Expansions at small Reynolds numbers for the flow past a porous circular cylinder

Abstract

The purpose of this article is to use the method of matched asymptotic expansions (MMAE) in order to study the two-dimensional steady low Reynolds number flow of a viscous incompressible fluid past a porous circular cylinder. We assume that the flow inside the porous body is described by the continuity and Brinkman equations, and the velocity and boundary traction fields are continuous across the interface between the fluid and porous media. Formal expansions for the corresponding stream functions are used. We show that the force exerted by the exterior flow on the porous cylinder admits an asymptotic expansion with respect to low Reynolds numbers, whose terms depend on the characteristics of the porous cylinder. In addition, by considering Darcy's law for the flow inside the porous circular cylinder, an asymptotic formula for the force on the cylinder is obtained. Also, a porous circular cylinder with a rigid core inside is considered with Brinkman equation inside the porous region. Stress jump condition is used at the porous–liquid interface together with the continuity of velocity components and continuity of normal stress. Some particular cases, which refer to the low Reynolds number flow past a solid circular cylinder, have also been investigated.

Keywords:

• Stokes flow
• Brinkman equation
• Oseen flow
• matched asymptotic expansion

AMS Subject Classifications:

• 76D05
• 76D07
• 76S05

Acknowledgements

G.P. Raja Sekhar acknowledges the support from the Alexander von Humboldt Foundation. Mirela Kohr is supported by the Romanian Ministry of Education and Research, UEFISCSU Grant, PN-II-ID-525/2007. Jai Prakash acknowledges the support of CSIR, India.