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The supersonic jet plumes that exhaust from the engines of tactical aircraft produce intense noise signatures that expose the Navy personnel working on the deck of aircraft carriers to dangerously high levels of noise that often results in hearing damage. Reducing the noise radiated by these supersonic plumes is of interest to the Department of Defense and is the primary motivation of this research. Fundamentally, jet noise reduction is achieved by manipulating the nozzle boundary condition to produce changes in the turbulence development and decrease the acoustic efficiency of coherent structures. The research presented here focuses on a novel jet noise reduction technique involving a centered thermal non-uniformity that alters the base flow by introducing a temperature-driven centerline velocity deficit into a perfectly expanded Mach 1.5 jet. The results indicate $2 pm 0.5$ dB reductions in peak narrowband spectral sound pressure levels upstream of peak directivity directions for the non-uniform jet compared to a thermally uniform baseline, even for static thrust matched conditions. This reduction is hypothesized to be related to perturbations induced by the thermal non-uniformity that convect inside the irrotational core and reduce the correlation length scales of turbulence at locations far downstream. This hypothesis was evaluated by studying the coherent turbulence via its convective hydrodynamic footprint in the near-field. An indirect investigation of the near-field using a far-field-informed model of the wavenumber-frequency spectra indicate a reduction in the energy contained in the tail of the wavenumber spectra amplitude, suggesting a reduction in the size of large scale structures. A direct evaluation of the spatio-temporal behavior of the near-field was performed using temporally resolved schlieren images. Space-time correlations of the frequency-filtered near-field identified high frequency acoustic waves radiated by compactly coherent turbulent structures and low frequency Mach waves produced by large scale instabilities. In the thermally non-uniform case these features and their sources were found to be decorrelated at downstream regions. These results provide strong evidence that a centered thermal non-uniformity reduces the radiated noise compared to a uniform baseline by shortening the correlation length scales of coherent structures in regions far from the nozzle exhaust. / Doctor of Philosophy / A more complete understanding of the intense noise sources present in supersonic jet plumes is of value to both government and industry, and is a necessary step towards optimizing noise reduction techniques. Tactical aircraft that operate on the deck of aircraft carriers expose Navy personnel to dangerously high levels of noise that often results in permanent hearing damage. Supersonic jet noise reduction is also of relevance to the recent efforts to revitalize supersonic air transport over land. For supersonic air transport to become a reality, the noise produced by these future aircraft during takeoff and landing must meet the increasingly stringent community noise requirements. Fundamental jet noise research is needed to guide the design of future engine architectures for these aircraft to ensure their commercial success. The research presented herein examines a novel noise reduction technique that involves a centered thermal non-uniformity consisting of a heated jet plume with a spot of locally cooler, slower moving air concentrated along the centerline of a Mach 1.5 jet. This temperature driven velocity deficit is shown to reduce the radiated noise by up to 2.5 dB at peak frequencies and at angles just outside of the peak directivity direction. The cause of the noise reduction is hypothesized be related to a reduction in the size of the coherent structures that radiate a majority of the noise produced by turbulent jets. This hypothesis is evaluated by examining the 'footprint' of the coherent structures in the ambient field directly outside of the jet shear layer in an area called the near-field. An indirect investigation of the near-field using a far-field informed analytic model suggests a reduction in the size of large scale structures. A direct evaluation of the space time structure of the near-field was performed using temporally resolved schlieren images. Statistical processing of the density gradient provided by the schlieren images revealed acoustically intense structures known as Mach waves and high frequency acoustic waves. These features and their sources, large scale instabilities and compactly coherent turbulence, were found to be decorrelated by the introduction of the thermal non-uniformity. These results provide strong evidence that the centered thermal non-uniformity produces a noise benefit by reducing the size of the turbulent structures.

