Extraction of Fluid Thermodynamic Modes from the Mean Flow of a Supersonic Jet

The aeroacoustic analysis and optimization of new nozzle designs and noise control technologies involves a large cost function which requires the continued development of instability models for noise prediction and control. These models are often carefully calibrated with high-fidelity numerical data. Recent work with Doak's Momentum Potential Theory (MPT) has revealed new insights in informing these instability models to accurately predict the noise generation process, by exactly separating the acoustic, vortical and thermal components (designated Fluid-Thermodynamic, or FT, components) from the flow. The application of Doak's MPT however, requires the use of large LES datasets. The goal of the present paper is to extend the application of Doak's MPT using the information from only the mean flow. Using a recently developed mean flow perturbation (MFP) approach with a carefully chosen initial condition, the evolution of perturbations about the mean flow of an ideally expanded Mach 1.3 jet is obtained and decomposed into its hydrodynamic and acoustic FT components. The acoustic perturbations are further analyzed using Dynamic Mode Decomposition. It is observed that noise radiation signatures exhibited by these acoustic perturbations show compelling agreement with those obtained from full LES. Moreover, the implicit nature of MFP allows the acoustic perturbations to exhibit intermittency without any additional considerations. Furthermore, it is demonstrated that by independently studying the growth rates of vorticity and acoustic perturbations, this approach can be used to guide noise control efforts.