Combined effects of velocity ratio and radii sizes of internal cylinder on the flow instability in a two-sided lid-driven cubical cavity

This paper computes the laminar flow in a three-dimensional (2D) two-sided lid-driven cubical cavity induced by a centrally located circular cylinder by Finite Volume Method and multigrid acceleration. The cavity has left and right parallel lid-driven walls and all the other walls completing the domain are motionless. Furthermore, different wake parameters are considered throughout this study; velocity ratios [alpha = 0, 0.25, 0.5 and 0.75] and radius size of the inner cylinder [R = 0.125, 0.15,0.175 and 0.2]. Thereafter, the study has been extended to the unsteady state by further increasing Reynolds number till reaching up to 2000. It is noticed that the highest critical Reynolds number corresponds to the lowest radius size and conversely. By further increasing the velocity ratio till reaching 0.25, 0.5 and 0.75, where the left moving lid began to have an effect, the opposite phenomenon occurs and we note that the highest critical Reynolds number corresponds to the highest radius. This can be explained by the fact that when the cavity is two-sided lid-driven, the velocity of the fluid particles accelerates. Besides, it has been proved that both parameters alpha = 0.75 and a radius size R = 0.125 promote faster transition to the unsteadiness rather than the remaining velocity ratios and radii sizes.