The noise generated by jet engines represents a significant environmental concern that still needs to be addressed. Accurate and efficient numerical predictions are a key step towards reducing jet noise. The current standard in highidelity prediction of jet noise is large eddy simulation (LES), which resolves the large turbulent scales responsible for the low and medium frequency noise and models the smallest turbulent scales that correspond to the high frequency noise. While LES requires significant computational resources to produce an accurate solution, it fails to resolve the noise in the high frequency range, which cannot be simply ignored. To circumvent this, in this dissertation the Coupled LES-Synthetic Turbulent method (CLST) was developed to model the missing frequencies that relate to un-resolved sub-grid scale fluctuations in the flow. The CLST method combines the resolved, large-scale turbulent fluctuations from very large eddy simulations (VLES) with modeled, small-scale fluctuations from a synthetic turbulence model. The noise field is predicted using a formulation of the linearized Euler equations (LEE), where the acoustic waves are generated by source terms from the combined fluctuations of the VLES and the synthetic fields. This research investigates both a Fourier mode-based stochastic turbulence model and a synthetic eddy-based turbulence model in the CLST framework. The Fourier mode-based method is computationally less expensive than the synthetic eddy method but does not account for sweeping. Sweeping and straining of the synthetic fluctuations by large flow scales from VLES are accounted for in the synthetic eddy method. The two models are tested on a Mach 0.9 jet at a moderately-high Reynolds number and at a low Reynolds number. The CLST method is an efficient and viable alternative to high resolution LES or DNS because it can resolve the high frequency range in the acoustic noise spectrum at a reasonable expense.

Key areas of noise sources are investigated through comparison of eddy convection velocity and turbulence measurements in three-stream nozzles. A Time-Resolved Doppler Global Velocimetry (TR-DGV) Instrument was applied to the Nozzle Acoustic Test Rig (NATR) at NASA's Aero-Acoustic Propulsion Lab (AAPL) to measure convection velocity. Particle image velocimetry (PIV) measurements provided mean velocity and turbulence intensity. Eddy convection velocity results were obtained from the TR-DGV data for three-stream nozzle configurations using a cross-correlation approach. The three-stream cases included an axisymmetric and an asymmetric nozzle configuration. Results of the VT TR-DGV convection velocity were compared to NASA PIV mean and turbulence intensity data. For the axisymmetric case, areas of high convection velocity and turbulence intensity were found to be from 4 to 6 diameters downstream. Comparison of convection velocity between the axisymmetric and offset case show this same region as the greatest reduction in convection velocity due to the offset. These findings suggest this region along the centerline near the end of the potential core is an important area for noise generation with jets and contribute to the noise reductions seen from three stream offset nozzles. An analysis of a one-dimensional wavepacket model was completed to provide understanding of the effect of the various convection velocities seen in the flow. Comparison of a wavepacket with a convection velocity of 0.6Uj to a wavepacket with a convection velocity of 0.8Uj showed that an increase in convection velocity shifts the wavenumber spectrum to higher wavenumbers as expected. It was also observed that for the higher convection velocity wavepacket, higher frequencies are more acoustically efficient, while mid frequencies are the most efficient radiators in the lower convection velocity case. Using mean velocity, turbulence intensity, and convection velocity areas of likely to generate noise are identified and possible fundamental mechanisms responsible for the noise generation are discussed. / Master of Science

Supersonic jet exhaust plumes produce noise in jet engines, which has been a problem in the aerospace field. Researchers are working on ways to reduce this turbulent mixing noise, with little modification to the engine and nozzle. Prior work has shown that total temperature non-uniformity is a noise reduction technique which introduces a stream of cold flow into the heated jet. This method has been shown to cause changes in the exhaust plume and result in a 2±0.5 dB reduction of peak sound pressure levels. The goal of this work is to reveal underlying changes in the spatial-temporal structure of plume instability and turbulence caused by non-uniform total temperature distributions. Studies have demonstrated several methods of jet noise reduction by modifying the turbulent mixing in the exhaust plume. Large-scale turbulent structures have been shown to be the dominant source of noise in heated supersonic jets, especially over long, streamwise distances. Therefore, a