THE OPTIMAL FLOW CONTROL BASED ON THE ADJOINT FLOWFIELD

The flow of the weak electrolyte solution can be controlled by Lorentz forces generated by magnetic and electric fields, which facilitates the drag reduction, the suppression of vortex shedding and the vortex street of a bluff body. In this paper, based on the nonlinear optimal control theory, taking the enstrophy as the optimal performance index, the adjoint equations of cylinder wake via Lorentz force are developed. With the introduction of the ‘play chess’ control method, numerical simulations based on the Navier-Stokes equations and their adjoint equations for nonlinear optimal control of cylinder wake are carried out. The variations of the optimal interaction parameters with time are obtained. The evolutions of the flow field and the variations of the drag and lift forces of the cylinder during the control process are discussed. It is shown that the reduction of drag force, suppression of vortex shedding and absorption of vibration are achieved by the optimal control.