Flow stability of axisymmetric shock-wave/boundary-layer interactions

Abstract

Shock-wave/boundary-layer interaction (SWBLI) is a fundamental flow problem that is widely encountered during hypersonic flights. It has received extensive attention since it can lead to laminar to turbulent transition, unsteadiness, and localized high pressure and heating regions. Understanding and predicting SWBLI are significant to the design and control of hypersonic vehicles. In this regard, numerous theoretical, experimental and numerical investigations have been performed over the decades. This thesis focuses on the flow stability of axisymmetric SWBLIs for both globally stable and unstable flows in the absence and presence of external perturbations. The intrinsic and convective instabilities of two canonical configurations, including a hollow­-cylinder/flare and a double cone, are investigated using different analytical tools. Supersonic flow over a hollow cylinder/flare with a free-stream Mach number of 2.25 is numerically studied. Axisymmetric computational fluid dynamics (CFD) simulations and global stability analysis (GSA) are performed for a wide range of cylinder radii and flare deflection angles. The onset of incipient and secondary separation is delayed as the cylinder radius is decreased due to the axisymmetric effects. The GSA reveals that a decrease in cylinder radius also postpones the emergence of global instability. The GSA results agree well with the results of direct numerical simulations (DNS) for a supercritical case in the linear stage. The saturated flow exhibits pairs of unsteady streamwise streaks downstream of reattachment. A criterion of the global stability boundary is established for supersonic flow over a hollow-­cylinder/flare. The influence of external forcings on globally stable flows over a hollow­-cylinder/flare and a double cone are investigated through resolvent analysis. The hollow-cylinder/flare flow with a free-stream Mach number of 2.25 is studied to illustrate the axisymmetric effects on the optimal disturbance. The increase of the cylinder radius is likely to result in a transition of the optimal response from the streamwise streaks to Mack’s first mode. For hypersonic flow over a double cone with a free-stream Mach number of 11.5, the impact of the shock interaction type on optimal disturbances to upstream forcings is studied. The optimal response is found to be insensitive to the shock interaction types (i.e. type VI and type V) due to the dominant role of modal resonance. Hypersonic flow over a canonical 25°−55° double-cone configuration with a free-stream Mach number of 10.38 is numerically investigated. Time-accurate axisymmetric and three-dimensional (3-D) simulations are performed for the double-cone flow to investigate the evolution of three-dimensionality and unsteadiness. Both the axisymmetric calculation and the 3-D simulation without exogenous perturbations exhibit a notably larger separation region than that in experiments and misrepresent the distributions of surface pressure and heat flux. The random forcing approach with two levels of noise amplitude is then applied to subsequent 3-D simulations. A better agreement with the measured data is observed for the time-averaged heat flux and pressure when the white noise is enforced. As the forcing amplitude is increased, the agreement is slightly improved. However, discrepancies between the 3-D results and experimental data still exist in the prediction of the heat flux and pressure distributions.