Steady and unsteady flow regimes in two-dimensional mixed convective flow of air past a heated square cylinder

Abstract

The present work involves a numerical investigation of bifurcations/transitions between unsteady to steady as well as steady to unsteady flow states found to exist in two-dimensional mixed convective laminar flow of air past a heated square cylinder. The unsteady flow governing equations, subjected to Oberbeck-Boussinesq approximation, are marched forward in time using a SMAC type pressure correction scheme on a structured body-fitted grid. A finite difference type discretization is employed to discretize the equations in space. Numerical simulations are carried out in the parametric space of Richardson number (Ri) and free-stream orientation (α) with respect to gravity for fixed values of Reynolds number (Re) in the range [20, 120] in steps of 20. Computations are carried out for 0 ≤ α ≤ 90° and 0 ≤ Ri ≤ 1.6. At Re = 20, only steady flows are observed for any (α, Ri) setting within the ranges considered. However for 40 ≤ Re ≤ 120, at a fixed (α, Re) with progressively increasing values of Ri, transitions from both unsteady to steady as well as steady to unsteady are observed. Stuart-Landau theory is employed to analyze the bifurcations and to estimate the critical Ri corresponding to the bifurcations/transitions. The critical Ri as a function of α (or neutral-curve) is obtained at different Re in the range 40 ≤ Re ≤ 120.