Numerical Study On The Unsteady Refraction Of Strong Shock Interacting With Light-heavy Interfaces

When a shock wave encounters an interface of different fluids,due to the difference of acoustic impedances for the fluids in both sides,the shock will refract on the interface.In recent years,due to the great significance in science and engineering practice,more and more attention has been paid to the study of shock refraction.More importantly,convergent shock wave refraction becomes attractive because of its application in high energy physics.In this work,we numerically study the influences of the continuous change of the incident angle and the Mach number on the unsteady refraction wave patterns and the wave transitions,respectively,for a light-heavy(Air/SF6)interface.For the purpose,we perform numerical simulations based on the HOWD(High Order WENO and Double-flux)solver that employs the compressible multicomponent Euler equation.The double flux algorithm is used to overcome the numerical oscillations caused by the difference of specific heat ratios in the vicinity of the material interface.The HOWD solver has high temporal resolution by using high order WENO and third order Runge-Kutta methods.The study of the plane shock wave refracting on the concave and the convex interfaces is performed to access the influence of the continuous change of the incident angle on the unsteady refraction phenomenon.The results show that there are two differences between pseudo-steady and unsteady refractions in the wave pattern structures and the wave pattern transitions as the incident angle changes from large to small:one is that CFR pattern affects the appearance of the MRR pattern,and the other is that a new type of refraction wave structure named TRRR appears.As the incident angle changes from small to large,there are also two differences of the wave patterns in pseudo-steady and unsteady refractions.On one side,the incident angle of MRR is delayed with a larger range.On the other side,the CFR disappears,but the Mach-stem of MRR in later stages is similar to the bottom deformation of CFR.The study of the refraction of the convergence shock waves on well-designed interfaces is performed to estimate the influence of the continuous change of the Mach number on the unsteady refraction phenomenon.The effect of simultaneous change of incident angle and the Mach number on the unsteady refraction phenomenon is studied by performing the convergent shock wave refraction on the flat interface.The results show that in comparison with the continuous change of the incident angle,under strong shock wave conditions the continuous change of the Mach number has much less influence on the unsteady refraction wave patterns.Moreover,similar conclusions can be drawn in the case of the simultaneous change of the incident angle and the Mach number,which appears in the process of the convergent shock wave refracting on the flat interface.