Exploring role of aspect ratio for compressible flow in a rectangular lid-driven cavity with a vertical temperature gradient

Numerical investigation of a compressible fluid in a two-dimensional rectangular lid-driven cavity (LDC) with a vertical temperature gradient is performed by solving the compressible Navier-Stokes equation. Here, we explore the role of aspect ratio (AR) (width/height) on the vorticity dynamics and redistribution by considering three ARs of 1:1, 2:1, and 3:1. The onset and propagation of the instability are explored via time-resolved and instantaneous distributions of vorticity, time-series of streamwise velocity, and its associated spectra. The flow physics reveal that the precessing vortical structures in certain square sub-cells of the rectangular LDC resemble that of orbital motion with a primary core eddy surrounded by gyrating satellite vortices, typical of a supercritical flow in a square LDC. Upon increasing the AR, there is a major shift in the vorticity transfer from the top right corner (acting as the source of maximum vorticity generation) toward the left square sub-cells in the domain. This is further aided by the convective motion due to the imposed destabilizing vertical thermal gradient. The spectra demonstrate that a multi-periodic, chaotic flow is the consistent flow feature for the rectangular LDC for Re = 5500, irrespective of the AR. The compressible enstrophy budget of the rectangular LDC with varying AR is computed for the first time. This shows the dominance of the baroclinic vorticity over the viscous diffusion terms, which was conceived of as the major contributor to the creation of rotational flow structures.

Automated summary

A numerical investigation is conducted to examine a compressible fluid flow in a two-dimensional rectangular lid-driven cavity with a vertical temperature gradient. The study focuses on the impact of the aspect ratio on the vorticity dynamics and redistribution. It is found that the vortical structures in specific sub-cells of the rectangular cavity resemble orbital motion and undergo a shift in vorticity transfer as the aspect ratio increases. The flow exhibits chaotic behavior regardless of the aspect ratio, and the dominance of baroclinic vorticity over viscous diffusion suggests its major contribution to rotational flow structures.