On the evolution mechanism of the shock-accelerated annular SF₆ cylinder

Based on the compressible multicomponent Navier-Stokes equations, the interaction of a planar shock wave (Ma=1.23) with an annular SF₆ cylinder whose inner and outer radii were set as 8 and 17.5 mm respectively was numerically studied. The simulation was conducted based on the finite volume method. For capturing the complex shock and vortex structures as well as the interfaces, the adaptive mesh refinement method, level set method, and fifth-order weighted essentially non-oscillatory scheme were used for the simulation. The adaptive mesh refinement method dynamically refined the uniform Cartesian grids around the multiple moving shocks and accelerated interfaces. The level set method tracked the interface, while the fifth-order weighted essentially non-oscillatory scheme captured discontinuities such as shock waves and contact surfaces. Time advancement was achieved with the third-order strong-stability-preserving Runge-Kutta method. Compared with the previous experimental results, numerical results revealed the complex evolution of shock wave structures generated in the process of four shock transmissions in the annular cylinder. It is found that the transition from free precursor refraction to free precursor von Neumann refraction occurs when the transmitted shock wave passes through the inner cylinder. In addition, the complex shock structures that developed between the inner and outer downstream interfaces cause the pressure gradient direction to reverse several times on the inner downstream interface, which eventually leads to three reversals of vorticity on the inner downstream interface. In the later stage, the “jet” structure formed on the inner cylinder would impact the downstream interfaces, and finally induces the interfaces to generate a pair of primary vortices, a pair of secondary vortices and a reverse “jet”. Quantitative analyses of the variation of the length, width, displacement, the circulation and mixing rate of the annular cylinder were conducted. The results demonstrate that the presence of the inner cylinder attenuates the influence on the height and length of the annular cylinder during the process of small vortexes merging into the large vortexes in the early stage, and increases the mixing rate of the heavy gas and the ambient gas.