Performance of characteristic numerical boundary conditions for mixed convective flows past a heated square cylinder using a non-Boussinesq approach

Abstract

This work represents an investigation of the performance of characteristic numerical boundary conditions on the unconfined 2D mixed convective flow of air past a heated square cylinder governed by a non-Boussinesq flow model. The working fluid (air) is taken to be thermally perfect with variable thermo-physical and transport properties. The fully compressible Navier-Stokes equations are transformed using body-fitted coordinates and solved using particle velocity upwind (PVU-M+) scheme on a structured O-type grid. To investigate the performance of characteristic numerical boundary conditions, the gravity aligned upward flow past a heated square cylinder at (α = 0°, M = 0.1 and 0.2, Re = 100, Fr = 0.5 and 1.0, Pr = 0.71, γ = 1.4, and ε = 0.07 and 1.0) is considered. The overheat ratio (ε) is defined as (Tw – T∞)/T∞, where Tw and T∞ are the uniform cylinder and free stream temperatures, respectively. In order to determine the proper choice of boundary conditions to be imposed on the far boundary, algebraic characteristic boundary conditions of Euler equations (AECBC) are considered in a local 1D sense normal to the far boundary. In this work, two sets of algebraic characteristic boundary conditions are considered. In one set (BC Set I), AECBC is used over the entire far boundary. While in the other set (BC Set II), AECBC is used over a portion of far boundary, that is characterized by normal flow velocity magnitude in excess of a threshold value, and entropy preserving extrapolating conditions for pressure and density over the remaining portion of the far boundary. It is shown that BC Set I generates spurious wave reflections and numerical noise from the far boundary, whereas BC Set II eliminates these numerical artifacts and captures the flow physics far more accurately.