Direct numerical simulation of turbulent flow and heat transfer over a heated cube placed in a matrix of unheated cubes

Abstract

Direct numerical simulation (DNS) of turbulent flow and heat transfer has been performed over a heated wall-mounted cube positioned in a non-heated cube matrix by applying periodic boundary conditions in both streamwise (X) and spanwise (Y) directions. Three different channel heights namely, 3.4H, 2.0H, 1.5H corresponding to blockage ratio (BR) of 0.0735, 0.125 and 0.167 with H as the size of the cube are employed. The Reynolds number defined for the present simulation is kept at 3,854 (based on the cube height and average streamwise velocity) while the Prandtl number is chosen to be 0.712. A second-order spatial and temporal discretization has been used to solve the Navier-Stokes and energy equations. The flow structures and the associated heat transfer have been compared and discussed at different BRs based on the results of instantaneous snapshots and statistical quantities of flow variables. The turbulent states for each BR has been compared using an anisotropic invariant map in the horseshoe vortex regime, top surface regime and in the wake regime. The total heat flux and turbulent heat flux quantities are compared near the cube’s surface to determine the contribution of both heat transfer by the thermal gradients, and due to the fluctuation induced heat flux. The overall Nusselt number is found to increase significantly with an increase in BR from 0.0735 to 0.125. However, at BR=0.167, no considerable augmentation in heat transfer has been observed as compared to BR=0.125. On the other hand, the friction factor increases monotonically but significantly with BR.