhanced and the n value lowered in the presence of sugars. Divalent cations of Mg(2+) and sucrose roughly showed more effect on rheological parameters than others.
A NEW METHOD FOR PREDICTION OF PRODUCTIVITY OF FRACTURED HORIZONTAL WELLS BASED ON NON-STEADY FLOW
无
2007-01-01
Hydraulic fracturing technologies of horizontal well are important ways to develop oil-gas field with low permeability. Productivity forecast of fractured horizontal wells is a difficult problem of hydraulic fracturing technologies. Basing on non-steady flow of fractures fluid during production, applying potential function principles, superposition principle and mathematical method for solving, coupling of seepage flow in the formation and pipe flow in the well bore, a new model on multi-fracture interference productivity forecast of fractured horizontal well is established in this article. The results indicate the coincidence rate between this model and practice is high. The pressure loss in the horizontal well bore has definite influence on the production status of fractured horizontal wells. The productions of different fractures in horizontal well bore are unequal, the productions of outer fractures are higher than middle fractures; the pressure in the well bore shows an uneven distribution, the pressure declines gradually from finger tip to heel end. Asymmetry of fractures may make productivity of fractured horizontal wells decline. The conclusions are instructive in designing fractured horizontal well for low permeability reservoir.
Si, Ting; Yin, Chuansheng; Gao, Peng; Li, Guangbin; Ding, Hang; He, Xiaoming; Xie, Bin; Xu, Ronald X.
2016-01-01
A compound-fluidic electro-flow focusing (CEFF) process is proposed to produce multicompartment microcapsules. The central device mainly consists of a needle assembly of two parallel inner needles and one outer needle mounted in a gas chamber with their tips facing a small orifice at the bottom of the chamber. As the outer and the inner fluids flow through the needle assembly, a high-speed gas stream elongates the liquid menisci in the vicinity of the orifice entrance. An electric field is further integrated into capillary flow focusing to promote the formation of steady cone-jet mode in a wide range of operation parameters. The multiphase liquid jet is broken up into droplets due to perturbation propagation along the jet surface. To estimate the diameter of the multiphase liquid jet as a function of process parameters, a modified scaling law is derived and experimentally validated. Microcapsules of around 100 μm with an alginate shell and multiple cores at a production rate of 103-105 per second are produced. Technical feasibility of stimulation triggered coalescence and drug release is demonstrated by benchtop experiments. The proposed CEFF process can be potentially used to encapsulate therapeutic agents and biological cargos for controlled micro-reaction and drug delivery.
Zhentao Wang
2014-07-01
Full Text Available A model based on the volume of fluid (VOF method and leaky dielectric theory is established to predict the deformation and internal flow of the droplet suspended in another vicious fluid under the influence of the electric field. Through coupling with hydrodynamics and electrostatics, the rate of deformation and internal flow of the single droplet are simulated and obtained under the different operating parameters. The calculated results show that the direction of deformation and internal flow depends on the physical properties of fluids. The numerical results are compared with Taylor's theory and experimental results by Torza et al. When the rate of deformation is small, the numerical results are consistent with theory and experimental results, and when the rate is large the numerical results are consistent with experimental results but are different from Taylor's theory. In addition, fluid viscosity hardly affects the deformation rate and mainly dominates the deformation velocity. For high viscosity droplet spends more time to attain the steady state. The conductivity ratio and permittivity ratio of two different liquids affect the direction of deformation. When fluid electric properties change, the charge distribution at the interface is various, which leads to the droplet different deformation shapes.
Analytical Model of an Asymmetric Sunspot with a Steady Plasma Flow in its Penumbra
Solov'ev, A. A.; Kirichek, E. A.
2016-08-01
A new exact analytical solution to the stationary problem of ideal magnetohydrodynamics is derived for an unipolar asymmetric sunspot immersed in a realistic solar atmosphere. The radial and vertical profiles of pressure, plasma density, and temperature in the visible layers of the sunspot are calculated. The reduction in plasma density in the magnetic funnel of the sunspot, corresponding to the Wilson depression, is also obtained. The magnetic structure of the sunspot is given analytically in a realistic way: a part of the magnetic flux of the sunspot approaches the surrounding photosphere at the outer edge of the penumbra. The magnetic field of the sunspot is not assumed to be axially symmetric. For the first time, the angular dependence of the physical variables in this model allows us to simulate not only a deviation from the circular shape of the sunspot, but also a fine filamentary structure of the sunspot penumbra. The Alfvén Mach number (the ratio of the plasma speed to the Alfvén speed) is zero at the center of the sunspot and rises slowly toward the periphery of the sunspot; this corresponds to the structure of the Evershed flow in the penumbra. The Evershed flow in our model is mainly concentrated in dark penumbral filaments, as is observed.
El Serafy, G.Y.H.; Mynett, A.E.
2008-01-01
Numerical models of a water system are always based on assumptions and simplifications that may result in errors in the model's predictions. Such errors can be reduced through the use of data assimilation and thus can significantly improve the success rate of the predictions and operational forecast
Steady Flow of a Second-Grade Fluid in an Annulus with Porous Walls
M. Emin Erdoğan
2008-01-01
Full Text Available An exact solution of an incompressible second-grade fluid for flow between two coaxial cylinders with porous walls is given. It is assumed that the inner cylinder is rotating with a constant angular velocity and the outer one is at rest. The solution is expressed in terms of the confluent hypergeometric functions and it is valid for all values of the cross-Reynolds number and the elastic number. The solutions for −2, +∞, and −∞ values of the cross-Reynolds number are obtained and a comparison with those of the Newtonian fluid is given. Furthermore, the torque exerted by the fluid on the inner cylinder is calculated. It is shown that the moment coefficient depends on the cross-Reynolds number, the elastic number, and the ratio of the radii of the cylinders. The variation of the moment coefficient with these numbers is discussed.
Flow under standing waves Part 1. Shear stress distribution, energy flux and steady streaming
Gislason, Kjartan; Fredsøe, Jørgen; Deigaard, Rolf
2009-01-01
The conditions for energy flux, momentum flux and the resulting streaming velocity are analysed for standing waves formed in front of a fully reflecting wall. The exchange of energy between the outer wave motion and the near bed oscillatory boundary layer is considered, determining the horizontal...... energy flux inside and outside the boundary layer. The momentum balance, the mean shear stress and the resulting time averaged streaming velocities are determined. For a laminar bed boundary layer the analysis of the wave drift gives results similar to the original work of Longuet-Higgins from 1953....... The work is extended to turbulent bed boundary layers by application of a numerical model. The similarities and differences between laminar and turbulent flow conditions are discussed, and quantitative results for the magnitude of the mean shear stress and drift velocity are presented. Full two...
Sarracino, A; Puglisi, A; Vulpiani, A
2016-01-01
We study the mobility and the diffusion coefficient of an inertial tracer advected by a two-dimensional incompressible laminar flow, in the presence of thermal noise and under the action of an external force. We show, with extensive numerical simulations, that the force-velocity relation for the tracer, in the nonlinear regime, displays complex and rich behaviors, including negative differential and absolute mobility. These effects rely upon a subtle coupling between inertia and applied force which induce the tracer to persist in particular regions of phase space with a velocity opposite to the force. The relevance of this coupling is revisited in the framework of non-equilibrium response theory, applying a generalized Einstein relation to our system. The possibility of experimental observation of these results is also discussed.
Mori, N.; Morimoto, J.; Nakamura, K. [Osaka University, Osaka (Japan). Faculty of Engineering
1996-04-25
Numerical simulations of the steady shear flows of a nematic phase are performed using nonequilibrium molecular dynamics. The SLLOD algorithm is developed for application to the steady shear flows of ellipsoids of revolution that interact via the Gay-Berne potential. The system composed of particles interacting via the Gay-Berne potential forms various phases including a nematic one. In the initial stage of simple shear flow of the nematic phase, the order parameter significantly decreases as the director rotates rapidly. The director, however, is inclined at a nearly constant angle regardless of shear rate in the steady state. Rheological properties, such as shear viscosity and normal stress differences, are examined. 18 refs., 9 figs.
Náraigh, L Ó; Matar, O; Zaki, T
2009-01-01
We investigate the linear stability of a flat interface that separates a liquid layer from a fully-developed turbulent gas flow. In this context, linear-stability analysis involves the study of the dynamics of a small-amplitude wave on the interface, and we develop a model that describes wave-induced perturbation turbulent stresses (PTS). We demonstrate the effect of the PTS on the stability properties of the system in two cases: for a laminar thin film, and for deep-water waves. In the first case, we find that the PTS have little effect on the growth rate of the waves, although they do affect the structure of the perturbation velocities. In the second case, the PTS enhance the maximum growth rate, although the overall shape of the dispersion curve is unchanged. Again, the PTS modify the structure of the velocity field, especially at longer wavelengths. Finally, we demonstrate a kind of parameter tuning that enables the production of the thin-film (slow) waves in a deep-water setting.
Jackman, C. M.; Thomsen, M. F.; Mitchell, D. G.; Sergis, N.; Arridge, C. S.; Felici, M.; Badman, S. V.; Paranicas, C.; Jia, X.; Hospodarksy, G. B.; Andriopoulou, M.; Khurana, K. K.; Smith, A. W.; Dougherty, M. K.
2015-05-01
We present a case study of an event from 20 August (day 232) of 2006, when the Cassini spacecraft was sampling the region near 32 RS and 22 h LT in Saturn's magnetotail. Cassini observed a strong northward-to-southward turning of the magnetic field, which is interpreted as the signature of dipolarization of the field as seen by the spacecraft planetward of the reconnection X line. This event was accompanied by very rapid (up to ~1500 km s-1) thermal plasma flow toward the planet. At energies above 28 keV, energetic hydrogen and oxygen ion flow bursts were observed to stream planetward from a reconnection site downtail of the spacecraft. Meanwhile, a strong field-aligned beam of energetic hydrogen was also observed to stream tailward, likely from an ionospheric source. Saturn kilometric radiation emissions were stimulated shortly after the observation of the dipolarization. We discuss the field, plasma, energetic particle, and radio observations in the context of the impact this reconnection event had on global magnetospheric dynamics.
Nwosu, Cajethan M.; Oti, Stephen E.; Ogbuka, Cosmas U.
2017-01-01
This paper presents transient and steady state performance analysis of power flow control in a 5.0 kW Doubly-Fed Induction Generator (DFIG) Variable Speed Wind Turbine (VSWT) under sub synchronous speed, super synchronous speed and synchronous speed modes of operation. Stator flux orientation is used for the control of the rotor-side converter (RSC) and DFIG whereas the grid (or stator) voltage orientation is the preferred choice for the control of the grid-side converter (GSC). In each of the three speeds modes, power is always supplied to the grid through the stator of the DFIG. The magnitude of net power (stator power plus rotor power) is less than stator power during the sub synchronous speed mode; it is greater than stator power during the super synchronous speed mode while it is equal to the stator power during the synchronous speed mode. In synchronous speed mode, the rotor power is zero indicating that power is neither supplied to the grid from the rotor nor supplied to the rotor from the grid; here the magnitude of net power is equal to stator power. The simulation results thus obtained in a MATLAB/SIMULINK environment laid credence to the controllability of power flow reversal in a DFIG-VSWT through back-to-back power electronic converter.
M. Ozgun Korukcu
2015-05-01
Full Text Available Energy and exergy characteristics of a square cylinder (SC in confined flow are investigated computationally by numerically handling the steady-state continuity, Navier-Stokes and energy equations in the Reynolds number range of Re = 10–50, where the blockage ratio (β = B/H is kept constant at the high level of β = 0.8. Computations indicated for the upstream region that, the mean non-dimensional streamwise (u/Uo and spanwise (v/Uo velocities attain the values of u/Uo = 0.840®0.879 and v/Uo = 0.236®0.386 (Re = 10®50 on the front-surface of the SC, implying that Reynolds number and blockage have stronger impact on the spanwise momentum activity. It is determined that flows with high Reynolds number interact with the front-surface of the SC developing thinner thermal boundary layers and greater temperature gradients, which promotes the thermal entropy generation values as well. The strict guidance of the throat, not only resulted in the fully developed flow character, but also imposed additional cooling; such that the analysis pointed out the drop of duct wall (y = 0.025 m non-dimensional temperature values (ζ from ζ = 0.387®0.926 (Re = 10®50 at xth = 0 mm to ζ = 0.002®0.266 at xth = 40 mm. In the downstream region, spanwise thermal disturbances are evaluated to be most inspectable in the vortex driven region, where the temperature values show decrease trends in the spanwise direction. In the corresponding domain, exergy destruction is determined to grow with Reynolds number and decrease in the streamwise direction (xds = 0®10 mm. Besides, asymmetric entropy distributions as well were recorded due to the comprehensive mixing caused by the vortex system.
