Turbulent Flow In Porous Media Research Articles

Multiscale modeling and simulation of turbulent flows in porous media

Numerical simulation is an important tool for understanding the physics of flows in porous media and for making predictions. The state of the art of multiscale modeling and simulation of turbulent flows in porous media is reviewed in this paper. Numerical simulations of flows in porous media can be classified as microscopic simulations, in which both macroscopic and pore-scale flows are directly resolved, and macroscopic simulations, in which the pore-scale motions are modeled while the volume-averaged equations are solved. Studies in the past few years have shown that microscopic simulations improve the understanding of turbulent flows in porous media considerably; this motivates the development of more efficient and more accurate turbulence models for macroscopic simulations. On the basis of this review, we believe that simulation of flows with higher Reynolds numbers, understanding the transport of macroscopic turbulence, modeling of turbulent flows in inhomogeneous and anisotropic porous media, simulation of compressible and multiphase turbulent flows in porous media, and fluid–structure interaction in deformable porous matrices are important topics to be studied in the future.

Non-intrusive, transferable model for coupled turbulent channel-porous media flow based upon neural networks

Turbulent flow over permeable interfaces is omnipresent featuring complex flow topology. In this work, a data-driven, end-to-end machine learning model has been developed to model the turbulent flow in porous media. For the same, we have derived a non-linear reduced order model (ROM) with a deep convolution autoencoder. This model can reduce highly resolved spatial dimensions, which is a prerequisite for direct numerical simulation, by 99%. A downstream recurrent neural network has been trained to capture the temporal trend of reduced modes; thus, it is able to provide future evolution of modes. We further evaluate the trained model's capability on a newer dataset with a different porosity. In such cases, fine-tuning could reduce the efforts (up to two-order of magnitude) to train a model with limited dataset (10%) and knowledge and still show a good agreement on the mean velocity profile. Especially, the fine-tuned model shows a better agreement in the porous domain than the channel and interface areas indicating the topological feature is less challenging for training than the multi-scale nature of the turbulent flows. Leveraging the current model, we find that even quick fine-tuning achieves an impressive order-of-magnitude reduction in training time by approximately O(102) and still results in effective flow predictions. This promising discovery encourages the fast development of a substantial amount of data-driven models tailored for various types of porous media. The diminished training time substantially lowers the computational cost when dealing with changing porous topologies, making it feasible to systematically explore interface engineering with different types of porous media.

Large‐eddy simulation of a channel flow over an irregular porous matrix

AbstractFor turbulent flows in porous media, it is often assumed that the irregularity of the matrix would not affect the macroscopic, double‐averaged (in time and space), parameters of turbulence. Hence, to improve currently used modelling techniques, the ongoing efforts of the community are focused on performing high‐fidelity, scale‐resolving simulations of flows in regular, periodically repeating porous structures. This approach allows for minimizing still large computational cost, however, it assumes that results obtained from those geometries are generalizable to more disordered configurations. We investigate this assumption numerically using large‐eddy simulation and analyse the influence of the irregularity of the porous structure on turbulent characteristics in a fully turbulent flow in a channel half‐filled with porous medium. The flow statistics are examined and compared between four simulations, a reference channel with regular three‐dimensional porous matrix consisting of an array of cubes and three similar geometries created from randomly perturbing the positions of the cubes, with increasing mean value of cube displacement. We study double‐averaged flow properties, the distributions of double‐averaged Reynolds stress tensor, including the anisotropy of macroscopic turbulence and the drag force induced by the flow in the porous region of the channel. The results confirm the idea that the averaged characteristics, including the anisotropy of the stress tensor and the drag force, are not greatly influenced by the moderate perturbation to the geometry of the porous matrix. Additionally, the macroscopic turbulence seems to exhibit a high degree of anisotropy in the porous region and the adjacent boundary layer, suggesting that second‐order closure could be an adequate modelling choice for such flows.

