Unsteady vortex roll structures in a mixed convective air flow through a horizontal plane channel: a numerical study

Abstract

A three-dimensional unsteady numerical simulation was conducted to investigate the buoyancy induced vortex flow structures in a forced air flow through a bottom heated horizontal plane channel. In particular, a third-order upwind finite difference scheme was chosen to solve the Navier-Stokes and energy equations. In the ranges of the Reynolds number Re from 20 to 50 and Rayleigh number Ra up to 31 000, several roll structures were predicted. In the steady flow at high Re and low Ra after the initial transient the longitudinal rolls possess spanwise symmetry and grow regularly to a fully developed state as it proceeds downstream. While in the time periodic flow at low Re and high Ra the rolls may tilt towards the right side wall and the flow is asymmetric or they may tilt to both sides and are symmetric, depending on the particular case studied. This roll tilting causes the rolls to terminate as they encounter the side walls. Meanwhile, new space is provided in the region near the other side of the duct or near the central vertical plane for the generation of new cells. It is also noted that the rolls are wavy in axial direction. Moreover, the rolls change their sizes during moving downstream and no fully developed state can be discerned. Based on the present data, correlating equations for the onset of convection and Hopf bifurcation were proposed.