Bartosiewicz, Yann [Universite Catholique de Louvain (UCL), Faculty of Applied Sciences, Mechanical Engineering Department, TERM Division, Place du Levant 2, 1348 Louvain-la-Neuve (Belgium)], E-mail: yann.bartosiewicz@uclouvain.be; Lavieville, Jerome [Universite Catholique de Louvain (UCL), Faculty of Applied Sciences, Mechanical Engineering Department, TERM Division, Place du Levant 2, 1348 Louvain-la-Neuve (Belgium); Seynhaeve, Jean-Marie [Universite Catholique de Louvain (UCL), Faculty of Applied Sciences, Mechanical Engineering Department, TERM Division, Place du Levant 2, 1348 Louvain-la-Neuve (Belgium)], E-mail: jm.seynhaeve@uclouvain.be
2008-04-15
This paper presents some results concerning a first benchmark for the new European research code for thermal hydraulics computations: NEPTUNE{sub C}FD. This benchmark relies on the Thorpe experiment to model the occurrence of instabilities in a stratified two-phase flow. The first part of this work is to create a numerical trial case with the VOF approach. The results, in terms of time of onset of the instability, critical wave-number or wave phase speed, are rather good compared to linear inviscid theory and experimental data. Additional numerical tests showed the effect of the surface tension and density ratio on the growing dynamics of the instability and the structure of the waves. In the second part, a code to code (VOF/multi-field) comparison is performed for a case with zero surface tension. The results showed some discrepancies in terms of wave amplitudes, growing rates and a time shifting in the global dynamics. Afterward, two surface tension formulations are proposed in the multi-field approach. Both formulations provided similar results. The time for onset of the instability, the most amplified wave-number and its amplitude were in rather good agreement with the linear analysis and VOF results. However, the time-shifted dynamics was still observed.
Irnawan, Roni; Silva, Filipe Miguel Faria da; Bak, Claus Leth
2017-01-01
of this MTDC system due to the inherited limit from point-to-point (PtP) configuration. An analytic method is proposed in order to estimate the steady-state DC voltage operational points of this MTDC system. The proposed method has been confirmed with a conventional DC power flow study result....
Sun, H; Chénier, Eric; Lauriat, Guy
2011-01-01
Abstract The physical model considered in the present numerical work is a square air-filled cavity cooled from below and above, with a heated square body located at the cavity center. The aim is to establish the effects of radiation interchanges amongst surfaces on the transition from steady, symmetric flows about the cavity centerline to complex periodic flows. Owing to the low temperature differences involved (1 K ? ?T ? 5 K), the two-dimensional model is based on the Boussinesq ...
Larsen, Poul Scheel; Riisgård, Hans Ulrik
2012-01-01
of particles cleared is in itself neither a criterion for valid CR measurement, nor an indicator of appropriate ‘chamber geometry’ as hitherto adapted in many studies. For the ‘steady-state method’ (SS), the design must ensure that inflow water becomes fully mixed with the bivalve’s excurrent flow to establish...... measurements depends on the percent reduction in particle concentration (1006P) from inlet to outlet of the ideal ‘chamber geomety’. For FTC, it decreases with increasing values of P while for SS it first decreases but then increases again, suggesting the use of an intermediate value of P. In practice......, the optimal value of P may depend on the given ‘chamber geometry’. The fundamental differences between the FTC and the SS methods and practical guidelines for their use are pointed out, and new data on CR for the blue mussel, Mytilus edulis, illustrate a design and use of the SS method which may be employed...
Huijun Feng, Lingen Chen, Fengrui Sun
2010-11-01
Full Text Available An irreversible universal steady flow heat pump cycle model with variable-temperature heat reservoirs and the losses of heat-resistance and internal irreversibility is established by using the theory of finite time thermodynamics. The universal heat pump cycle model consists of two heat-absorbing branches, two heat-releasing branches and two adiabatic branches. Expressions of heating load, coefficient of performance (COP and profit rate of the universal heat pump cycle model are derived, respectively. By means of numerical calculations, heat conductance distributions between hot- and cold-side heat exchangers are optimized by taking the maximum profit rate as objective. There exist an optimal heat conductance distribution and an optimal thermal capacity rate matching between the working fluid and heat reservoirs which lead to a double maximum profit rate. The effects of internal irreversibility, total heat exchanger inventory, thermal capacity rate of the working fluid and heat capacity ratio of the heat reservoirs on the optimal finite time exergoeconomic performance of the cycle are discussed in detail. The results obtained herein include the optimal finite time exergoeconomic performances of endoreversible and irreversible, constant- and variable-temperature heat reservoir Brayton, Otto, Diesel, Atkinson, Dual, Miller and Carnot heat pump cycles.
LI; Sheng; SCHERER; Ronald; C.; WAN; Mingxi
2006-01-01
Vocal fold geometry plays an important role in human phonation. The intraglottal quasi- steady pressure and velocity distributions depend upon the shape, size, and diameter of the glottis. This study reports the effects of the variation of glottal shapes on intraglottal pressures and velocities using a Plexiglas model with a glottis having nine symmetric glottal angles (uniform, as well as convergent and divergent 5°, 10°, 20° and 40°), while the minimal glottal diameter was held constant at 0.06 cm. The empirical data were supported by penalty finite element computational results. The results suggest that larger convergent glottal angles correspond to increased pressures and decreased velocities in the glottis upstream of the minimum glottal location, with a reversal of this pattern at the minimal glottal diameter location. The pressure dip near the glottal entrance for divergent glottal angles was greatest for the 10° divergence angle condition, and was sequentially less for 5°, 20°, and 40°. Flow resistance was greater for a convergent angle than a divergent angle of the same value, and least for the 10° divergent condition. Pressure recovery in the glottis suggested that the optimal glottal diffuser angle was near 10°. Results suggest that the glottal geometry has a critical relationship with phonation (especially for vocal efficiency), and therefore important significance to understanding artistic voice and clinical voice management.
Bing Yang; Fuping Gao; DongSheng Jeng; Yingxiang Wu
2009-01-01
In this study, the vortex-induced vibrations of a cylinder near a rigid plane boundary in a steady flow are studied experimentally. The phenomenon of vortex-induced vibrations of the cylinder near the rigid plane boundary is reproduced in the flume. The vortex shedding frequency and mode are also measured by the methods of hot film velocime-ter and hydrogen bubbles. A parametric study is carded out to investigate the influences of reduced velocity, gap-to-diame-ter ratio, stability parameter and mass ratio on the amplitude and frequency responses of the cylinder. Experimental results indicate: (1) the Strouhal number (St) is around 0.2 for the stationary cylinder near a plane boundary in the sub-criti-cal flow regime; (2) with increasing gap-to-diameter ratio (eo/D), the amplitude ratio (A/D) gets larger but frequency ratio (f/fn) has a slight variation for the case of larger val-ues of e0/D(e0/D 0.66 in this study); (3) there is a clear difference of amplitude and frequency responses of the cylin-der between the larger gap-to-diameter ratios (e0/D 0.66) and the smaller ones (e0/D < 0.3); (4) the vibration of the cylinder is easier to occur and the range of vibration in terms of Vr number becomes more extensive with decrease of the stability parameter, but the frequency response is affected slightly by the stability parameter; (5) with decreasing mass ratio,the width of the lock-in ranges in terms of Vr and the frequency ratio(f/fn)become large.
U.S. Geological Survey, Department of the Interior — This digital data set defines the lateral boundary of the area simulated by the steady-state ground-water flow model of the Death Valley regional ground-water flow...
Schmidt, John C.; Topping, David J.; Rubin, David M.; Hazel, Joseph E.; Kaplinski, Matt; Wiele, Stephen M.; Goeking, Sara A.
2007-01-01
The low summer steady flows (LSSF) experiment of 2000 further demonstrated that spike flows released from Glen Canyon Dam redistribute sand from the channel bed and lower elevation parts of eddy sandbars to channel-margin deposits and the higher elevation parts of eddy sandbars. Unfortunately, summer 2000 was a period of unusually low tributary influx of sediment and there was little fine sediment (i.e., sand and finer material) available for redistribution. Nevertheless, the low steady flows, which held releases from the dam steady at 230 m3/s (8,100 ft3/s), during the summer of 2000 effectively retained on the channel bed the little sediment that was supplied by tributaries, and a subsequent 4-day, 870 m3/s (30,700 ft3/s) spike flow caused modest increases in the area of the mid-elevation zone of eddy sandbars.
Reynolds, C. A.; Menke, H. P.; Blunt, M. J.; Krevor, S. C.
2015-12-01
We observe a new type of non-wetting phase flow using time-resolved pore scale imaging. The traditional conceptual model of drainage involves a non-wetting phase invading a porous medium saturated with a wetting phase as either a fixed, connected flow path through the centres of pores or as discrete ganglia which move individually through the pore space, depending on the capillary number. We observe a new type of flow behaviour at low capillary number in which the flow of the non-wetting phase occurs through networks of persistent ganglia that occupy the large pores but continuously rearrange their connectivity (Figure 1). Disconnections and reconnections occur randomly to provide short-lived pseudo-steady state flow paths between pores. This process is distinctly different to the notion of flowing ganglia which coalesce and break-up. The size distribution of ganglia is dependent on capillary number. Experiments were performed by co-injecting N2and 25 wt% KI brine into a Bentheimer sandstone core (4mm diameter, 35mm length) at 50°C and 10 MPa. Drainage was performed at three flow rates (0.04, 0.3 and 1 ml/min) at a constant fractional flow of 0.5 and the variation in ganglia populations and connectivity observed. We obtained images of the pore space during steady state flow with a time resolution of 43 s over 1-2 hours. Experiments were performed at the Diamond Light Source synchrotron. Figure 1. The position of N2 in the pore space during steady state flow is summed over 40 time steps. White indicates that N2 occupies the space over >38 time steps and red <5 time steps.
Pasquier-Guilbert, N.
2004-12-15
Simultaneous knowledge of local velocity and equivalence ratio is very important in numerous combustion applications and especially for direct injection engines where the flame propagates through a heterogeneous concentration distribution of fuel-air mixture. This study reproduce heterogeneities of equivalence ratio with propane and air in a constant volume combustion vessel. The local influence of velocity and equivalence ratio on the propagation of a spark-ignited flame is studied. To create a stratification, a rich axisymmetric pulsed jet is injected in a leaner chamber and the mixing is ignited. Two optical diagnostics are used simultaneously, PIV for velocity and FARLIF for equivalence ratio, with or without combustion. All properties and range of applications of PIV and FARLIF have been verified. These methods were then used to study the characteristics of stratified combustion. (author)
Miller, R.E.
1977-01-01
A steady-state simulation model was applied to the shallow hydrothermal system in the East Mesa area of Imperial Valley, Calif. The steady-state equations of flow and heat transport were solved by use of a Galerkin, finite-element method. A solution was obtained by iterating between the temperature and pressure equations, using updated densities and viscosities. Temperature and pressure were obtained for each node, and corresponding head values were calculated. The simulated temperature and pressure patterns correlated well with the observed patterns. Additional data, mainly from test drilling, would be required for construction of a similar model of the deep hydrothermal system.
King, G P [Instituto de Oceanografia, Faculdade de Ciencias, Universidade de Lisboa, Campo Grande, 1749-016 Lisboa (Portugal); Rudman, Murray [CSIRO Manufacturing and Infrastructure Technology, P.O. Box 56, Highett, Vic. 3190 (Australia); Rowlands, G [Department of Physics, University of Warwick, Coventry CV4 7AL (United Kingdom)], E-mail: gkinglisboa@gmail.com, E-mail: Murray.Rudman@csiro.au, E-mail: G.Rowlands@warwick.ac.uk
2008-01-31
The dimensionless effective axial diffusion coefficient, D{sub z}, calculated from particle trajectories in steady wavy vortex flow in a narrow gap Taylor-Couette system, has been determined as a function of Reynolds number (R = Re/Re{sub c}), axial wavelength ({lambda}{sub z}), and the number of azimuthal waves (m). Two regimes of Reynolds number were found: (i) when R < 3.5, D{sub z} has a complex and sometimes multi-modal dependence on Reynolds number; (ii) when R > 3.5, D{sub z} decreases monotonically. Eulerian quantities measuring the departure from rotational symmetry, {psi}{sub {theta}}, and flexion-free flow, {psi}{sub {nu}}, were calculated. The space-averaged quantities {phi}-bar{sub {theta}} and {phi}-bar{sub {nu}} were found to have, unlike D{sub z}, a simple unimodal dependence on R. In the low R regime the correlation between D{sub z} and {psi}{sub {theta}}{psi}{sub {nu}} was complicated and was attributed to variations in the spatial distribution of the wavy disturbance occurring in this range of R. In the large R regime, however, the correlation simplified to D{sub z}{approx}{phi}-bar{sub {theta}}{phi}-bar{sub {nu}} for all wave states, and this was attributed to the growth of an integrable vortex core and the concentration of the wavy disturbance into narrow regions near the outflow and inflow jets. A reservoir model of a wavy vortex was used to determine the rate of escape across the outflow and inflow boundaries, the size of the 'escape basins' (associated with escape across the outflow and inflow boundaries), and the size of the trapping region in the vortex core. In the low R regime after the breakup of all KAM tori, the outflow basin ({gamma}{sub O}) is larger than the inflow basin ({gamma}{sub I}), and both {gamma}{sub O} and {gamma}{sub I} are (approximately) independent of R. In the large R regime, with increasing Reynolds number the trapping region grows, the outflow basin decreases, and the inflow basin shows a slight increase
Aisopou, Angeliki; Stoianov, Ivan; Graham, Nigel J D
2012-01-01
Monitoring the quality of drinking water from the treatment plant to the consumers tap is critical to ensure compliance with national standards and/or WHO guideline levels. There are a number of processes and factors affecting the water quality during transmission and distribution which are little understood. A significant obstacle for gaining a detailed knowledge of various physical and chemical processes and the effect of the hydraulic conditions on the water quality deterioration within water supply systems is the lack of reliable and low-cost (both capital and O & M) water quality sensors for continuous monitoring. This paper has two objectives. The first one is to present a detailed evaluation of the performance of a novel in-pipe multi-parameter sensor probe for reagent- and membrane-free continuous water quality monitoring in water supply systems. The second objective is to describe the results from experimental research which was conducted to acquire continuous water quality and high-frequency hydraulic data for the quantitative assessment of the water quality changes occurring under steady and unsteady-state flow conditions. The laboratory and field evaluation of the multi-parameter sensor probe showed that the sensors have a rapid dynamic response, average repeatability and unreliable accuracy. The uncertainties in the sensor data present significant challenges for the analysis and interpretation of the acquired data and their use for water quality modelling, decision support and control in operational systems. Notwithstanding these uncertainties, the unique data sets acquired from transmission and distribution systems demonstrated the deleterious effect of unsteady state flow conditions on various water quality parameters. These studies demonstrate: (i) the significant impact of the unsteady-state hydraulic conditions on the disinfectant residual, turbidity and colour caused by the re-suspension of sediments, scouring of biofilms and tubercles from the
Voss, Clifford I.; Simmons, Craig T.; Robinson, Neville I.
