Flow and mixing in shock-accelerated elliptic helium gas cylinder process

Abstract

In shock bubble interaction (SBI), the baroclinic vorticity generated by misalignment of pressure and density gradient will lead to flow instability which promotes the mixing between the bubbles and surrounding gas. A numerical study on the flow and mixing of shock-accelerated elliptic helium cylinder with the surrounding air is presented in this study. To well simulate the SBI, compressible multi-component two-dimensional Navier-Stokes equations are solved by combining with double-flux model and five-order weighted essentially non-oscillatory scheme. Both the wave system evolution and the interface deformation are clearly illustrated by using the present numerical method. Quantitatively, the length scales of distorted interface, compressibility of helium cylinder, circulation, and total mixing rates of helium are measured and compared to investigate the mixing mechanism and structure effect of the helium cylinder. It is found that the evolution of elliptic interface is closely related to its shape. In the case of elliptic gas cylinder shock-accelerated along major axis, the most remarkable feature is the air jet which grows constantly with time and penetrates the downstream interface boundary, forming two independent vortices. The penetration speed of the air jet is found to increase with ellipse eccentricity increasing. In addition, like the case of the circular helium cylinder, typical free-precursor irregular shock wave refraction occurs when incident shock wave passes through the interface. In the case of shock-accelerated elliptic gas cylinder along minor axis, a distinct flat structure appears due to the shock compression during the evolution of interface, and then vorticity concentrates at the two ends of the ellipses, which finally bends the interface severely. Simple regular shock wave refraction occurs in the large frontal area of the helium cylinder. These features also grow intensely with the eccentricity of the initial elliptic interface increasing. The distinct morphologies of these elliptic interfaces also lead to the different behaviors of the interface features including the length and height. The comprehensive analysis shows that for the elliptic helium cylinder, the structure effect not only affects the interface evolution in a length-scale manner but also plays a role in their mixing process. The mixing rate of helium cylinder shocked along the major axis is significantly superior to that along the minor axis.