Analysis of Aspect Ratio Effects of Left Heated 2D Cavity Using Energy Streamlines and Field Synergy Principle

Abstract

In the present study natural convective flow of air in a two dimensional cavity with three different aspect ratios (AR) are analyzed using direct numerical simulation. Established open source CFD package OpenFOAM, has been utilized to run the simulation. In this problem, the vertical walls are assumed to be maintained at an isothermal temperature with left vertical wall has high temperature than the right wall and the other walls are assumed to be thermally insulated. The governing equations of this problem are expressed in dimensionless form and are solved by using the finite volume method. For spatial derivatives, the second order upwind linearization technique was used. The CGS method was employed as an effective acceleration means. The divergent and Laplacian terms in the governing equations are discretized by the QUICK and Gauss linear schemes, respectively. The computations are conducted for Rayleigh number until 10 6. An attempt has been made to gather the visualization techniques such as streamlines, isotherms, energy streamlines and field synergy principle to analyse the flow behavior. When Ra is small, vertical energy streamlines appeared, as Ra further increases, free energy streamlines at the boundary are observed whereas trapped energy streamlines at the centre appeared in the horizontal direction. For a fixed Ra, as AR increases, average synergy angle () increases. This result implies that synergy between temperature field and velocity gets worse, which leads to the mild growth rate of ̅̅̅̅. The field synergy principle shows that the improving synergy between the temperature gradient and velocity vector, the heat transfer can be enhanced with less increased flow resistance.