2010-01-01
This benchmark for three-dimensional (3D) numerical simulators of variable-density groundwater flow and solute or energy transport consists of matching simulation results with the semi-analytical solution for the transition from one steady-state convective mode to another in a porous box. Previous experimental and analytical studies of natural convective flow in an inclined porous layer have shown that there are a variety of convective modes possible depending on system parameters, geometry and inclination. In particular, there is a well-defined transition from the helicoidal mode consisting of downslope longitudinal rolls superimposed upon an upslope unicellular roll to a mode consisting of purely an upslope unicellular roll. Three-dimensional benchmarks for variable-density simulators are currently (2009) lacking and comparison of simulation results with this transition locus provides an unambiguous means to test the ability of such simulators to represent steady-state unstable 3D variable-density physics.
Double criticality and the two-way Boussinesq equation in stratified shallow water hydrodynamics
Bridges, Thomas J.; Ratliff, Daniel J.
2016-06-01
Double criticality and its nonlinear implications are considered for stratified N-layer shallow water flows with N = 1, 2, 3. Double criticality arises when the linearization of the steady problem about a uniform flow has a double zero eigenvalue. We find that there are two types of double criticality: non-semisimple (one eigenvector and one generalized eigenvector) and semi-simple (two independent eigenvectors). Using a multiple scales argument, dictated by the type of singularity, it is shown that the weakly nonlinear problem near double criticality is governed by a two-way Boussinesq equation (non-semisimple case) and a coupled Korteweg-de Vries equation (semisimple case). Parameter values and reduced equations are constructed for the examples of two-layer and three-layer stratified shallow water hydrodynamics.
El-Asrag, Hossam A.; Ju, Yiguang
2013-04-01
Direct numerical simulations (DNSs) of a stratified flow in a homogeneous compression charge ignition (HCCI) engine are performed to investigate the exhaust gas recirculation (EGR) and temperature/mixture stratification effects on the autoignition of synthetic dimethyl ether (DME) in the negative temperature combustion region. Detailed chemistry for a DME/air mixture is employed and solved by a hybrid multi-time scale (HMTS) algorithm to reduce the computational cost. The effect of ? to mimic the EGR effect on autoignition are studied. The results show that adding ? enhances autoignition by rapid OH radical pool formation (34-46% reduction in ignition delay time) and changes the ignition heat release rates at different ignition stages. Sensitivity analysis is performed and the important reactions pathways affecting the autoignition are specified. The DNS results show that the scales introduced by thermal and mixture stratifications have a strong effect after the low temperature chemistry (LTC) ignition especially at the locations of high scalar dissipation rates. Compared to homogenous ignition, stratified ignitions show similar first autoignition delay times, but 18% reduction in the second and third ignition delay times. The results also show that molecular transport plays an important role in stratified low temperature ignition, and that the scalar mixing time scale is strongly affected by local ignition in the stratified flow. Two ignition-kernel propagation modes are observed: a wave-like, low-speed, deflagrative mode and a spontaneous, high-speed, ignition mode. Three criteria are introduced to distinguish these modes by different characteristic time scales and Damkhöler numbers using a progress variable conditioned by an ignition kernel indicator. The low scalar dissipation rate flame front is characterized by high displacement speeds and high mixing Damkhöler number. The proposed criteria are applied successfully at the different ignition stages and
Ralston, Barbara E.
2011-01-01
In the spring and summer of 2000, a series of steady discharges of water from Glen Canyon Dam on the Colorado River were used to evaluate the effects of aquatic habitat stability and water temperatures on native fish growth and survival, with a special focus on the endangered humpback chub (Gila cypha), downstream from the dam in Grand Canyon. The steady releases were bracketed by peak powerplant releases in late-May and early-September. The duration and volume of releases from the dam varied between spring and summer. The intent of the experimental hydrograph was to mimic predam river discharge patterns by including a high, steady discharge in the spring and a low, steady discharge in the summer. The hydrologic experiment was called the Low Steady Summer Flow (LSSF) experiment because steady discharges of 226 m3/s dominated the hydrograph for 4 months from June through September 2000. The experimental hydrograph was developed in response to one of the U.S. Fish and Wildlife Service's Recommended and Prudent Alternatives (RPA) in its Biological Opinion of the Operation of Glen Canyon Dam Final Environmental Impact Statement. The RPA focused on the hypothesis that seasonally adjusted steady flows were dam operations that might benefit humpback chub more than the Record of Decision operations, known as Modified Low Fluctuating Flow (MLFF) operations. Condensed timelines between planning and implementation (2 months) of the experiment and the time required for logistics, purchasing, and contracting resulted in limited data collection during the high-release part of the experiment that occurred in spring. The LSSF experiment is the longest planned hydrograph that departed from the MLFF operations since Record of Decision operations began in 1996. As part of the experiment, several studies focused on the responses of physical properties related to environments that young-of-year (YOY) native fish might occupy (for example, measuring mainstem and shoreline water
Fisher, J. C.; Ackerman, D. J.; Rousseau, J. P.; Rattray, G. W.
2009-12-01
Three-dimensional steady-state and transient models of groundwater flow and advective transport through the fractured basalts and interbedded sediments of the Eastern Snake River Plain (ESRP) aquifer were developed by the U.S. Geological Survey in cooperation with the U.S. Department of Energy. The model domain covers an area of 1,940 square miles that includes most of the Idaho National Laboratory (INL). A 50-year history of waste disposal at the INL has resulted in measurable concentrations of waste contaminants in the aquifer. Numerical models simulated 1980 steady-state conditions and transient flow for 1980-95. In the transient model, streamflow infiltration was the major stress. The models were calibrated using the parameter-estimation program incorporated in MODFLOW-2000. The steady-state model reasonably simulated the observed water-table altitude and gradients. Simulation of transient conditions reproduced changes in the flow system resulting from episodic infiltration from the Big Lost River. Analysis of simulations shows that flow is (1) dominantly horizontal through interflow zones in basalt, vertical anisotropy resulting from contrasts in hydraulic conductivity of different types of basalt and the interbedded sediments, (2) temporally variable due to streamflow infiltration from the Big Lost River, and (3) moving downward downgradient of the INL. Particle-tracking simulations were used to evaluate how simulated groundwater flow paths and travel times differ between the steady-state and transient flow models, and how well model-derived groundwater flow directions and velocities compare to independently-derived estimates. Particle tracking also was used to simulate the growth of tritium plumes originating at two INL facilities over a 16 year period under steady-state and transient flow conditions (1953-68). The shape, dimensions, and areal extent of these plumes were compared to a map of the plumes for 1968 from tritium releases beginning in 1952
Reda, G. Abdel-Rahman; M. Khader, M.; Ahmed, M. Megahed
2013-03-01
The Lie group method is applied to present an analysis of the magneto hydro-dynamics (MHD) steady laminar flow and the heat transfer from a warm laminar liquid flow to a melting moving surface in the presence of thermal radiation. By using the Lie group method, we have presented the transformation groups for the problem apart from the scaling group. The application of this method reduces the partial differential equations (PDEs) with their boundary conditions governing the flow and heat transfer to a system of nonlinear ordinary differential equations (ODEs) with appropriate boundary conditions. The resulting nonlinear system of ODEs is solved numerically using the implicit finite difference method (FDM). The local skin-friction coefficients and the local Nusselt numbers for different physical parameters are presented in a table.
Baccouche, Ryan; Tahar, Mabrouk Ben; Moreau, Solène
2016-09-01
A Perfectly Matched Layer (PML) for aeroacoustic problems using Galbrun's equation in the presence of an axial and a swirling steady mean flow is investigated in a cylindrical coordinates system. This equation is based on an Eulerian-Lagrangian description and leads to a wave equation written only in terms of the Lagrangian perturbation of the displacement. Galbrun's equation is solved by a mixed pressure-displacement Finite Element Method (FEM). To avoid instabilities in the presence of mean flow, a geometric transformation is presented. The validity and efficiency of the proposed PML formulation are established through comparisons with analytical, semi-analytical model based on Pridmore-Brown equation (extended to an axial and a swirling mean flow) and with multiple-scale models. The interest of the formulation is shown through an example of aeroacoustic radiation.
Reda G.Abdel-Rahman; M.M.Khader; Ahmed M.Megahed
2013-01-01
The Lie group method is applied to present an analysis of the magneto hydro-dynamics (MHD) steady laminar flow and the heat transfer from a warm laminar liquid flow to a melting moving surface in the presence of thermal radiation.By using the Lie group method,we have presented the transformation groups for the problem apart from the scaling group.The application of this method reduces the partial differential equations (PDEs) with their boundary conditions governing the flow and heat transfer to a system of nonlinear ordinary differential equations (ODEs) with appropriate boundary conditions.The resulting nonlinear system of ODEs is solved numerically using the implicit finite difference method (FDM).The local skin-friction coefficients and the local Nusselt numbers for different physical parameters are presented in a table.
Suppression of stratified explosive interactions
Meeks, M.K.; Shamoun, B.I.; Bonazza, R.; Corradini, M.L. [Wisconsin Univ., Madison, WI (United States). Dept. of Nuclear Engineering and Engineering Physics
1998-01-01
Stratified Fuel-Coolant Interaction (FCI) experiments with Refrigerant-134a and water were performed in a large-scale system. Air was uniformly injected into the coolant pool to establish a pre-existing void which could suppress the explosion. Two competing effects due to the variation of the air flow rate seem to influence the intensity of the explosion in this geometrical configuration. At low flow rates, although the injected air increases the void fraction, the concurrent agitation and mixing increases the intensity of the interaction. At higher flow rates, the increase in void fraction tends to attenuate the propagated pressure wave generated by the explosion. Experimental results show a complete suppression of the vapor explosion at high rates of air injection, corresponding to an average void fraction of larger than 30%. (author)
H. Saathoff
2003-01-01
Full Text Available This article describes an investigation of the casingwall flow phenomena in a single-stage, axial-flow, low-speed compressor at part-load conditions, utilizing an oil-flow technique to visualize the boundary layer development and highfrequency sensors to measure ensemble-averaged velocity and flow-angle distributions as well as unsteady total pressure distributions. Representative results are shown and discussed. The results enable different sources of endwall blockage to be identified and changes with flow rate to be determined.
Steady periodic gravity waves with surface tension
Walsh, Samuel
2009-01-01
In this paper we consider two-dimensional, stratified, steady water waves propagating over an impermeable flat bed and with a free surface. The motion is assumed to be driven by capillarity (that is, surface tension) on the surface and a gravitational force acting on the body of the fluid. We prove the existence of global continua of classical solutions that are periodic and traveling. This is accomplished by first constructing a 1-parameter family of laminar flow solutions, $\\mathcal{T}$, then applying bifurcation theory methods to obtain local curves of small amplitude solutions branching from $\\mathcal{T}$ at an eigenvalue of the linearized problem. Each solution curve is then continued globally by means of a degree theoretic theorem in the spirit of Rabinowitz. Finally, we complement the degree theoretic picture by proving an alternate global bifurcation theorem via the analytic continuation method of Dancer.
Tyree, M T; Christy, A L; Ferrier, J M
1974-10-01
A simple steady state iterative solution of Münch pressure-flow in unbranched sieve tubes containing only water and sucrose is derived. The iterative equations can be solved on a programmable desk calculator. Solutions are presented for steady state transport with specific mass transfer rates up to 1.5 x 10(-5) mole second(-1) centimeters(-2) (= 18.5 grams hour(-1) centimeters(-2)) over distances in excess of 50 meters. The calculations clearly indicate that a Münch pressure-flow system can operate over long distances provided (a) the sieve tube is surrounded by a semipermeable membrane; (b) sugars are actively loaded in one region and unloaded at another; (c) the sieve pores are unblocked so that the sieve tube hydraulic conductivity is high (around 4 centimeters(2) second(-1) bar(-1)); (d) the sugar concentration is kept high (around one molar in the source region); and (e) the average sap velocity is kept low (around 20-50 centimeters hour(-1)). The dimensions of sieve cells in several species of plants are reviewed and sieve tube hydraulic conductivities are calculated; the values range from 0.2 to 20 centimeters(2) second(-1) bar(-1). For long distance pressure-flow to occur, the hydraulic conductivity of the sieve cell membranes must be about 5 x 10(-7) centimeters second(-1) bar(-1) or greater.
Park, Sung-Hong; Wang, Danny J.J.; Duong, Timothy Q.
