Numerical analysis for the flow past a porous square cylinder based on the stress‐jump interfacial‐conditions

Abstract

Purpose

The purpose of this paper is to report on the flow past a porous square cylinder, implementing the stress jump treatments for the porous‐fluid interface.

Design/methodology/approach

The numerical method was developed for flows involving an interface between a homogenous fluid and a porous medium. It is based on the finite volume method with body‐fitted and multi‐block grids. The Brinkman‐Forcheimmer extended model was used to govern the flow in the porous medium region. At its interface, a shear stress jump that includes the inertial effect was imposed, together with a continuity of normal stress.

Findings

The present model is validated by comparing with those for the flow around a solid circular cylinder. Results for flow around porous square cylinder are presented with flow configurations for different Darcy number, 10⁻² to 10⁻⁵, porosity from 0.4 to 0.8, and Reynolds number 20 to 250. The flow develops from steady to unsteady periodic vortex shedding state. It was found that the stress jump interface condition can cause flow instability. The first coefficient β has a more noticeable effect whereas the second coefficient β₁ has very small effect, even for Re=200. The effects of the porosity, Darcy number, and Reynolds number on lift and drag coefficients, and the length of circulation zone or shedding period are studied.

Originality/value

The present study implements the numerical method based on finite volume method with a collocated variable arrangement to treat the stress jump condition.

Citation

Chen, X., Yu, P., Winoto, S.H. and Low, H. (2008), "Numerical analysis for the flow past a porous square cylinder based on the stress‐jump interfacial‐conditions", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 18 No. 5, pp. 635-655. https://doi.org/10.1108/09615530810879756