Numerical Investigations Of The Richtmyer-Meshkov Instability(RMI) In The Control Of Magnetic Fields

Due to the interaction between shock waves and density interfaces,the interface separating different density fluids is becoming unstable and develop to turbulence.This kind of phenomenon is called the Richtmyer-Meshkov instability(RMI)which has wide applications in high energy fields such as weapons,aerospace and astrophysics.In this thesis,the magnetohydrodynamic(MHD)equations are solved by using the CTU+CT(corner transport upwind+constrained transport)numerical method.Based on the numerical results,we investigated the RMI in the hydrodynamics(hydro)and magnetohydrodynamic(MHD)involving closed interfaces.First of all,consider the simple regular triangular interface in which the incident shock angle is a constant,the evolution of the RMI in hydro and MHD cases is investigated in both light and heavy triangular cylinders.The numerical results show that whether there exist external magnetic fields or not,different wave patterns and jet phenomena could be distinguished under the impact of the incident shock wave.More specifically,the regular refraction occurs in the heavy cases while irregular refraction occurs in the light cases.Interiror jets phenomenon occurs in the heavy cases whereas ambient gas jets phenomenon occurs in the light cases.In addition,a large amount of vortex sequences deposit on density interfaces for both cases,the main vortex pair formed from the top and bottom corners of the triangular cylinder dominates the flow fields of the heavy case,while the vortex dipole dominates the flow fields of the light case.However,in the presence of magnetic fields,the vortex sequences,the main vortex pair and the vortex dipole disappear for both heavy and light cylinders.Detailed investigation of the Lorentz force distribution demonstrates that the unstable vorticities induced by the RMI are transported to the Alfvén wave front by the Lorentz forces.Consequently,the vorticity depositing on the interface is reduced and the interface becomes stable.Quantitatively,the movement of the upstream interface is accelerated while the movement of the downstream is decelerated,less deformation can be seen in the light cylinder.Furthermore,based on more representative circular cylinder interfaces in which the incident shock angle changes continuously,the development of the RMI is also investigated in hydrodynamics,transverse and longitudinal magnetic fields.The goal is to find out the ideal magnetic field configuration to provide reference for future experiments and numerical investigations.The numerical results show that the grow of the RMI is compressed by these two kinds of magnetic field configurations,especially by the transverse magnetic field.In the absence of magnetic fields,the SF₆ jet can penetrate the downstream interface and a great deal of vorticities would deposit on density interfaces.However,density interfaces become rather smooth in the presence of external magnetic fields.Concretely,in the transverse magnetic field configuration,the SF₆ jet can not penetrate the downstream interface,and the density interface is smoother than that in the longitudinal magnetic field.Besides,due to the RMI,the magnetic field lines become kinked near the interfaces.More serious kinked magnetic field lines can be seen near the upstream density interface,resulting in stronger Lorentz forces and the bigger distance between two vortex sheets at that place.Near the downstram interfaces,the Lorentz forces is smallere in longitudinal magnetic fields.Consequently,the vortex sheets could interact with each other,resulting in the growth of instability.In addition,the dynamic mode decomposition(DMD)technique is primarily used in the investigation of the RMI in the magnetohydrodynamic.Some conclusions can be obtained from the DMD results.Small disturbance can also be distinguished even in the presence of magnetic fields.More disturbance can be seen in the longitudinal magnetic field,which demonstrates that the transverse magnetic field is more efficient in compressing the growth of the RMI.In addition,the DMD first mode can extract the main stable vortex structure.The frequencies of small vorticities increase with the increase of modes.Under the same mode,the highest and lowest frequencies of small vorticities appear in the hydro(no magnetic fields)and transverse magnetic cases,respectively.Besides,the frequencies of small vortex sequences are reduced by external magnetic field.Therefore,the DMD results also demonstrate that the growth of the RMI is compressed by external magnetic fields.