2013-01-01
We implemented pseudo-continuous ASL (pCASL) with 2D and 3D balanced steady state free precession (bSSFP) readout for mapping blood flow in the human brain, retina, and kidney, free of distortion and signal dropout, which are typically observed in the most commonly used echo-planar imaging acquisition. High resolution functional brain imaging in the human visual cortex was feasible with 3D bSSFP pCASL. Blood flow of the human retina could be imaged with pCASL and bSSFP in conjunction with a phase cycling approach to suppress the banding artifacts associated with bSSFP. Furthermore, bSSFP based pCASL enabled us to map renal blood flow within a single breath hold. Control and test-retest experiments suggested that the measured blood flow values in retina and kidney were reliable. Because there is no specific imaging tool for mapping human retina blood flow and the standard contrast agent technique for mapping renal blood flow can cause problems for patients with kidney dysfunction, bSSFP based pCASL may provide a useful tool for the diagnosis of retinal and renal diseases and can complement existing imaging techniques. PMID:23664680
Zhiyin Yang
2014-12-01
Full Text Available A complex flow field is created when a vertical/short take-off and landing aircraft is operating near ground. One major concern for this kind of aircraft in ground effect is the possibility of ingestion of hot gases from the jet engine exhausts back into the engine, known as hot gas ingestion, which can increase the intake air temperature and also reduce the oxygen content in the intake air, potentially leading to compressor stall, low combustion efficiency and causing a dramatic loss of lift. This flow field can be represented by the configuration of twin impinging jets in a cross-flow. Accurate prediction of this complicated flow field under the Reynolds averaged Navier–Stokes (RANS approach (current practise in industry is a great challenge as previous studies suggest that some important flow features cannot be captured by the Steady-RANS (SRANS approach even with a second-order Reynolds stress model (RSM. This paper presents a numerical study of this flow using the Unsteady-RANS (URANS approach with a RSM and the results clearly indicate that the URANS approach is superior than the SRANS approach but still the predictions of Reynolds stress are not accurate enough.
Vernieu, William S.; Anderson, Craig R.
2013-01-01
Water releases from Glen Canyon Dam, Arizona, are the primary determinant of streamflow, sediment transport, water quality, and aquatic and riparian habitat availability in the Colorado River downstream of the dam in Grand Canyon. The presence and operation of the dam have transformed the seasonally warm Colorado River into a consistently cold river because of hypolimnetic, or deep-water, releases from the penstock withdrawal structures on the dam. These releases have substantially altered the thermal regime of the downstream riverine environment. This, in turn, has affected the biota of the river corridor, particularly native and nonnative fish communities and the aquatic food web. In the spring and summer of 2000, a Low Steady Summer Flow experiment was conducted by the U.S. Geological Survey and the Bureau of Reclamation to evaluate the effects of the experimental flow on physical and biological resources of the Colorado River ecosystem downstream from Glen Canyon Dam to Lake Mead on the Arizona-Nevada border. This report describes the water temperatures collected during the experimental flow from 14 nearshore sites in the river corridor in Grand Canyon to assess the effects of steady releases on the thermal dynamics of nearshore environments. These nearshore areas are characterized by low-velocity flows with some degree of isolation from the higher velocity flows in the main channel and are hypothesized to be important rearing environments for young native fish. Water-temperature measurements were made at 14 sites, ranging from backwater to open-channel environments. Warming during daylight hours, relative to main-channel temperatures, was measured at all sites in relation to the amount of isolation from the main-channel current. Boat traffic, amount of direct solar radiation, and degree of isolation from the main-channel current appear to be the primary factors affecting the differential warming of the nearshore environment.
Jun, Brian H; Saikrishnan, Neelakantan; Yoganathan, Ajit P
2014-03-01
A number of clinical, in vitro and computational studies have shown the potential for thromboembolic complications in bileaflet mechanical heart valves (BMHV), primarily due to the complex and unsteady flows in the valve hinges. These studies have focused on quantitative and qualitative parameters such as velocity magnitude, turbulent shear stresses, vortex formation, and platelet activation to identify potential for blood damage. However, experimental characterization of the whole flow fields within the valve hinges has not yet been conducted. This information can be utilized to investigate instantaneous damage to blood elements and also to validate numerical studies focusing on the hinge's complex fluid dynamics. The objective of this study was therefore to develop a high-resolution imaging system to characterize the flow fields and global velocity maps in a BMHV hinge. In this study, the steady leakage hinge flow fields representing the diastolic phase during the cardiac cycle in a 23 mm St. Jude Medical regent BMHV in the aortic position were characterized using a two-dimensional micro particle image velocimetry system. Diastolic flow was simulated by imposing a static pressure head on the aortic side. Under these conditions, a reverse flow jet from the aortic to the ventricular side was observed with velocities in the range of 1.47-3.24 m/s, whereas low flow regions were observed on the ventricular side of the hinge with viscous shear stress magnitude up to 60 N/m². High velocities and viscous shearing may be associated with platelet activation and hemolysis, while low flow zones can cause thrombosis due to increased residence time in the hinge. Overall, this study provides a high spatial resolution experimental technique to map the fluid velocity in the BMHV hinge, which can be extended to investigate micron-scale flow domains in various prosthetic devices under different hemodynamic conditions.
Wirestam, R.; Knutsson, L.; Risberg, J.; Boerjesson, S.; Larsson, E.M.; Gustafson, L.; Passant, U.; Staahlberg, F. [Depts. of Medical Radiation Physics, Diagnostic Radiology, Psychiatry, and Psychogeriatrics, Lund Univ, Lund (Sweden)
2007-07-15
Background: Attempts to retrieve absolute values of cerebral blood flow (CBF) by dynamic susceptibility contrast magnetic resonance imaging (DSC-MRI) have typically resulted in overestimations. Purpose: To improve DSC-MRI CBF estimates by calibrating the DSC-MRI-based cerebral blood volume (CBV) with a corresponding T1-weighted (T1W) steady-state (ss) CBV estimate. Material and Methods: 17 volunteers were investigated by DSC-MRI and 133Xe SPECT. Steady-state CBV calculation, assuming no water exchange, was accomplished using signal values from blood and tissue, before and after contrast agent, obtained by T1W spin-echo imaging. Using steady-state and DSC-MRI CBV estimates, a calibration factor K = CBV(ss)/CBV(DSC) was obtained for each individual. Average whole-brain CBF(DSC) was calculated, and the corrected MRI-based CBF estimate was given by CBF(ss) = KxCBF(DSC). Results: Average whole-brain SPECT CBF was 40.1{+-}6.9 ml/min 100 g, while the corresponding uncorrected DSC-MRI-based value was 69.2{+-}13.8 ml/mi 100 g. After correction with the calibration factor, a CBF(ss) of 42.7{+-}14.0 ml/min 100 g was obtained. The linear fit to CBF(ss)-versus-CBF(SPECT) data was close to proportionality (R = 0.52). Conclusion: Calibration by steady-state CBV reduced the population average CBF to a reasonable level, and a modest linear correlation with the reference 133Xe SPECT technique was observed. Possible explanations for the limited accuracy are, for example, large-vessel partial-volume effects, low post-contrast signal enhancement in T1W images, and water-exchange effects.
Zhu, H P; Yu, A B [Centre for Simulation and Modeling of Particulate Systems, School of Materials Science and Engineering, University of New South Wales, Sydney, NSW 2052 (Australia)
2004-05-21
Granular flow in a cylindrical hopper with flat bottom is investigated based on the results generated by the discrete element method. The dependence of flow behaviour on the geometric and physical parameters of the hopper and particles, such as the orifice size and wall roughness of hoppers, and frictional and damping coefficients between particles, is analysed to establish the spatial and statistical distributions of microdynamic variables related to flow and force structures such as velocity, porosity, coordination number, and interaction forces between particles and between particles and walls. It is shown from the velocity field that there are four different zones in the hopper flow: a stagnant zone, a plug flow zone, a converging flow zone, and a transition zone from plug flow to converging flow. The Beverloo equation can describe the relationship between discharge rate and orifice size; however, the constants in the equation may vary with the wall friction coefficient, particle friction and damping coefficients. The flow and force structures of particles in the hopper are spatially non-uniform. In particular, porosity is high in the region near the orifice and low in the upper part and around the bottom corner of the hopper, whilst the coordination number has an opposite distribution. Large contact forces are experienced by particles around the bottom corner whereas small forces are experienced by particles in the upper part and the region near the orifice. However, there is a region above the orifice where particles experience the maximum total interaction forces between particles; the forces gradually propagate from this region into the bed and have a minimum value in the central upper part. The velocity distribution, flow and force structures are affected by the geometric and physical parameters of the hopper and particles.
Strongly Stratified Turbulence Wakes and Mixing Produced by Fractal Wakes
Dimitrieva, Natalia; Redondo, Jose Manuel; Chashechkin, Yuli; Fraunie, Philippe; Velascos, David
2017-04-01
This paper describes Shliering and Shadowgraph experiments of the wake induced mixing produced by tranversing a vertical or horizontal fractal grid through the interfase between two miscible fluids at low Atwood and Reynolds numbers. This is a configuration design to models the mixing across isopycnals in stably-stratified flows in many environmental relevant situations (either in the atmosphere or in the ocean. The initial unstable stratification is characterized by a reduced gravity: g' = gΔρ ρ where g is gravity, Δρ being the initial density step and ρ the reference density. Here the Atwood number is A = g' _ 2 g . The topology of the fractal wake within the strong stratification, and the internal wave field produces both a turbulent cascade and a wave cascade, with frecuen parametric resonances, the envelope of the mixing front is found to follow a complex non steady 3rd order polinomial function with a maximum at about 4-5 Brunt-Vaisalla non-dimensional time scales: t/N δ = c1(t/N) + c2g Δρ ρ (t/N)2 -c3(t/N)3. Conductivity probes and Shliering and Shadowgraph visual techniques, including CIV with (Laser induced fluorescence and digitization of the light attenuation across the tank) are used in order to investigate the density gradients and the three-dimensionality of the expanding and contracting wake. Fractal analysis is also used in order to estimate the fastest and slowest growing wavelengths. The large scale structures are observed to increase in wave-length as the mixing progresses, and the processes involved in this increase in scale are also examined.Measurements of the pointwise and horizontally averaged concentrations confirm the picture obtained from past flow visualization studies. They show that the fluid passes through the mixing region with relatively small amounts of molecular mixing,and the molecular effects only dominate on longer time scales when the small scales have penetrated through the large scale structures. The Non
Kernodle, J.M.; Scott, W.B.
1986-01-01
As part of the Southwest Alluvial Basins study, model was constructed to simulate the alluvial aquifer system underlying the Albuquerque-Belen Basin. The model was used to simulate the steady-state flow condition assumed to have existed prior to 1960. Until this time there apparently were no long-term groundwater level changes of a significant magnitude outside the immediate vicinity of Albuquerque. Therefore, the construction of a steady-state flow model of the aquifer system based on reported hydrologic data predating 1960 was justified. During construction of the steady-state model, simulated hydraulic conductivity values were adjusted, within acceptable physical limits, until a best fit between measured or reported and computed heads at 34 control wells was achieved. The modeled area was divided into six sub-areas, or zones, within each of which hydraulic conductivity was assumed to be uniform. The model consisted of six layers for each of which simulated transmissivity was proportional to the layer thickness. Adjustments to simulated hydraulic conductivity values in the different zones resulted in final values that ranged from a low of 0.25 ft/day in the west to 50 ft/day in the eastern part of the basin. The error of the simulation, defined as the absolute difference between the computed and the measured or reported water level at the corresponding point in the physical system being modeled, ranged from 0.6 ft to 36 ft, with an average of 14.6 ft for the 34 control wells. (Author 's abstract)
Ellahi, Rahmat; Wang, Xinil; Hameed, Muhammad
2014-02-01
This article is concerned with the study of heat transfer and nonlinear slip effects on the Couette flow of a third-grade fluid. Numerical solutions are obtained by solving nonlinear differential equations using the higher-order Chebyshev spectral method. The results for no slip and no thermal slip become special cases of this study. Moreover, the results for Poiseuille flow can be obtained as a special case from the generalized Couette flow analysis by setting the plate velocity to zero. Graphical results for involved pertinent parameters are sketched and examined.
Zhao, Peng; Li, Qiang; Kuang, S. B.; Zou, Zongshu
2017-02-01
Transient flow structures in a continuous casting mold can strongly influence the slag entrainment in liquid steel and the bubbles capture in the initial solidified shell, both of which are associated with the quality of the final product. This paper presents a numerical study of the turbulent flow with a top free surface in the continuous casting mold at a meso-scale level by a three-dimensional combined approach of Free Surface Lattice Boltzmann Method and Large Eddy Simulation (FSLBM-LES). The validity of the model is verified by the good agreement between the calculated results and the measurements from various water experiments in terms of the flow velocity and free surface profile. The mathematical model is then used to reveal the transient and spatiotemporal asymmetric characteristics associated with the transient flow field and the free surface fluctuation, although the steady state operation is considered during the continuous casting process. The results show that the locations of the jets of liquid steel from the two out ports of the Submerged Entry Nozzle (SEN) always fluctuate alternatively within a certain range, and periodically deviate from the design angle of the SEN within the same time period. The oscillating behavior of the jets promotes the asymmetric flow patterns and multi-scale vortices at both sides of the SEN. By introducing the Q-criterion in the results analysis, the formation, development, and shedding of the coherent structure (CS) of the turbulent flow are quantitatively characterized. The interaction between the transient flow patterns and the fluctuations of the top free surface as well as the evolution of the transient profile and velocities of the free surface are also demonstrated. The results obtained from the current study suggest that the FSLBM-LES model offers a promising way to study the complex flows and related transfer phenomena in the continuous casting process.
