Role of Atwood number on flow morphology of a planar shock-accelerated square bubble : a numerical study

Abstract

The Atwood number plays a critical role in describing the physics of fluids behind the hydrodynamic instabilities in gas dynamics. In order to investigate the impacts of the Atwood number (At), the evolution of a shock-accelerated square bubble containing either SF6, Kr, Ar, Ne, or He and surrounded by N2 is investigated numerically. For this purpose, the unsteady compressible Navier-Stokes-Fourier equations are solved using an explicit modal discontinuous Galerkin method. For validation, the numerical results are compared with available experimental results and are found to be in good agreement. The results demonstrate that the Atwood number has a significant influence on flow morphology with wave patterns, vortex creation, vorticity generation, and bubble deformation. For At > 0, the speed of the shock wave traveling along with the bubble inner surface is often less than that of the incident shock wave and greater than that of the transmitted shock wave. Moreover, vortex pairs from the upstream and downstream corners are generated, and the former vortex pair ultimately dominates the flow morphology. For At ≈ 0, the incident and transmitted shock waves move at the same speeds, whereas for At < 0, the transmitted shock wave travels faster than the incident shock wave. Moreover, only one vortex pair at the upstream corners is generated, which dominates the flow morphology. Furthermore, a detailed study of Atwood number impacts is investigated through the vorticity generation at interfaces. A quantitative analysis based on the shock trajectories, the interface features, and the integral diagnostics is also studied in detail to investigate the impacts of the Atwood number on the flow structure. Finally, a comparative study of the flow physics between the shock-accelerated square and cylindrical bubbles is conducted to examine their natural differences.