Unsteady state fluid structure of two-sided nonfacing lid-driven cavity induced by a semicircle at different radii sizes and velocity ratios

This paper aims in analyzing the effect of velocity ratio α and Radius size of an inner semicircle inserted at the bottom wall of two-sided nonfacing lid-driven cavity on the bifurcation occurrence phenomena. The study has been performed by using finite volume method (FVM) and multigrid acceleration for certain pertinent parameters; Reynolds number, velocity ratios (0≤α≤1) by step of 0.25 and Radius size of the inner semicircle (0.1≤R≤0.25) by step of 0.05. An analysis of the flow evolution shows that, when increasing Re beyond a certain critical value, the flow becomes unstable then bifurcates for various velocity ratios and radius size of the semicircle. Therefore, critical Reynolds numbers are determined for each case. It is worth to mention that the transition to unsteadiness follows the classical scheme of a Hopf bifurcation. Results show also that in the standard case of a single lid-driven cavity (α=0), the highest critical Reynolds number corresponds to the lowest radius of the semicircle and the same for (α=0.25). Conversely, from (α=0.5) where the left moving lid take effect, the opposite phenomenon occurs. In harmony with this, it has been found that elongating the cylinder radius accelerates the appearance of the unsteady regime and delays it in the opposite case. Flow periodicity has been verified through time history plots for the velocity component and phase-space trajectories as a function of Reynolds number. The numerical results are correlated in a sophisticated correlation of the critical Reynolds number with other parameters.