Bifurcation Techniques of Fluid Flow in Lid-Driven Cavity with Different Wake Parameters
Numerical simulations were conducted to analyze the effects of aspect ratios A and aspect velocity ratios α on the bifurcation occurrence phenomena in lid-driven cavity by using Finite volume method (FVM) and multigrid acceleration. In this study, the transition of the flow regime from the steady state to the unsteady state and consequent Hopf bifurcation, giving rise to a perfectly periodic state were investigated by means of wide range of the Reynolds number values, aspect ratios ranging from 0.25 to 1, as well as various velocity ratios taken from 0.25 to 0.825. Flow periodicity has been verified through time history plots for the velocity component and phase-space trajectories as a function of Reynolds number. Flow characteristics inside the cavity have been presented and discussed in terms of streamline patterns and vorticity contours at a fixed Reynolds number (Re = 5000) for various aspect ratios at α = 0. Overall, it was particularly found that the critical Reynolds number value Rec is weak for low velocity ratio values, then augments by further increasing this value for both fixed aspect ratios A= 0.5 and A=0.75.
Keywords - Critical Reynolds number, lid-driven cavity, fluid mechanics, shallow aspect ratios, velocity ratio.