Vortex-shedding suppression in two-dimensional mixed convective flows past circular and square cylinders

Abstract

Vortex-shedding suppression in two-dimensional mixed convective flows past circular and square cylinders is investigated numerically at two supercritical Reynolds numbers, Re = 60 and 100, at a fixed Prandtl (Pr) number of 0.71. The Richardson number (Ri) and free-stream orientation (α) are varied in the range [0, 1.6] and [0, π/2], respectively. The investigations involve the numerical solutions of mass, momentum, and energy equations subject to Boussinesq approximation in generalized curvilinear body-fitted coordinates. The critical Richardson numbers corresponding to the onset of suppression of vortex-shedding are determined for different free-stream orientations using the numerical data and the Stuart-Landau theory. For the case of circular cylinder, the critical Richardson number exhibits a “cosine-law” with respect to the free-stream orientation, while a non-monotonic trend is observed for the case of the square cylinder. By examining the near critical steady flow field data, two distinct components of the baroclinic vorticity generation rate are identified that appear to control the shedding suppression laws (relationships between the critical Richardson number and free-stream orientation) in theRi-α parametric space for the circular and the square cylinders. Supported by numerical experiments, the plausible roles of these baroclinic vorticity generation rate components are identified and utilized to theoretically deduce the functional forms of the shedding suppression laws that agree with the laws observed in the numerical experiments.