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

Abstract

A theoretical model is presented to predict the circulation generation in the interaction of a shock wave with elliptical heavy gas cylinders with various elongations. The focus is to introduce the interface geometrical relation into circulation modeling. This high-speed multifluid flow is simulated by solving the Navier-Stokes (NS) equations in a finite difference frame. The second-order Strang time-splitting scheme is used to decouple the NS equations into the hyperbolic and parabolic steps. The fifth-order weighted essentially nonoscillatory scheme and the three-order total variation diminishing Runge-Kutta scheme are applied in the hyperbolic step. The fourth-order central difference scheme and the second-order explicit Runge-Kutta-Chebyshev scheme are applied to handle the viscosity term in the parabolic step. Nine elliptical heavy gas interfaces filled with SF6/air mixture are examined under the impact of incident shock with Mach number 1.2. The evolutions of the wave system are presented, and the interfaces are correspondingly classified based on a shock wave competition between the incident shock and the transmitted shock. The distributions of vorticity and generations of circulations on different interfaces are computed. Based on the present numerical results, a unified circulation model is proposed for the elliptical interfaces considering both the interface classification and the geometrical relation between the incident shock and the initial interface. This model is found to provide an accurate prediction of the circulation generation. For the cases being studied, the maximum prediction error is 8%, and the minimum error reaches 1.6%. It highlights the geometric role as an independent factor that played in the interaction of shock with gas inhomogeneities.