Mode transition and oscillation suppression in supersonic cavity flow

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.

Model reduction for supersonic cavity flow using proper orthogonal decomposition(POD)and Galerkin projection

The reduced-order model （ROM） for the two-dimensional supersonic cavity flow based on proper orthogonal decomposition （POD） and Galerkin projection is investigated. Presently, popular ROMs in cavity flows are based on an isentropic assumption, valid only for flows at low or moderate Mach numbers. A new ROM is constructed involving primitive variables of the fully compressible Navier-Stokes （N-S） equations, which is suitable for flows at high Mach numbers. Compared with the direct numerical simulation （DNS） results, the proposed model predicts flow dynamics （e.g., dominant frequency and amplitude） accurately for supersonic cavity flows, and is robust. The comparison between the present transient flow fields and those of the DNS shows that the proposed ROM can capture self-sustained oscillations of a shear layer. In addition, the present model reduction method can be easily extended to other supersonic flows.

Effects of multiple subcavities with floor subcavity in supersonic cavity flow

Experimental and computational analysis has been carried out by many researchers on supersonic cavity flow,but detailed analysis based on Rossiter’s model still requires some insight.In the current study an open rectangular cavity with a length to depth ratio of 2(L/D=2)and Mach number at the inlet as 1.71,was considered as a baseline configuration for experimental analysis.Statistical techniques such as power spectral density(PSD),correlation,and overall sound pressure level(OASPL)were carried out on the unsteady pressure data,to analyze the aero-acoustic flow physics.High-speed schlieren images were processed to obtain spatially coherent modes by proper orthogonal decomposition(POD).The analysis was extended for different dimensions of subcavities on the aft,floor,and front wall.This detailed analysis of these configurations with different dimensions and combinations revealed the various flow features and mode frequencies in supersonic cavity.As the front wall subcavity act as a passive control device,reducing the overall sound pressure level inside the cavity whereas,the aft wall subcavity acts as a passive resonator with distinct harmonic fluidresonant modes,a similar phenomenon was observed for floor subcavity at different locations.A novel method was employed to analyze Rossiter’s model and its applicability in estimating experimental modes was verified,as it accurately predicted the dominant frequencies with a maximum of 2.74% uncertainty among all the configurations.

A Weighted Multi-Domain Spectral Penalty Method with Inhomogeneous Grid for Supersonic Injective Cavity Flows

In[J.Comput.Phys.192(1),pp.325-354(2003)],we have developed a multidomain spectral method with stable and conservative penalty interface conditions for the numerical simulation of supersonic reactive recessed cavity flows with homogeneous grid.In this work,the previously developed methodology is generalized to inhomogeneous grid to simulate the two dimensional supersonic injector-cavity system.Non-physical modes in the solution generated at the domain interfaces due to the spatial grid inhomogeneity are minimized using the new weighted multi-domain spectral penalty method.The proposed method yields accurate and stable solutions of the injector-cavity system which agree well with experiments qualitatively.Through the direct numerical simulation of the injector-cavity system using the weighted method,the geometric effect of the cavity wall on pressure fluctuations is investigated.It is shown that the recessed slanted cavity attenuates pressure fluctuations inside cavity enabling the cavity to act potentially as a stable flameholder for scramjet engine.