High Reynolds number incompressible turbulent flow inside a lid-driven cavity with multiple aspect ratios

Abstract

The numerical simulation of incompressible turbulent flow at Re = 11 800 (equivalent Reynolds number Rem = 10 030) inside lid-driven cavities with varying spanwise aspect ratio and depthwise aspect ratio (DAR) has been carried out using the dynamic Smagorinsky model. A better comparison of central line averaged velocities and second order turbulent properties is obtained with the existing experimental result of Prasad and Koseff [“Reynolds number and end-wall effects on a lid-driven cavity flow,” Phys. Fluids A 1, 208–218 (1989)] than with the one provided by Leriche and Gavrilakis [“Direct numerical simulation of the flow in a lid-driven cubical cavity,” Phys. Fluids 12, 1363–1376 (2000)]. It is noticed that the size of the downstream secondary vortex increases with an increase in the aspect ratio. Lower DAR cavities are found to be having the maximum turbulent kinetic energy (TKE) and turbulent production, which is further confirmed by the TKE spectra shown at the point of maximum turbulent production on the symmetrical mid-plane. The power spectra maintain a slope of −53 in the inertial subrange as proposed by Kolmogorov and show a steeper slope in the dissipating range. The time integral scale shows that in low DAR cavities, eddies are formed and undergo complete distortion more frequently. The joint probability density function confirms the anisotropy in turbulence, and the anisotropy invariant map (Lumley triangle) shows the type of turbulent anisotropy which shows whether the turbulence is either one-component or two-component near the walls.