The present work investigates the bubble formation and vortex shedding phenomena in the viscous flow of a compressible gas seeded with dust particles. A new modal discontinuous Galerkin method was developed for solving the two-fluid model of dusty gas flows. Most previous studies have been limited to flows with low Mach numbers without the presence of shock waves. This study considered a wider Mach number range, from subsonic to supersonic, in the presence of shock waves. We also investigated in detail the effects of the presence of solid particles on flow properties such as bubble size and frequency and the amplitude of the Bérnard-von Kármán vortex street. A novel approach was employed to circumvent the non-strictly hyperbolic nature of the equations of the dusty-gas flow model caused by the non-existence of the pressure term. This allowed the same inviscid numerical flux functions to be applicable for both the gaseous Euler and solid pressureless-Euler systems. The simulation results revealed that the transition from stationary flow to unsteady flow is dependent on both the Reynolds and Mach numbers of the flow. Moreover, it was shown that in stark contrast with the pure gas case above the critical Reynolds number in the supersonic regime, where no flow instability was observed, in the multiphase flows, adding particles produced flow instability. This unusual behavior is because the two-way coupling effects between the gas phase and solid phase override the compressibility effect and cause severe flow instability and spontaneous symmetry breaking in the coherent dynamics of the vortices.

本工作研究了用粉尘颗粒播种的可压缩气体在粘性流中的气泡形成和涡流脱落现象。开发了一种新的模态间断Galerkin方法，用于求解含尘气体的双流体模型。以前的大多数研究仅限于马赫数低而没有冲击波的流动。这项研究认为，在存在冲击波的情况下，从亚音速到超音速，马赫数范围更大。我们还详细研究了固体颗粒的存在对流动特性（如气泡大小和频率以及Bérnard-vonKármán涡街的振幅）的影响。采用了一种新颖的方法来避免由于压力项的不存在而引起的含尘气体流量模型方程的非严格双曲性质。这使得相同的无粘性数值通量函数适用于气态欧拉和固体无压欧拉系统。仿真结果表明，从固定流到非恒定流的过渡取决于流的雷诺数和马赫数。此外，表明在多相流中，与没有观察到流动不稳定性的超音速状态中高于临界雷诺数的纯气体情况形成鲜明对比，增加了颗粒产生了流动不稳定性。这种不正常的行为是因为气相和固相之间的双向耦合效应超过了可压缩性效应，并导致严重的流动不稳定性和自发对称性破坏了涡旋的相干动力学。