Numerical study of shear rate effect on unsteady flow separation from the surface of the square cylinder using structural bifurcation analysis

Abstract

In this paper, an incompressible two-dimensional shear flow past a square cylinder problem is investigated numerically using a higher order compact finite difference scheme. Simulations are presented for three sets of Reynolds numbers, 100, 200, and 500, with various shear parameter (K) values ranging from 0.0 to 0.4. The purpose of the present study is to elaborate the influence of shear rate on the vortex shedding phenomenon behind the square cylinder. The results presented here show that the vortex shedding phenomenon strongly depends on Re as well as K. The strength and size of vortices shed behind the cylinder vary as a function of Re and K. When K is larger than a critical value, the vortex shedding phenomenon has completely disappeared depending on the Reynolds number. Apart from the numerical study, a thorough theoretical investigation has been done by using a topology based structural bifurcation analysis for unsteady flow separations from the walls of the cylinder. Through this analysis, we study the exact locations of the bifurcation points associated with secondary and tertiary vortices with appropriate non-dimensional time of occurrence. To the best of our knowledge, this is the first time, a topological aspect based structural bifurcation analysis has been done to understand the vortex shedding phenomenon and flow separation for this problem.