Low-frequency unsteadiness of shock wave/boundary layer interactions in high-speed flows

Abstract

Shock wave/boundary layer interaction (SBLI) is one of the classical problems in high-speed vehicles. The interactions are featured by separated flows, which are normally associated with low-frequency unsteadiness. As the unsteadiness can be the cause of severe buffeting of the aircraft structures, yielding structural failure and possible dam­age of the payload, it is necessary and important to figure out the mechanism behind such unsteadiness. However, different mechanisms have been proposed to explain the unsteadiness from various points of view, which lead to the cause of such an unsteady phenomenon being the subject of debate. Thus, the aim of the thesis is to provide a physical interpretation of low-frequency unsteadiness applicable to various SBLI flows. Specifically, the SBLI flow is regarded as a dynamics system, and the flow is divided into four scenarios according to the concepts of amplifier and oscillator from the stability analysis. The first part of the thesis focuses on investigating the unsteady dynamics of the shock wave/laminar boundary layer interaction (SLBLI) flow to understand the intrinsic mech­anism solely. Hypersonic laminar flow over a canonical 25-55° double cone is studied using computational fluid dynamics [direct numerical simulation (DNS)], global stability analysis (GSA), bispectrum analysis, and dynamic mode decomposition (DMD) with a freestream Mach number of 11.5 and unit Reynolds number of 1.6 × 105m−1. The DNS and GSA results revealed that the development of perturbations in the early stage of flow evolutions is due to the intrinsic global instability, which is suggested by a con­sistent linear-growth rate between the most unstable global mode and the temporal DNS history of the azimuthal velocity. Besides, the evolutions and nonlinear behav­ior of perturbation modes in the flow are also studied. By examining the evolution of such interactions, the frequency-broadening phenomenon of the fully saturated flow is explained, and the unsteady dynamics of the fully saturated flow are recognized to be caused by the nonlinear saturation of linear instability in the flow. The origins and dynamics of unsteady saturated flow in the flow are therefore demonstrated. The second part of the thesis focuses on investing the unsteady dynamics of the shock wave/turbulent boundary layer interaction (STBLI) flow to identify the contribution of coherent structures in the incoming wall-bounded turbulence to the low-frequency unsteadiness. In this work, supersonic turbulent flow over a 15° compression ramp is studied using wall-resolved large eddy simulation (LES) with a freestream Mach number of 2.95. The LES results are analyzed by Linear And Nonlinear Disambiguation Opti­mization (LANDO), Spectral Proper Orthogonal Decomposition (SPOD), and resolvent analysis. The LANDO results reveal the very-large-scale motions (VLSMs) presenting in the incoming very-long wall-bounded turbulence featured by low-frequency dynamics. Such VLSMs are then observed in the most energetic SPOD mode with a low-frequency dynamic consistent with the peak of the wall-pressure spectrum. A resolvent analysis is also performed to further confirm that the origins of low-frequency dynamics of the present flow are contributed by the VLSMs. The third part of the thesis focuses on investigating the unsteady dynamics of the STBLI flow to identify the coexistence of the intrinsic/convective mechanisms in the flow. Supersonic turbulent flow over a 25° compression ramp is studied using LES, local stability analysis (LSA), GSA, and LANDO with a freestream Mach number of 2.95 and Reynolds number (based on incoming boundary layer thickness δ0) of 6.3 × 104 . By analyzing the dynamic system for the STBLI flow, three dynamically important modes with characteristic spanwise wavelengths of 2δ0,3δ0, and 6δ0 are captured, which are then identified to be associated with G¨ortler instability, a convective mechanism that is excited and maintained by VLSMs, and global instability. The coexistence of these three mechanisms is therefore confirmed. Discussion and summary on the above findings finally provided a complete physical interpretation of low-frequency unsteadiness applicable to various SBLI flows.