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The influence of nonlinearities on jet noise modeling based on parabolized stability equation

With the aid of a large eddy simulation (LES) model of a turbulent jet, we study the modeling of jet noise based on wavepackets by considering a certain degree of nonlinearity. Linear parabolized stability equations (PSEs) are utilized to solve the spatial evolution of wavepackets with the base flow obtained from the LES. The spectral proper orthogonal decomposition (SPOD) is performed to extract the most energetic coherent structures. Since the mean flow includes partial nonlinearity, improved agreement of hydrodynamic pressure fields between SPOD-filtered results and linear-PSE solutions is obtained in the near field. Deviations only occur when the coherent structures decay. Although linear-PSE solutions represent the near-field hydrodynamics reasonably, the far-field noise propagated from this linear model shows a large deviation from the LES results. Then, a small external harmonic forcing is added to the right-hand side of the PSE to mimic the effects of nonlinearity due to incoherent fluctuations on the late evolution of near-field wavepackets, and an adjoint approach is further utilized to search for optimal forcing distribution. Optimized forcing is mainly located near the critical layer; enhances the energy of wavepackets; and raises the sound radiation efficiency, but to a limited extent. Meanwhile, the coherence-matched PSE wavepacket is proposed to incorporate the coherence decay of wavepackets calculated based on LES. An improved agreement in far-field sound pressure levels for low-frequency components is achieved. In short, these findings all prove the vital role of nonlinearity in jet noise modeling, and the current modeling approaches have made some progress. However, a more physics-based and generalized nonlinear model is still required.