The dynamical behaviour and stability properties of the circular cylinder wake subject to passive control is investigated using Direct Numerical Simulation (DNS) and stability analysis. The control action consists of either suction or blowing at a steady flow rate from a control arc symmetrically placed at the cylinder base. The study is limited to two-dimensional flows, at low Reynolds numbers (Re < 90), where the non-manipulated flow is either steady or characterized by vortex shedding.
DNS results show that, in the supercritical Reynolds number regime (Re > 47), slight blowing or high enough suction stabilizes the wake; in the subcritical regime, suction can destabilize the wake for Re > 17, and result in vortex shedding, whereas blowing does not affect the flow stability in this regime.
At supercritical Reynolds numbers, suction can strongly modify the dynamics of vortex shedding, in comparison to the uncontrolled flow. With increasing suction, the flow frequency can drastically decrease, while the fluctuation amplitudes increase. At a, critical suction flow rate, the flow undergoes a first; bifurcation: it becomes steady and asymmetric simultaneously. At a higher critical suction flow rate, the flow undergoes a second bifurcation and becomes steady symmetric.
With increasing suction flow rate, the flow state is naturally affected away from the cylinder base. However, the computational domains used have finite size, and the assumption of free stream velocity is made at the inflow and lateral boundaries. The study of the effects of computational domain size on the simulation results suggests that the transition from a, steady asymmetric flow to a steady symmetric flow at very high suction flow rates, found with the use of computational domains of finite size, may not exist in an infinite flow domain. This transition occurs at increasing suction flow rate with increasing domain size.
Global linear stability analysis calculations confirm the main results of the numerical simulations. They show furthermore that, at supercritical. Reynolds numbers, small suction has an even further destabilizing effect, as it increases the global growth rate of small perturbations superimposed on the steady symmetric base flow solutions. High enough suction is necessary to inverse the global growth rate trend and lead to negative values, as also deduced from DNS. Stability analysis strongly supports the hypothesis that the transition from steady asymmetric to steady symmetric flow would not exist in an infinite flow domain.