In a recent publication Hornung (2019) showed that the shock wave stand-off distance and the drag coefficient of a cone in inviscid hypersonic flow of a perfect gas can be expressed as the product of a function of the inverse normal-shock density ratio and a function of a cone-angle parameter, thus reducing the number of independent parameters from three (Mach number, specific heat ratio and angle) to two. By making a large number of Euler computations, analytic forms of the functions were obtained. In this article the same approach is applied to the symmetrical flow over a wedge. It turns out that the same simplification applies and corresponding analytical forms of the functions are obtained. The functions of the normal-shock density ratio are compared with newly determined corresponding functions for flow over a circular cylinder.
Linear Instability of Shock-Dominated Laminar Hypersonic Separated Flows
采用动力学直接模拟蒙特卡罗（DSMC）方法研究了双楔高超声速氮分子绕流中激波/边界层相互作用（SWBLI）系统的展向自激均匀扰动。流动的过渡努森数和单位雷诺数分别为3.4 x 10 $^{-3}$和5.2 x 10 $^4$ m $^{-1}$。由于上楔面产生的马赫数为7的分离（弓形）激波下游存在着强烈的热不平衡。线性不稳定性机制预计使预先计算的二维基流在展向扰动下可能不稳定。具体的目的是评估不稳定模式的增长率，波长，位置，和起源的展向周期性流动结构，以及在这种相互作用中存在的特征频率。
Kinetic modelling of three-dimensional shock/laminar separation bubble instabilities in hypersonic flows over a double wedge
本文研究了由激波/边界层干扰（SBLI）引起的三维展向均匀层流分离泡（LSB）的线性整体不稳定性。在对应于自由流动单位雷诺数$Re_1=5.2\times 10^{4}$ m $^{-1}$的这些条件下，流动表现出稀疏效应，激波厚度与分离时附面层的大小相当。这反过来又需要使用高保真直接模拟蒙特卡罗（DSMC）方法来准确地解决非定常流特征。我们第一次表明，LSB维持自激，小振幅，3-D扰动，导致展向周期性的流动结构不仅在和下游的分离区域，如在众多的实验和数值模拟，而且在内部结构的分离和分离激波层。发现两个区域中结构的展向周期长度和生长速率相同。结果表明，线性整体不稳定性导致分离激波与分离激波相交形成的三相点的低频不稳定，对应的Strouhal数为$St\sim0.02$。展向均匀基流和主导的三维流动本征模的线性叠加提供了LSB和激波层中线性不稳定性之间强耦合的进一步证据。
