Numerical investigation of buoyancy-aided mixed convective flow past a square cylinder inclined at 45 degrees

Abstract

The present study numerically investigates the two-dimensional mixed convective flow of air past a square cylinder placed at an angle of incidence $\alpha = 45^{\circ}$ to the free-stream. We perform direct numerical simulations (DNS) for a Reynolds number (Re) of 100, a range of Richardson numbers (Ri) between 0.0 and 1.0, and a Prandtl number (Pr) of 0.7. The critical Richardson number at which the near-field becomes a steady flow from an unsteady one lies between $0.65$ and $0.7$, along with a simultaneous emergence of the far-field unsteadiness. There is no range of Ri for which the entire flow field is seen to be steady. At a relatively moderate Ri, the flow field reveals the presence of vorticity inversion through the momentum addition in the downstream region. We discuss the dual wake-plume nature of the flow behind the cylinder. The wake exhibits characteristics similar to those of a plume, revealing a self-similar behavior in the far-field at increased buoyancy. We explore the cause of the far-field unsteadiness and discuss the mechanism of the observed flow physics using instantaneous and time-averaged flow fields. The important flow quantities, such as force coefficients, vortex shedding frequency, and Nusselt number, are discussed at various Richardson numbers.