Numerical investigations on shock oscillations ahead of a hemispherical shell in supersonic flow

A clear understanding of the mechanism responsible for large amplitude shock pulsations ahead of a hemispherical cavity in supersonic flow is presented for the first time in this article. This has applications in supersonic parachute decelerators during the atmospheric descent stage of aerospace vehicles. A cell-centered finite volume code FaSTAR is used to solve the full Navier-Stokes equations on a hemispherical shell facing a Mach 4.0 supersonic free stream. The numerical method is validated against earlier experimental results. First, Flow Configuration A appears consisting of an axisymmetric shock that undergoes low-amplitude oscillations. This flow transitions to Flow Configuration B that has an asymmetric shock structure and undergoes large-amplitude non-stationary shock pulsations. The shock stand-off distance in Flow Configuration B is 1.65 times that in Flow Configuration A. The generation of vortices from the curved shock, amplification of vortices of one kind due to the dynamics of the cavity flow, and further interaction of these amplified vortices with the shock in a loop causes the large-amplitude shock pulsations. The oscillation frequencies as determined from cavity pressure and shock stand-off distance signals extracted from the unsteady results are 1.26 kHz during Flow Configuration A, and 859 and 863 Hz during the non-stationary pulsations of Flow Configuration B. The Helmholtz resonator model predicts quite accurately the frequency of Flow Configuration A (1.27 kHz), and to a good extent the frequency in Flow Configuration B (916.7 Hz).