Latest papers in fluid mechanics

Flow field prediction of supercritical airfoils via variational autoencoder based deep learning framework

Physics of Fluids - Thu, 08/19/2021 - 11:53
Physics of Fluids, Volume 33, Issue 8, August 2021.
Effective access to obtain the complex flow fields around an airfoil is crucial in improving the quality of supercritical wings. In this study, a systematic method based on generative deep learning is developed to extract features for depicting the flow fields and predict the steady flow fields around supercritical airfoils. To begin with, a variational autoencoder (VAE) network is designed to extract representative features of the flow fields. Specifically, the principal component analysis technique is adopted to realize feature reduction, aiming to obtain the optimal dimension of features in VAE. Afterward, the extracted features are incorporated into the dataset, followed by the mapping from the airfoil shapes to features via a multilayer perception (MLP) model. Eventually, a composite network is adopted to connect the MLP and the decoder of VAE for predicting the flow fields given the airfoil. The proposed VAE network achieves compression of high-dimensional flow field data into ten representative features. The statistical results indicate the accurate and generalized performance of the proposed method in reconstructing and predicting flow fields around a supercritical airfoil. Especially, our method obtains accurate prediction results over the shock area, indicating its superiority in conducting turbulent flow under high Reynolds number.

Lattice Boltzmann method to simulate three-dimensional ion channel flow using fourth order Poisson–Nernst–Planck–Bikerman model

Physics of Fluids - Thu, 08/19/2021 - 11:53
Physics of Fluids, Volume 33, Issue 8, August 2021.
Over the past three decades, the lattice Boltzmann method (LBM) has been applied to a vast range of hydrodynamic and non-hydrodynamic (e.g., ion transport) systems. In conjunction with the immersed boundary method (IBM), the LBM has been successfully implemented to solve systems with complex geometries. In this study, the immersed boundary–lattice Boltzmann method (IB-LBM) is implemented to simulate nanoscale ion transport. Traditionally, ion transport is described through the Poisson–Nernst–Planck (PNP) equations where ionic interactions are included. In the current paper, the fourth order Poisson–Nernst–Planck–Bikerman (4PNPBik) model has been used. In addition to ionic interactions, the 4PNPBik model includes the effects of the finite size of particles (ions and water) and interactions between ions and its surrounding medium. Applicability of the 4PNPBik model is demonstrated through comparison of the experimental and predicted ion activity. Implementation of the 4PNPBik model has been validated by comparing the predicted current–voltage curve with the analytical result. The transient receptor potential (TRP) ion channel of the vanilloid group (TRPV4) is used to demonstrate the applicability of this approach. The TRPV4 is a nonselective cation channel that prefers divalent cationic species over monovalent cations. In this study, this selectivity is demonstrated by comparing the concentration profiles of calcium, sodium, and chloride ions. Further, the role of the finite size of particles and nonlocal electrostatics is discussed by comparing the results obtained from the PNP and 4PNPBik models under identical initial and boundary conditions.

Simulation of imbibition in porous media with a tree-shaped fracture following the level-set method

Physics of Fluids - Thu, 08/19/2021 - 06:46
Physics of Fluids, Volume 33, Issue 8, August 2021.
Imbibition is an important mechanism for enhancing oil recovery in low-permeability reservoirs, such as shale and tight sandstone, and a tree-shaped network has been successfully used to characterize fracturing fracture. Therefore, understanding the imbibition mechanism in porous media with a tree-shaped fracture (TFPM) is important for developing low-permeability reservoirs. In this study, a simulation model for imbibition in TFPM was established based on the level-set method, and the model was verified by comparing it with an analytical solution. The influences of the fracture width, bifurcation angle, tortuosity, and water flow rate on imbibition in TFPM were then discussed. Based on the results, the following points have been established: (1) During the early stage, the imbibition in TFPM included countercurrent and a combined imbibition, and only countercurrent imbibition occurred during the later stage. (2) At a constant fracture width ratio, increasing the primary fracture width could reduce the residual oil in the TFPM, thereby improving the oil recovery factor. (3) At a fracture bifurcation angle ranging from 0° to 45°, the oil recovery factor increased as the bifurcation angle increased. (4) At a fracture tortuosity of 1.0 to 1.24, changes in tortuosity had little effect on the oil recovery factor during the early stage of imbibition, while it significantly affected the distribution of the residual oil. (5) At a water flow rate of 5 mm/s, the simulated oil recovery factor in the TFPM was highest. This investigation can provide a reference for the development of low-permeability reservoirs.