large field-of-view measurement is desirable for studying these structures. Time-Resolved Doppler Global Velocimetry (TR-DGV) with a sampling frequency of 50 kHz is used to collect flow velocity data that is resolved in both time and space. The experiments for data collection were performed on a heated supersonic jet at the Virginia Tech Advanced Propulsion and Power Laboratory. A converging-diverging nozzle with a diameter Reynolds number of 850,000 was used to generate a perfectly expanded, heated flow of Mach 1.5 and a nozzle pressure ratio (NPR) of 3.67. The unheated plume was introduced at the center of the nozzle, with a total temperature ratio (TTR) of 2. Comparison of the mean velocity fields shows that the introduction of the cooler temperature flow in the thermally non-uniform case results in a velocity deficit of about 10% compared to the thermally uniform case. The method of spectral proper orthogonal decomposition (SPOD) was used to reveal the large-scale, coherent noise producing mechanisms. SPOD results indicate that the thermally non-uniform case showed a decrease in turbulent kinetic energy compared to the uniform case at all frequencies. Coherent fluctuations start developing further upstream in the thermally non-uniform case. The addition of the unheated plume results in a disruption in the propagation of the Mach waves from the shear layer into the ambient. The results indicate that the total temperature non-uniformity results in a modified exhaust plume and mean flow distribution at the nozzle exit, compared to that of a thermally uniform flow, which past studies have indicated is a method to reduce jet noise. / Master of Science / Supersonic jet exhaust plumes produce noise in jet engines, which has been a problem in the aerospace field. Researchers are working on ways to reduce this turbulent mixing noise, with little modification to the engine and nozzle. Traditionally, nozzles produce a single stream of uniform temperature flow. This work identifies a method of reducing jet noise, known as thermal non-uniformity. A stream of cold flow is introduced at the center of the nozzle. Applying this method to jet engines can result in quieter aircraft. Large-scale turbulent structures are the dominant noise producing source in supersonic free jets. To further understand the relationship between coherent structures and acoustic jet noise, spectral analysis is used to educe these structures from the flow. This study uses velocity data collected using Time-Resolved Doppler Global Velocimetry (TR-DGV). The study compares the results of a thermally uniform and a thermally non-uniform heated supersonic jet of Mach 1.5. The goal of this study is to determine the effects of thermal non-uniformity on large-scale coherent structures using a modal decomposition analysis known as spectral proper orthogonal decomposition (SPOD). The results from this study show that the thermally non-uniform cases contained less turbulent kinetic energy compared to the thermally uniform cases. Coherent fluctuations start developing further upstream in the thermally non-uniform case. The addition of the unheated plume results in a disruption in the propagation of the Mach waves from the shear layer into the ambient. The results indicate that the total temperature non-uniformity results in a modified exhaust plume and mean flow distribution at the nozzle exit, compared to that of a thermally uniform flow, which past studies have indicated is a method to reduce jet noise.

Cette étude porte sur le développement d’une méthodologie de calcul pour évaluer les effets d’installation. Ce phénomène, qui représente le bruit d’interaction entre un jet double flux et un profil, constitue un problème modèle pour l’étude du bruit de jet installé en aéronautique. L’écoulement moyen est déterminé à partir de la résolution des équations de Navier-Stokes moyennées et du modèle de turbulence k - ω BSL de Menter. Lorsque le jet est isolé, il est possible ensuite d’utiliser le modèle de Tam & Auriault. Dans des configurations plus complexes, comme l’interaction jet-voilure considérée ici, la formulation statistique des termes sources de ce modèle est retenue à la place du modèle complet. Un propagateur acoustique, basé sur les équations d’Euler linéarisées, est utilisé pour compléter la modélisation. Dans un premier temps, une tuyère double flux avec plug est simulée et les résultats obtenus sont comparés aux données d’essais dans le but de valider la simulation numérique. De bons résultats sont obtenus. La même étude est ensuite réalisée sur une configuration installée, prenant en compte la même tuyère installée sous un profil. La simplicité de la configuration se justifie par le fait qu’il s’agit de développer une méthodologie de calcul permettant d’avoir un effet qualitatif de l’installation sur le développement du jet. En comparant les résultats aérodynamiques avec ceux obtenus numériquement pour la tuyère isolée, l’impact du profil sur le jet est mis en évidence au travers de la déviation