A novel model for air velocities in airblast events in block caving mining

An airblast is a sudden collapse of a large volume of rock that causes air to rapidly flow through an underground opening as a result of air being compressed in a small space. Through the solution of the Ergun equation for turbulent flows in porous media, we have modeled air gusts in this paper. To resolve the issue, we use the finite element method (FEM). At a drawbell’s associated drawpoints, air flows and velocities are calculated. A series of numerical simulations are run while taking into account different arrangements of the average size of the rocks in the fractured zone and the air gap length, Lag, which is implicitly represented as the boundary condition for incoming air velocity at the muckpile. We propose a novel mathematical function that, using scaling arguments, expresses the maximum air gust velocity at the drawpoints as a function of the air gap height and average particle diameter. Designing geomechanical risk mitigation strategies for airblast events during block caving mining can take advantage of the findings in this paper.

The evolution of turbulent micro-vortices and their effect on convection heat transfer in porous media

New insight into the contribution of the microscale vortex evolution to convection heat transfer in porous media is presented in this paper. The objective is to determine how the microscale vortices influence convection heat transfer in turbulent flow inside porous media. The microscale temperature distribution is analysed using flow visualization in two dimensions using streamlines and in three dimensions using the Q-criterion. The pertinent observations are supplemented with a comparison of surface skin friction and heat transfer using: (i) surface skin-friction lines and (ii) the joint probability density function of the pressure and skin-friction coefficients, along with the Nusselt number. The microscale flow phenomena observed are corroborated with the features of the frequency spectra of the drag coefficient and macroscale Nusselt number. The large eddy simulation technique is used in this study to investigate the flow field inside a periodic porous medium. The Reynolds numbers of the flow are 300 and 500. The porous medium consists of solid obstacles in the shape of square and circular cylinders. Two distinct flow regimes are represented by using the porosities of 0.50 and 0.87. The results show that the surface Nusselt number distribution is dependent on whether the micro-vortices are attached to or detached from the surface of the obstacle. The spectra of the macroscale Nusselt number and the pressure drag are similar, signifying a correlation between the dynamics of heat transfer and the microscale turbulent structures. Both vortex shedding and secondary flow instabilities are observed that significantly influence the Nusselt number. The fundamental insight gained in this paper can inform the development of more robust macroscale models of convection heat transfer in turbulent flow in porous media.

Modeling Turbulence in Permeable Media: The Double-Decomposition Concept Revisited

In this article, a concept named double decomposition, which is used to model turbulent flows in porous media, is examined. This concept is based on the idea that in a turbulent flow through a porous matrix, local instantaneous variables can be averaged in time and space, simultaneously. Depending on how these operators are applied, averaged equations take different forms. In this article, instantaneous local equations are averaged using both operators and a different set of equations resulting from such operations are commented upon. Additional terms proposed for the averaged equations are discussed.

Symmetry breaking of turbulent flow in porous media composed of periodically arranged solid obstacles

The focus of this paper is a numerical simulation study of the flow dynamics in a periodic porous medium to analyse the physics of a symmetry-breaking phenomenon, which causes a deviation in the direction of the macroscale flow from that of the applied pressure gradient. The phenomenon is prominent in the range of porosity from 0.43 to 0.72 for circular solid obstacles. It is the result of the flow instabilities formed when the surface forces on the solid obstacles compete with the inertial force of the fluid flow in the turbulent regime. We report the origin and mechanism of the symmetry-breaking phenomenon in periodic porous media. Large-eddy simulation (LES) is used to simulate turbulent flow in a homogeneous porous medium consisting of a periodic, square lattice arrangement of cylindrical solid obstacles. Direct numerical simulation is used to simulate the transient stages during symmetry breakdown and also to validate the LES method. Quantitative and qualitative observations are made from the following approaches: (1) macroscale momentum budget and (2) two- and three-dimensional flow visualization. The phenomenon draws its roots from the amplification of a flow instability that emerges from the vortex shedding process. The symmetry-breaking phenomenon is a pitchfork bifurcation that can exhibit multiple modes depending on the local vortex shedding process. The phenomenon is observed to be sensitive to the porosity, solid obstacle shape and Reynolds number. It is a source of macroscale turbulence anisotropy in porous media for symmetric solid-obstacle geometries. In the macroscale, the principal axis of the Reynolds stress tensor is not aligned with any of the geometric axes of symmetry, nor with the direction of flow. Thus, symmetry breaking in porous media involves unresolved flow physics that should be taken into consideration while modelling flow inhomogeneity in the macroscale.