How coronavirus survives for hours in aerosols

Physics of Fluids - Wed, 08/18/2021 - 12:36
Physics of Fluids, Volume 33, Issue 8, August 2021.
COVID (CoronaVirus Disease)-19, caused by severe acute respiratory syndrome-CoronaVirus-2 (SARS-CoV-2) virus, predominantly transmits via airborne route, as highlighted by recent studies. Furthermore, recently published titer measurements of SARS-CoV-2 in aerosols have disclosed that the coronavirus can survive for hours. A consolidated knowledge on the physical mechanism and governing rules behind the significantly long survival of coronavirus in aerosols is lacking, which is the subject of the present investigation. We model the evaporation of aerosolized droplets of diameter [math]m. The conventional diffusion-limited evaporation is not valid to model the evaporation of small size (μm–nm) droplets since it predicts drying time on the order of milliseconds. Also, the sedimentation timescale of desiccated droplets is on the order of days and overpredicts the virus survival time; hence, it does not corroborate with the above-mentioned titer-decay timescale. We attribute the virus survival timescale to the fact that the drying of small ([math]m–nm) droplets is governed, in principle, by the excess internal pressure within the droplet, which stems from the disjoining pressure due to the cohesive intermolecular interaction between the liquid molecules and the Laplace-pressure. The model predictions for the temporal reduction in the aerosolized droplet number density agree well with the temporal decay of virus titer. The findings, therefore, provide insight on the survival of coronavirus in aerosols, which is particularly important to mitigate the spread of COVID-19 from indoors.

The study of shallow water flow with bottom topography by high-order compact gas-kinetic scheme on unstructured mesh

Physics of Fluids - Wed, 08/18/2021 - 12:36
Physics of Fluids, Volume 33, Issue 8, August 2021.
A well-balanced compact high-order gas-kinetic scheme (GKS) on unstructured mesh is first developed for solving the shallow water equations with source terms. The distinguishable feature of the finite volume GKS is that based on the gas-kinetic formulation, a time-accurate gas distribution function can be constructed, from which both the fluxes and the flow variables can be explicitly evaluated at the cell interface. As a result, besides the update of cell-averaged conservative variables, the cell-averaged slopes of the flow variables can be updated as well. Equipped with both flow variables and their slopes, a fourth-order compact spatial reconstruction on unstructured mesh can be obtained as the initial condition at the beginning of each time step. For the shallow water flow, in order to preserve the well-balanced property, the advection and the source terms in the flux function have to be balanced properly. The current compact GKS achieves high-order accuracy, keeps the well-balanced property, and has super-robustness in the simulation of bore waves. The scheme is used in the shallow water flow studies, such as dam breaking and bore wave propagation. In addition, the pollution transport, morphodynamics, and bottom friction in the shallow water flow have been included in the scheme. In the end, the water discharge in the Pearl River estuary and the dam-break experiment with movable bed topography have been simulated.

Forced flow response analysis of a turbulent swirling annular jet flame

Physics of Fluids - Wed, 08/18/2021 - 12:35
Physics of Fluids, Volume 33, Issue 8, August 2021.
This study of an externally forced, amplifier-type turbulent reacting swirling annular jet presents a low-order model for the flow response to transverse acoustic excitation and compares the model's predictions with experimental measurements. The model is formulated based on linear stability calculations about the turbulent mean flow and eddy viscosity fields obtained from separate measurements of the unforced flow. The stability calculations yield weakly global spatial modes associated with the forcing frequency, which serve as a basis upon which to project the forcing input. Thus, the model constitutes a hydrodynamic transfer function connecting the input forcing to the output coherent flow response through the linearized low Mach number compressible Navier–Stokes equations. Following a detailed presentation of the stability analysis underlying the model, the response predictions are evaluated against previously reported experiments where the jet was transversely excited at both an acoustic pressure node and an antinode. The results reveal excellent agreement between the predicted response and the measured fluctuating fields, suggesting that the low-order linear model based on the turbulent mean flow field captures the essential physics of the mode selection process in this forced configuration. This work provides further evidence that linear hydrodynamics govern the growth and decay of spatiotemporally coherent vortical structures in the swirling, turbulent jet flame, and, in particular, explains the dominance of co-rotating spiral structures.

