A non-primitive boundary integral formulation for modeling flow through composite porous channel. (December 2019) - Nishad, Chandra Shekhar; Karmakar, Timir; Chandra, Anirban; Raja Sekhar, G.P.
Abstract: In this study, we develop a non-primitive boundary integral formulation (BIF) for modeling flow through composite porous channel. We consider a planar channel having two packings that are filled with fully saturated porous media. We assume that the two porous media are isotropic and homogeneous in nature, but with different permeabilities. Brinkman equation is used to model fluid flow through porous media. Stress-jump condition is utilized at the porous-porous interface to account the flow exchange due to two layers porous media. We present BIF for steady two-dimensional flow of a viscous incompressible fluid through a composite porous channel with two layers having different permeabilities (Brinkman-Brinkman problem). The BIF developed is in terms of non-primitive variables namely, stream-function and vorticity. In the limit of large permeability Brinkman equation approaches Stokes equation. Hence, in order to assert the accuracy of our BEM code, we have considered the corresponding Stokes-Brinkman system. We derive the Brinkman layer thickness for Brinkman-Brinkman system as a function of various flow parameters. It is observed that Darcy number, stress-jump coefficients and the thickness parameter have significant effect on the flow mechanics.