A comparative study of different heat transfer enhancement mechanisms in a partially porous pipe

The effect of porous material position on the heat transfer inside a pipe working in a turbulent regime is studied here to obtain a detailed understanding of the heat transfer enchantment mechanisms in different porous substrate positions. To this end, an in-house Fortran code is developed to solve the governing equations using the finite volume method and SIMPLE algorithm. Turbulent flow in porous media is modeled using a modified version of k–ε model. The flow field and heat transfer inside the partially filled pipe are investigated for the two cases of central and boundary configurations. The porous and flow characteristics including Reynolds number, Darcy number, the conductivity ratios of solid to fluid and the thickness of inserted porous layer are varied and the heat transfer performance is studied in different cases. It is observed that two entirely different phenomena enhance the heat transfer in central and boundary configurations. While the channeling of fluid between the porous media and the pipe wall highly affects the heat transfer performance in the former, the thermal conductivity of porous media plays a highly critical role in the latter configuration. It is shown that, for the same filling ratio, inserting the porous layer at the core of the pipe is more effective than placing it at the wall. Investigating porous materials with different solid conductivities revealed that covering the pipe wall with a porous material is justified only for solid matrixes with high thermal conductivities.

Modeling Turbulent Flows in Porous Media

Turbulent flows in porous media occur in a wide variety of applications, from catalysis in packed beds to heat exchange in nuclear reactor vessels. In this review, we summarize the current state of the literature on methods to model such flows. We focus on a range of Reynolds numbers, covering the inertial regime through the asymptotic turbulent regime. The review emphasizes both numerical modeling and the development of averaged (spatially filtered) balances over representative volumes of media. For modeling the pore scale, we examine the recent literature on Reynolds-averaged Navier–Stokes (RANS) models, large-eddy simulation (LES) models, and direct numerical simulations (DNS). We focus on the role of DNS and discuss how spatially averaged models might be closed using data computed from DNS simulations. A Darcy–Forchheimer-type law is derived, and a prior computation of the permeability and Forchheimer coefficient is presented and compared with existing data.

A Subgrid-Scale Model for Turbulent Flow in Porous Media

Given the analogy between the filtered equations of large eddy simulation and volume-averaged Navier–Stokes equations in porous media, a subgrid-scale model is presented to account for the residual stresses within the porous medium. The proposed model is based on the kinetic energy balance of the filtered velocity field within a pore; hence, when using the model, numerical simulations of the turbulent flow in the pores are not required. The accuracy of the model is validated with available data in the literature on turbulent flow through packed beds and staggered arrangement of square cylinders. The validation yields that the model successfully captures the effect of the pore-scale turbulent motion. The model is then used to study turbulent flow in a wall-bounded porous media to assess its accuracy.

Direct numerical simulation of convective heat transfer in porous media

Convective heat transfer in turbulent flow in porous media is, in general, less understood compared to laminar and creeping flows. It is broadly integrated into industrial applications even though a lack of understanding in microscale. In the present study, we report a direct numerical simulation (DNS) based microscopic analysis of heat and fluid flow in synthetic porous media with an aim to link the macroscopic statistics and qualitative observations with pore-scale signatures of the same. DNS is conducted with two computational codes with a cautious validation on the microscale. The conventional finite-volume solver shows an excellent agreement with high-order spectral/hp element solvers. The synthetic porous media are comprised of square cylinders in a staggered array. Macroscopic observation indicates an increased pressure loss and increased Nusselt number (Nu) as a result of high Reynolds numbers. However, a further examination of the ratio of Stanton number to skin friction coefficient St/Cf reveals that increasing Reynolds numbers lead to more pressure loss than improved heat transfer. Microscopic analysis shows that Nu is highest on the impinging surface, whereas lowest on the wake surface. In addition, it tends to be homogeneously distributed on surface area in the high porosity case. In the low porosity case, Nu on the sharp corners, is significantly higher than on other locations. Probability density function (PDF) of streamwise velocity fluctuation u′ shows Gaussian like distribution within two standard deviation. The high porosity group owns a spike around zero abscissa on PDF of both u′ and temperature fluctuation T′, which is an indication of less chaotic flow motions.

Angular multiscale statistics of turbulence in a porous bed

The physics of turbulent flow in porous media is explored in the Lagrangian frame. The evolution of curvature angles along the fluid trajectories reveals the multiscale nature of turbulence. The asymptotic value of the curvature angle quantifies the effect of geometric confinement on turbulence.