Fluid dynamics of respiratory droplets in the context of COVID-19: Airborne and surfaceborne transmissions

Physics of Fluids - Wed, 08/18/2021 - 12:35
Physics of Fluids, Volume 33, Issue 8, August 2021.
The World Health Organization has declared COVID-19 a global pandemic. Several countries have experienced repeated periods of major spreading over the last two years. Many people have lost their lives, employment, and the socioeconomic situation has been severely impacted. Thus, it is considered to be one of the major health and economic disasters in modern history. Over the last two years, several researchers have contributed significantly to the study of droplet formation, transmission, and lifetime in the context of understanding the spread of such respiratory infections from a fluid dynamics perspective. The current review emphasizes the numerous ways in which fluid dynamics aids in the comprehension of these aspects. The biology of the virus, as well as other statistical studies to forecast the pandemic, is significant, but they are not included in this review.

Dynamic iterative approximate deconvolution models for large-eddy simulation of turbulence

Physics of Fluids - Wed, 08/18/2021 - 12:35
Physics of Fluids, Volume 33, Issue 8, August 2021.
Dynamic iterative approximate deconvolution (DIAD) models with Galilean invariance are developed for subgrid-scale (SGS) stress in the large-eddy simulation (LES) of turbulence. The DIAD models recover the unfiltered variables using the filtered variables at neighboring points and iteratively update model coefficients without any a priori knowledge of direct numerical simulation (DNS) data. The a priori analysis indicates that the DIAD models reconstruct the unclosed SGS stress much better than the classical velocity gradient model and approximate deconvolution model with different filter scales ranging from viscous to inertial regions. We also propose a small-scale eddy viscosity (SSEV) model as an artificial dissipation to suppress the numerical instability based on a scale-similarity-based dynamic method without affecting large-scale flow structures. The SSEV model can predict a velocity spectrum very close to that of DNS data, similar to the traditional implicit large-eddy simulation. In the a posteriori testing, the SSEV-enhanced DIAD model is superior to the SSEV model, dynamic Smagorinsky model, and dynamic mixed model, which predicts a variety of statistics and instantaneous spatial structures of turbulence much closer to those of filtered DNS data without significantly increasing the computational cost. The types of explicit filters, local spatial averaging methods, and initial conditions do not significantly affect the accuracy of DIAD models. We further successfully apply DIAD models to the homogeneous shear turbulence. These results illustrate that the current SSEV-enhanced DIAD approach is promising in the development of advanced SGS models in the LES of turbulence.

Experiments on thermal drift

Physics of Fluids - Wed, 08/18/2021 - 12:32
Physics of Fluids, Volume 33, Issue 8, August 2021.
Thermal drift is a horizontal flow driven by a pattern interaction effect occurring on a solid surface; that is, the flow is driven by an interaction between surface topography and the heating pattern applied to the surface. The interaction generates surface forces through projection of the convective pressure field onto the surface topography—these forces drive the flow. The existence of thermal drift is demonstrated experimentally. Its basic characteristics, that is, variations of the strength and direction of the resulting flow as a function of the relative position of both patterns, were determined experimentally and theoretically. An excellent agreement between both sets of data has been demonstrated.

Self-diffusivity of dense confined fluids

Physics of Fluids - Wed, 08/18/2021 - 12:32
Physics of Fluids, Volume 33, Issue 8, August 2021.
Molecular transport through tight porous media is crucial to shale gas exploration, but deeper insights of the elemental physics are still required, particularly under high pressures and nanoscale confinements, where Navier–Stokes and Boltzmann solutions are no longer valid. In this work, we carry out a fundamental and systematic study of self-diffusion using event-driven molecular dynamics simulations, varying fluid rarefaction, confinement, and surface friction. We differentiate between fluid–fluid and fluid-wall collisions to identify the interplay of the underpinning diffusive mechanisms, namely, molecular and Knudsen diffusion. We find that the Bosanquet formula, which has been used for describing rarefied gases, is also able to provide a good semi-analytical description of self-diffusivities in confined dense fluids, as long as the pore height is not smaller than five molecular diameters. Importantly, this allows us to predict the self-diffusion coefficient, regardless of the fluid rarefaction, confinement state, and surface roughness, in a wide range of Knudsen numbers that were not possible before. Often as a source of debate, we prove here that despite strong fluid inhomogeneities arising in these conditions, the Einstein self-diffusivity can still be used within Fick's law, provided boundary effects are considered when using Fick's setup. Finally, we notice that a previously identified linear scaling of self-diffusivities with confinement is only valid in the limit of low densities and frictionless walls, which is not representative of shale reservoirs. This work will serve as a foundation for investigating the anomalous gas transport behavior observed in the recent work of dense, confined fluids.

