Slip and no-slip velocity boundary conditions at interface of porous, plain media (original) (raw)
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Computation
In this work, Finite Element Method (FEM) is applied to obtain the condition at the boundary of the interface between a channel and a porous medium. The boundary conditions that should be applied to the inhomogeneous interface zone between the two homogeneous regions of free fluid and porous medium are derived. The comparison has been performed for porous material characterizations to provide the velocity at the inhomogeneous interface zone with variable permeability between the two homogeneous regions of free fluid and porous medium. Also, the dependence of the slip coefficient on the thickness of the transition zone is established and the values of the thickness are so justified that the numerical results and the numerical results of our proposed technique are found to be in good agreement with experimental results in the literature.
Slip effects on shearing flows in a porous medium
Acta Mechanica Sinica, 2008
This paper deals with the magnetohydrodynamic (MHD) flow of an Oldroyd 8-constant fluid in a porous medium when no-slip condition is no longer valid. Modified Darcy's law is used in the flow modelling. The non-linear differential equation with non-linear boundary conditions is solved numerically using finite difference scheme in combination with an iterative technique. Numerical results are obtained for the Couette, Poiseuille and generalized Couette flows. The effects of slip parameters on the velocity profile are discussed.
Fluid mechanics of the interface region between two porous layers
Applied Mathematics and Computation, 2002
Flow through and over a fluid-saturated porous layer is investigated. The flow through a porous channel (which is assumed to be governed by Forchheimer equation) is terminated by a porous layer possessing a different structure (the flow through which is governed by the Brinkman equation). At the interface between the physical regions, matching conditions on the velocity and shear stress are imposed. The flow through this configuration admits solutions which are linear combinations of polynomial and exponential functions. The effect of the Reynolds number and the Darcy numbers on the interface velocity is presented in this work. Ó
Verification of the boundary condition at the porous medium–fluid interface
We study the hydrodynamic stability of liquid flowing down over the inclined layer of uniform porous medium and compare the results obtained in the different frameworks. The flow in porous medium is described by the Brinkman model and by the Darcy model with corresponding boundary conditions at the interface between the homogeneous fluid and porous medium. It is shown the critical Reynolds number is calculated for the Darcy model much lower than in case of the Brinkman model, while the flow velocity is the same in the both models. It is a pure mathematical effect, which can be used to verify the models and to determine the empirical coefficients in the boundary conditions from an experimental study of flow instability.
Slip at a uniformly porous boundary: effect on fluid flow and mass transfer
Journal of Engineering Mathematics, 1992
An approximate solution to the 2-D Navier-Stokes equations for steady, isothermal, incompressible, laminar flow in a channel bounded by one porous wall subject to uniform suction is derived. The solution is valid for small values of the Reynolds number based on the suction velocity and channel height. Solute transport is considered numerically by decoupling the equations representing momentum and mass transfer. The effect of fluid slip at the porous boundary on the axial and transverse components of fluid velocity, axial pressure drop and mass transfer is investigated.
WSEAS TRANSACTIONS ON HEAT AND MASS TRANSFER, 2021
Coupled parallel flow of fluid with pressure-dependent viscosity through an inclined channel underlain by a porous layer of variable permeability and variable thickness is initiated in this work. Conditions at the interface between the channel and the porous layer reflect continuity assumptions of velocity, shear stress, pressure and viscosity. Viscosity is assumed to vary in terms of a continuous pressure function that is valid throughout the channel and the porous layer. Model equations are cast in a form where the pressure as an independent variable and solutions are obtained to illustrate the effects of flow and media parameters on the dynamics behaviour of pressure-dependent viscosity fluid. A permeability and a viscosity adjustable control parameters are introduced to avoid unrealistic values of permeability and viscosity. This work could serve as a model for flow over a mushy zone.
Boundary conditions at a planar fluid–porous interface for a Poiseuille flow
International Journal of Heat and Mass Transfer, 2006
The velocity boundary condition that must be imposed at an interface between a porous medium and a free fluid is investigated. A heterogeneous transition zone characterized by rapidly varying properties is introduced between the two homogeneous porous and free fluid regions. The problem is solved using the method of matched asymptotic expansions and boundary conditions between the two homogeneous regions are obtained. The continuity of the velocity is recovered and a jump in the stress built using the viscosity (and not the effective viscosity) appears. This result also provides an explicit dependence of the stress jump coefficient to the internal structure of the transition zone and its sensitivity to this micro structure is recovered.
Modeling and simulation of flows over and through fibrous porous media
2018
Any natural surface is in essence non-smooth, consisting of more or less regular roughness and/or mobile structures of different scales. From a fluid mechanics point of view, these natural surfaces offer better aerodynamic performances when they cover moving bodies, in terms of drag reduction, lift enhancement or control of boundary layer separation; this has been shown for boundary layer or wake flows around thick bodies. The numerical simulation of microscopic flows around "natural" surfaces is still out of reach today. Therefore, the goal of this thesis is to study the modeling of the apparent flow slip occurring on this kind of surfaces, modeled as a porous medium, applying Whitaker's volume averaging theory. This mathematical model makes it possible to capture details of the microstructure while preserving a satisfactory description of the physical phenomena which occur. The first chapter of this manuscript provides an overview of previous efforts to model these s...