激波在air/SF_6气体界面上非定常折射的数值研究

Numerical investigation on unsteady refraction of planar shock wave at air/SF_6 gas interface

本文数值研究了平面激波在air/SF_6凹形(凸形)界面上的非定常折射,着重关注入射角变化带来的波系结构变化.数值程序利用有限差分法离散可压缩多组分欧拉方程,采用双通量算法成功克服了物质界面附近由于比热比不同导致的数值振荡问题,并将该算法与高阶WENO以及三阶Runge-Kutta耦合,使得程序具有较高的时空分辨率.结果表明,相比于准定常折射,平面激波在凹形(凸形)界面上传播时由于入射角的连续变化会出现波系结构的转变现象.随着入射角由大变小,平面激波在凹形界面上依次出现了前曲折射、规则反射折射以及过渡规则折射.相比准定常折射,没有出现Mach反射折射,但出现新的折射波系——过渡规则折射,由流场的迟滞效应导致.随着入射角由小变大,平面激波在凸形界面上依次出现规则反射折射以及Mach反射折射.相比准定常折射,没有出现前曲折射,但Mach折射出现的角度区域推迟且范围变大.研究表明,流场的非定常性对激波折射波系具有重要影响.

The unsteady refractions of a planar shock wave at a concave（convex） air/SF6 interface are numerically studied. The finite di ff erence method is utilized to solve the compressible multi-component Euler equations. Pressure oscillation near the interface due to the di ff erence of the specific heat ratio is successfully overcome using Double-Flux algorithm. High temporal and spatial resolutions are achieved through combining the Double-Fluid algorithm with 5 th WENO and 3 rd Runge-Kutta. Di ff erent from pseudo-steady refraction, the continuous change of incident angle when a planar shock wave moves at a concave or convex interface will result in the transitions between di ff erent refraction wave patterns. It turns out that when the incident angle changes from 90？to 0？during the shock propagating along the concave interface, the refraction patterns of concave-forwards refraction（CFR）, regular refraction with reflected shock（RRR） and transitioned regular refraction with reflected shock（TRRR） are observed in sequence. Compared with pseudo-steady refraction, the Mach type irregular refraction（MRR） is not observed while a new refraction pattern of TRRR occurs, which is possibly caused by hypothesis e ff ect of the flow. With the incident angle increasing from 0？to 90？when the shock moves along the convex interface, only two refraction types of RRR and MRR are captured, and CFR, which occurs under pseudo-steady condition, does not occur. However, at the late stage, the Mach stem becomes curved and resembles the incident shock wave near the interface in CFR. Besides, the critical angle when RRR transits into MRR is delayed while the range of MRR is extended. From this work, it is shown that the flow unsteadiness has a significant influence on the refraction wave pattern.