Noise mitigation in rectangular jets through plasma actuator-based shear layer control

A computational analysis is performed to study the three-dimensional response of rectangular shear layers to plasma actuator-based control, in the context of sound mitigation of supersonic non-axisymmetric jets. A Mach $1.5$ rectangular jet with an aspect ratio $2:1$ is controlled using experimentally informed actuation patterns, referred to as M0, M1, M2, M3, M${\rm \pi}$ and M+/$-$1. While the first five progressively increase the phase difference between successive actuators thus enhancing three-dimensionality of the shear layer structures, the latter corresponds to the flapping mode of the jet. A preliminary linear analysis identifies that the frequency, $St\sim 1$, has a relatively high overall amplification within the baseline shear layer, and is hence utilized for control in the subsequent nonlinear simulations. Each actuation reveals unique near-field vortical and acoustic responses that have a profound impact on far-field noise levels. The M0 actuation induces circumferentially interconnected strong streamwise vortices, while M1 actuation enhances the circumferential variability in the coherent structures. The M2 actuation encompasses both these effects, and along with a very low tonal impact of forcing, produces the most desirable far-field noise mitigation (${\sim }2.6\,{\rm dB}$), contributed by a broadband reduction around the column-mode peak of the baseline jet. Beyond M2 actuation, effectiveness of control saturates, particularly along the direction of peak noise radiation. Through a near-field analysis of the acoustic component, the efficacy of M2 actuation is attributed to the attenuation of the radiative efficiency of the jet, including reduced energy in the supersonic phase speeds, and redistribution of energy into the higher helical modes. Further, it curtails the nonlinear difference interactions in the plume that energize column-mode frequencies, which often appear as strong intermittent sound-producing events. While the shear layer turbulent kinetic energy decreases with actuation, the controlled jets show minimal variations in mean flow properties, particularly under M2 actuation, suggesting this to be a promising small-perturbation-based noise control strategy.