Author: Unnikrishnan Sasidharan Nair

Publisher:

Published: 2017

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The exact mechanism by which turbulent fluctuations in jets are converted into acoustic energy remains unexplained. The current work aims to improve our understanding of this problem by localizing acoustic sources and identifying its causal dynamics. We use Large-Eddy Simulations of a Mach 1.3 turbulent cold jet for this purpose. The localization question is resolved by using a novel technique, termed Synchronous Large-Eddy Simulations (SLES), that tracks the non-linear evolution of small perturbations from any region (window) in a time-varying base flow. This provides superior insights into the generation of intermittency and directivity compared to traditional approaches that use linear stability analyses based on steady basic states or backward correlations between different regions of the flow. In SLES, two simulations are performed in a lock-step manner. At each step, native fluctuations from a desired spatial window in the first (or baseline simulation) are scaled to small values and then injected into the second (or twin simulation) to provide a forcing in the targeted region. At subsequent times, the difference between the two simulations provides a snapshot of the evolution of the perturbation field associated with the continuous forcing in the chosen spatial window. The perturbation field, which is equivalent to the solution of the forced Navier-Stokes equations linearized about the time-evolving base flow, is then statistically analyzed to identify its modulation by the turbulent region of the jet. Results are distilled by examining forcing at lipline and centerline locations in detail. The end of the potential core is found to be a sensitive zone where perturbations are amplified and lead to secondary sources. Perturbations within the shear layer on the other hand, are initially channeled toward the core and undergo higher amplification compared to those originating from the centerline, before propagating outward. Statistical analyses quantify intermittent events which have a major role in creating the nearfield sound signature and yield polar variation of the most significant frequency band. The flowfield is decomposed into its acoustic, hydrodynamic and thermal modes (which are referred to as the Fluid-Thermodynamic (FT) modes) using the Momentum Potential Theory to identify the acoustic sources and extract the propagated field of the jet. The hydrodynamic mode highlights the shear layer roll up and turbulent mixing, while the acoustic and thermal modes exhibit a wavepacket nature in the core. The acoustic wavepacket develops into the nearfield radiation pattern of the jet, with spatio-temporal amplifications in the core due to the presence of vorticity resulting in nearfield intermittent events. The acoustic and hydrodynamic modes closely follow the theoretical decay rates and the former possess the features of experimentally observed model sound spectra along the downstream and sideline polar angles. Inter-modal energy transfers in the non-linear flow are analyzed using the transport equation for the universal acoustic variable, Total Fluctuating Enthalpy (TFE). Production terms of TFE identify intruding vortices in the potential core as the principal physical mechanism by which intermittent acoustic sources are generated in the jet. The acoustic wavepacket and its nearfield fluctuations play a central role in transporting TFE utward from the core, resulting in the near and farfield sound signature of the jet. The present work provides unique insights into time-accurate linear response of a turbulent jet, and quantifies the relative prominence of various core locations in generating the nearfield acoustic signature. The evolution of the linear perturbation field highlights the modulation of random turbulent fluctuations into spatio-temporally persistent intermittent events. While the intermediate frequencies in the jet propagate in the upstream direction, the highest and lowest frequency-bands prevail in the sideline and downstream directions respectively. The FT mode decomposition elucidates the energy transfer mechanisms in the jet. It provides a phenomenological model to explain the amplification of the acoustic mode, leading to intermittent sound events in the nearfield as well as generation of acoustic sources. The FT modes also quantify the net energy flux scattered and transmitted out of the jet, delineating the stochastic turbulence from a relatively orderly acoustic transport.