Numerical study on shock-accelerated gas rings

Abstract

The morphologies of shock-accelerated gas rings are presented numerically, based on which a straightforward circulation prediction approach is proposed. Sulfur hexafluoride (SF6) and helium (He) rings shocked in air are examined in the present study. The circulation prediction approach is derived from the direct linear superposition of the Samtaney and Zabusky model and the Yang, Kubota, and Zukoski model. We solved Euler equations using the fifth-order weighted essentially non-oscillatory scheme and third-order total variation diminishing Runge-Kutta scheme to demonstrate the complex shock–interface interactions. The numerical results show that, after the shock impact, the mass of the SF6 ring accumulates to its upstream part, while the mass of the He ring accumulates to its downstream part. The circulation prediction approach is found to be easy to implement and is proved reliable in predicting the total circulations of a series of SF6 rings under weak shock conditions.