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

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.

In the field of supersonic jet noise, measurements of full-scale afterburning jet engines are infrequent and provide unique opportunities to better understand jet noise phenomena. This thesis represents a phenomenological jet noise analysis using far-field noise data collected from a T-7A-installed GE F404-103 turbofan engine. One issue with the far-field acoustic data from the T-7A was the effects of ground reflections present in the spectra generated from the measured waveforms. A previously developed ground reflection model was implemented into the data to account for this interference. This work represents the first time this model has been implemented in data collected from a full-scale aircraft. Spectra and spatiospectral maps are used to show that, while imperfect, this model represents a step in the right direction for accounting for ground reflections. From the ground reflection-corrected data, sound power values were calculated at varying engine powers. These values were compared against mechanical power values calculated using provided engine parameters at the corresponding engine conditions. It is shown that the observed increase in sound power with mechanical power at supersonic engine conditions follows classical jet noise theory, while the increase between transonic engine conditions is much greater than predicted by classical jet noise theory. This divergence is currently unexplained. Finally, far-field noise directivity measured from the T-7A is connected back to both physics-based and empirically derived definitions of the convective Mach number, a dimensionless parameter used to describe the velocities of coherent structures in the turbulent mixing layer of a jet. For supersonic jets, where Mach wave radiation is the dominant noise source, the convective Mach number should be useful for predicting peak directivity angles. The evaluated definitions show that the convective Mach number associated with Kelvin-Helmholtz instability waves best predicts the peak directivity of the T-7A.

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Rapid mixing and spreading of supersonic jets are two important characteristics in supersonic ejectors, noise reduction in jets and fuel mixing in supersonic combustion. It helps in changing the acoustic and thermal signature in supersonic exhaust. The supersonic nozzles in most cases result in compressible mixing layers. The subsonic nozzles form incompressible mixing layers but at high Mach numbers even they form compressible mixing layers. Compressible mixing layers have been found to have much lower mixing and spreading rates than incompressible mixing layer Birch & Eggers (1972). In order to enhance the spreading and mixing of mixing layers from supersonic nozzles various active and passive methods have been deviced. Active methods include fluid injection, fluid lobes and plasma actuation. Passive methods are mostly based on modifying the nozzle geometry such that the fluid expansion is ideal or the shock cell is broken. Many nozzles with exotic shapes have been developed to obtain mixing enhancements in supersonic jets Gutmark et al. (1995). To achieve enhanced mixing an innovative nozzle named as the Elliptic Sharp Tipped Shallow (ESTS) lobed nozzle has been developed in L.H.S.R., I.I.Sc., India Rao & Jagadeesh (2014). This nozzle has a unique geometry involving elliptical lobes and sharp tips. These lobes are generated using a simple manufacturing process from the throat to the exit. This lobed and sharp tipped structure introduces stream wise vortices and azimuthal velocity components which must help in enhanced mixing and spreading. The ESTS lobed nozzle has shown mixing enhancement with 4 lobes. The spreading rate was found to be double of the reference conical nozzle. This thesis is motivated by the need to investigate the flow physics involved in the ESTS lobed nozzle. The effect of varying the number of lobes and the design Mach number of the nozzle on the mixing and spreading characteristics will be further discussed. Visualisation studies have been performed. The schlieren and planar LASER Mie scattering techniques have been used to probe the flow. Instantaneous images were taken at axial planes with the reference conical and ESTS nozzles with three, four, five and six lobes. The nozzles are for design Mach number 2.0 and 2.5. The stagnation chamber pressure was maintained to obtain over expanded, ideally expanded and under expanded flows. LASER scattering was obtained by seeding the flow with water to observe the behaviour of the primary flow. The condensation of moisture due to the cold primary flow mixing with the ambient air was exploited to scatter laser and observe the flow structures in the mixing layer. A comparison of the images of the reference conical nozzle and the ESTS lobed nozzles shows changes in the mixing layers due to the ESTS lobed nozzles. The image of the reference conical nozzle shows a distinct potential core and mixing layers all along the length of the image. For the ESTS lobed nozzles this distinction becomes unclear shortly after the nozzle exit. Thus mixing of the primary flow and ambient air is seen to be enhanced in the case of all the ESTS lobed nozzles. The flow in the case of the ESTS lobed nozzles if found to be highly non axis symmetric. The starting process of the nozzles has been visualised using time resolved schlieren. Image processing was performed on the nozzles to quantify the spread rate. The shock structure of the nozzles has been studied and found to be modified due to the lobed geometry. The level of convolution of the mixing layer due to the lobed structure has been studied using fractal analysis. The four lobed nozzle was found to have the highest spread rate and th most convoluted shear layer. Hence this nozzle was further studied using background oriented schlieren and particle image velocimetry to quantify the flow field. These experimental results have been compared with CFD simulations using the commercial software CFX5. The computations and experiments don’t match accurately but the trends match. This allows for simulations to be used as a good first approximation. The acoustic properties of a jet are dependent on the flow structure behaviour. The ESTS lobes have been found to change the flow structure. Hence the ESTS lobed nozzle was predicted to change the acoustic signature of the flow. The acoustic measurements of the flow were carried out at National Aerospace Laboratories, Bengaluru. The screech of the overexpanded flow was seen to be eliminated and the overall sound levels were found to have been reduced in all cases. Thus the lobed nozzle was found to have acoustic benefits over the reference conical nozzle. Thus the ESTS lobed nozzle has been studied and compared with the conical nozzle using several methods. The changes due to the lobed structure have been studied quantitatively. Future studies would focus on the change in thrust due to the lobed structure. Also new geometries have been proposed inspired by the current design but with possible thrust benefits or manufacturing benefits.

