Non-modal Stability Analysis Of Hunt's Flow

Magnetohydrodynamics(MHD)is a study of the interaction between the magnetic field and the conducting fluid.The common conducting fluid includes liquid metal,electrolyte and so on.The characteristics of flow will change when the conducting fluid flowing in the presence of magnetic field,and the stability of the fluid flow is also effected,which will further affect the heat transfer efficiency and safety of the tube.The study of the stability of conducting fluid flow under magnetic field can provide theoretical support for the prediction and control the conducting fluid flow and the application in industry.In this paper,the stability and flow structure of a specific MHD duct flow which is known as Hunt's flow,are investigated using non-modal stability analysis and numerical simulation,respectively.The main contents are as follows:(1)The stability analysis of Hunt's flow is performed,the amplification and distribution of optimal primary perturbations are obtained by solving iteratively the direct and adjoint governing equations with respect of the perturbation variables.Four modes of perturbations with different symmetries in the space are considered,and the effect of the low-intensity magnetic field is also taken into account.The results show that two weak jets appear in the centre of the duct at a relatively magnetic field and the velocity of the jet increases while the thickness of the side layer decreases by suppression of magnetic field,with the increase of the intensity of the magnetic field.when the Hartmann number Ha is small(Ha=0,5),the perturbations in the form of different modes exhibit transient growth.By contrast,when Ha is large(Ha=8,10,15,20),these perturbations grow differently: the perturbations in the form of mode I,III and IV grow transiently;the perturbations of mode II grows exponentially,meanwhile,flow field stability is related to the jets.(2)The large eddy simulation of Hunt's flow under low-intensity magnetic field is carried out,and the influence of magnetic field on the flow structure is analyzed.The results show that,the flow structure of the Hunt's flow is similar,and the formation and evolution of the vortex structure appear with and without magnetic field.The streamwise vortices are distributed at different cross-sections of the duct along streamwise direction,which are similar to the vortex structures found in the stability analysis of Hunt's flow.