A Numerical Study of Unsteady Mixed Convection in a Square Cavity: Transition From Laminar to Turbulent Flow

Abstract

A study was conducted to simulate the circulation patterns and heat transfer characteristics of flows in a square cavity during transition from laminar to turbulent mixed convection conditions using numerical techniques. The cavity under study is assumed to be filled with a compressible fluid. The bottom of the cavity is insulated and stationary where as the top of the cavity (the lid) is assumed to be stationary initially and then pulled at constant speed for times greater than zero. The vertical walls of the cavity are kept at constant but unequal temperatures. A two-dimensional, physics based mathematical model is adopted to predict the momentum and heat transfer inside this rectangular cavity. A standard two equation turbulence model is used to model the turbulent flow inside the enclosure and the compressibility of the working fluid is represented by an ideal gas relation. The numerical solution techniques adopted in this study is a hybrid one (implicit-explicit) where the conservation equations for the velocity, temperature, and pressure are solved using an implicit technique (Coupled Modified Strongly Implicit Procedure -CMSIP) whereas the equations for the standard K-ε turbulence model are solved using an explicit (MacCormack) technique. In both techniques, a second order accurate finite difference technique is used to discretize the governing equations. Then numerical experiments were carried out to simulate the unsteady flow and heat transfer characteristics of mixed convection flow inside a square cavity filled with air (Pr = 0.72) for different Richardson numbers in the range of 0.00868–0.03470; corresponding to Reynolds numbers ranging from 2000 to 4000, respectively, when the Rayleigh number was kept constant at 105. Vertical and horizontal temperature and velocity profiles were generated while the flow goes through transition from laminar to turbulent. Changes in wall heat flux were calculated and average Nusselt numbers were determined for each parametric study.