Lors d’un lancement spatial, le bruit des jets supersoniques chauds, générés par les moteurs-fusées au décollage et en interaction avec le pas de tir, est dommageable pour le lanceur et en particulier sa charge utile. Par conséquent, les acteurs du spatial cherchent à renforcer leur compréhension et leur maîtrise de cette ambiance acoustique, entre autres grâce à des méthodes et outils numériques. Toutefois, ils ne disposent pas d’une approche numérique globale capable de prendre en compte simultanément la génération fidèle du bruit, la propagation acoustique non-linéaire, les effets d’installation complexes et les géométries réalistes, pourtant inhérents aux applications spatiales. Dans cette optique, cette étude consiste à mettre en place et valider une méthodologie de simulation numérique par couplage fort Navier-Stokes − Euler, puis à l’appliquer à des cas réalistes de bruit de jet supersonique. L’objectif est d’affiner les capacités de prévision et de contribuer à la compréhension des mécanismes de génération de bruit dans de tels jets. Le solveur Navier-Stokes repose sur une méthode LES sur maillage non-structuré et le solveur acoustique sur une méthode de Galerkine discontinue d’ordre élevé sur maillage non-structuré. La méthodologie est tout d’abord évaluée sur des cas académiques visant à valider la simulation par couplage fort. Après des calculs préliminaires, la méthodologie est appliquée à la simulation du bruit d’un jet libre supersonique à Mach 3.1. Une méthode de déclenchement géométrique de la turbulence est implémentée sous la forme d’une marche à la paroi de la tuyère. La simulation aboutit à des estimations du bruit très proches des mesures réalisées au banc MARTEL et met en évidence des effets non-linéaires significatifs ainsi qu’un mécanisme singulier de rayonnement des ondes de Mach. Dans une démarche de progression vers des cas toujours plus réalistes, l’ensemble de l’approche numérique est finalement adaptée avec succès à la simulation du bruit d’un jet en présence d’un carneau. À terme, elle pourra être étendue à des configurations multi-jets réactifs, avec injection d’eau, voire à l’échelle 1. / During a space launch, the noise from hot supersonic jets, generated by rocket engines at liftoff and interacting with the launch pad, is harmful to the launcher and in particular its payload. Consequently, space actors are seeking to strengthen their understanding and control of this acoustic environment through numerical methods and tools, among the others. However, they do not dispose of a comprehensive numerical strategy that can simultaneously take into account accurate noise generation, nonlinear acoustic propagation, complex installation effects and realistic geometries, which are inherent to space applications. For this purpose, the present study consists in setting up and validating a numerical simulation methodology using a Navier-Stokes − Euler two-way coupling approach, then applying it to realistic cases of supersonic jet noise in order to improve prediction capabilities and contribute to the understanding of the noise generation mechanisms in such jets. The Navier-Stokes solver is based on an LES method on unstructured mesh and the acoustic solver on a high-order discontinuous Galerkin method on unstructured mesh. The methodology is first assessed on academic cases to validate the use of the two-way coupling. After preliminary computations, the methodology is applied to the simulation of the noise from a supersonic free jet at Mach 3.1. A geometric turbulence tripping method is implemented via a step at the nozzle wall. The computation leads to noise predictions very close to the experimental measurements performed at the MARTEL test bench and highlights significant nonlinear effects as well as a quite particular Mach waves radiation mechanism. Targeting even more realistic cases, the entire numerical approach is finally successfully adapted to the simulation of the noise from a supersonic jet configuration including a flame trench. In the future, it may be extended to configurations with clustered reactive jets, water injection devices or even at full scale.