MHD Control Of Instabilities On The Interface

The interactions between shock waves and fluid interface are widely existed in areas such as aviation,aerospace,celestial mechanics,nuclear energy and industrial explosion,so that it is of great academic and industrial value to study the instabilities they induced and the control mechanism.This dissertation based on the non-ideal MHD equations and CTU+CT algorithm,combined with roe linear Riemann solver and third-order reconstruction with characteristic variables limits,and then we study numerically on the problems such as planar and spherical heavy gas cloud explosion,the interaction between shock waves and heavy/light gas cylinder with different shapes and the interaction between shock waves and heavy gas cloud separately.The main research contents and achievements are as follows:The processes of planar and spherical heavy gas cloud explosion are studied in the dissertation.The results indicate that the magnetic field can effectively suppress the RM instability,the bigger the magnetic field strength,the better the control effect.When the part of interface is parallel to the initial magnetic field,the effect of magnetic pressure there is not significant.With the growing of perturbation amplitude on interface,the normal magnetic pressure there is increasing too.Meanwhile,the magnetic field has no significant effect on the propagation velocities of transmitted shock wave and the reflected rarefaction wave.A variety of dissipation effects based on non-ideal MHD equations are studied in this dissertation,the results indicate that the Ohmic dissipation,the Hall effect and ambipolar diffusion can promote the development of instability.The numerical results of heavy gas cloud explosion with magnetic field indicate that the magnetic field can also control the RM instability on the interface in 3-dimentional case.In addition,the magnetic field can reduce the range of λ2 and can control the vorticity,this effect is more obvious when the magnetic filed strength is increasing.Then the coherent structures of cross section in the flow field are studied using Snapshots-POD method.The results indicate the magnetic field can change the coherent structures in the flow field and increase the proportion of the tubulence energy in the low order modes.The magnetic field makes the energy distribution more concentrated in the flow field,and makes the flow field more regular.The interactions of shock waves and heavy/light gas cylinder with different shapes are numerically studied in the dissertation,the results show the wave structures in the flow field and the developing process of instabilities on the interface,reveal the influence mechanism of magnetic field during the process and the change of vorticity,enstrophy,change-tolerance rate and aberration rate in the flow field.The results indicate the magnetic field has inhibiting effect on the instabilities during the process,with the magnetic field strength increasing,the inhibiting effect on the instabilities is more obvious.Meanwhile,the normal magnetic field has better suppression effect than the magnetic field on the flow direction.The study on jet flow indicates the magnetic has little effect on the tail jet,the magnetic fields in different direction can accelerate the pressure and velocity decay behind shock wave slightly and slow down the velocity of jet to some extent.In addition,although the magnetic field can not reduce the average vorticity in the flow field,it can greatly reduce the peak value of vorticity,so that it can restrain the enstrophy.Then the Okubo-Weiss function at different initial conditions is studied,the results always meet 9=S12+S22-Ω2>0 during the process so that deformation is the main factor in the flow field.When the shock waves interacting with the gas cylinder,the magnetic field can suppress the change-tolerance rate,aberration rate and enstrophy,with the increase of magnetic field,this effect is more significant.Meanwhile,the suppression effect of normal magnetic field is better than the effect of magnetic field parallel to the flow direction,especially for the enstrophy.When the shock waves leave the gas cylinder interface,the magnetic field can promote the aberration rate and enstrophy,this effect is also more obvious with the magnetic field increasing,the promotion effect of normal magnetic field is better than the effect of magnetic field parallel to the flow direction.compared the results of the heavy/light columns with the same shape,we can find the tendencies of S12,S22 and Ω2 with time are related with the shape of interface.Meanwhile,the effect of magnetic field on the average vorticity is related to the shape of interface too.In addition,the interactions between shock waves and SF6 heavy gas cloud are studied,the results indicate the magnetic field has little influence on the interaction process between shock waves and gas cloud,it mainly affects the interfacial disturbance and the flow structure in the late period.We can conclude that the magnetic field can restrain the instabilities on interface of the gas cloud by studying and discussing the 3D density contours and λ2 contours,especially in the late period.the normal magnetic field has the best control effect,though only both sides in y direction can be affected,the instabilities on both sides in z direction can not be controlled effectively.The bigger the magnetic field strength,the better the control effect.Meanwhile,the vortex ring structure thickens under 0.01T initial magnetic field,along with its number decreases.The vortex layers attached to the interface appear under 0.05T initial magnetic field,the typical vortex structure disappears,and the vortex layer gradually separated from the interface with time.The normal magnetic field can suppress the gas cloud along the y axis direction,and two flake vortex structures will form at the tail of gas cloud later.Then the Snapshots-POD method is applied to study the coherent structure of xy section in the flow field.The results indicate the magnetic field can reduce the energy dissipation and increase the flow regularity,and the bigger the magnetic field strength,the flow field is more regular.Meanwhile,the normal magnetic field has better influence than the magnetic field parallel to the flow direction.In addition,the magnetic field can control the small scale coherent structure in late period for this kind of problem,the same as before,the normal magnetic field has better effect than the parallel magnetic field,this phenomenon is more obvious when the magnetic field strength is growing.