Multivariate Analysis of Prandtl, Reynolds, and Richardson Numbers in Lid-Driven Cavity Flow

Abstract

This study presents Direct Numerical Simulations (DNS) of a two-dimensional lid-driven cavity flow, investigating the influence of heating of the bottom wall and movement of the top lid on the flow characteristics. The simulations are performed at Reynolds numbers (Re) of 500, 1000, 2500, 5000, and 10000, and Prandtl numbers (Pr) of 0.03, 0.72, 7.1, and 100 using different working fluids, namely mercury, air, water, and glycerol. The sidewalls of the enclosure are considered adiabatic, while the bottom wall is heated, and the top plate is kept at a lower temperature. Validation of the developed numerical code is performed by comparing the results with Ghia et al. for the non-heating case and Moallemi et al. for the heating case. Temperature and streamline profiles are obtained for various Richardson numbers (Ri) ranging from 0 to 30 for Re values of 500, 1000, 2500, 5000, and 10000, where Ri represents the ratio of buoyancy effects to viscous effects and is varied to examine low and moderate magnitudes within the limits of the Boussinesq approximation.The investigation of the time-averaged drag reveals its dependency on Richardson numbers for the range of Ri=0 to Ri=100, considering Re values of 500, 1000, 2500, 5000, and 10000.The findings from this study provide valuable insights into the thermal and dynamic behavior of lid-driven cavity flows with varied heating and movement effects, contributing to a better understanding of convective heat transfer and fluid motion in similar engineering and natural systems.