Lagrangian analysis of the formation and mass transport of compressible vortex rings generated by a shock tube*

Abstract

In order to understand the mass transport and the dynamic genesis associated with a compressible vortex formation, a dynamic analysis of compressible vortex rings (CVRs) generated by shock tubes by using the framework of Lagrangian coherent structures (LCSs) and finite-time Lyapunov exponents field (FTLE) is performed. Numerical calculation is performed to simulate the evolution of CVRs generated by shock tubes with 70 mm, 100 mm, and 165 mm of the driver section at the circumstances of pressure ratio = 3. The formation of CVRs is studied according to FTLE fields. The mass transport during the formation is obviously seen by the material manifold reveled by FTLE fields. A non-universal formation number for the three CVRs is obtained. Then the elliptic LCSs is implemented on three CVRs. Fluid particles separated by elliptic LCSs and ridges of FTLE are traced back to t = 0 to identify the fluid that eventually forms the CVRs. The elliptic LCSs encompass around 60% fluid material of the advected bulk but contain the majority of the circulation of the ring. The other parts of the ring carrying almost zero circulation advect along with the ring. Combining the ridges of FTLE and the elliptic LCS, the whole CVR can be divided into three distinct dynamic parts: vortex part, entrainment part, and advected part. In addition, a criterion based on the vortex part formation is suggested to identify the formation number of CVRs.