Investigation on shear layer instabilities and generation of vortices during shock wave and boundary layer interaction

Abstract

The interaction of a reflected shock with the boundary layer inside the shock tubes is an important engineering problem. Studies related to shock wave mitigation and attenuation are performed inside the shock tubes. A proper understanding of the flow behind the reflected shock and the separated zone involving multiple vortical structures is highly essential for estimating the effectiveness of the shock wave mitigation/ attenuation. Such complex flows consist of Lambda shock, shear layer originating from the triple point, multiple shocklets, Mach stems, and vortices. Experimentally the shock structures are obtained through optical techniques. The vortices present in the compressible flow can be obtained through numerical simulations. The complex flows consisting of the above- mentioned features have been simulated numerically so far for the Reynolds numbers up to 1000 [ Zhou G, Xu K, Liu F. Grid-converged solution and analysis of the unsteady viscous flow in a two-dimensional shock tube. Phys Fluids 2018;30(016102):1-21.]. In the present investigation, the shock-wave boundary-layer interaction is simulated for the Reynolds numbers of 1000 and 2500 using a 13th order hybrid scheme to discern the distinct flow features. First, the solver [Kundu A, De S. Navier-Stokes simulation of shock-heavy bubble interaction: Comparison of upwind and WENO schemes. Comput Fluids 2017;157:131-145.] was validated with the benchmark wall density data for a Reynolds number of 1000. Next, the simulations were performed using 50 and 109.5 million cells for the Reynolds number of 2500. The density gradients, vorticity, wall density, and Fourier spectra were used for comparing the flow field for the Reynolds numbers of interest. The Lambda shock, Kelvin-Helmholtz (K-H) vortices in the shear layer, shocklets, the height of lambda shock, and Mach stems were obtained using a grid-mesh of 109.5 million cells. It is observed that the number of vortices generated inside the separated flow region increased with the increase in Reynolds number from 1000 to 2500. Furthermore, the triple point height and the number of K-H vortices generated at the shear layer also increase with an increase in Reynolds number. The present simulations revealed the formation of vortices close to the wall at a Reynolds number of 2500. Such flow structures have an important role in shock / blast wave mitigation and the associated aeroacoustics.