Optimal flow control of vortex breakdown in a laminar swirling flow

Abstract

Abstract In highly swirling flows, such as hydraulic turbines operating under part-load (PL) conditions, vortex breakdown occurs and performance is impaired. Consequently, it is imperative that mitigation measures are taken. In the present study, a laminar swirling flow with a vortex breakdown at a Reynolds number of 180 is investigated. At the inlet, a swirling velocity profile with a swirl number of 1.095 is set. A stability analysis is conducted to identify unstable modes based on the assumption that vortex breakdown is a global instability. The results indicate that spiral modes with wave number 1 are unstable. An optimal flow control method based on the Adjoint method is then utilized to mitigate vortex breakdown. In the present study, the control method targets vorticity using a minimization algorithm. Control variables include radial and axial body forces. According to the results, the method was effective in mitigating vortex breakdown. A stability analysis conducted during the control process revealed that as the vorticity decreased, the growth-rate of the eigenvalue decreased, indicating that the flow is stabilized.