Computation of Viscous Incompressible Flows with Heat Transfer Using Godunov-Projection Method

摘要

In this study, the Godunov-projection method has been used to solve for the viscous incompressible flow with heat transfer in a lid-driven cavity. This projection method circumvents the problem arising from the lack of the time dependency of the density in the continuity equation. The energy equation is included with the momentum equations to solve the temperature field. The comparison between the numerical results and the experimental data shows good agreement thereby demonstrating the feasibility of using this algorithm for fluid flows with heat transfer. The maximum percentage error is about 10% and is mostly due to the large conduction error at the bottom of the cavity. The numerical simulation of the cavity flow reveals clearly the viscous effects at the wall boundaries and the shear force at the moving lid boundary. Grid convergence studies indicate that a grid size of 168 x 56 x 28 and above is required to obtain numerical results that are within 1.25% of the experimental results. The present study has only focused on the feasibility of the numerical scheme to study steady-state convective flows. Future work will address the more general unsteady cavity flow in which perturbations will be imposed on the boundary conditions to simulate unsteady thermal and flow effects and the steady-state solutions obtained here will be used as the initial conditions to capture the evolving unsteady flowfields. The assumption of constant fluid properties will be discarded, and the governing equations will be modified to take into account the temperature dependency by way of coupling.