Study of flow through and around a pair of porous cylinders covering steady and unsteady regimes

Abstract

The present article focuses on the incompressible flow around two identical porous cylinders for a side-by-side configuration in a closed channel. The formation of various flow patterns behind permeable cylinders is more intriguing and further compelling to assimilate the underlying flow physics. The effects of three critical parameters, gap ratio (s/d), Reynolds number ( Re), and the Darcy number ( Da), on the flow behavior are investigated for the ranges of s/d = 1.5–6, Re =  5–100, and Da =  10−6–10−2. Both attached standing and detached vortices are observed in a steady flow regime. One secondary wake structure is also observed for s/d = 1.5, whose size gradually reduces with increased permeability. In an unsteady flow regime, the jet-like flow in the gap section mainly governs the unsteady wake patterns. In the low range of Darcy numbers (10−6–10−3), asymmetric flip-flopping patterns are observed for s/d = 1.5 and 2; and synchronized wake patterns either in anti-phase or in-phase mode are observed for higher gap ratios. The velocity profiles in the gap and free sides of the cylinders and pressure distribution along the porous surface are also discussed to facilitate the understanding of different wake patterns. Surprisingly, a case of pattern shifting from anti-phase to in-phase mode is observed when permeability is altered for the same flow-time. Symmetric and clustered strands of vorticity near the centerline are observed for all cases of s/d at Da =  10−2. The effects of Re, s/d, and Da on the drag coefficient and critical Reynolds number are also discussed. A jump in the drag values, a maximum of 13.9% for s/d = 3.5, is witnessed for the mid-range of Da at higher Re.