电磁力作用下槽道流速度响应的放大机理

Amplification mechanism of the velocity response with the effect of electro-magnetic force in channel flow

在电解质溶液中,电磁场产生的电磁力可以控制流体的运动,从而达到很好的减阻、增升、减振等效果。但由于所施加的电磁力较大,导致控制效率很低,因此以较小的电磁力诱导出大的流动响应成为提高流动控制效率的关键。以层流槽道流动作为研究对象,在槽道的下壁面施加沿展向余弦分布的展向电磁力,推导了线性条件下流向响应速度的解析解,并通过直接数值模拟对非线性条件下的响应进行了计算。结合解析解和数值解,揭示了流场中速度响应的放大机制,讨论了电磁力和流场参数对响应放大效果的影响。结果表明:当振幅较小时,速度响应处于线性范围内,其放大倍数与Re^2成正比,随着渗透深度的增大,先迅速增大后缓慢减小;随着展向波数Kz的增大单调减小。随着振幅的增大,放大倍数进入非线性范围,其值逐渐减小,但速度响应值先增大后减小。在振幅处于10^-3~10^-2量级时,速度响应可达到的最大值超过0.2,此时的放大倍数在102量级。因此,利用流场的放大效应,是实现高效流动控制的重要环节。

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 a large amplitude for the 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 are induced by the electromagnetic force,which 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 deduced with linear stability theory,and 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 of the parameters of electromagnetic forces and flow field are discussed.The results show that the amplification of velocity response along the streamwise direction is proportional to Re^2 for small amplitude,i.e.,the responses in the linear stage.Moreover,the amplification of response increases firstly and then decreases with the increase of the effective penetrationΔ,while the amplification monotonically decreases with the increase of wave number along the spanwise direction.However,with the increase of amplitude,the response amplification approaches the nonlinear stage.The amplification monotonically decreases,while the amplitude value of velocity response increases firstly and then decreases.Moreover,the amplitude value reaches the maximum which is more than 0.2,and the corresponding amplification is the order of 10^2.Therefore,the flow induced by the electromagnetic force is amplified with the effect of flow field,which is the key to enhance the efficiency of flow control.