Numerical Simulation And Control Of Supersonic Cavity Flows

Cavity flow can be widely seen in the realm of Aeronautics and Astronautics, strong pressure oscillations may be generated under some flow conditions, which cause environmental pollution and damage of the devices in cavity. Meanwhile, cavity flow involves many problems in the fluid mechanics such as the unsteady flow, vortex dynam-ics, shear layer instability and so on. Hence, it attracts more and more concerns from scientific researchers and engineers. The two-dimensional supersonic cavity flow and control of the pressure oscillations are investigated by the direct numerical simulation in this thesis. The main work includes following aspects:(1) For 2D cavity of the length-to-depth ratio L/D= 4, direct numerical simulation is performed with different inflow boundary layer thicknesses and Mach numbers at a low Reynolds number. For a given Mach number Ma= 1.8, as the decline of boundary layer thickness, cavity flow mode transition from steady mode to Rossiter Ⅱ mode, then to dominant Rossiter Ⅱ mode with secondary Rossiter Ⅲ mode and low-frequency mode, then to dominant Rossiter Ⅲ mode with secondary Rossiter Ⅱ mode and low-frequency mode has been observed because of the change of vortex-corner interactions. In the shear layer mode, the dominant oscillating frequency is increased. Because of the enhanced shear layer instability and the interaction between the shear layer and the recirculation zone, the amplitude of the pressure oscillations is also increased. For a given initial inflow boundary layer thickness, as the increase of the Mach number, cavity flow mode transition from wake mode (when the boundary layer thickness is sufficiently small) to shear layer mode, then to steady mode has been observed. In the shear layer mode, the amplitude of the pressure oscillations is decreased because of the weakened shear layer instability. The dominant mode transition can be clearly showed by the dynamic modes obtained from the dynamic mode decomposition (DMD), and the energy spectra are consistent with the local power spectral density (PSD) analysis at the monitor in the flow fields.(2) With a given boundary layer velocity profile of Ma= 1.8 at the cavity inlet, the passive control by substituting the cavity trailing edge with a quarter-circle and the active control using steady subsonic mass injection upstream of the cavity leading edge are numerically studied. Under the passive control, as the radius of the quarter-circle increases, cavity flow mode transition from dominant Rossiter Ⅱ mode with secondary Rossiter Ⅲ mode and low-frequency mode to dominant Rossiter Ⅲ mode with sec-ondary Rossiter Ⅱ mode and low-frequency mode, then to Rossiter Ⅲ mode has been observed because of the change of vortex-corner interactions. The amplitude of the pressure oscillations is decreased for the reason of the weakened shear layer instability and the interaction between the shear layer and the recirculation zone. Under the active control, the shear layer is lifted up to alleviate the downstream shear layer impingement, the shear layer is thickened to reduce the receptivity to the pressure disturbance, the shear layer instability and the interaction between the shear layer and the recirculation zone are also weakened. Hence, the pressure oscillations can be suppressed.(3) A new reduced-order model (ROM) named approximate full N-S model in-volving the primitive variables (ρ, u, v, T) of the 2D fully compressible Navier-Stokes equations is constructed based on proper orthogonal decomposition (POD) with visu-alized weighting inner product and Galerkin projection, which is theoretically valid for flows at high Mach numbers. Comparison with the widely used isentropic N-S model valid for flows at low or moderate Mach numbers is performed. For 2D supersonic cavity flow with relatively thick boundary layer, the approximate full N-S model can predict the flow dynamics accurately using less POD modes compared with the isentropic N-S model. The dominant frequency and amplitude given by the spectra at the monitor are in agreement with the DNS results, comparison of the transient streamwise velocity fields with the DNS results also proves that the new model can capture dominant flow features of supersonic cavity flow very well. When the boundary layer is relatively thin, the Runge-Kutta integration to obtain the coefficients of the POD modes will diverge finally with the isentropic N-S model. However, the same process for the approximate full N-S model can stably proceed, indicating that our new model has better robustness. To predict the flow dynamics accurately, there is a need to add dissipative model in the new ROM. Additionally, present model reduction method is relatively simple, and can be easily extended to other supersonic flows.