A General Macroscopic Model for Turbulent Flow in Porous Media

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Nima F. Jouybari ◽  
Mehdi Maerefat ◽  
T. Staffan Lundström ◽  
Majid E. Nimvari ◽  
Zahra Gholami
Keyword(s):  
Porous Media ◽  
Turbulent Flow ◽  
Present Model ◽  
Flow Characteristics ◽  
Flow In Porous Media ◽  
Macroscopic Model ◽  
Solid Matrix ◽  
Turbulent Regime ◽  
Rod Bundles ◽  
Capillary Model

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.

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

2001 ◽  
Vol 123 (4) ◽  
pp. 941-947 ◽  
Author(s):  
Marcos H. J. Pedras ◽  
Marcelo J. S. de Lemos
Keyword(s):  
Turbulent Flow ◽  
Porous Structure ◽  
Volume Averaging ◽  
Flow In Porous Media ◽  
Macroscopic Model ◽  
Turbulence Structure ◽  
Turbulent Regime ◽  
Periodic Cell ◽  
Initial Work ◽  
Adjusted Model

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.

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

2021 ◽  
Vol 929 ◽  
Author(s):  
Vishal Srikanth ◽  
Ching-Wei Huang ◽  
Timothy S. Su ◽  
Andrey V. Kuznetsov
Keyword(s):  
Numerical Simulation ◽  
Porous Medium ◽  
Porous Media ◽  
Symmetry Breaking ◽  
Turbulent Flow ◽  
Vortex Shedding ◽  
Flow Instability ◽  
Flow In Porous Media ◽  
Turbulent Regime ◽  
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.

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

2015 ◽  
Vol 766 ◽  
pp. 76-103 ◽  
Author(s):  
Y. Jin ◽  
M.-F. Uth ◽  
A. V. Kuznetsov ◽  
H. Herwig
Keyword(s):  
Numerical Simulation ◽  
Porous Medium ◽  
Porous Media ◽  
Direct Numerical Simulation ◽  
Turbulent Flow ◽  
Flow In Porous Media ◽  
Minimum Size ◽  
Solid Matrix ◽  
Pore Scale ◽  
Turbulent Structures

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.

Phase-Field Models of Gravity-Driven Unsaturated Flow in Porous Media

2008 ◽  
Author(s):  
Luis Cueto-Felgueroso ◽  
Ruben Juanes
Keyword(s):  
Porous Media ◽  
Preferential Flow ◽  
Unsaturated Flow ◽  
Flow In Porous Media ◽  
Macroscopic Model ◽  
Wetting Front ◽  
Forming Mechanism ◽  
Gravity Driven ◽  
Pattern Forming ◽  
Models Of Gravity

Existing continuum models of multiphase flow in porous media are unable to explain why preferential flow (fingering) occurs during infiltration into homogeneous, dry soil. We identify a relevant pattern-forming mechanism in the dynamics of the wetting front, and present a macroscopic model that reproduces the experimentally observed features of fingered flows. The proposed model reveals a scaling between local and nonlocal interface phenomena in imbibition, and does not introduce new independent parameters. The predictions based on this model are consistent with experiments and theories of scaling in porous media.

A Functional Scaling Relationship for Laminar to Turbulent Flow Regimes

2011 ◽  
Author(s):  
George Papadopoulos
Keyword(s):  
Turbulent Flow ◽  
Stokes Equations ◽  
Initial Conditions ◽  
Flow Characteristics ◽  
Flow Region ◽  
Flow Regimes ◽  
Transitional Flow ◽  
Turbulent Regime ◽  
Flow Profile ◽  
Scaling Relationship

A dimensional analysis that is based on the scaling of the two-dimensional Navier-Stokes equations is presented for correlating bulk flow characteristics arising from a variety of initial conditions. The analysis yields a functional relationship between the characteristic variable of the flow region and the Reynolds number for each of the two independent flow regimes. A linear relationship is realized for the laminar regime, while a nonlinear relationship is realized for the turbulent regime. Both relationships incorporate mass-flow profile characteristics to fully capture the effects of initial conditions on the variation of the characteristic variables. The union of these two independent relationships is formed utilizing the concept of flow intermittency to further expand into a generic scaling relationship that incorporates transitional flow effects to fully encompass solutions spanning the laminar to turbulent flow regimes. The results of the analysis are discussed within the context of several flow phenomena (e.g. pipe flow, jet flow & separated flow) resulting from various initial and boundary conditions.

A Mechanistic Explanation of Channels in Debris Beds

1986 ◽  
Vol 108 (1) ◽  
pp. 125-131 ◽  
Author(s):  
A. W. Reed
Keyword(s):  
Porous Media ◽  
Mechanistic Explanation ◽  
Flow In Porous Media ◽  
Spherical Particles ◽  
Solid Matrix ◽  
Saturation Curve ◽  
Two Phase ◽  
Flow Equations ◽  
Free Body ◽  
Particulate Debris

A mechanistic explanation of channeling during boiling in unconsolidated particulate debris beds is formulated by combining a free-body force diagram and the capillary pressure-saturation curve for porous media. The model is consistent with the principles of two-phase flow in porous media and provides boundary conditions for the flow equations in the unchanneled region. Experimental evidence for spherical particles presented here implies that the solid matrix in the channeled region cannot maintain a shear force and therefore behaves like a fluid without being fluidized in the classical sense.

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