Zlotnik, V A; Zurbuchen, B R; Ptak, T
2001-01-01
Over the last decade the dipole-flow test (DFT) evolved from the general idea of using recirculatory flow to evaluate aquifer properties, to the development of prototype instrumentation and feasibility studies, to a reliable tool for characterization of aquifer heterogeneity. The DFT involves the interpretation of head in recirculatory flow between injection and extraction sections (chambers) in a single well isolated from each other by a multipacker system. In this study, the steady-state dipole flow test (DFT) has been used to characterize the statistics of horizontal hydraulic conductivity (Kr) of the highly permeable, heterogeneous, and thin aquifer at the Horkheimer Insel site, Germany. In previous studies, Kr estimates were based on the steady-state head difference between chambers. A new by-chamber interpretation is proposed that is based on drawdown within each individual chamber. This interpretation yields more detailed information on structure of heterogeneity of the aquifer without introducing complexity into the analysis. The DFT results indicate that Kr ranges from 49 to 6000 m/day (mean ln Kr [(m/s)] approximately -4, and variance of ln Kr [(m/s)] approximately 1-2). Descriptive statistics from the DFT compare well with those from previous field and laboratory tests (pumping, borehole flowmeter, and permeameter tests and grain-size analysis) at this site. It is shown that the role of confining boundaries in the DFT interpretation is negligible even in this case of a thin (< 4 m thick) aquifer. This study demonstrates the flexibility of the DFT and expands the potential application of this method to a wide range of hydrogeologic settings.
张晓俊; 权龙; 赵斌
2016-01-01
针对现有液压阀流场(Computational fluid dynamics，CFD)仿真研究中，采用单相流模型进行计算，忽略了流体气化现象对流体密度及其流场的影响，仿真所得相对压力过低与实际不符的问题，运用Fluent软件，采用两相流模型，研究内流式滑阀流场分布，分析阀口开度、流量变化对于阀芯壁面压力分布及其稳态液动力的影响；设计一种壁面压力分布测量的试验方案，测量得到阀芯壁面的压力分布，并通过表面积积分法求出阀芯所受稳态液动力。结果表明：试验所得的内流式滑阀的壁面压力分布及其稳态液动力与仿真结果趋势一致，壁面压力峰值随着阀口开度的增大而减小；阀口开度较小时，稳态液动力的方向为阀口关闭的方向，在阀口开度达到临界点时，稳态液动力的方向为阀口打开的方向；滑阀稳态液动力公式计算由于忽略了入口射流角的变化及其出口处的动量，得到的稳态液动力误差较大，且方向始终指向阀口打开的方向。%In view of the existing problem which does not accord with the fact, that is, in the hydraulic valve flow field CFD study, the single-phase flow model ignores the influence on fluid density and fluid flow field under the condition of cavitation occurred, which leads to the result of the lower relative pressure, by using Fluent software and multiphase model, field distribution is studied on the converged flow sliding valve,and the influence by the change in the flow rate and valve orifice is analyzed on the spool wall pressure distribution and the steady-state flow force. A measurement scheme of wall pressure distribution is designed. The surface integral of the measurement value is the steady flow force. The result is the experimental data is consistent with the simulation’s, and the peak of the wall pressure distribution decreases with the increasing of the orifice area. the orifice area
New considerations on the mass and energy balances in one-dimensional two-phase flow at steady state
Collado, F.J. [Zaragoza Univ. (Spain). Dept. de Ingenieria Mecanica; Munoz, M. [Zaragoza Univ. (Spain). Dept. de Ingenieria Mecanica
1997-08-01
A new equation to be added to the classical mass balance expressions for two-phase flow is presented. It is based on the definition of new differential control volumes of variable length which are proportional to the gas velocity in a compressible flow. The new equation is equivalent to the gas-solids velocity ratio being constant throughout the duct, and it is used to derive a new expression of the energy balance for a two-phase, non-reacting flow. Through this energy balance, new correlations for the pressure drop in pneumatic conveying lines are obtained, showing an excellent agreement with experimental data from the high-pressure research facility of the Institute of Gas Technology, Chicago, IL. Finally, a more general equation, which is also valid for the mass balance of reacting flows, is supplied. (orig.)
Takenaka, N; Fujii, T; Mizubata, M; Yoshii, K
1999-01-01
Three-dimensional void fraction distribution of air-water two-phase flow in a 4x4 rod-bundle near a spacer was visualized by fast neutron radiography using a CT method. One-dimensional cross sectional averaged void fraction distribution was also calculated. The behaviors of low void fraction (thick water) two-phase flow in the rod bundle around the spacer were clearly visualized. It was shown that the void fraction distributions were visualized with a quality similar to those by thermal neutron radiography for low void fraction two-phase flow which is difficult to visualize by thermal neutron radiography. It is concluded that the fast neutron radiography is efficiently applicable to two-phase flow studies.
Abdel-wahed, Mohamed S.
2017-03-01
A mathematical simulation to the cooling process of a flat moving surface using a weak concentration micropolar-nanofluid as a cooling medium has been investigated. The modelling based on the conservation equations of the unsteady case for the momentum and thermal boundary layer taking into consider the effect of suction process and thermal radiation. Using similarity transformation technique, the conservation equations have been transformed to ordinary differential equations that are solved numerically for general case and analytically for the steady case. Surface shear stress, couple shear stress, and the rate of heat transfer are deduced, and the impact of these physical characteristics on the final quality and the mechanical properties of the surface to be cooled discussed.
Abdullah Ahmed Foisal
2016-01-01
Full Text Available MHD free convection over an inclined plate in a thermally stratified high porous medium in the presence of a magnetic field has been studied. The dimensionless momentum and temperature equations have been solved numerically by explicit finite difference technique with the help of a computer programming language Compaq Visual Fortran 6.6a. The obtained results of these studies have been discussed for the different values of well known parameters with different time steps. Also, the stability conditions and convergence criteria of the explicit finite difference scheme has been analyzed for finding the restriction of the values of various parameters to get more accuracy. The effects of various governing parameters on the fluid velocity, temperature, local and average shear stress and Nusselt number has been investigated and presented graphically.
Minakov, A.; Platonov, D.; Sentyabov, A.; Gavrilov, A.
2017-01-01
We performed numerical simulation of flow in a laboratory model of a Francis hydroturbine at three regimes, using two eddy-viscosity- (EVM) and a Reynolds stress (RSM) RANS models (realizable k-ɛ, k-ω SST, LRR) and detached-eddy-simulations (DES), as well as large-eddy simulations (LES). Comparison of calculation results with the experimental data was carried out. Unlike the linear EVMs, the RSM, DES, and LES reproduced well the mean velocity components, and pressure pulsations in the diffusor draft tube. Despite relatively coarse meshes and insufficient resolution of the near-wall region, LES, DES also reproduced well the intrinsic flow unsteadiness and the dominant flow structures and the associated pressure pulsations in the draft tube.
On the existence of steady flow in a channel with one porous wall or two accelerating walls
Chunqing Lu
1998-11-01
Full Text Available channel either with no-slip at one wall and constant uniform suction or injection through another wall, or with two accelerating walls. The flows are governed by the fourth order nonlinear differential equation $F^{iv}+R(FF'''-F'F''=0$. In the former case, the flow is subject to the boundary conditions $F(-1=F'(-1=F'(1=0$, $F(1=-1$. In the latter case, the boundary conditions are $F(-1=F(1=0$, $F'(-1=-1$, $F'(1 = 1$.
A. Mohammadebrahim
2013-01-01
Full Text Available The present paper is an account of an experimental analysis carried out to investigate to what extent the flow characteristics in the intake system of a 4-valve, spark ignition internal combustion engine depend on the experimental conditions at the steady flow test bench. In this respect, the study is aimed at determining the influences of the intake adaptor, test pressure, adaptor length and diameter, adaptor roughness, paddle wheel diameter, and asymmetric valves lifting on the flow coefficient and the swirl intensity measurements. In studies of this kind, researchers generally tend to adopt different test parameters to arrive at a nonuniform base to compare results from several investigations. This work is aimed at verifying the quantitative differences detected using these test parameters. The findings revealed that the swirl intensity depends on the pressure test, adaptor length, and the entry type to a significant degree. Moreover, it was observed that the intake adaptor is the most effective test parameter on the flow coefficient. Finally, the sensitivity analysis has been performed in order to investigate the experimental results and to correlate them with the test parameters.
Wu, Youjun; Yu, Wei; Zhou, Chixing; Xu, Yuanze
2007-04-01
The morphology evolution of immiscible polymer-liquid crystal systems is quite different from flexible polymer-polymer mixtures due to the anisotropic properties of liquid crystals. The deformation and retraction of a single low molar mass liquid crystal 4' -pentyl-4-biphenylcarbonitrile (5CB) droplet and 4' -octyl-4-biphenylcarbonitrile (8CB) dispersed in polydimethyl-siloxane under two-dimensional linear flow was investigated by a computer-controlled four-roll mill, which is equipped with an optical microscope and a digital camera. The deformation parameter and orientation angle during deformation versus capillary number was obtained and compared with calculations using the Maffettone-Minale (MM) model and the Yu-Zhou liquid-crystal (YZ-LC) model. The MM model can describe the behavior of a Newtonian droplet in another Newtonian matrix whereas the YZ-LC model can describe the behavior of a LC droplet in a Newtonian matrix. The results showed that the deformation and rotation of a LC droplet is more difficult than viscoelastic droplets, possibly because of the resistance of the nematic elastic energy induced by the nematic mesogens deformation and orientation under flow field. Furthermore, the different behavior between flow-aligning 5CB and flow-tumbling 8CB droplets and the influence of droplet size of LC on deformation and retraction were discussed by experiment and calculation; the results reveal that the different size LC droplets show different evolution curves.
López-Barrón, Carlos R., E-mail: carlos.r.lopez-barron@exxonmobil.com [ExxonMobil Chemical Company, Baytown Technology and Engineering Complex, Baytown, Texas 77520 (United States); Wagner, Norman J. [Center for Neutron Science, Department of Chemical and Biomolecular Engineering, University of Delaware, Newark, Delaware 19716 (United States); Porcar, Lionel [Institute Laue-Langevin, BP 156, F38042 Grenoble Cedex 9 (France)
2015-05-15
The rheology and three-dimensional microstructure of a concentrated viscoelastic solution of the triblock copolymer poly(ethylene oxide){sub 106}-poly(propylene oxide){sub 68}-poly(ethylene oxide){sub 106} (Pluronic F127) in the protic ionic liquid ethylammonium nitrate are measured by small angle neutron scattering (SANS) under flow in three orthogonal planes. This solution's shear-thinning viscosity is due to the formation of two-dimensional hexagonal close-packed (HCP) sliding layer structure. Shear-melting of the crystalline structure is observed without disruption of the self-assembled micelles, resulting in a change in flow properties. Spatially resolved measurements in the 1–2 plane reveal that both shear-melting and sliding are not uniform across the Couette gap. Melting and recrystallization of the HCP layers occur cyclically during a single large amplitude oscillatory shear (LAOS) cycle, in agreement with the “stick-slip” flow mechanism proposed by Hamley et al. [Phys. Rev. E 58, 7620–7628 (1998)]. Analysis of 3D “structural” Lissajous curves show that the cyclic melting and sliding are direct functions of the strain rate amplitude and show perfect correlation with the cyclic stress response during LAOS. Both viscosity and structural order obey the Delaware–Rutgers rule. Combining rheology with in situ spatiotemporally resolved SANS is demonstrated to elucidate the structural origins of the nonlinear rheology of complex fluids.
Udina, Mireia; Sun, Jielun; Kosović, Branko; Soler, Maria Rosa
2016-11-01
Following Sun et al. (J Atmos Sci 69(1):338-351, 2012), vertical variations of turbulent mixing in stably stratified and neutral environments as functions of wind speed are investigated using the large-eddy simulation capability in the Weather Research and Forecasting model. The simulations with a surface cooling rate for the stable boundary layer (SBL) and a range of geostrophic winds for both stable and neutral boundary layers are compared with observations from the Cooperative Atmosphere-Surface Exchange Study 1999 (CASES-99). To avoid the uncertainty of the subgrid scheme, the investigation focuses on the vertical domain when the ratio between the subgrid and the resolved turbulence is small. The results qualitatively capture the observed dependence of turbulence intensity on wind speed under neutral conditions; however, its vertical variation is affected by the damping layer used in absorbing undesirable numerical waves at the top of the domain as a result of relatively large neutral turbulent eddies. The simulated SBL fails to capture the observed temperature variance with wind speed and the observed transition from the SBL to the near-neutral atmosphere with increasing wind speed, although the vertical temperature profile of the simulated SBL resembles the observed profile. The study suggests that molecular thermal conduction responsible for the thermal coupling between the surface and atmosphere cannot be parameterized through the Monin-Obukhov bulk relation for turbulent heat transfer by applying the surface radiation temperature, as is common practice when modelling air-surface interactions.
Reddy Gnaneswara M.
2012-01-01
Full Text Available In this paper, an analysis has been carried out to study heat and mass transfer effects on steady two-dimensional flow of an electrically conducting incompressible dissipating fluid past an inclined semi-infinite porous surface with heat generation. A scaling group of transformations is applied to the governing equations. The system remains invariant due to some relations among the parameters of the transformations. After finding three absolute invariants, a third-order ordinary differential equation corresponding to the momentum equation, and two secondorder ordinary differential equations corresponding to energy and diffusion equations are derived. The coupled ordinary differential equations along with the boundary conditions are solved numerically. Many results are obtained and a representative set is displayed graphically to illustrate the influence of the various parameters on the dimensionless velocity, temperature and concentration profiles. Comparisons with previously published work are performed and the results are found to be in very good agreement.
