Optimal ‘quiet’ inlet perturbation using adjoint-based PSE in supersonic jets

Abstract

The adjoint-based control of noise emission for two supersonic turbulent jets with different temperature ratios is attempted by modifying the inlet perturbations. The major noise emission of supersonic jets can be modeled by the spatially developing instability waves, which are obtained by solving parabolized stability equation (PSE) based on the solution of Reynolds-averaged Navier–Stokes equations. The closed-loop control system based on the adjoint PSE is constructed, with the objective function of both total perturbation energy and pressure perturbations. The final objective of this work is to modify the inlet Kelvin–Helmholtz modes, which produce lowest-level far-field noise in supersonic turbulent jets. The results show that the near-field coherent structures acting as sound sources and far-field noise intensity generated by optimal perturbations in isothermal and heated jets could be decreased greatly compared with the original inlet perturbations from linear stability theory. Moreover, the energy-based and pressure-based optimization give similar control efficiency in the noise reduction, although there are some minor differences in optimal inlet perturbations. This indicates that by considering the near-field disturbance energy in the noise control framework, which is easier to measure in real experiments, one can obtain the same benefits as the measurement of far-field pressure.