Turbulent Flow In Porous Media Research Articles

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.

Scale estimation for turbulent flows in porous media

The results of an experimental study to determine the smallest, dissipative scales of the turbulent flow in a randomly packed porous bed are presented and discussed. Particle Image Velocimetry was used to obtain time dependent two-dimensional velocity fields within the bed, which were then used to obtain turbulent statistical measures within the flow field. Results are presented for representative pores for a range of pore Reynolds numbers, Repore, from 839 to 3964, which include integral length and velocity scales and estimates of the Kolmogorov scales of length, velocity and time. The results show an asymptotic region at sufficiently high Repore, on the order of 2800, where scaling is normalized using the bed pore scales. It is also shown that the turbulent Reynolds number for this flow in the asymptotic limit is on the order of 0.07Repore, for the range of pores studied.

On the Budget Terms of the Double Averaged Turbulent Stress Transport Equations in Porous Media

To provide information for modeling turbulent flows in porous media, LES (large eddy simulation) of fully developed flows in porous media is performed. The numerical scheme used for the LES is the D3Q27 (three dimensional 27 discrete velocity) MRT (multiple relaxation time) LBM (lattice Boltzmann method) coupled with the WALE (wall-adapting local eddy-viscosity) sub- grid-scale turbulence model. The considered porous medium configurations are square rod arrays, cube arrays and BCC (body centered cube) foams. Using the statistical data by the LES, the behaviors of the budget terms of the double averaged turbulent stress transport equations are investigated carefully for modeling those transport equations.

Three-Dimensional Numerical Analysis of Turbulent Flow in Porous Media Formed by Periodic Arrays of Cubic, Spherical, or Ellipsoidal Particles

In the present paper, three-dimensional (3D) turbulent flow in the porous media formed by periodic arrays of particles is numerically investigated. 3D Navier–Stokes equations and a standard k-ε turbulence model with enhanced wall function are adopted to model the turbulent flow inside the pores. Both local and macroscopic turbulence characteristics for different particle types (cubic, spherical, and ellipsoidal particles) and array forms [simple cubic (SC) and body center cubic arrays (BCC)] with different pore Reynolds numbers and porosities are carefully examined. It is revealed that, in the structural arrays of particles, the effects of particle shape and array form would be remarkable. With the same Reynolds number and porosity, the magnitudes of turbulence kinetic energy and its dissipation rate for the simple cubic array of spheres (SC-S) would be higher than those for the other arrays. Furthermore, with a nonlinear fitting method, the macroscopic correlations for extra turbulence quantities k∞ and ɛ∞ in the structural arrays for different particle types and array forms are extracted. The forms of present correlations can fit well with those of Nakayama and Kuwahara's correlations [Nakayama and Kuwahara, 1999, “A Macroscopic Turbulence Model for Flow in Porous Media,” ASME J. Fluids Eng., 121(2), pp. 427–433], but some model constants would be lower.

Macroscopic Turbulence Models and Their Application in Turbulent Vegetated Flows

Turbulent flow in porous media, terrestrial and aquatic canopies, and urbanlike roughness is usually investigated using the macroscopic approach, which is based on the volume average theory (VAT). Two different methodologies have been developed in the past leading to different equations for both the mean and the turbulence quantities: time-averaging the volume-averaged equations and volume-averaging the time-averaged equations. In this study four models of the volume-averaging methodology are applied for modeling the flow in open channels with submerged vegetation. The vegetation is considered rigid, simulated as cylindrical roughness in a staggered or nonstaggered arrangement. Three of the models are of the k-e type and one is of the Reynolds stress type. The latter has been applied using a modified e equation to account for the extra dissipation attributable to vegetation. Numerical results for both mean and turbulence flow characteristics are compared against available experimental measurements for dense canopies under shallow and deep flow conditions. In addition, relevant characteristics (displacement thickness, canopy shear layer parameter, mixing length, penetration length scale, and etc.) are calculated for both computed and experimental data for assessing the performance of the models.

