Investigation of vortex shedding behind a porous square cylinder using lattice Boltzmann method

Abstract

Incompressible, two-dimensional flow around a porous square cylinder placed in an infinite stream is simulated using the d2q9i model of the lattice Boltzmann method. The Reynolds number (based on the height of the cylinder) is kept at 100. The porosity ϕ of the cylinder is varied from 0.25 to 0.9 and permeability through the Darcy number Da from 0.0001 to 0.1. The velocity data at a point downstream of the cylinder are collected at each time step. Discrete Fourier transform analysis of this data is carried out to extract the dominant frequencies of the unsteady flow field behind the cylinder. Strouhal numbers (St) calculated using these dominant frequencies are compared with those of corresponding solid cylinder to bring out the effect of the porous medium on the wake structure and the vortex shedding. At Re=100, as the nondimensional permeability Da is increased from the solid cylinder limit, more flow results through the porous cylinder. The reduction in the value of the dominant frequency with increasing porous medium permeability Da and porosity ϕ indicates a substantial reduction in the vortex shedding. Corresponding static pressure plots and St values corroborate this observation at Re=100 and 200.