Rafik Bouakkaz
2017-06-01
Full Text Available In this work, steady flow-field and heat transfer through a copper–water nanofluid around a circular cylinder, under the influence of both the standard thermal boundary conditions i.e. uniform heat flux (UHF and constant wall temperature (CWT was investigated numerically by using a finite-volume method for Reynolds numbers of 10 to 40. Furthermore, the range of nanoparticle volume fractions (φ considered is 0 ≤ φ ≤ 5%. The variation of the local and the average Nusselt numbers with Reynolds number, and volume fractions are presented for the range of conditions. The average Nusselt number is found to increase with increasing the nanoparticle volume fractions.
Adjali Saadia
2015-01-01
Full Text Available Accurate simulation of turbulent free surface flows around surface ships has a central role in the optimal design of such naval vessels. The flow problem to be simulated is rich in complexity and poses many modeling challenges because of the existence of breaking waves around the ship hull, and because of the interaction of the two-phase flow with the turbulent boundary layer. In this paper, our goal is to estimate the lift and drag coefficients for NACA 0012 of hydrofoil advancing in calm water under steady conditions with free surface and emerged NACA 0015. The commercial CFD software FLUENT version 14 is used for the computations in the present study. The calculated grid is established using the code computer GAMBIT 2.3.26.The shear stress k-ωSST model is used for turbulence modeling and the volume of fluid technique is employed to simulate the free-surface motion. In this computation, the second order upwind scheme is used for discretizing the convection terms in the momentum transport equations, the Modified HRIC scheme for VOF discretisation. The results obtained compare well with the experimental data.
Adjali, Saadia; Belkadi, Mustapha; Aounallah, Mohammed; Imine, Omar
2015-05-01
Accurate simulation of turbulent free surface flows around surface ships has a central role in the optimal design of such naval vessels. The flow problem to be simulated is rich in complexity and poses many modeling challenges because of the existence of breaking waves around the ship hull, and because of the interaction of the two-phase flow with the turbulent boundary layer. In this paper, our goal is to estimate the lift and drag coefficients for NACA 0012 of hydrofoil advancing in calm water under steady conditions with free surface and emerged NACA 0015. The commercial CFD software FLUENT version 14 is used for the computations in the present study. The calculated grid is established using the code computer GAMBIT 2.3.26.The shear stress k-ωSST model is used for turbulence modeling and the volume of fluid technique is employed to simulate the free-surface motion. In this computation, the second order upwind scheme is used for discretizing the convection terms in the momentum transport equations, the Modified HRIC scheme for VOF discretisation. The results obtained compare well with the experimental data.
Mori, N.; Nakamura, K. [Osaka University, Osaka (Japan)
1998-03-15
Numerical simulation was carried out by a nonequilibrium molecular dynamics method to clarify the system structure and rhelogical properties in the steady shear flow of the isotropic and nematic phases of liquid crystalline molecules. The F-GB potential (Lennard-Jones type that represents the model potential of liquid crystalline molecules and that has the dependency of orientation) that has both attractive force and repulsive force as the potential between molecules and the WCA-GB potential in which only repulsive force is considered were used. In an equilibrium system, it was known that the attractive force between molecules facilitates the phase transition of isotropic phase to liquid crystalline phase. In a shear flow, four systems between the isotropic and nematic phases were calculated, and the effect of the shear flow on each system was clarified. Moreover, the effect of the attractive force between the molecules in isotropic and nematic phases was investigated. The result showed that the attractive force between molecules influences the orientation order parameter of the system at a low shear rate. The degree of influence at that time differs in isotropic and nematic phases. 21 refs., 7 figs.
Irvine, Dylan J.; Cartwright, Ian; Post, Vincent E. A.; Simmons, Craig T.; Banks, Eddie W.
2016-02-01
Steady state 1-D analytical solutions to estimate groundwater fluxes from temperature profiles are an attractive option because they are simple to apply, with no complex boundary or initial conditions. Steady state solutions have been applied to estimate both aquifer scale fluxes as well as to estimate groundwater discharge to streams. This study explores the sources of uncertainty in flux estimates from regional scale aquifers caused by sensor precision, aquifer heterogeneity, multidimensional flow and variations in surface temperature due to climate change. Synthetic temperature profiles were generated using 2-D groundwater flow and heat transport models with homogeneous and heterogeneous hydraulic and thermal properties. Temperature profiles were analyzed assuming temperature can be determined with a precision between 0.1°C and 0.001°C. Analysis of synthetic temperature profiles show that the Bredehoeft and Papadopulos (1965) method can provide good estimates of the mean vertical Darcy flux over the length of the temperature profile. Reliable flux estimates were obtained when the ratio of vertical to horizontal flux was as low as 0.1, and in heterogeneous media, providing that temperature at the upper boundary was constant in time. However, temporal increases in surface temperature led to over-estimation of fluxes. Overestimates increased with time since the onset of, and with the rate of surface warming. Overall, the Bredehoeft and Papadopulos (1965) method may be more robust for the conditions with constant temperature distributions than previously thought, but that transient methods that account for surface warming should be used to determine fluxes in shallow aquifers.
Stevenson, D M; Yoganathan, A P; Williams, F P
1985-01-01
Turbulent flow simulations are run for five aortic trileaflet valve geometries, ranging from a valve leaflet orifice area of 1.1 cm2 (Model A1--very stenotic) to 5.0 cm2 (Model A5--natural valve). The simulated data compares well with experimental measurements made downstream of various aortic trileaflet valves by Woo (PhD Thesis, 1984). The location and approximate width and length of recirculation regions are correctly predicted. The less stenotic valve models reattach at the end of the aortic sinus region, 1.1 diameters downstream of the valve. The central jet exiting the less stenotic valve models is not significantly different from fully developed flow, and therefore recovers very quickly downstream of the reattachment point. The more stenotic valves disturb the flow to a greater degree, generating recirculation regions large enough to escape the sinuses and reattach further downstream. Peak turbulent shear stress values downstream of the aortic valve models which approximated prosthetic valves are 125 and 300 Nm-2, very near experimental observations of 150 to 350 Nm-2. The predicted Reynolds stress profiles also present the correct shape, a double peak profile, with the location of the peak occurring at the location of maximum velocity gradient, which occurs near the recirculation region. The pressure drop across model A2 (leaflet orifice area 1.6 cm2) is 20 mmHg at 1.6 diameters downstream. This compares well with values ranging from 19.5 to 26.2 mmHg for valves of similar orifice areas. The pressure drop decreases with decreasing valve stenosis, to a negligible value across the least stenotic valve model. Based on the good agreement between experimental measurements of velocity, shear stress and pressure drop, compared to the simulated data, the model has the potential to be a valuable tool in the analysis of heart valve designs.
Steadiness of a “water bell” surface to a destruction at a flow around of the thin rods assembly
Slesareva Ekaterina; Dekhtyar Ruslan; Ovchinnikov Valeriy
2015-01-01
The experimental research of hydrodynamic stability of a dome-shaped film liquid at a flow around a thin plate has been carried out. Experiments were carry out with a film in shape a «water bell». The film was formed by a leak-in jet of water width 10 mm on a hard disk with diameter 14.5 mm. The width of a plate ζ changed from 0.05 to 3.5 mm. The plate placed along or across relative to the vector of velocity of a liquid in a film. Experiments have shown, that stability of a film of liquid at...
贾俊梅; 刘宇陆
2012-01-01
采用大涡模拟的方法,研究了均匀剪切稳定分层流动.主要对不同梯度Richardson数下湍流动量和标量输运特性进行分析研究.结果表明:随着梯度Richardson数的增大,湍流动能减小,湍流势能增大；垂向热通量和雷诺应力减弱,流向热通量增强；并且在强分层情况下,存在动量和热量的逆梯度输运现象.%LES method is applied to study the sheared homogeneous stratified turbulent flows. The turbulent momentum and scalar transport properties of different gradient Richardson numbers are mainly analyzed. The primary conclusions are; with the increase of gradient Richardson number, turbulent kinetic energy decreases, while the turbulent potential energy increases; vertical heat flux and the Reynolds stress decrease,but the streamwise heat flux increases;Turbulent momentum and heat CGT in strong stratification are more obvious than those of the weak stratified turbulence.
Adeli, Mostafa; Samavati, Vahid
2015-01-01
The extraction of water-soluble polysaccharide from Ziziphus lotus fruit (WPZL) was performed by ultrasonic-assisted extraction method. A Box-Behnken design (BBD) was applied to evaluate the effects of three independent variables (ultrasonic power (X1: 70-100 W), extraction time (X2: 10-30 min), extraction temperature (X3: 55-95 °C), and water to raw material ratio (X4: 5-25)) on the extraction yield of APH. The effect of temperature and concentration on flow behavior of gum solution was studied. WPZL solutions exhibited shear-thinning non-Newtonian flow behavior for concentrations above 0.5% (w/v). The viscosity of fully hydrated gum solutions decreased as temperature increase. The correlation analysis of the mathematical-regression model indicated that quadratic polynomial model could be employed to optimize the extraction of WPZL. The optimal conditions to obtain the highest extraction of WPZL (13.398 ± 0.019%) were as follows: ultrasonic power, 88.77 W; extraction time, 29.96 min, extraction temperature, 77.73 °C and water to raw material ratio 24.44 mL/g. Copyright © 2014 Elsevier B.V. All rights reserved.
Mixing by microorganisms in stratified fluids
Wagner, Gregory L; Lauga, Eric
2014-01-01
We examine the vertical mixing induced by the swimming of microorganisms at low Reynolds and P\\'eclet numbers in a stably stratified ocean, and show that the global contribution of oceanic microswimmers to vertical mixing is negligible. We propose two approaches to estimating the mixing efficiency, $\\eta$, or the ratio of the rate of potential energy creation to the total rate-of-working on the ocean by microswimmers. The first is based on scaling arguments and estimates $\\eta$ in terms of the ratio between the typical organism size, $a$, and an intrinsic length scale for the stratified flow, $\\ell = \\left ( \
Ishiguro, Masaki; Liu Haiqing; Tokunaga, Tomonori; Tashima, Saya [Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga 816-8580 (Japan); Hanada, Kazuaki; Zushi, Hideki; Yoshida, Naoaki; Nakamura, Kazuo; Fujisawa, Akihide; Idei, Hiroshi; Sakamoto, Mizuki; Hasegawa, Makoto; Kawasaki, Shoji; Nakashima, Hisatoshi; Higashijima, Aki [Research Institute for Applied Mechanics, Kyushu University, Kasuga 816-8580 (Japan); Takase, Yuichi [Graduate School of Frontier Science, University Tokyo, Kashiwa 277-8561 (Japan); Maekawa, Takashi; Kishimoto, Yasuaki [Graduate School of Energy Science, Kyoto University, Kyoto 606-8502 (Japan); Mitarai, Osamu [Liberal Arts Education Center, Kumamoto Campus, Tokai University, 9-1-1 Toroku, Kumamoto 862-8652 (Japan)
2011-11-15
In magnetized plasmas, the presence of a significant number of energetic electrons has been observed but quantitative characteristics of these electrons are proving difficult to investigate. A Langmuir probe offers a means to provide quantitative measurement of these energetic electrons that takes into account electron emissions (secondary electron emission and electron reflection) from the probe tips and sheath expansion around the probe tips caused by a considerable negative potential. In this paper, these effects are experimentally confirmed and an analytical means to measure energetic electron characteristics are proposed. An analysis of plasmas produced by a high frequency wave is then applied leading to the successful detection of an asymmetric flow of energetic electrons. The estimated electron temperature and current density were approximately 4-5 keV and 2-3 kA/m{sup 2}.
Prasser, H.M. [ed.
1999-12-01
The emphasis of the conference was on methods of measurement that show spatial distributions of phase fractions and velocity, particle sizes and bubbles of the disperse phase. Among the methods described were 3D X-ray tomography, grid sensor measurement of velocity profiles, and simultaneous measurement of bubble sizes and gas and liquid flow rates using an optical particle tracking method. Also presented were interesting developments in the field of local probes, e.g. an electrodiffusion probe. Another new development was the attempt to use optical tomography for investigations of two-phase flows. [German] Am 14. Oktober 1999 wurde in Rossendorf die dritte Veranstaltung in einer Serie von Workshops ueber Messtechnik fuer stationaere und transiente Mehrphasenstroemungen durchgefuehrt. Dieses Jahr koennen wir auf 11 interessante Vortraege zurueckblicken. Besonders hervorzuheben sind die beiden Hauptvortraege, die von Herrn Professor Hetsroni aus Haifa und Herrn Dr. Sengpiel aus Karlsruhe gehalten wurden. Ihnen und allen anderen Vortragenden moechten wir herzlich fuer ihren Beitrag zum Gelingen des Workshops danken. Erneut lag ein wichtiger Schwerpunkt auf Messverfahren, die raeumliche Verteilungen von Phasenanteilen und Geschwindigkeiten sowie die Groesse von Partikeln bzw. Blasen der dispersen Phase zugaenglich machen. So wurde ueber einen dreidimensional arbeitenden Roentgentomographen, ein Verfahren zur Messung von Geschwindigkeitsprofilen mit Gittersensoren und eine Methode zur simultanen Messung von Blasengroessen sowie Feldern von Gas- und Fluessigkeitsgeschwindigkeit mit einer optischen Partikelverfolgungstechnik vorgetragen. Daneben wurden interessante Entwicklungen auf dem Gebiet der lokalen Sonden vorgestellt, wie z.B. eine Elektrodiffusionssonde. Neue messtechnische Ansaetze waren ebenfalls vertreten; hervorzuheben ist der Versuch, die Methode der optischen Tomographie fuer die Untersuchung von Zweiphasenstroemungen nutzbar zu machen. (orig.)
