有限导Hartmann壁对Hunt流线性稳定性的影响
The effect of finite-conductvity Hartmann walls on the linear stability of Hunt's flow
摘要：
本文用数值方法分析了具有绝缘侧壁和薄导电水平壁的方形管道中充分发展的液态金属流动的线性稳定性，其中壁电导比为$c=0.01\cdots 1$，垂直磁场的哈特曼数为$c=0.01\cdots 1$。流动由两个位于侧壁的射流和一个靠近侧壁的射流组成，对于相对速度为$\sim(cHa)^{-1}.$的停滞核我们发现对于$Ha\gtrsim300,$，壁面电导率对流动稳定性的影响主要取决于对于$cHa.$，磁场或壁电导率的增加对流动具有不稳定的影响。流动的最大不稳定发生在$Ha\approx30/c.$处。在具有$cHa\gtrsim 30,$的较强磁场中，不稳定效应消失，并且恢复了Priede等人[J. Fluid Mech.649，115，2010]对于具有完美传导哈特曼壁的理想亨特流动的渐近结果。
英文摘要：
We analyse numerically the linear stability of the fully developed liquid metal flow in a square duct with insulating side walls and thin electrically conducting horizontal walls with the wall conductance ratio $c=0.01\cdots 1$ subject to a vertical magnetic field with the Hartmann numbers up to $Ha=10^{4}.$ In a sufficiently strong magnetic field, the flow consists of two jets at the side walls walls and a near-stagnant core with the relative velocity $\sim(cHa)^{-1}.$ We find that for $Ha\gtrsim300,$ the effect of wall conductivity on the stability of the flow is mainly determined by the effective Hartmann wall conductance ratio $cHa.$ For $c\ll 1,$ the increase of the magnetic field or that of the wall conductivity has a destabilizing effect on the flow. Maximal destabilization of the flow occurs at $Ha\approx30/c.$ In a stronger magnetic field with $cHa\gtrsim 30,$ the destabilizing effect vanishes and the asymptotic results of Priede et al. [J. Fluid Mech. 649, 115, 2010] for the ideal Hunt's flow with perfectly conducting Hartmann walls are recovered.
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