Effects of heating and free-stream orientation in two-dimensional forced convective flow of air past a square cylinder

Abstract

A numerical investigation of the combined effects of heating and flow orientation on the forced convective flow of air past a square cylinder is carried out. In order to account for the effects of large-scale heating like thermal straining of the fluid particles, variations in thermo-physical and transport properties, a fully compressible flow model is utilized. The numerical simulations are carried out using a new flux-based particle velocity upwind scheme (PVU-M+). The computations are carried out in the parametric space of free stream Reynolds number (Re) in the range [60, 140], free stream orientation (α) in the range [0, 45°] and the Over-heat ratio, ε = (TW−T∞)/T∞ in the range [0, 1] where TW and T∞ are the uniform cylinder and free stream temperatures.At all parameter combinations the flow is found to be unsteady with vortex-shedding except for (Re = 60, α = 0, ε = 0.8, 1.0) and (Re = 60, α = 15, ε = 1.0) where vortex-shedding is suppressed resulting in a steady flow. By comparing the data for the global parameters like Strouhal number, mean drag coefficient and mean Nusselt number, with that obtained from a constant property incompressible flow model (Boussinesq type model), a quantification of “large-scale” heating scenario is carried out. Utilizing a novel mathematical procedure, it is shown that the data obtained for the global parameters at different Re and ε can be transformed into appropriate scaling parameters that yield an optimal collapse of the data at different (Re, ε) combinations for a fixed free-stream orientation.