Prasser, H.M. [ed.
1997-12-01
There is hardly another area of physics which has a comparable multiplicity of phenomena, like flow in multi-phase mixtures. The wishes of experimenters regarding measurement technique are correspondingly great: Apart from the conventional parameters of pressure, temperature and speed of flow, as great a collection with resolution of the instantaneous phase distribution is required. Also, the phases themselves frequently consists of several components, whose concentration should also be measured. The enormous progress which has recently been made with laser optics and tomographic processes, must be compared with a long list of unsolved problems, above all where non-contact measurement is concerned. The attempts at solutions are multifarious, the need for the exchange of experience is great and the comparson of measurement processes with one another must be strengthened. The workshop has set itself these targets. (orig.) [Deutsch] Es gibt kaum ein anderes Gebiet der Physik, das eine vergleichbare Vielfalt der Erscheinungen aufweist wie Stroemungen von Mehrphasengemischen. Entsprechend gross sind die Wuensche der Experimentatoren hinsichtlich der Messtechnik: Neben den klassischen Parametern Druck, Temperatur und Stroemungsgeschwindigkeit wird eine moeglichst hoch aufloesende Erfassung der momentanen Phasenverteilung benoetigt. Ausserdem bestehen die Phasen selbst haeufig aus mehreren Komponenten, deren Konzentration ebenfalls gemessen werden soll. Den enormen Fortschritten, ie mit laseroptischen und tomographischen Verfahren in letzter Zeit gemacht wurden, steht nach wie vor eine lange Liste bisher ungeloester Aufgaben gegenueber, vor allen Dingen, wenn beruehrungslos gemessen werden soll. Die Loesungsansaetze sind vielfaeltig, der Bedarf an Erfahrungsaustausch ist gross, der Vergleich der Messverfahren untereinander muss verstaerkt werden. Diesen Zielen hatte sich der Workshop ``Messtechnik fuer tationaere und transiente Mehrphasenstroemungen`` verschrieben.
水平和倾斜管内气液分层流界而稳定性%Stability of Stratified Gas-Liquid Flow in Horizontal and Near Horizontal Pipes
顾汉洋; 郭烈锦
2007-01-01
A viscous Kelvin-Helmholtz criterion of the interfacial wave instability is proposed in this paper based on the linear stability analysis of a transient one-dimensional two-fluid model. In this model, the pressure is evaluated using the local momentum balance rather than the hydrostatic approximation. The criterion predicts well the stability limit of stratified flow in horizontal and nearly horizontal pipes. The experimental and theoretical investigation on the effect of pipe inclination on the inteffacial instability are carried out. It is found that the critical liquid height at the onset of interfacial wave instability is insensitive to the pipe inclination. However, the pipe inclination significantly affects critical superficial liquid velocity and wave velocity especially for low gas velocities.
Prasser, H.M. [ed.
1998-11-01
The 2nd Workshop on measuring systems for steady-state and transient multiphase flows was held at Rossendorf on September 24/25, 1988. 14 Papers were presented, whose subjects ranged from optical and radiometric methods to impedance sensors, hot film probes and model-assisted methods of measurement. In the field of computer simulation of multiphase flow, a trend towards 3D models was identified which makes higher demands on the spatial and time resolution and on the information volume to be acquired and processed. [German] Vom 24.-25. September 1998 fand in Rossendorf der 2. Workshop ueber Messtechnik fuer stationaere und transiente Mehrphasenstroemungen statt. Es standen 14 Vortraege auf dem Programm, das Spektrum reichte von optischen ueber radiometrische Methoden bis hin zu verschiedenen Impedanzsensoren, Heissfilmsonden und modellgestuetzten Messverfahren. Auf dem Gebiet der Computersimulation von Mehrphasenstroemungen zeichnet sich zunehmend der Uebergang zu dreidimensionalen Modellen ab. Hieraus ergeben sich neue Anforderungen an die Messtechnik, sowohl hinsichtlich der raeumlich-zeitlichen Aufloesung als auch was den Umfang der zu erfassenden Informationen betrifft. (orig./AKF)
Hunt, Julian C. R.; Moustaoui, Mohamed; Mahalov, Alex
2015-09-01
High resolution three-dimensional simulations are presented of the interactions between turbulent shear flows moving with mean relative velocity ΔU below a stably stratified region with buoyancy frequency (N+). An artificial forcing in the simulation, with a similar effect as a small negative eddy viscosity, leads to a steady state flow which models thin interfaces. Characteristic eddies of the turbulence have length scale L. If the bulk Richardson number Rib=(LN+/ΔU)2 lies between lower and upper critical values denoted as Ri∗(temperature. Comparisons are made with shear turbulent interfaces with no stratification. When Rib>R~i, vertical propagating waves are generated, with shear stresses carrying significant momentum flux and progressively less as Rib increases. Simulations for a jet and a turbulent mixing layer show similar results. A perturbation analysis, using inhomogeneous Rapid Distortion Theory, models the transition zone between shear eddies below the interface and the fluctuations in the stratified region, consistent with the simulations. It demonstrates how the wave-momentum-flux has a maximum when Rib˜2 and then decreases as Rib increases. This coupling mechanism between eddies and waves, which is neglected in eddy viscosity models for shear layers, can drive flows in the stratosphere and the deeper ocean, with significant consequences for short- and long-term flow phenomena. The "detached layer" is a mechanism that contributes to the formation of stratus clouds and polluted layers above the atmospheric boundary layer.
郑平; 赵梁
2016-01-01
The gas-liquid two-phase stratified flow has complex momentum and energy transmission phenomena at interface,although its pattern is simple. There are still no unified conclusions for interfacial shear stress in stratified flow. Current progress of interfacial shear stress in horizontal pipes were elaborated by theoretical models,experimental models and numerical simulations. As for theoretical models,closure models were established by models simplification and empirical correlations. Empirical correlations were corrected with closure relations in experiments. Due to simplifying assumptions and experimental conditions,there are some limitations in predicting the interfacial shear stress with theoretical and experimental ways. The detailed flow fields were studied by numerical simulations,but closure relations have been less obtained so far. Five existing models are compared according to liquid holdup and pressure drop. The future research trends of gas-liquid two-phase stratified flow interfacial shear stress in horizontal pipes were further discussed. More detailed local models are needed to be proposed and engineering practice should be taken into account. It is necessary to develop new methods of gas-liquid interface calculations and closure relations for numerical simulations.%水平管气液两相分层流虽流型简单，但由于界面存在复杂的动量和能量传递，分层流的界面剪切预测至今没有一致的结论。本文从理论模型、实验模型、数值计算3个角度出发，详细阐述水平管气液两相分层流界面剪切预测的研究现状，得出不同研究方法的优势和缺陷。针对3种研究方法，指出理论模型通过模型简化和经验关联式来建立封闭模型，实验模型则在封闭关系上修正经验关联式，但由于简化假设和实验条件的限制，使得这两种研究方法对界面剪切应力的预测具有一定的局限性；数值计算能够弥补机理模型在流场细
Drainage in a model stratified porous medium
Datta, Sujit S; 10.1209/0295-5075/101/14002
2013-01-01
We show that when a non-wetting fluid drains a stratified porous medium at sufficiently small capillary numbers Ca, it flows only through the coarsest stratum of the medium; by contrast, above a threshold Ca, the non-wetting fluid is also forced laterally, into part of the adjacent, finer strata. The spatial extent of this partial invasion increases with Ca. We quantitatively understand this behavior by balancing the stratum-scale viscous pressure driving the flow with the capillary pressure required to invade individual pores. Because geological formations are frequently stratified, we anticipate that our results will be relevant to a number of important applications, including understanding oil migration, preventing groundwater contamination, and sub-surface CO$_{2}$ storage.
Arnold, L.R.
2010-01-01
The Lost Creek Designated Ground Water Basin (Lost Creek basin) is an important alluvial aquifer for irrigation, public supply, and domestic water uses in northeastern Colorado. Beginning in 2005, the U.S. Geological Survey, in cooperation with the Lost Creek Ground Water Management District and the Colorado Water Conservation Board, collected hydrologic data and constructed a steady-state numerical groundwater flow model of the Lost Creek basin. The model builds upon the work of previous investigators to provide an updated tool for simulating the potential effects of various hydrologic stresses on groundwater flow and evaluating possible aquifer-management strategies. As part of model development, the thickness and extent of regolith sediments in the basin were mapped, and data were collected concerning aquifer recharge beneath native grassland, nonirrigated agricultural fields, irrigated agricultural fields, and ephemeral stream channels. The thickness and extent of regolith in the Lost Creek basin indicate the presence of a 2- to 7-mile-wide buried paleovalley that extends along the Lost Creek basin from south to north, where it joins the alluvial valley of the South Platte River valley. Regolith that fills the paleovalley is as much as about 190 ft thick. Average annual recharge from infiltration of precipitation on native grassland and nonirrigated agricultural fields was estimated by using the chloride mass-balance method to range from 0.1 to 0.6 inch, which represents about 1-4 percent of long-term average precipitation. Average annual recharge from infiltration of ephemeral streamflow was estimated by using apparent downward velocities of chloride peaks to range from 5.7 to 8.2 inches. Average annual recharge beneath irrigated agricultural fields was estimated by using passive-wick lysimeters and a water-balance approach to range from 0 to 11.3 inches, depending on irrigation method, soil type, crop type, and the net quantity of irrigation water applied
Berenbrock, Charles E.
2015-01-01
Reduction of cross-sectional data using a genetic algorithm method, and the effects of data reduction on channel geometry and steady-flow profiles, were analyzed. Two reduction methods─standard and genetic algorithms─were used to reduce cross-sectional data from the Kootenai River in northern Idaho. Cross sections that are representative of meander, straight, braided, and canyon reaches were used to evalutate the reduction methods. Visual and hydraulic analyses were used to assess the methods. The genetic algorithm-reduced cross sections approximated the shape of the original cross sections better than the standard-reduced cross sections. A greater number of cross-sectional data points were needed for reduced cross sections in the straight reach, and even more in the braided reach, because a greater amount of data points are needed to adequately define cross sections that have greater topographic varability. For the genetic algorithm-reduction method, about 40 data points were needed to adequately define the shape of a reduced cross section in the braided reach compared to 10 to 20 data points in the meander and canyon reaches. The standard-reduction method needed about 70 data points for the braided reach and more than 30 points for the meander and canyon reaches. The genetic algorithm can effectively reduce data while staying within the threshold set by the maximum number of points to be included in the reduced dataset.
Yoon, Inkyoung; Ohm, Inyong [Seoul Nat’l Univ. of Science and Technology, Seoul (Korea, Republic of)
2017-02-15
This study is the second investigation on the steady flow characteristics of an SI engine with a semi-edge combustion chamber as a function of the port shape with varying evaluation positions. For this purpose, the planar velocity profiles were measured from 1.75B, 1.75 times of bore position apart from the bottom of head, to 6.00B positions using particle – image velocimetry. The flow patterns were examined with both a straight and a helical port. The velocity profiles, streamlines, and centers of swirl were almost the same at the same valve lift regardless of the measuring position, which is quite different from the case of the pent-roof combustion chamber. All the eccentricity values of the straight port were out of distortion criterion 0.15 through the lifts and the position. However, the values of the helical port exceeded the distortion criterion by up to 4 mm lift, but decreased rapidly above the 3.00B position and the 5 mm lift. There always existed a relative offset effect in the evaluation of the swirl coefficient using the PIV method due to the difference of the ideal impulse swirl meter velocity profile assumption, except for the cylinder-center-base estimation that was below 4 mm of the straight port. Finally, it was concluded that taking the center as an evaluation basis and the assumption about the axial velocity profile did not have any qualitative effect on swirl evaluation, but affected the value owing to the detailed profile.
Thermal stratification built up in hot water tank with different inlet stratifiers
Dragsted, Janne; Furbo, Simon; Dannemand, Mark
2017-01-01
H is a rigid plastic pipe with holes for each 30 cm. The holes are designed with flaps preventing counter flow into the pipe. The inlet stratifier from EyeCular Technologies ApS is made of a flexible polymer with openings all along the side and in the full length of the stratifier. The flexibility...... in order to elucidate how well thermal stratification is established in the tank with differently designed inlet stratifiers under different controlled laboratory conditions. The investigated inlet stratifiers are from Solvis GmbH & Co KG and EyeCular Technologies ApS. The inlet stratifier from Solvis Gmb...... of the stratifier prevents counterflow. The tests have shown that both types of inlet stratifiers had an ability to create stratification in the test tank under the different test conditions. The stratifier from EyeCular Technologies ApS had a better performance at low flows of 1-2 l/min and the stratifier...
Lapuerta, C
2006-10-15
During an hypothetical major accident in a pressurized water reactor, the deterioration of the core can produce a stratified pool crossed by a bubbly flow. This latter strongly impacts the heat transfers, whose intensities are crucial in the progression of the accident. In this context, this work is devoted to the diffuse interface modelling for the study of an-isothermal incompressible flows, composed of three immiscible components, with no phase change. In the diffuse interface methods, the system evolution is driven by the minimization of a free energy. The originality of our approach, derived from the Cahn-Hilliard model, is based on the particular form of the energy we proposed, which enables to have an algebraically and dynamically consistent model, in the following sense: on the one hand, the triphasic free energy is equal to the diphasic one when only two phases are present; on the other, if a phase is not initially present then it will not appear during system evolution, this last property being stable with respect to numerical errors. The existence and the uniqueness of weak and strong solutions are proved in two and three dimensions as well as a stability result for metastable states. The modelling of an an-isothermal three phase flow is further accomplished by coupling the Cahn-Hilliard equations with the energy balance and Navier-Stokes equations where surface tensions are taken into account through volume capillary forces. These equations are discretized in time and space in order to preserve properties of continuous model (volume conservation, energy estimate). Different numerical results are given, from the validation case of the lens spreading between two phases, to the study of the heat and mass transfers through a liquid/liquid interface crossed by a single bubble or a series of bubbles. (author)
How stratified is mantle convection?
