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

ZHANG Chenglong; ZHANG Hui; JIANG Daiwen

doi:10.7638/kqdlxxb-2019.0165

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

更新时间：2026-05-28

- Amplification mechanism of the velocity response with the effect of electro-magnetic force in channel flow
- Vol. 38, Issue 3, Pages: 490-499(2020)
- 作者机构：
  
  1. 南京理工大学瞬态物理国家重点实验室,南京,210094
  2. 帝国理工学院数学系,伦敦,英国,SW7 2AZ
- 作者简介：
- 基金信息：
- DOI：10.7638/kqdlxxb-2019.0165
  CLC： O361
- Published：2020
- 稿件说明：
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张成龙, 张辉, 江代文. 电磁力作用下槽道流速度响应的放大机理[J]. 空气动力学学报, 2020, 38(3): 490-499.

ZHANG Chenglong, ZHANG Hui, JIANG Daiwen. Amplification mechanism of the velocity response with the effect of electro-magnetic force in channel flow[J]. 2020, 38(3): 490-499.
张成龙, 张辉, 江代文. 电磁力作用下槽道流速度响应的放大机理[J]. 空气动力学学报, 2020, 38(3): 490-499. DOI： 10.7638/kqdlxxb-2019.0165.

ZHANG Chenglong, ZHANG Hui, JIANG Daiwen. Amplification mechanism of the velocity response with the effect of electro-magnetic force in channel flow[J]. 2020, 38(3): 490-499. DOI： 10.7638/kqdlxxb-2019.0165.

摘要

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

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

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10

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。

Abstract

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 effic

iency. 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

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 penetration

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

. 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.

关键词

Keywords

references

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