Eulerian-Eulerian simulation of dusty gas flows past a prism from subsonic to supersonic regimes using a modal discontinuous Galerkin method

•A DG method is developed for solving the Eulerian-Eulerian model of dusty gas flows.•The study investigates a wider Mach number range in the presence of shock waves.•Two-way coupling effect overrides compressibility effect and causes flow instability. 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.