Sub-cavity Induced Passive Control of Confined Supersonic Cavity Flows Across Varying Freestream Mach Numbers

TL;DR

The paper investigates passive control of confined supersonic cavity oscillations by inserting sub-cavities at the front or aft walls, across $M_ty=2$ and $M_ty=3$. Using Large-Eddy Simulations with a Dynamic WALE model in OpenFOAM, coupled with PSD, CWT, flow visualization, cross-correlation, and Dynamic Mode Decomposition, the study reveals that aft-wall sub-cavities best suppress the dominant frequency at $M_ty=2$ while front-wall sub-cavities are more effective at $M_ty=3$, achieving reductions of about $5.45\%$ and $23.4\%$, respectively. The suppression arises from different mechanisms: mass entrainment disruption and vortex interaction at $M_ty=2$, and suppression of compressibility-driven acoustic coupling near the leading edge at $M_ty=3$. These insights offer practical passive-flow-control options for confined cavity configurations in high-speed aerospace applications, validated by cross-correlation and DMD analyses that corroborate the identified mechanisms.

Abstract

The self-sustaining oscillations in cavity flows enhance fluid mixing and promote energy and momentum transport. However, the associated oscillation frequencies can amplify acoustic loading, potentially damaging surrounding structures. Hence, understanding cavity dynamics across geometries and freestream conditions and developing strategies to regulate these oscillations without compromising performance are essential. This study examines the influence of sub-cavities placed at the front and aft walls of a cavity confined by a top wall with a deflection angle of 2.29 degrees, under freestream Mach numbers 2 and 3. Large eddy simulations (LES) are performed using OpenFOAM, and unsteady pressure signals are analyzed through spectral methods. Results show that the aft-wall sub-cavity most effectively suppresses the dominant oscillation at Mach number 2, while the front-wall sub-cavity achieves greater suppression at Mach number 3. Density gradient (numerical Schlieren) and vorticity fields, normalized acoustic impedance, and global wavelet power reveal the mechanisms responsible for this attenuation. At Mach number 2, the aft-wall sub-cavity entrains mass and disrupts the convective feedback loop. At Mach number 3, the front-wall sub-cavity weakens the hydrodynamic-acoustic coupling near the leading edge, disrupting the compressibility-driven feedback. These configurations suppress dominant frequencies by 5.45 and 23.4 percent for Mach numbers 2 and 3, respectively. Cross-correlation between pressure probes and Dynamic Mode Decomposition (DMD) further confirm the mechanisms behind the observed frequency suppression

Figures (34)

• Figure 1: Schematic of the confined cavity with a) front-wall b) aft-wall subcavity with probe locations.
• Figure 2: Schematic of cavity geometry illustrating the deflection angle ($\theta$), the shock angle ($\beta$), the origin of the shock (a), and the impinging point (b).
• Figure 3: Validation of the present simulation against the experimental data of Gruber et al.gruber2001fundamental.
• Figure 4: Normalized Power Spectral Density (PSD) (fGxx(p)/$(p_\infty)^2$) vs the Strouhal number (St=fL/$U_\infty$)obtained from the pressure fluctuation data recorded by probes P1, P2 and P3 for cavity (a) without sub-cavity (R2) (b) with front-wall sub-cavity (F2) (c) with aft-wall sub-cavity (A2) at M$_\infty$ = 2.
• Figure 5: Normalized Power Spectral Density (PSD) (fGxx(p)/$(p_\infty)^2$) vs the Strouhal number (St=fL/$U_\infty$) obtained from the pressure fluctuation data recorded by probes P1, P2 and P3 for cavity (a) without sub cavity (R3) (b) with front-wall sub-cavity (F3) (c) with aft-wall sub-cavity (A3) at M$_\infty$ = 3