Effect of Buoyancy on Three-Dimensional Flow Around a Heated Square Cylinder in Mixed Convection

Abstract

Three-dimensional flow around a heated square cylinder is studied using direct numerical simulation (DNS) in a mixed convective flow regime. In this study, an infinite square cylinder is immersed in horizontal free-stream crossflow (air, Prandtl number $Pr=0.7$) at right angles to gravity. Numerical results are shown with different heat levels defined by the over-heat ratio $\epsilon =(T_w-T_\infty )/T_\infty$, where $T_w$ and $T_\infty$ are equal to the surface and surrounding temperature. At large-scale heating $\epsilon \thicksim O(1)$, the thermal straining and transport properties of the fluid particles are varied. To capture this variation, an in-house solver of the compressible flow model is employed. The compressible flow governing equations in Cartesian coordinates are transformed into a body-fitted coordinate system and solved using the flux-based particle velocity upwind-modified+ (PVU-M+) scheme. The low Mach number $M=0.1$ is used for all computations. The results obtained using the in-house solver are validated with the values reported in the literature achieved by experimental, DNS, and Floquet methods. The disordered vortical structure of the mode B transition changes its shape and spanwise wavelength with the increase of the heating level from $\epsilon =0$ to $\epsilon =1$ at the Reynolds number $Re=500$. In addition, a very significant change in the force coefficient and the vortex shedding frequency is observed upon increasing the heating level. Variations in the frequency spectra of the lift coefficient are observed with varying heating.