du jet vers le profil et d’un déficit de l’énergie cinétique turbulente. La dernière étape consiste à caractériser l’impact de ces modifications sur les sources de bruit. Pour cela, le logiciel de propagation industriel Actran DGM est utilisé. Les sources calculées statistiquement par le modèle de Tam & Auriault sont introduites dans les équations d’Euler linéarisées. En première approche pour mettre en œuvre la méthodologie, les sources de bruit de jet sont assimilées à une distribution de monopoles équivalents. Cette modélisation permet de mettre en évidence les effets de diffraction et de masquage de l’onde causés par le profil. Le rayonnement en champ lointain est quant à lui obtenu avec la méthode intégrale de Ffowcs-Williams & Hawkings. / Excess noise induced by installation effects is numerically investigated in this work. Interaction noise between a turbofan jet engine and an airfoil is a simplified but relevant problem to address installed jet noise in aeronautics. The mean flow is determined from Reynolds-Averaged Navier-Stokes equations, using Menter k - ω BSL turbulence model. With jet only, fine scale turbulence model of Tam & Auriault can be used directly for jet noise prediction. To assess jet-wing interaction in industrial configuration, the statistical formulation of the source terms is retained from this stochastic model, and the acoustic propagation is performed using linearised Euler equations. A dual stream jet is firstly computed and the results are compared to available data in order to validate the numerical simulation. Satisfactory results are obtained. The same study is then performed on an installed configuration, taking into account the same nozzle installed under a profile. This first configuration is is used to develop a methodology of calculation by having a qualitative effect of the installation on the jet behaviour. By comparing the aerodynamic results with those obtained numerically for the isolated nozzle, the impact of the jet profile is highlighted through the jet deflection and a modification of the turbulent kinetic energy field. The last step is to characterize the impact of these modifications on the noise sources. For this, the industrial propagation software Actran DGM is used. The statistical formulation of the source calculated by Tam & Auriault model is introduced into the linearised Euler equations. As a first step, the jet sources are defined as a distribution of equivalent monopoles. This modeling allows highlighting the effects of diffraction and the masking effects caused by the profile. The radiation in the far field is obtained with the integral method of Ffowcs-Williams & Hawkings.

A scaling model based on an effective Gol'dberg number is proposed for predicting the presence of cumulative nonlinear distortions in the acoustic waveforms produced by high-speed jets. Two acoustic length scales, the shock formation distance and the absorption length are expressed in terms of jet exit parameters. This approach allows one to compute the degree of cumulative nonlinear distortion in a full-scale scenario, from laboratory-scale observations, or vice versa. Surveys of the acoustic pressure waveforms emitted by a laboratory-scale, shock-free and unheated Mach 3 jet are used to support the findings of the model. These acoustic waveforms are acquired on a planar grid in an acoustically treated and range-restricted environment. Various statistical metrics are employed to examine the degree of local and cumulative nonlinearity in the measured waveforms and their temporal derivatives. This includes skewness, kurtosis, the number of zero crossings in the waveform, a wave steepening factor, the Morfey-Howell nonlinearity indicator and an application of the generalized Burgers equation. It is advocated that in order for the Morfey-Howell indicator to be used as an investigative tool for the presence of cumulative nonlinear waveform distortion, that it be applied as a multi-point indicator. Based on findings of the model and the spatial topography of the metrics, it is concluded that cumulative nonlinear steepening effects are absent in the current data set. This implies that acoustic shock-structures in the waveforms are generated by local mechanisms in, or in close vicinity to, the jet's hydrodynamic region. Furthermore, these shock-structures induce the crackle noise component. The research aims to quantify crackle in a temporal and spectral fashion, and is motivated by the fact that (1) it is perceived as the most annoying component of jet noise, (2) no unique measures of crackle exist, and (3) significant reductions in jet noise will be achieved when crackle can be controlled. A unique detection algorithm is introduced which isolates the shock-structures in the temporal waveform that are responsible for crackle. Ensemble-averages of the identified waveform sections are employed to gain an in-depth understanding of the crackling structures. Moreover, PDF's of the temporal intermittence of these shocks reveal modal trends and show evidence that crackling shock-structures are present in groups of multiple shocks. A spectral measure of crackle is considered by using wavelet-based time-frequency analyses. The increase in sound energy is computed by considering the global pressure spectra of the waveforms and the ones that represent the spectral behavior during instances of crackle. This energy-based metric is postulated to be an appropriate metric for the level of crackle. / text

