Aeroacoustic noise prediction and the dynamics of shear layers and jets using the nonlinear parabolized stability equations

The study of jet noise has long remained an important problem due to the challenges of accurately predicting aeroacoustic noise, and the practical consequences of environmental noise pollution. Previous investigations into jet noise have relied on large scale Direct Numerical Simulations (DNS) or Large Eddy Simulations (LES) to resolve the relevant scales and features of the problem, but their relatively high computational cost is prohibitive. In this study, we present a more efficient method to predict aeroacoustic radiation based on the Parabolized Stability Equations (PSE), which seek to represent flow disturbances as a set of slowly evolving instability waves. As applied in our work, the PSE is used to compute the near field hydrodynamics and noise sources in the problem, which can then be coupled to an acoustic analogy approach to predict the far field noise. For slowly developing flows where the PSE approximations are valid, we find that using the hybrid PSE-acoustic analogy method results in predictions with accuracy similar to DNS, but with an order of magnitude improvement in speed.; This method is first applied to subsonic and supersonic compressible two-dimensional shear layers, both with and without heating effects. For supersonic shear layers we find the PSE method itself captures the Mach wave radiation in the far-field, as well as the large scale phenomena occurring inside the shear layer. In the computations of the subsonic cases, we observe that the PSE solution captures the near field hydrodynamics and underpredicts the acoustic radiation. However, when combined with Lilley's acoustic analogy, reasonable agreement is found with DNS calculations. When this method is applied to supersonic and subsonic jet flows, similar results are also obtained.; In the last portion of this study, we present an extension to the PSE that is based on the method of multiple scales. We show how the multiple scale PSE method can be used to handle more general inlet forcing schemes and capture additional frequencies not present in the traditional nonlinear PSE approach. This extended method is also applied to supersonic and subsonic shear layers, and compared to results from DNS calculations.