Numerical investigation of respiratory drops dynamics released during vocalization

Physics of Fluids - Wed, 08/18/2021 - 12:32
Physics of Fluids, Volume 33, Issue 8, August 2021.
Release of drops from a human body has been the focus of many recent investigations because of the current COVID-19 pandemic. Indirect virus transmission from asymptomatic individuals has been proved to be one of the major infectious routes and difficult to quantify, detect, and mitigate. We show in this work a detailed and novel numerical investigation of drops released during vocalization from a thermal manikin using a large eddy simulation coupled with Lagrangian tracking of drops. The vocalization experiment was modeled using existing data from the literature for modeling exhaled airflow, emission rate, and size distribution. Particular focus was on the definition of the boundary conditions for the exhalation process. Turbulence was compared with experimental data for the near mouth region for 75 exhalation breathing cycles and showed the sensitivity of different modeling assumptions at the mouth inlet. The results provide insights of special interest for understanding drop dynamics in speech-like exhalation modes, modeling the mouth inlet boundary conditions, and providing data for verifying other more simplified models.

Experimental investigation on backflow of power-law fluids in planar fractures

Physics of Fluids - Wed, 08/18/2021 - 12:32
Physics of Fluids, Volume 33, Issue 8, August 2021.
In hydrofracturing, we model the backflow of a non-Newtonian fluid in a single flat-walled fracture of planar geometry and support our conceptualization with laboratory experiments. We consider a power-law fluid, a spatially homogeneous fracture aperture, and its variation in time depending on the internal fluid pressure and the elastic relaxation of the walls. The relationship between the latter quantities may be linear, akin to a Winkler soil, or nonlinear, due to the progressive softening or stiffening of the boundary associated with the properties of the surrounding rock. The result is an integrodifferential problem that generally admits a closed-form solution, albeit implicit for some quantities. In particular, a comparison is conducted between the drainage time in the present configuration and point drainage in radial geometry. The approach is generalized by introducing a leak-off, i.e., a loss of fluid at the fracture boundaries that accelerates the fracture closure, when compared to the no leak-off case. To validate the theoretical results, 14 experiments are conducted with an ad hoc replica of a rectangular fracture of aspect ratio 2.5–2.7, with a maximum height of [math]; the elastic reaction of the walls is due to o-rings, also sealing the fracture without adding friction disturbances. Fluids with different rheology, both Newtonian and shear-thinning, are associated with different boundary conditions of external pressure and overload. The match between theory and experiments is fairly good, with discrepancies of a few percent essentially due to the approximations of the theoretical model, and, for shear-thinning fluids, to the simplified constitutive equation.

Rheotaxis of active droplets

Physics of Fluids - Wed, 08/18/2021 - 12:01
Physics of Fluids, Volume 33, Issue 8, August 2021.
Rheotaxis is a well-known phenomenon among microbial organisms and artificial active colloids, wherein the swimmers respond to an imposed flow. We report the first experimental evidence of upstream rheotaxis by spherical active droplets. It is shown that the presence of a nearby wall and the resulting strong flow-gradient at the droplet level is at the root of this phenomenon. Experiments with optical cells of different heights reveal that rheotaxis is observed only for a finite range of shear rates, independent of the bulk flow rate. We conjecture that the flow induced distortion of an otherwise isotropic distribution of filled/empty micelles around the droplet propels it against the flow. We also show that nematic droplets exhibit elastic stress-induced oscillations during their rheotactic flight. A promising potential of manipulating the rheotactic behavior to trap as well as shuttle droplets between target locations is demonstrated, paving way to potentially significant advancement in bio-medical applications.

