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We use resolvent analysis to determine an unsteady active control setup toattenuate pressure fluctuations in turbulent supersonic flow over a rectangularcavity with a length-to-depth ratio of 6 at a Mach number of 1.4 and a Reynoldsnumber based on cavity depth of 10,000. Large-eddy simulations (LES) anddynamic modal decomposition (DMD) of the supersonic cavity flow reveal thedominance of two-dimensional Rossiter modes II and IV. These predominantlytwo-dimensional vortical structures generate high-amplitude unsteadiness overthe cavity through trailing-edge impingement and create oblique shock waves byobstructing the freestream. To disrupt the undesired formation of vorticalstructures, we introduce three-dimensional unsteady forcing along the cavityleading edge to generate streamwise vortical structures. Resolvent analysiswith respect to the time-averaged base flow is leveraged to determine theoptimal combination of forcing frequency and spanwise wavenumber. Instead ofselecting the most amplified resolvent forcing modes, we seek the combinationof control parameters that yields sustained amplification of the primaryresolvent-based kinetic energy distribution over the entire length of thecavity. The sustained amplification is critical to ensure that the selectedforcing input remains effective to prevent the formation of the large spanwisevortices. This resolvent-analysis-based flow control guideline is validatedwith a number of companion LES of the controlled cavity flows. The optimalcontrol setup is verified to be the most effective in reducing the pressureroot-mean-square level up to 52% along the aft and bottom cavity walls comparedto the baseline cavity flow. The present flow control guideline derived fromresolvent analysis should be applicable to flows that require the actuationinput to remain effective over an extended region of interest.

Unsteady control of supersonic turbulent cavity flow based on resolvent analysis