This thesis studies the prediction and reduction of installed jet noise, combining both analytical and experimental techniques. In the prediction part, it starts with formulating a low-order but robust isolated jet noise prediction model, based on which a remarkably fast code with pre-informed data is developed. A semi-empirical low-order model is then developed to predict installed jet noise. The model consists of two parts, the first of which is based on the Lighthill's acoustic analogy theory. The second part embraces Amiet's approach to model the sound due to the scattering of jet instability waves. It is shown that the significant low-frequency noise enhancement observed in installed jet experiments is due to the scattering of near-field instability waves. The trailing edge scattering model can successfully predict noise spectra at all distinct angles. The quadrupole-induced high-frequency sound is either efficiently shielded at $90^\circ$ to the jet axis on the shielded side or enhanced by around $3$ dB at $90^\circ$ on the reflected side. But these effects gradually diminish as the observer angle decreases. The high-frequency spectra can be robustly predicted at large observer angles while deviation occurs at low observer angles due to jet refraction effects. An experimental study on installed jet noise is then conducted. The effects of plate positions and Mach numbers are studied. Excellent agreement between the experimental results and model predictions is achieved at low frequencies for all plate positions and Mach numbers tested. At high frequencies, the noise spectra at $90^\circ$ on the reflected side can also be correctly predicted. At lower observer angles, deviations occur due to jet refraction effects. In the noise reduction part, an experimental study is firstly carried out to study the effects of lobed nozzles on installed jet noise at constant flow rates. It is found that lobed nozzles do not noticeably change the installed jet noise spectra at low frequencies. However, they do result in a slight noise reduction at high frequencies. To understand why lobed nozzles hardly change low-frequency installed jet noise, an analytical stability analysis for lobed vortex sheets is performed. The results show that lobed jets change both the convection velocity and the temporal growth rate of instability waves. The changes become more pronounced as the number of lobes $N$ and the penetration ratio $\epsilon$ increase. A second set of experiments is carried out to explore the possibility of reducing installed jet noise by using two pylons. The results show that even in the most conservative case installed jet noise is reduced by around $2\sim3$ dB at low frequencies. It is concluded that using two pylons to reduce installed jet noise has significant practical potential.

Cette thèse est consacrée au développement de méthodes numériques pour la prévision du bruit des jets par la simulation des grandes échelles (LES). L’approche LES suivie s’appuie sur l’utilisation de schémas de discrétisation spatiale implicites d’ordre élevé peu dissipatifs et peu dispersifs en volumes finis. Elle permet de calculer directement les sources acoustiques dans les écoulements turbulents et de propager les ondes sonores avec précision. Deux méthodes numériques sont développées en vue de faciliter la réalisation des simulations. La première méthode est la mise en œuvre d’une modélisation de paroi pour s’affranchir des contraintes liées à la résolution des couches limites qui se développent près des parois. Un modèle de paroi analytique est couplé aux schémas d’ordre élevé de discrétisation spatiale. Une discrétisation spatiale particulière, s’appuyant sur la reconstruction de cellules fictives, est proposée près des parois. Sa performance est évaluée en simulant un écoulement turbulent de canal à un nombre de Mach de 0.2 et un nombre de Reynolds de frottement de 2000, puis un écoulement de jet simple subsonique et isotherme à un nombre de Mach de 0.6 et un nombre de Reynolds basé sur le diamètre du jet de 570 000. Les caractéristiques aérodynamiques et acoustiques des écoulements sont comparées avec succès aux résultats des simulations numériques directes et aux mesures expérimentales de la littérature. La seconde méthode porte sur le développement d’un traitement aux interfaces des maillages non conformes. Ces maillages présentent des discontinuités aux interfaces entre les blocs ce qui permet l’utilisation de maillages plus simples pour les calculs. Le traitement proposé assure la compatibilité entre les schémas de discrétisation spatiale