Mode transition and oscillation suppression in supersonic cavity flow

Abstract

Supersonic flows past two-dimensional cavities with/without control are investigated by the direct numerical simulation (DNS). For an uncontrolled cavity, as the thickness of the boundary layer declines, transition of the dominant mode from the steady mode to the Rossiter II mode and then to the Rossiter III mode is observed due to the change of vortex-corner interactions. Meanwhile, a low frequency mode appears. However, the wake mode observed in a subsonic cavity flow is absent in the current simulation. The oscillation frequencies obtained from a global dynamic mode decomposition (DMD) approach are consistent with the local power spectral density (PSD) analysis. The dominant mode transition is clearly shown by the dynamic modes obtained from the DMD. A passive control technique of substituting the cavity trailing edge with a quarter-circle is studied. As the effective cavity length increases, the dominant mode transition from the Rossiter II mode to the Rossiter III mode occurs. With the control, the pressure oscillations are reduced significantly. The interaction of the shear layer and the recirculation zone is greatly weakened, combined with weaker shear layer instability, responsible for the suppression of pressure oscillations. Moreover, active control using steady subsonic mass injection upstream of a cavity leading edge can stabilize the flow.

Pressure oscillation suppression and mode transition for supersonic cavity flows controlled by upstream mass injections

“…The effect of the boundary layer thickness on the pressure oscillation and mode transition for uncontrolled supersonic cavity flows was studied in our previous work. 33 Here, we performed three simulation cases, and the flow conditions are listed in Table 3.…”

“…Our previous works 33,45 have reported that the flow mode in supersonic cavity flows could be divided into the steady mode, the shear layer mode (the Rossiter mode), and the wake mode. The dash-dot and dashed lines in Figure 7 show the oscillation frequencies of the Rossiter modes based on equations ( 4) and ( 5), respectively, and m = 1-4.…”

“…DNS is quite suitable for description of a compressible flow with a small Reynolds number, and one can achieve a good resolution with easy flow visualization. To identify the deterministic structures of flow modes, the proper orthogonal decomposition (POD) 29,30 and the dynamic mode decomposition (DMD) [31][32][33] are two effective mode decomposition methods. The central idea of POD is to determine an optimal subspace of reduced dimension by decomposing a set of complex original distributions into a linear approximation of basic functions and the corresponding coefficients.…”

Reduced‐Order Modeling of Cavity Flow Oscillations across Multi‐Mach Numbers Using Deep Learning

“…CFD numerical simulation mainly includes direct numerical simulation (DNS) [12][13][14], Reynolds averaged Navier-Stokes (RANS) [15,16], and large eddy simulation (LES) [17][18][19]. DNS is a direct high-fidelity method for solving Navier-Stokes equations, which requires very fine grids.…”