A new turbulence model for porous media flows. Part II: Analysis and validation using microscopic simulations

A new model for turbulent flows in porous media developed in an accompanying paper [F.E. Teruel, Rizwan-uddin, A new turbulence model for porous media flows. Part I: Constitutive equations and model closure, Int. J. Heat Mass Transfer (2009), doi: 10.1016/j.ijheatmasstransfer.2009.04.017.], in which new definitions of the macroscopic turbulence quantities are introduced, is analyzed and validated. The model is validated using a simple but often used porous medium consisting of a staggered arrangement of square cylinders. Theoretically predicted values of the newly defined turbulence variables, under fully developed conditions, are compared with corresponding variables used in existing turbulence models. Additionally, evolution of the macroscopic turbulence quantities obtained numerically using the model developed here are compared with reference results, obtained by averaging over space the microscopic level solution of the RANS equations. Comparison exercise for the 75% porosity case is carried out for a range of turbulence intensity at the entrance of the porous medium. Comparison of results shows very good agreement. The spatial evolution of the dispersive kinetic energy, which is included in the definition of the macroscopic turbulent kinetic energy introduced here, is computed using the microscopic solution. Its magnitude relative to the conventional turbulent kinetic energy shows the importance of this quantity in the representation of turbulence effects in porous media flows.

A new turbulence model for porous media flows. Part I: Constitutive equations and model closure

A new model for turbulent flows in porous media is developed. The spatial- and time fluctuations in this new model are tied together and treated as a single quantity. This novel treatment of the fluctuations leads to a natural construction of the k and ε type equations for rigid and isotropic porous media in which all the kinetic energy filtered in the averaging process is modeled. The same terms as those found in the corresponding equations for clear flow, plus additional terms resulting from the interaction between solid walls in the porous media and the fluid characterize the model. These extra terms arise in a boundary integral form, facilitating their modeling. The model is closed by assuming the eddy viscosity approximation to be valid, and using simple models to represent the interaction between the walls in the porous media and the fluid.

Exact and approximate analytical solutions for unsteady fully developed turbulent flow in porous media and fractures for time dependent boundary conditions

Summary The problem of recharge of water to an initially dry, semi-infinite aquifer is investigated, where the occurrence of turbulent flow is considered. By applying a similarity transform an analytical solution is obtained by the Adomian’s decomposition method. The integration constant of the power series is determined by examining the mathematical structure of the solution at the downstream part of the front. It is demonstrated that for two specific cases the Adomian’s series are reduced to exact solutions. The analytical solutions above, derived on the basis of fully developed turbulent flow regime are compared to the water table profile computed on the basis of the Forchheimer equation. Four specific cases in real world coordinated are investigated: (a) the propagation of a linear traveling wave, (b) injection of fluid at constant flow-rate in a fracture or aquifer, (c) flow induced by a sudden raise of the piezometric head, (d) redistribution of a finite quantity of water in a porous medium. Potential applications of the above cited results are water body–aquifers interaction, and exploitation of hot dry rocks.

Hydrodynamic Modeling of Porous Media; Analytical model ofWater Filtration

Hydrodynamic modeling of viscous flow in porous media was investigated for fourselected filter media crushed silica, crushed anthracite coal, glass beads and crushed garnet.Typical constants that can be used to estimate head loss for some of the most common designof granular media filters were correlated. The effect of several parameters such as porosity(35%-60%) , temperature(20oC-80oC) and media grain size (0.5-2mm) was studied. Empiricalrelationships were developed using a plot of friction vs. Reynolds number similar to those thathad been successfully used for the flow of fluids in pipes. Analytical models were made todevelop an equation for viscous turbulent flow in porous media from first hydraulic principles.Empirical equation was developed to predict pressure drop in porous media as a function ofbed porosity and evaluated the friction factor as a function to flow type.

