Dissertation Defense: Development of a Semi-Lagrangian Methodology for Jet Aeroacoustics Analysis

Committee

• Professor Datta Gaitonde, Chair (AE)
• Professor Mo Samimy (ME)
• Professor Mei Zhuang (AE)
• Professor Jen-Ping Chen (AE)
• Mark Lewis

Abstract

Over the course of several decades, much has been learned on the nature and evolution of jet noise. Early developments focused on connecting mixing layer turbulence to radiated noise. With the evolving knowledge of turbulence and the discovery of highly organized structures in turbulent shear layers, focus later turned to exploring the connection of large-scale coherent structures to farfield noise signatures, with great success. The leading theory on farfield noise shows that sideline-radiated noise is dominated by high-frequency (small scale) turbulence while aft-propagated noise is intimately tied to the low-frequency, large-scale coherent structures. More importantly, research has shown that intermittency, whereby the bulk of the acoustic energy in the farfield is accounted for in small fractions of the total length of the signal, is a key aspect of jet noise. While these conclusions have been widely accepted, a theory describing a direct mechanism for the induction of these noise components has proven elusive. Experimental and analytic techniques primarily leverage statistical and correlation-based analyses to connect far field pressure signals to jet near-field events. An inevitable result of such analyses is the loss of connection to instantaneous events. The current research targets this loss of temporal information by developing, validating, and testing a novel Lagrangian-based method for the study of jet aeroacoustics. The finite-time Lyapunov exponent (FTLE), a technique developed to identify Lagrangian coherent structures in incompressible flows, is extended for use in compressible flows and applied for the study of wave phenomena in the near-field of a Mach 0.9 jet. It is demonstrated that a dilatational operator is at the heart of the FTLE, providing a direct link between the semi-Lagrangian procedure and acoustics. Temporal integration parameters effectively act as a pseudo-filter, identifying the dominant convective structures in the jet and the emergence and propagation of acoustic radiation connected to said structures in a time-accurate manner. In the jets of interest, FTLE reveals intermittent flow entrainment and ejection events in the vicinity of the shear layer that contribute significantly to farfield-radiated noise, especially in the surrounding area of the potential core collapse. The analysis also resolves the genesis and modulation of wavepackets within the potential core as a direct consequence of vortex interactions and pairing events in the shear layer. These events significantly alter the structure of the wavepackets and are intimately tied to flow entrainment/ejection events throughout the shear layer. Finally, it is demonstrated that attracting and repelling Lagrangian coherent structures, which are representative of stable and unstable manifolds, each have a significant role in establishing the structure of the acoustic near-field. While the stable (attracting) manifolds represent the contributions of large-scale coherent structures, the repelling structures establish a favorable environment for vortex pairing events, subsequently leading to the generation of radiated acoustic energy. In fact, repelling structures are more highly correlated to near-field acoustic signals than the large-scale coherent structures.