et les maillages non conformes, tout en répondant aux exigences de précision imposées par les simulations aéroacoustiques. Ce traitement s’appuie sur la réalisation d’interpolations de type meshless. Sa validité est examinée en simulant la convection d’un tourbillon et le développement d’une couche de mélange en 2-D. Les résultats obtenus montrent que le traitement proposé ne génère pas d’oscillations parasites d’amplitude significative et ne perturbe pas le développement de l’écoulement au voisinage des raccords de bloc. / This thesis is devoted to the development of numerical methods to predict jet noise using Large-Eddy Simulation (LES). The LES approach used in this work relies on high-order low-dissipation and low-dispersion implicit finite-volume schemes for spatial discretization. It allows the direct calculation of acoustic sources in turbulent flows and the propagation of sound waves with accuracy. Two numerical methods are developed in order to facilitate the LES computations. The first method focuses on using wall modeling in the near-wall regions instead of resolving the boundary layers. An analytical wall model is combined with the high-order schemes for spatial discretization. A specific spatial discretization, based on a ghost cell reconstruction, is proposed near the walls. Its performance is assessed by performing the LES of a turbulent channel flow at a Mach number of 0.2 and a friction Reynolds number of 2,000, and the LES of an isothermal subsonic round jet at a Mach number of 0.6 and a Reynolds number based on the jet diameter of 570,000. The aerodynamic and the acoustic properties of the flows are in agreement with the direct numerical simulation data and the experimental results of the literature. The second method deals with the development of a treatment at the non-conforming grid interfaces. Non-conforming grids involve discontinuous block interfaces, allowing the use of simplified meshes for the computations. The proposed treatment ensures the compatibility between the spatial discretization schemes and non-conforming meshes. Particular attention is paid to meet the accuracy requirements imposed in computational aeroacoustics. This treatment relies on meshless interpolations. Its validity is evaluated by simulating a vortex convection and a mixing layer development in two dimensions. The results show that the treatment does not produce significant spurious numerical waves nor disturb the flow development near the grid interfaces.

Crackle is a perceptual feature of supersonic jet noise that is related to the presence of acoustic shocks. The skewness of the time-derivative of the pressure waveform, or derivative skewness, is used as a metric indicative of crackle perception. The three main objectives of this work are: 1) Determine the potential spatial origin of crackle-related events in the near field of a high-performance military aircraft via an event-based beamforming method. 2) Investigate the potential for nonlinear, irregular shock reflections occurring along the near-field ground array and their implications on derivative skewness. 3) Relate the near-field, crackle-related events to far-field crackle perception by comparing nonlinearly propagated waveforms with measured far-field data. The event-based beamforming method used to determine source and far-field relationship of shock-like events utilizes the cross correlation between adjacent microphone waveform segments to determine the angle of propagation for an ensemble of crackle-related events within the waveform. The angle of propagation is traced towards the source for each event to find its apparent origin along the jet lipline. Beamforming results indicate that crackle-related events appear to originate anywhere from 2 to 14.5 m downstream along the jet lipline, with distributions that shift downstream and broaden with increasing engine power. The shock reflection classification method builds on the event-based beamforming method to calculate angle of incidence relative to the ground for an ensemble of shock events. The combination of angles of incidence and the measured shock strengths of the events reveal that irregular reflections are likely to occur over the majority of the array, which likely elevates the derivative skewness values due to steeper shocks with greater peak-to-peak pressures relative to off-ground measurements. Near-field, crackle-related events are extrapolated to the far field using a nonlinear propagation model to determine their prevalence in the far field. Cross-correlation coefficients of waveform segments centered about the propagated events indicates that for farther aft angles, near-field events are more related to far-field measurements. Waveform observations show that shock-like events in the near field that are more spiked in nature tend not propagate into the far field. However, near-field, large-derivative events with broader, high-pressure peaks nonlinearly steepen and form shocks in the far field that are likely contribute to crackle perception.