Simulation of turbulent natural convection in a porous cylindrical annulus using a macroscopic two-equation model

This work presents numerical computations for laminar and turbulent natural convection within a horizontal cylindrical annulus filled with a fluid saturated porous medium. Computations covered the range 25 < Ra m < 500 and 3.2 × 10 −4 > Da > 3.2 × 10 −6 and made use of the finite volume method. The inner and outer walls are maintained at constant but different temperatures. The macroscopic k– ε turbulence model with wall function is used to handle turbulent flows in porous media. First, the turbulence model is switched off and the laminar branch of the solution is found when increasing the Rayleigh number, Ra m. Subsequently, the turbulence model is included and calculations start at high Ra m, merging to the laminar branch for a reducing Ra m. This convergence of results as Ra m decreases can be seen as an estimate of the so-called laminarization phenomenon. Here, a critical Rayleigh number was not identified and results indicated that when the porosity, Prandtl number, conductivity ratio between the fluid and the solid matrix and Ra m are kept fixed, the lower the Darcy number, the higher is the difference of the average Nusselt number given by the laminar and turbulent models.

Large eddy simulation of turbulent flow in porous media

An LES (large eddy simulation) study was conducted using one of standard numerical models for a porous medium, namely, a flow through a periodic array of square cylinders. The LES results were processed to extract macroscopic results such as the macroscopic turbulent kinetic energy and the macroscopic pressure gradient. These macroscopic results are compared against those obtained using conventional models of turbulent kinetic energy and its dissipation rate, so as to examine the validity of extending the conventional two equation models of turbulence to the flow in porous media. The spectrum of turbulence was also examined to appreciate the onset of turbulence.

Fundamentals of the double - decomposition concept for turbulent transport in permeable media

Environmental impact analyses as well as engineering equipment design can both benefit from reliable modeling of turbulent flow in porous media. A number of natural and engineering systems can be characterized by a permeable structure through which a working fluid permeates. Turbulence models proposed for such flows depend on the order of application of time and volume average operators. Two methodologies, following the two orders of integration, lead to different governing equations for the statistical quantities. This paper reviews recently published methodologies to mathematically characterize turbulent transport in porous media. A new concept, called double-decomposition, is here discussed and models for turbulent transport in porous media are classified in terms of the order of application of the time and volume averaging operators, among other peculiarities. Within this paper Instantaneous Local Transport Equations are reviewed for clear flow before Time and Volume Averaging Procedures are applied to them. The Double-Decomposition Concept is presented and thoroughly discussed prior the derivation of macroscopic governing equations. Equations for Turbulent Transport follow, showing detailed derivation for the mean and turbulent field quantities.

301 多孔質構造体における乱流への遷移過程(OS3-1,OS3 多孔質体内流動・伝熱・燃焼研究の新展開)

301 多孔質構造体における乱流への遷移過程(OS3-1,OS3 多孔質体内流動・伝熱・燃焼研究の新展開)

Turbulent natural convection in a porous square cavity computed with a macroscopic κ– ε model

Detailed numerical computations for laminar and turbulent natural convection within a square cavity filled with a fluid saturated porous medium are presented. Heated vertical walls are maintained at constant but different temperatures, while horizontal surfaces are kept insulated. The macroscopic κ– ε turbulence model with wall function is used to handle turbulent flows in porous media. In this work, the turbulence model is first switched off and the laminar branch of the solution is found when increasing the Rayleigh number, Ra m. Computations covered the range 10 < Ra m < 10 6 and 10 −7 < Da < 10 −10 and made use of the finite volume method. Subsequently, the turbulence model is included and calculations start at high Ra m, merging to the laminar branch for a reducing Ra m and for Ra m less than a certain critical Rayleigh number, Ra cr. This convergence of results as Ra m decreases can be seen as a characterization of the laminarization phenomenon. For Ra m values less than around 10 4, both laminar and turbulent flow solutions merge, indicating that such critical value for Ra m was reached. Results further indicate that when the parameters porosity, Pr, conductivity ratio between the fluid and the solid matrix and the Ra m are kept fixed, the lower the Darcy number, the higher the average Nusselt number at the hot wall.