Influence of thermal stratification on vertical natural convection—Experimental investigations on the example of thermal energy storage systems

Physics of Fluids - Wed, 08/18/2021 - 12:00
Physics of Fluids, Volume 33, Issue 8, August 2021.
Stratified thermal energy storages (TESs) are a promising solution for the large-scale energy storage problem of surplus renewable energy. Recent studies have shown parasitic convection occurring in near-wall regions inside such storage tanks, decreasing the working fluid's thermal stratification and reducing their exergy efficiency. This paper presents an experimental investigation of vertical convective flows in thermally stratified environments to complement the theoretical studies in this field. Specifically, we consider natural convection within a stratified laminar flow driven not by active heating but by the temperature gradient along a vertical wall, as is the case in real TES systems. The insights gained into the fundamental physical mechanisms of stratified vertical convection can promote efficiency improvements in TES systems. Therefore, we combine multiple particle image velocimetry and temperature measurements at different heights and thus obtain high-resolution vector fields of the entire wall jet flow and vertical temperature profiles for a TES model experiment. We appropriately modify scaling arguments found in the literature to develop a theory specifically suited to the experimental setup. The experimental data agree well with the modified theory. The results show two laminar counter-directed jets next to the vertical sidewall. In regions with high temperature gradients, the wall jets slow down, and flow reversals occur next to them. Moreover, the wall jets are asymmetric due to temperature-dependent fluid properties in conjunction with the ambient fluid stratification. In the stratification's upper, hot part, the wall jet is thinner and faster than the bottom jet in the cold region.

A priori analysis of subgrid-scale terms in compressible transcritical real gas flows

Physics of Fluids - Wed, 08/18/2021 - 12:00
Physics of Fluids, Volume 33, Issue 8, August 2021.
Of interest to the research community dealing with real gas flows, this study analyzes the influence of the physical complexity of real gases on the amplitude of subgrid-scale (SGS) terms present in the filtered Navier–Stokes equations to be solved in large eddy simulations. The direct numerical simulation results of three academic configurations (homogeneous isotropic turbulence, mixing layer, and channel flow) are filtered from the largest scale in the domain down to the Kolmogorov length scale. The analysis of the filtered flow variables consistently shows that the SGS turbulent stress and the SGS pressure cannot be neglected in the momentum equation. In the total energy equation, SGS pressure work and SGS internal and kinetic fluxes are found to be significant in the inertial zone of the turbulent kinetic energy spectrum. Since in the inertial zone, which corresponds to large filter sizes, specific models have not yet been designed for some of these terms, this study calls for such a modeling effort that will benefit the real gas and organic Rankine cycles research communities.

Reproduction of vortex lattices in the simulations of rotating liquid helium-4 by numerically solving the two-fluid model using smoothed-particle hydrodynamics incorporating vortex dynamics

Physics of Fluids - Wed, 08/18/2021 - 12:00
Physics of Fluids, Volume 33, Issue 8, August 2021.
Our recent study has shown that the representative phenomena of liquid helium-4 rotating in a cylinder could be simulated by solving the two-fluid model using smoothed-particle hydrodynamics (SPH) after reformulating the viscosity to conserve the rotational angular momentum. Specifically, the emergence of multiple parallel vortices and their rigid-body rotations were observed in our previous SPH simulations. The reported scheme is based on a classical approximation that assumes the fluid forces of both components and their interactions, with the expectation of functioning as a coarse-grained model of existing approximations that couple a microscopic model and the Navier–Stokes equation. Based on previous studies, this paper proposes an improved SPH scheme that explicitly incorporates vortex dynamics into SPH to reproduce vortex lattices, which was not possible in previous studies. Consequently, our improved scheme was observed to reproduce vortex lattices by introducing the Magnus force and interaction forces among vortices into the reformulated two-fluid model. The spinning of the vortices and rigid-body rotations were also observed. The number of vortices showed a certain agreement with Feynman's rule after the model parameter was optimized. Notably, from a scientific point of view, such vortex lattices are reproduced by the classical-mechanical approximation. We hope that our model will help physicists studying low-temperature physics find a new way of approaching this bizarre phenomenon that has attracted attention for more than 80 years.

Spatial wake transition past a thin pitching plate

Physical Review E - Wed, 08/18/2021 - 11:00

Author(s): Arnab Kumar De and Sandip Sarkar

The spatial transition of the wake behind a thin pitching plate in the thrust regime is studied. The drag-to-thrust transition is seen to occur at a threshold pitching frequency which becomes smaller for higher pitching angle and aspect ratio. The reverse von Kármán wake shows deflected asymmetric v...


