Phase-based analysis and control of a supersonic turbulent cavity flow

We present a phase-based framework for reducing the pressure fluctuations within a spanwise-periodic supersonic turbulent cavity flow with an incoming free-stream Mach number of 1.4 and a depth-based Reynolds number of 10 Superscript 4 10 4 $10^4$ . Open cavity flows exhibit large fluctuations due to the feedback between the shear-layer instabilities and the acoustic field. The dominant flow physics includes the formation, convection and impingement of large-scale spanwise-oriented vortical structures into the aft wall. We implement a phase-reduction approach to identify the flow response about this time-varying convective process by defining a phase variable using dynamic mode decomposition. Three-dimensional impulse perturbations with various spanwise actuation wavenumbers, beta β $\beta$ , are introduced from the cavity leading edge to characterise the phase advancement or delay of convection. We perform open-loop flow control through unsteady blowing using actuation frequencies slightly different from the vortex-convection frequency to disrupt the feedback loop. After designing a phase-sensitivity-based actuation waveform optimised for quick flow modification, we investigate the speed of fluctuation reduction and compare it with a sinusoidal waveform actuation. At a spanwise actuation wavenumber of beta equals 2 pi β = 2 π $\beta =2\pi$ , both perform similarly, achieving a 46 % reduction of pressure fluctuations within five convective times. At beta equals pi β = π $\beta =\pi$ , the phase-sensitivity-based actuation performs better by achieving a 40 % reduction compared with the 30 % with a sinusoidal waveform within six convective times. The present method explicitly targets the temporal dynamics to achieve rapid suppression within a few convective times. This study shows the potential of phase-based analysis for timing-based (event-based) flow control and rapid flow modification of unsteady turbulent flows.