Variable-density mixing in shock bubble interaction, a canonical flow of Richtermyer-Meshkov instability, is studied by the high-resolution simulation. While the dissipation mainly controls the passive scalar mixing rate, an objective definition of variable-density mixing rate characterizing the macroscopic mixing formation is still lacking, and the fundamental behavior of mixing rate evolution is not yet well understood. Here, we first show that the variable-density mixing of shock bubble interaction is distinctly different from the previous observations in the passive scalar mixing. The widely-accepted hyperbolic conservation of the first moment of concentration in the scalar mixing, i.e., the conservation of the mean concentration, is violated in variable-density flows. We further combine the compositional transport equation and the divergence relation for the miscible flows to provide the evidence that the existence of density gradient accelerated mixing rate, decomposed by the accelerated dissipation term and redistributed diffusion term, contributes to the anomalous decrease or increase of the mean concentration depending on Atwood number. Further analyzing a number of simulations for the cylindrical or spherical bubbles under a broad range of shock Mach numbers, Reynolds numbers, and Peclet numbers, the density gradient accelerated mixing rate exhibits weak dependent on Peclet numbers, and identifies an Atwood number range with high mixing rate, which can be theoretically predicted based on the mode of hyperbolic conservation violation behavior.
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。
激波与球形密度不均匀体的相互作用通过斜压涡度的脉冲沉积导致涡环的发展。目前的流体动力学视频显示这种现象，并在威斯康星州激波管实验室（WiSTL）的9.2米，向下射击激波管进行了实验研究。该管具有方形内部横截面（0.25 m x 0.25 m），具有用于光学访问的多个熔融石英窗口。球形肥皂泡是由一个可伸缩的注射器产生的，并释放到自由落体200毫秒前的初始冲击加速。向下运动的M = 2.07的冲击波使气泡冲动地加速并从管端壁反射。反射的冲击波使气泡重新加速（再冲击），气泡现在已经发展成涡环，沉积了额外的涡量。在没有任何流动扰动的情况下，反射激波后面的流动是静止的。因此，任何观察到的涡环运动都是由于环流造成的。冲击涡环成像在12,500 fps的平面米氏散射。
