Analysis of the Momentum Transport Boundary Conditions at a Fluid-Porous Interface

The porous composite system is consists of porous medium and free fluid layer, which has extensive industrial applications. The study method for the flow field in the porous composite system includes the microscopic, mesoscopic and macroscopic approaches. When the two-domain approach is adopted, which is one of the macroscopic methods, the momentum transport boundary conditions at the interface between porous medium and free fluid layer is essential to analyze the flow field in the system. When Darcy equation is adopted to describe the flow in porous region, the Beavers-Joseph (BJ) interface condition can be used. When Darcy-Brinkman equation is adopted to describe the flow in porous region, the stress-jump (Ochoa-Tapia & Whitaker: OTW) interface condition can be used. To utilize these interface conditions, the velocity slip coefficient used in the BJ interface condition and the stress-jump coefficient used in the OTW interface condition should be specified. In this paper, a brush configuration is approximately treated as the equivalent porous media in the composite system. A numerical simulation method is used to obtain the microscopic solution for the flow in the system based on the Navier-Stokes equation applied in whole system, and an analytical method is used to obtain the corresponding macroscopic solution based on the two-domain approach. By comparing the microscopic and macroscopic solutions, the velocity slip coefficient and the stress-jump coefficient are determined since they can be treated as adjustable parameters. The influence of different flow types, including Poiseuille flow, Couette flow, and free boundary flow, are investigated. Also the impact of free fluid layer thickness and porous structure on the velocity slip coefficient and the stress-jump coefficient are discussed. The results indicate that, the velocity slip coefficient and the stress-jump coefficient are not only the parameters which depend on the porous structure, but also depend on the thickness of free fluid layer and flow type. When the thickness of free fluid layer is lower than a certain value, the impact of free fluid layer thickness on the velocity slip coefficient and the stress-jump coefficient is much obvious. In addition, when the thickness of free fluid layer is small, these coefficients are found to be dependent on the flow type. However, when the thickness of free fluid layer is large, the stress jump coefficient is independent of the thickness of free fluid layer and the flow type. Thus the stress jump coefficient obtained for a specific case can be used to predict velocity for different flow types and different thickness of free fluid layers.