On the circulation prediction of shock-accelerated polygonal heavy gas cylinders

A modified theoretical model is presented to predict the circulation generation in the interactions of a shock wave with polygonal heavy gas cylinders. In the present work, numerical methods are used to examine the interactions of square-, circular-, and diamond-shaped cylinders that filled with SF6/air mixture under the impact of incident shock with Mach numbers ranging from 1.21 to 2.50. The evolution of shock wave systems, vorticity deposition, and cylinder deformation are demonstrated; the static area measurements resulting from the shock compression and hydrodynamic instabilities and circulation measurements calculated over the entire computational domain and cylinder interface region are analyzed. It is found that the initial cylinder geometry determines the shock refraction types, which in turn determines the vorticity deposition. Different from the circular-shaped cylinder, large vorticity deposition and thus large vortex pairs are concentrated at the corners of the square and diamond-shaped cylinders, so that inaccurate prediction of the original circulation model results. The geometry of the cylinders does not apparently affect the area variation driven by the wave system effect but does affect the area driven by the hydrodynamic instability effect, which can be well manifested by the fast interface diffusion at the late stage. For the square- and diamond-shaped cylinders, the previous circulation prediction is found to agree well with the simulated circulation deposited over the cylinder interface region rather than over the entire computational domain. Finally, a modified circulation model is proposed for the polygonal cylinders considering both the influence of large vorticity generation at interface corners and shock strength reduction. This model provides an interface circulation prediction with relative errors of 0.55%–6.24% and 0.12%–3.04% for the square and diamond-shaped cylinders, respectively.