电磁场作用下磁流体在管道内的稳定流速研究

Steady Velocity of Magnetofluid in Pipe under Electromagnetic Field

研究磁流体在磁场和电场作用下的流动速度,对于一些基于磁流体动力学原理的工程应用,如磁流体动量轮等,具有重要意义。基于层流和轴对称假设,构建了截面速度二维分布的傅里叶级数解析模型。分析了无沿管道方向的压力梯度情况下,截面速度和诱导磁场耦合傅里叶级数解的不可解性;基于纳维-斯托克斯方程推导了电磁场作用下稳态截面速度的傅里叶级数解析式,并利用MATLAB对解析式进行计算,与Ansys仿真结果对比分析;对不同驱动方式的速度分布进行了分析,给出了截面速度在各点的分布与该点处的电场、磁场大小及磁流体特性参数等的关系。

It is of great significance to study the velocity of magnetofluid under electromagnetic field for some engineering applications based on magnetohydrodynamics,such as magnetohydrodynamic momentum wheel.Based on the assumption of laminar flow and symmetry,the two-dimensional analytical model of cross-section velocity is constructed in terms of Fourier series.The Fourier series coupling solution of cross-section velocity and induced magnetic field is proved insolvable in the case of none pressure gradient along the pipeline.Based on Navier-Stokes equation,the Fourier series analytic formula of steady velocity under electromagnetic field is derived.The two-dimensional distribution of velocity in different driving modes is calculated by MATLAB according to the analytic formula,and then compared with Ansys simulation results.The relationship between velocity and the electric field,magnetic field as well as the characteristic parameters of magnetofluid is given.