A time-domain linear method for jet noise prediction and control trend analysis

Large-scale turbulent structures in the form of coherent wavepackets play a significant role in the generation of prominent shallow-angle noise radiation of jets. Economical prediction tools often model these wavepackets in the frequency-domain using stability modes of the mean flow. Simplifying choices, such as parabolized equations and azimuthal decomposition, provide efficient prediction methods but can impose constraints on rate of streamwise variation of the mean state or geometric complexity, thus limiting the range of application to mostly perfectly-expanded circular jets. The current investigation develops a time-domain linearized Navier-Stokes-based approach predicated on the mean basic state with two goals: (i) to obtain the radiated shallow-angle noise field, including that from imperfectly-expanded jets containing shock trains, and (ii) to estimate noise control trends with frequency imposed by a notional actuator. Implicit linearization about the mean flow is achieved through a general method that repurposes native non-linear Navier-Stokes code capabilities; this avoids any additional constraints on nozzle geometry or flow features such as shocks. A crucial step is to sift the linearized perturbations to isolate the acoustic component according to Doak's momentum potential theory (MPT). Comparisons with well-validated Large Eddy Simulation (LES) databases in different spectral ranges show accurate model predictions for super-radiative shallow angle noise, including for hot jets from military-style nozzles. Transient pulse response enabled by the time-domain nature of the procedure also facilitates estimation of control frequency effectiveness. For this, the transient perturbation growth characteristics are segregated into the distinct effects of the excitation on vorticity relative to the MPT acoustic variable. For a jet with extensive published experimental data using plasma actuators, it is shown that the method correctly predicts noise amplification at lower frequencies and reduction at higher values, at the observed crossover location. Considerations on the costs associated with the approach, which exploits linearity to extract results at multiple frequencies with each simulation, are outlined.