Abstract: The flow of the weak electrolyte solution can be controlled by Lorentz forces generated by the suitably chosen magnetic and electric fields, which can be used for the drag reduction, the suppression of vortex shedding and the vortex street in the flow over a bluff body. In order to get a large control effect with small power input, the interaction parameter N, the ratio of the electromagnetic force to the inertia force serving as control input in the control process, should be optimized according to the instantaneous flow field. An adjoint-based ensemble optimization method of control algorithms was developed via Lorentz forces. The performance index and adjoint equations in the expolential-polar coordinates were derived. Numerical simulations based on the Navier-Stokes equations and its adjoint equations for optimal control of cylinder wake were carried out for Reynolds number Re=200. Based on the Navier-Stokes equations considering the electromagnetic body force, i.e. Lorentz force, in the exponential-polar coordinates, the numerical investigations were carried out by means of an alternative-direction implicit algorithm and a fast Fourier transform algorithm. The variation of the optimal interaction parameters with time were described based on calculated results, and the evolution of the flow field and the variation of the drag and lift forces on the cylinder surface in the control process were discussed. The results show that the suppression of vortex shedding, reduction in drag force, absorption of vibration and suppression of noise can be implemented by the optimal control.

Key words: fluid mechanics, flow control, adjoint optimal control, cylinder wake, nonlinear optimal control