A General Macroscopic Model for Turbulent Flow in Porous Media

The present study deals with the generalization of a macroscopic turbulence model in porous media using a capillary model. The additional source terms associated with the production and dissipation of turbulent kinetic energy due to the presence of solid matrix are calculated using the capillary model. The present model does not require any prior pore scale simulation of turbulent flow in a specific porous geometry in order to close the macroscopic turbulence equations. Validation of the results in packed beds, periodic arrangement of square cylinders, synthetic foams, and longitudinal flows such as pipes, channels, and rod bundles against available data in the literature reveals the ability of the present model in predicting turbulent flow characteristics in different types of porous media. Transition to the fully turbulent regime in porous media and different approaches to treat this phenomenon are also discussed in the present study. Finally, the general model is modified so that it can be applied to lower Reynolds numbers below the range of fully turbulent regime in porous media.

Turbulence modeling for flows in wall bounded porous media: An analysis based on direct numerical simulations

Various models are available for simulating turbulent flows in porous media. Models based on the eddy viscosity assumption are often adopted to close the Reynolds stress term. In order to validate the assumptions behind such turbulence models, we studied the dynamics of macroscopic momentum and turbulence kinetic energy in porous media flows by utilizing Direct Numerical Simulation (DNS). The generic porous matrix is composed of regularly arranged spheres. The resulting periodic porous medium is bounded by two walls. The DNS analyses with a Lattice Boltzmann method were performed for various values of the applied pressure gradient, pore size to channel width ratio, and porosity. The DNS results were averaged over time and volume to obtain macroscopic results. The results show that the macroscopic shear Reynolds stress in all Representative Elementary Volumes (REVs), independent of their location, is negligibly small, although the mean velocity gradient takes nonzero values near the wall. The turbulence kinetic energy production rate is generally balanced by the dissipation rate in each REV. The DNS results support a zero-equation turbulence model that accounts for the fact that turbulent structures are restricted in size by the pore scale. The DNS results also suggest that the Brinkman term, which expresses the diffusion of momentum, has an important effect near the wall where the gradient of the shear stress is large. Therefore, the Brinkman term should be taken into account in the macroscopic momentum equation as a component of the total drag. A preliminary macroscopic model for calculating turbulent porous media flows has been proposed and compared with our DNS results.

A study of turbulent flow in large-scale porous media at high Reynolds numbers. Part II: flow physics

ABSTRACTThe evaluation of hydraulic performance of coarse porous media at high Reynolds numbers is of significant importance for dam safety assessment. To address this task, the present study uses a numerical approach based on a rigorous theoretical framework. The novelty of the study lies in the application of a fully calibrated and validated numerical three-dimensional model and a set of modified equations for momentum transfer and the associated coefficients for flow in porous media. A Lagrangian particle tracking model was used to estimate the lengths of the flow channels that developed in the porous media. Gamma distributions were fitted to the normalized channel lengths, and the scale and shape parameters of the gamma distribution were found to be Reynolds number dependent. These shape parameters can be estimated from the suggested polynomial equations. The proposed normalized length parameter can be used to evaluate permeability, energy dissipation, induced forces, and diffusion. It was found that shear forces exerted on the coarse particles depend on the inertial forces of the flow and can be estimated using the proposed equation for the developed turbulent flows in porous media.

Renormalization Group Analysis of the Stability of Turbulent Flows in Porous Media

The concept of renormalization groups for modeling the parameters of flow in porous media is considered. An algorithm for the renormalization of the equations from the k–e model of turbulence is given. An expression is obtained for the coefficient of renormalized viscosity. Based on the model developed, conditions of the turbulent flow instability in a porous medium have been analyzed.

Large eddy simulations of pore-scale turbulent flows in porous media by the lattice Boltzmann method

To discuss turbulent transport processes inside porous media, high resolution large eddy simulations by the D3Q27 multiple relaxation time lattice Boltzmann method and their data analysis are performed. The focused porous medium structures are square rod arrays, staggered cube arrays, fractal cube arrays and open cell foam. Although the second moments appearing in the double averaged momentum equation in porous media are the macro-scale Reynolds stress, the micro-scale Reynolds stress and the dispersive covariance, it is found that the micro-scale Reynolds stress and the dispersive covariance become dominant in the present porous medium flows. It is also found that the turbulent anisotropy and the magnitudes of those second moments are totally different among the cases due to the porous structures. Their transport mechanisms are discussed through the budget terms of the transport equations.

