The Investigations Of The Velocity Responses By Electro-magnetic Force In Channel Flow

The flow of the weak electrolyte solution can be controlled by electromagnetic forces generated by the suitably chosen magnetic and electric fields,which has significant effects for applications in the drag reduction,lift amplification and oscillatory suppression.However,the control efficiency is very low due to the application of large amplitude for electromagnetic force.Therefore,the large response,induced by a small electromagnetic force,is the key to enhance the flow control efficiency.In this paper,based on the laminar flow of a weakly conductive fluid in a channel,the flow responses induced by the electromagnetic force are discussed with the aim of the optimal design of electromagnetic actuator.This force is applied on the lower wall of the channel and is cosine distribution along the spanwise direction.The analytic solutions of the velocity responses in linear stage are derived with linear stability theory,when the amplitude of electromagnetic force is very small.From the discussions of the analytic solutions,the mechanism is revealed on large responses which is induced by the small Lorentz force in the flow field.When the velocity response approaches to the nonlinear stage,the numerical solutions of these responses in nonlinear stage are calculated with direct numerical simulation(DNS).For the periodic characters of the channel flow in the streamwise and spanwise directions,the dealiased Fourier method is used in these two directions,while the Chebyshev-tau method is used in the wall normal direction.Moreover,the usual no-slip and no-penetration conditions are used on the walls.The time advancement is performed with third-order accuracy by using a semi-implicit back-differentiation formula method.To eliminate residual divergence,the pressure term and the linear term are solved with a Chebyshev-tau influence matrix method.For the non-linear term,a spectral truncation method is used to remove aliasing errors.Combing the analytic and numerical solutions,the amplification mechanisms are revealed and the influences with the parameters of electromagnetic forces and flow field are discussed.Moreover,the electromagnetic actuator,which can induce a large velocity response,is designed on the base of the optimal parameters.The conclusions show as:(1)The flow along the spanwise direction is induced by electromagnetic force,and the pressure effects of fluid motion along the spanwise direction lead to the momentum exchange of fluids in the wall-normal direction.Therefore,the large responses of velocity along the streamwise direction are generated due to the high-speed fluids transferring to the wall;(2)The velocity response along the streamwise direction is proportional to amplitude A and the square of Reynolds numbers for small amplitude,i.e.,the responses in the linear stage.The velocity response increases firstly and then decreases with the increase of the effective penetration,while the response monotonically decreases with the increase of wave number along the spanwise direction.Moreover,the response approaches to the nonlinear stage with the increase of amplitude.The amplitude value of velocity response increases firstly and then decreases,while the amplification monotonically decreases.Furthermore,the amplitude value reaches the maximum which is more than 0.2 and the corresponding amplification is the order of 100;(3)Based on the large response mechanism and parameters optimization above,a new arrangement of electrode and magnetic pole is applied to design the electromagnetic actuator,which can induce a large velocity response under some working conditions.