A Numerical Study of Lid Driven Cavity with Mixed Convection

TL;DR

This study uses direct numerical simulation to analyze two-dimensional lid-driven cavity flow with mixed convection, examining the effects of heating and lid movement at different Richardson numbers, and validating the results against established data.

Contribution

It introduces a numerical code to study mixed convection in lid-driven cavities, comparing heating, shear, and combined effects, and validates results with existing benchmarks.

Findings

Heating influences the flow and drag force on the lid.

Shear and heating effects significantly alter flow patterns.

The developed code accurately predicts flow behavior in mixed convection.

Abstract

Direct Numerical Simulation have been carried out for a two dimensional flow in a Lid driven cavity at Reynolds number 5000 and Prandtl number 7 with water as the working fluid. Both the side walls of the enclosure are insulated(i.e. adiabatic boundary condition), while the bottom plate is at higher temperature and the top wall is at colder temperature. Effects of heating of the bottom wall and movement of the top lid have been investigated by conducting numerical simulations at different Richardson numbers by varying from low and moderate magnitudes within the limits of Boussinesq-approximation. Three standard cases has been compared, in the first case heating effects are not taken into account and only the flow due to shear action of the plate is studied. In the second case only the heating effects are taken into account and shear effects are neglected. In the third case effects of both heating and shear action is taken into consideration(i.e. mixed convection). Drag force on the moving plate is calculated in all the three cases and effect of temperature on the drag force is studied. For running the above simulation a code has been developed which is validated by comparing the results with Ghia et al for non-heating case.