Development of an engineering approach to computations of turbulent flows in composite porous/fluid domains

The purpose of this paper is to develop an engineering approach to computations of turbulent flows in composite domains partly occupied by a clear fluid and partly by a fluid saturated porous medium. Previous research concerning turbulent flows in porous media indicates that the effect of porous media is to dampen turbulence. Therefore, in porous/fluid domains the penetration depth of turbulent eddies into the porous region is expected to be small. The authors suggest assuming that the flow over the whole porous region remains laminar and matching turbulent flow solution in the clear fluid region with the laminar flow solution in the turbulent flow region. Although the flow in the porous region is assumed to be laminar, linear Darcy or Brinkman–Darcy models cannot be utilized to describe momentum transport in the porous region because of large filtration velocity. The momentum transport model in the porous layer utilized in this research is based on the Brinkman–Forchheimer-extended Darcy equation, which allows the accounting for deviation from linearity and also allows a smooth matching of the filtration velocity at the porous/fluid interface. Because of the large filtration velocity in the porous region, the energy equation in the porous region also accounts for the thermal dispersion effects.

On the Mathematical Description and Simulation of Turbulent Flow in a Porous Medium Formed by an Array of Elliptic Rods

Many engineering and environmental system analyses can benefit from appropriate modeling of turbulent flow in porous media. Through the volumetric averaging of the microscopic transport equations for the turbulent kinetic energy, k, and its dissipation rate, ε, a macroscopic model was proposed for such media (IJHMT, 44(6), 1081-1093, 2001). In that initial work, the medium was simulated as an infinite array of cylindrical rods. As an outcome of the volume averaging process, additional terms appeared in the equations for k and ε. These terms were here adjusted assuming now the porous structure to be modeled as an array of elliptic rods instead. Such an adjustment was obtained by numerically solving the microscopic flow governing equations, using a low Reynolds formulation, in the periodic cell composing the medium. Different porosity and Reynolds numbers were investigated. The fine turbulence structure of the flow was computed and integral parameters were presented. The adjusted model constant was compared to similar results for square and cylindrical rods. It is expected that the contribution herein provide some insight to modelers devoted to the analysis of engineering and a environmental systems characterized by a porous structure saturated by a fluid flowing in turbulent regime.

Macroscopic turbulence modeling for incompressible flow through undeformable porous media

The literature presents two different methodologies for developing turbulent models for flow in a porous medium. The first one starts with the macroscopic equations using the extended Darcy–Forchheimer model. The second method makes use, first, of the Reynolds-averaged equations. These two methodologies lead to distinct set of equations for the k– ε model. The present work details a mathematical model for turbulent flow in porous media following the second path, or say, space-integrating the equations for turbulent flow in clear fluid. In order to account for the porous structure, an additional term is included in the sources for k and ε. A methodology is followed for determining the additional constant proposed. The equations for the microscopic flow were numerically solved inside a periodic elementary cell. The porous structure was approximated by an infinite array of circular rods. The method SIMPLE and a non-orthogonal boundary-fitted coordinate system were employed. Integrated parameters where compared to the existing data for fully developed homogeneous flow through porous media. Preliminary results are in agreement with numerical experiments presented in the literature.

High-velocity laminar and turbulent flow in porous media

We model high-velocity flow in porous media with the multiple scale homogenization technique and basic fluid mechanics. Momentum and mechanical energy theorems are derived. In idealized porous media inviscid irrotational flow in the pores and wall boundary layers give a pressure loss with a power of 3/2 in average velocity. This model has support from flow in simple model media. In complex media the flow separates from the solid surface. Pressure loss effects of flow separation, wall and free shear layers, pressure drag, flow tube velocity and developing flow are discussed by using phenomenological arguments. We propose that the square pressure loss in the laminar Forchheimer equation is caused by development of strong localized dissipation zones around flow separation, that is, in the viscous boundary layer in triple decks. For turbulent flow, the resulting pressure loss due to average dissipation is a power 2 term in velocity.

Numerical Modeling of Turbulent Flow in Porous Media Using a Spatially Periodic Array

Numerical Modeling of Turbulent Flow in Porous Media Using a Spatially Periodic Array

Field Solutions for Turbulent Seepage Flow

A finite element solution is presented for obtaining field solutions for turbulent flow in porous media. Such problems are frequently of the free surface type. They are associated with rockfill dams and flood diversion, and with some natural slopes. Comparisons are drawn between laminar and turbulent states; the latter is shown to produce higher pore pressures, and a significant result is deduced relating to requirements for mesh protection.