[Phys. Rev. E 104, 025106] Published Wed Aug 18, 2021

The influence of nonlinearities on jet noise modeling based on parabolized stability equation

Physics of Fluids - Wed, 08/18/2021 - 02:00
Physics of Fluids, Volume 33, Issue 8, August 2021.
With the aid of a large eddy simulation (LES) model of a turbulent jet, we study the modeling of jet noise based on wavepackets by considering a certain degree of nonlinearity. Linear parabolized stability equations (PSEs) are utilized to solve the spatial evolution of wavepackets with the base flow obtained from the LES. The spectral proper orthogonal decomposition (SPOD) is performed to extract the most energetic coherent structures. Since the mean flow includes partial nonlinearity, improved agreement of hydrodynamic pressure fields between SPOD-filtered results and linear-PSE solutions is obtained in the near field. Deviations only occur when the coherent structures decay. Although linear-PSE solutions represent the near-field hydrodynamics reasonably, the far-field noise propagated from this linear model shows a large deviation from the LES results. Then, a small external harmonic forcing is added to the right-hand side of the PSE to mimic the effects of nonlinearity due to incoherent fluctuations on the late evolution of near-field wavepackets, and an adjoint approach is further utilized to search for optimal forcing distribution. Optimized forcing is mainly located near the critical layer; enhances the energy of wavepackets; and raises the sound radiation efficiency, but to a limited extent. Meanwhile, the coherence-matched PSE wavepacket is proposed to incorporate the coherence decay of wavepackets calculated based on LES. An improved agreement in far-field sound pressure levels for low-frequency components is achieved. In short, these findings all prove the vital role of nonlinearity in jet noise modeling, and the current modeling approaches have made some progress. However, a more physics-based and generalized nonlinear model is still required.

Energy stability analysis of turbulent incompressible flow based on the triple decomposition of the velocity gradient tensor

Physics of Fluids - Tue, 08/17/2021 - 13:40
Physics of Fluids, Volume 33, Issue 8, August 2021.
In the context of flow visualization, a triple decomposition of the velocity gradient into irrotational straining flow, shear flow, and rigid body rotational flow was proposed by Kolář in 2007 [V. Kolář, “Vortex identification: New requirements and limitations,” Int. J. Heat Fluid Flow, 28, 638–652 (2007)], which has recently received renewed interest. The triple decomposition opens for a refined energy stability analysis of the Navier–Stokes equations, with implications for the mathematical analysis of the structure, computability, and regularity of turbulent flow. We here perform an energy stability analysis of turbulent incompressible flow, which suggests a scenario where at macroscopic scales, any exponentially unstable irrotational straining flow structures rapidly evolve toward linearly unstable shear flow and stable rigid body rotational flow. This scenario does not rule out irrotational straining flow close to the Kolmogorov microscales, since there viscous dissipation stabilizes the unstable flow structures. In contrast to worst case energy stability estimates, this refined stability analysis reflects the existence of stable flow structures in turbulence over extended time.

Onset of instability in Hadley–Prats flow in a weakly heterogeneous porous layer with viscous dissipation

Physics of Fluids - Tue, 08/17/2021 - 13:04
Physics of Fluids, Volume 33, Issue 8, August 2021.
The stability of a flow subjected to an inclined temperature gradient (Hadley-type flow) in a horizontal porous media is studied in the presence of a basic horizontal mass flow (Prats flow). Therefore, the basic flow is called the Hadley–Prats flow. A weak vertical heterogeneity in permeability and conductivity is considered. The effect of viscous dissipation is taken to be non-negligible. The Rayleigh number corresponding to the vertical thermal gradient RaC is considered as an eigenvalue. Other parameters are the Péclet number (Pe) associated with the horizontal through flow, horizontal Rayleigh number [math] associated with the horizontal temperature gradient, Gebhart number (Ge) associated with viscous dissipation; parameters γ1 and γ2 represent the changes in permeability and conductivity, respectively. A linear stability analysis is done and the governing equations are solved numerically to obtain the critical Rayleigh number and wave number. Longitudinal and transverse rolls are discussed. Longitudinal rolls are the preferred modes for instability in most scenarios. It is found that when throughflow is present, the heterogeneity in permeability can show a stabilizing effect for longitudinal rolls but destabilizing effect for transverse rolls and vice versa depending on the direction of the throughflow. Increase in conductivity also may stabilize or destabilize the flow depending on the mass flow and viscous heating. The horizontal thermal gradient shows interesting effects in the presence of weak heterogeneity and horizontal throughflow. Significant change in the critical Rayleigh number is observed even for small values of the horizontal Rayleigh number.

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