Puster, Peter; Jordan, Thomas H.
1997-04-01
We quantify the flow stratification in the Earth's mid-mantle (600-1500 km) in terms of a stratification index for the vertical mass flux, Sƒ (z) = 1 - ƒ(z) / ƒref (z), in which the reference value ƒref(z) approximates the local flux at depth z expected for unstratified convection (Sƒ=0). Although this flux stratification index cannot be directly constrained by observations, we show from a series of two-dimensional convection simulations that its value can be related to a thermal stratification index ST(Z) defined in terms of the radial correlation length of the temperature-perturbation field δT(z, Ω). ST is a good proxy for Sƒ at low stratifications (SƒUniformitarian Principle. The bound obtained here from global tomography is consistent with local seismological evidence for slab flux into the lower mantle; however, the total material flux has to be significantly greater (by a factor of 2-3) than that due to slabs alone. A stratification index, Sƒ≲0.2, is sufficient to exclude many stratified convection models still under active consideration, including most forms of chemical layering between the upper and lower mantle, as well as the more extreme versions of avalanching convection governed by a strong endothermic phase change.
Numerical Study of Stratified Charge Combustion in Wave Rotors
Nalim, M. Razi
1997-01-01
A wave rotor may be used as a pressure-gain combustor effecting non-steady flow, and intermittent, confined combustion to enhance gas turbine engine performance. It will be more compact and probably lighter than an equivalent pressure-exchange wave rotor, yet will have similar thermodynamic and mechanical characteristics. Because the allowable turbine blade temperature limits overall fuel/air ratio to sub-flammable values, premixed stratification techniques are necessary to burn hydrocarbon fuels in small engines with compressor discharge temperature well below autoignition conditions. One-dimensional, unsteady numerical simulations of stratified-charge combustion are performed using an eddy-diffusivity turbulence model and a simple reaction model incorporating a flammability limit temperature. For good combustion efficiency, a stratification strategy is developed which concentrates fuel at the leading and trailing edges of the inlet port. Rotor and exhaust temperature profiles and performance predictions are presented at three representative operating conditions of the engine: full design load, 40% load, and idle. The results indicate that peak local gas temperatures will result in excessive temperatures within the rotor housing unless additional cooling methods are used. The rotor itself will have acceptable temperatures, but the pattern factor presented to the turbine may be of concern, depending on exhaust duct design and duct-rotor interaction.
Geometric structure of pseudo-plane quadratic flows
Sun, Che
2017-03-01
Quadratic flows have the unique property of uniform strain and are commonly used in turbulence modeling and hydrodynamic analysis. While previous applications focused on two-dimensional homogeneous fluid, this study examines the geometric structure of three-dimensional quadratic flows in stratified fluid by solving a steady-state pseudo-plane flow model. The complete set of exact solutions reveals that steady quadratic flows have an invariant conic type in the non-rotating frame and a non-rotatory vertical structure in the rotating frame. Three baroclinic solutions with vertically non-aligned formulation disprove an earlier conjecture. All elliptic and hyperbolic solutions, except for the inertial ones, exhibit vertical concentricity. The rich geometry of quadratic flows stands in contrast to the depleted geometry of high-degree polynomial flows. A paradox in the steady solutions of shallow-water reduced-gravity models is also explained.
Bertin H.
2006-11-01
Full Text Available Nous abordons l'étude des écoulements polyphasiques en milieu poreux hétérogène d'un point de vue théorique (méthodologie de la prise de moyenne à grande échelle et expérimental. Dans une première partie nous présentons la méthodologie permettant d'obtenir les équations à grande échelle. Le point de départ de l'étude est les équations locales, analogues aux équations de Darcy généralisées obtenues par prise de moyenne des équations de Stokes à l'échelle du pore. La prise de moyenne à grande échelle de ces équations permet d'écrire un système d'équations où les coefficients de transport équivalents sont calculés à partir des données locales, par la résolution d'un problème de fermeture explicité dans le cas quasi-statique (effets capillaires dominants. La seconde partie de notre travail concerne l'étude expérimentale d'un écoulement eau-huile dans un milieu poreux stratifié constitué de deux régions de caractéristiques physiques différentes. Les champs de saturation bidimensionnels sont mesurés tout au long de l'imbibition par absorption d'un rayonnement gamma. Les résultats expérimentaux, évolution de la fraction volumique moyenne par section en fonction du temps, sont comparés aux résultats d'une simulation numérique des équations de transport où les coefficients utilisés ont été déterminés par la méthode de prise de moyenne à grande échelle. Two-phase flow in heterogeneous porous media is studied from a theoretical point of view (the large-scale averaging method and experimentally. In the first part, we present the methodology leading to the large-scale equations. The starting point of the study is the local equation, analogous to the generalized Darcy's law obtained by averaging the Stokes equation at the pore level. The large-scale averaging of these equations leads to a system where the equivalent transport coefficients are computed from the local data by solving a closure
杨春元; 朱天宇; 蔡一凡
2015-01-01
Using a numerical simulation of a nelliptical cavity absorber and vacuum absorber, heat transfer coefficient and thermal gradient of the stratified flow areas of both absorbers are ana-lyzed.The results show an increase of heat trans-fer coefficient in the cavity absorber,but the struc-ture still needs to be improved,because the ther-mal gradient remains high.%针对一种椭圆形腔体式集热管和真空集热管，通过数值模拟的方法，对该集热管在分层流区域的换热系数和温度梯度进行分析研究。结果表明该腔体式集热管能够提高分层流区域的换热系数，但是集热管壁面的温度梯度并没有得到有效的降低，结构有待进一步改进。
Dupuit稳定井流公式的模型分析%Model analysis of Dupuit’s steady well flow formula
王晓明; 王秀辉; 文望; 李功宇
2014-01-01
It has been more than 100 years, spanning three centuries since Dupuit proposed the steady well flow model and the Dupit formula. Due to the simple principle and the concise formula, Dupit formula is still in use. However, there have been a lot of disputes and misunderstandings about Dupuit’s model, Dupuit’s formula and relative concepts. Through analyzing Dupuit model and Dupit formula, this paper points out that the Dupuit model and the formula itself do not contain the concept of radius of influence. The concept of the influence radius was understood as one of aquifer parameters, trying to seek a representative average influence radius is lack of enough theoretical basis.%Dupuit稳定井流模型和公式自1863年提出，至今已有一百多年了，时间横跨3个世纪。由于其原理的简单及公式的简洁，人们仍在使用。而人们对Dupuit模型以及有关概念的认识，仍然存在很大的差异和误区。通过分析Dupuit稳定流模型及公式，指出Dupuit模型及公式中本身就不含有影响半径的概念。将 Thiem提出的影响半径的概念理解为含水层的一个参数，一个不变的常数，并试图寻求一个具有代表性的平均影响半径是没有理论依据的。
NUMERICAL SIMULATION OF STEADY/UNSTEADY FLOW IN FRACTURED ROCK MASSES%裂隙岩体稳定/非稳定渗流数值模拟
张丽; 刘晓宇; 李世海
2009-01-01
A numerical model of steady/unsteady flow in fractured rock mass is developed. On the one hand,by using Monte Carlo technique,an intact rock is cut into 3D irregular block elements in term of the statistical distribution of density,orientation,position,size and aperture of fractures. A 3D fracture network is then constructed,which is composed of fracture elements between adjacent rock elements. The hydraulic properties are attached to the fracture elements. On the other hand,the fracture elements are discretized into triangular mesh,and the flow finite element equations are derived based on the variational principle. The dynamic relaxation technique in discrete element method is introduced to solve the permeability field without assembling the global matrix. Finally,the reliability and applicability of the program are validated by typical examples.%发展裂隙岩体稳定/非稳定的渗流数值模型,一方面,依照裂隙面的密度、产状、位置、大小和开度的统计分布规律,使用蒙特卡罗模拟技术将完整岩石切割为三维不规则块体集合.根据相邻块体单元间产生的裂隙单元,构建三维裂隙网络系统,并附加各裂隙单元的水力特性;另一方面,对裂隙单元进行三角形单元的有限元网格划分,运用变分原理导出裂隙单元的渗流有限元求解方程.采用离散元方法中的动态松驰技术,在无须组装整体渗透矩阵的情况下求解裂隙网格各结点的水头值.最后,通过典型算例验证程序的可靠性及适用性.
Liu, Xin; Fan, Zhaoyang; Zhang, Na; Yang, Qi; Feng, Fei; Liu, Pengcheng; Li, Debiao
2014-01-01
Purpose To assess image quality and diagnostic performance of unenhanced magnetic resonance (MR) angiography with use of flow-sensitive dephasing (FSD)–prepared steady-state free precession (SSFP) of the foot arteries in patients with diabetes. Materials and Methods This prospective study was approved by institutional review board. Informed consent was obtained from all subjects. Thirty-two healthy volunteers and 38 diabetic patients who had been scheduled for lower-extremity contrast material–enhanced MR angiography were recruited to undergo unenhanced MR angiography with a 1.5-T MR unit. Image quality and diagnostic accuracy of unenhanced MR angiography in the detection of significant arterial stenosis (≥50%) were assessed by two independent reviewers. Contrast-enhanced MR angiography was used as the reference standard. The difference in the percentage of diagnostic arterial segments at unenhanced MR angiography between healthy volunteers and diabetic patients was evaluated with the McNemar test and generalized estimating equation for correlated data. Signal-to-noise ratio (SNR) and artery-to-muscle contrast-to-noise ratio (CNR) of pedal arteries were measured and compared between the two MR angiography techniques by using the paired t test. Results All subjects successfully underwent unenhanced MR angiography of the foot. Unenhanced MR angiography yielded a high percentage of diagnostic arterial segments in both healthy volunteers (303 of 320 segments, 95%) and patients (341 of 370 segments, 92%), and there was no difference in the percentage between the two populations (P = .195). In patients, the average SNR and CNR at unenhanced MR angiography were higher than those at contrast-enhanced MR angiography (SNR: 90.7 ± 38.1 vs 81.7 ± 34.7, respectively, P = .023; CNR: 85.2 ± 33.2 vs 76.6 ± 33.5, respectively, P = .013). The average sensitivity, specificity, positive predictive value, negative predictive value, and accuracy of unenhanced MR angiography
Liu, Xin; Fan, Zhaoyang; Zhang, Na; Yang, Qi; Feng, Fei; Liu, Pengcheng; Zheng, Hairong; Li, Debiao
2014-09-01
To assess image quality and diagnostic performance of unenhanced magnetic resonance (MR) angiography with use of flow-sensitive dephasing (FSD)-prepared steady-state free precession (SSFP) of the foot arteries in patients with diabetes. This prospective study was approved by institutional review board. Informed consent was obtained from all subjects. Thirty-two healthy volunteers and 38 diabetic patients who had been scheduled for lower-extremity contrast material-enhanced MR angiography were recruited to undergo unenhanced MR angiography with a 1.5-T MR unit. Image quality and diagnostic accuracy of unenhanced MR angiography in the detection of significant arterial stenosis (≥50%) were assessed by two independent reviewers. Contrast-enhanced MR angiography was used as the reference standard. The difference in the percentage of diagnostic arterial segments at unenhanced MR angiography between healthy volunteers and diabetic patients was evaluated with the McNemar test and generalized estimating equation for correlated data. Signal-to-noise ratio (SNR) and artery-to-muscle contrast-to-noise ratio (CNR) of pedal arteries were measured and compared between the two MR angiography techniques by using the paired t test. All subjects successfully underwent unenhanced MR angiography of the foot. Unenhanced MR angiography yielded a high percentage of diagnostic arterial segments in both healthy volunteers (303 of 320 segments, 95%) and patients (341 of 370 segments, 92%), and there was no difference in the percentage between the two populations (P = .195). In patients, the average SNR and CNR at unenhanced MR angiography were higher than those at contrast-enhanced MR angiography (SNR: 90.7 ± 38.1 vs 81.7 ± 34.7, respectively, P = .023; CNR: 85.2 ± 33.2 vs 76.6 ± 33.5, respectively, P = .013). The average sensitivity, specificity, positive predictive value, negative predictive value, and accuracy of unenhanced MR angiography were 88% (35 of 40 segments), 93% (107 of
Helicity dynamics in stratified turbulence in the absence of forcing
Rorai, C; Pouquet, A; Mininni, P D
2012-01-01
A numerical study of decaying stably-stratified flows is performed. Relatively high stratification and moderate Reynolds numbers are considered, and a particular emphasis is placed on the role of helicity (velocity-vorticity correlations). The problem is tackled by integrating the Boussinesq equations in a periodic cubical domain using different initial conditions: a non-helical Taylor-Green (TG) flow, a fully helical Beltrami (ABC) flow, and random flows with a tunable helicity. We show that for stratified ABC flows helicity undergoes a substantially slower decay than for unstratified ABC flows. This fact is likely associated to the combined effect of stratification and large scale coherent structures. Indeed, when the latter are missing, as in random flows, helicity is rapidly destroyed by the onset of gravitational waves. A type of large-scale dissipative "cyclostrophic" balance can be invoked to explain this behavior. When helicity survives in the system it strongly affects the temporal energy decay and t...