Interaction of steady jets with an array of permeable screens

Turbulent flows in porous media have important practical applications such as enhanced mixing of fuel and air, food drying, and cooling of electronics. However, experimental studies of turbulence in porous media are sparse due to the difficulties of measuring the complex flow environment. To this end, the interactions of steady jets with a porous medium formed from several parallel, transparent, permeable screens are studied using digital particle image velocimetry in a refractive indexed-matched environment. The permeable screens had porosities (open area ratios, ϕ) of 83.8, 69.0, 55.7, and 49.5 % and were held by a transparent frame that allowed the screen spacing to be changed. The steady jet results for Reynolds number (Re), which is defined based on the jet exit velocity and jet diameter, of 1000 showed laminar, predominantly steady flow that was segregated inside the porous medium, but for Re ≥ 2000, the flow was unsteady and turbulent with a mean velocity field that was relatively smooth inside the porous medium. As a result, more traditional jet features of self-similarity and increasing jet width were compared for the Re ≥ 2000 results. Decreasing the porosity was observed to increase the width of the jet significantly, especially for low porosity screens, and slowed the jet flow speed. Some of the typical features for axisymmetric jets were observed, even though the flow impinged on the permeable screens. In particular, self-similarity (or near self-similar behavior) was observed for the cross-sectional mean velocity profiles and for turbulence quantities for porosities larger than 55.7 % inside the porous medium. The effect of ϕ on turbulence quantities was significant for Re ≥ 2000. Although turbulence intensity increased on the downstream side of the first screen, the high dissipation forced drastic decrease of turbulence levels further downstream in the porous domain. Finally, the screens increased the removal of momentum from the jet as porosity decreased and screen spacing had a significant effect on the removal rate.

Numerical investigation of the possibility of macroscopic turbulence in porous media: a direct numerical simulation study

AbstractWhen a turbulent flow in a porous medium is determined numerically, the crucial question is whether turbulence models should account only for turbulent structures restricted in size to the pore scale or whether the size of turbulent structures could exceed the pore scale. The latter would mean the existence of macroscopic turbulence in porous media, when turbulent eddies exceed the pore size. In order to determine the real size of turbulent structures in a porous medium, we simulated the turbulent flow by direct numerical simulation (DNS) calculations, thus avoiding turbulence modelling of any kind. With this study, which for the first time uses DNS calculations, we provide benchmark data for turbulent flow in porous media. Since perfect DNS calculations require the resolution of scales down to the Kolmogorov scale, often only approximate DNS solutions can be obtained, especially for high Reynolds numbers. This is accounted for by using and comparing two different DNS approaches, a finite volume method (FVM) with grid refinement towards the wall and a lattice Boltzmann method (LBM) with equal grid distribution. The solid matrix was simulated by a large number of rectangular bars arranged periodically. The number of bars in the solution domain with periodic boundary conditions was reduced systematically until a minimum size was found that does not suppress any large-scale turbulent structures. Two-point correlations, integral length scales and energy spectra were determined in order to answer the question of whether or not macroscopic turbulence can be found in porous media.

Simulation of Flows through Submerged Vegetation Patches Using Macroscopic Turbulence Models

Macroscopic approach incorporating the spatial averaging procedure is commonly used to investigate turbulent flows in porous media, terrestrial and aquatic canopies. In this work the hydrodynamics of flows through a semi-rigid vegetation patch (VP) was investigated with two macroscopic turbulence models. We modified the Reynolods Averaged Navier Stokes (RANS) equations to obtain the Volume Averaged (VARANS) equations and performed simulations using the open source code OpenFOAM. The numerical results of gradually varied flows over submerged VPs are compared with the corresponding experimental measurements. The results show that the macroscopic turbulence models simulate the velocity profiles with acceptable accuracy. The increase of vegetation density generates higher Reynolds stress around the top of vegetation and smaller velocity inside the VP. The two models perform differently in the computation of Reynolds stress, with the profiles from the model of Uittenbogaard (2003) requiring a shorter distance to reach the uniform state for the case of low vegetation density. Further works will be carried out to identify the cause of difference and to achieve a refined macroscopic turbulence model.