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.

Particle-laden supersonic jets impinging on a flat surface are of interest to cold gas-dynamic spray technology. Solid particles are propelled to a high velocity through a convergent-divergent nozzle, and upon impact on a substrate surface, they undergo plastic deformation and adhere to the surface. For given particle and substrate materials, particle velocity and temperature at impact are the primary parameters that determine the success of particle deposition. Depending on the particle diameter and density, interactions of particles with the turbulent supersonic jet and the compressed gas region near the substrate surface can have significant effects on particle velocity and temperature. Unlike previous numerical simulations of cold spray, in this dissertation we track solid particles in the instantaneous turbulent fluctuating flow field from the nozzle exit to the substrate surface. Thus, we capture the effects of particle-turbulence interactions on particle velocity and temperature at impact. The flow field is obtained by direct numerical simulations of a supersonic rectangular particle-laden air jet impinging on a flat substrate. An Eulerian-Lagrangian approach with two-way coupling between solid particles and gas phase is used. Unsteady three-dimensional Navier-Stokes equations are solved using a six-order compact scheme with a tenth-order compact filter combined with WENO dissipation, almost everywhere except in a region around the bow shock where a fifth-order WENO scheme is used. A fourth-order low-storage Runge-Kutta scheme is used for time integration of gas dynamics equations simultaneously with solid particles equations of motion and energy equation for particle temperature. Particles are tracked in instantaneous turbulent jet flow rather than in a mean flow that is commonly used in the previous studies. Supersonic jets for air and helium at Mach number 2.5 and 2.8, respectively, are simulated for two cases for the standoff distance between the nozzle exit and the substrate. Flow structures, mean flow properties, particles impact velocity and particles deposition efficiency on a flat substrate surface are presented. Different grid resolutions are tested using 2, 4 and 8 million points. Good agreement between DNS results and experimental data is obtained for the pressure distribution on the wall and the maximum Mach number profile in wall jet. Probability density functions for particle velocity and temperature at impact are presented. Deposition efficiency for aluminum and copper particles of diameter in the range 1 micron to 40 microns is calculated. Instantaneous flow fields for the two standoff distances considered exhibit different flow characteristics. For large standoff distance, the jet is unsteady and flaps both for air (Mach number 2.5) and for helium (Mach number 2.8), in the direction normal to the large cross-section of the jet. Linear stability analysis of the mean jet profile validates the oscillation frequency observed in the present numerical study. Available experimental data also validate oscillation frequency. After impingement, the flow re-expands from the compressed gas region into a supersonic wall jet. The pressure on the wall in the expansion region is locally lower than ambient pressure. Strong bow shock only occurs for small standoff distance. For large standoff distance multiple/oblique shocks are observed due to the flapping of the jet. The one-dimensional model based on isentropic flow calculations produces reliable results for particle velocity and temperature. It is found that the low efficiency in the low-pressure cold spray (LPCS) compared to high-pressure cold spray (HPCS) is mainly due to low temperature of the particles at the exit of the nozzle. Three-dimensional simulations show that small particles are readily influenced by the large-scale turbulent structures developing on jet shear layers, and they drift sideways. However, large particles are less influenced by the turbulent flow. Particles velocity and temperature are affected by the compressed gas layer and remain fairly constant in the jet region. With a small increase in the particles initial temperature, the deposition efficiency in LPCS can be maximized. There is an optimum particle diameter range for maximum deposition efficiency. / Ph. D.

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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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Im Rahmen dieser Arbeit wurden verschiedene Teilchendetektoren zur Verwendung in einem gepulsten Überschallmolekularstrahlexperiment entworfen und hergestellt. In den hier durchgeführten Experimenten kollidiert ein Molekularstrahl mit einer sensitiven Detektoroberfläche, nämlich einer Polyvinylidenfluorid(PVDF)-Folie. Da PVDF sowohl pyroelektrisch wie auch piezoelektrisch ist, entstehen durch die Kollision der Molekularstrahlteilchen auf der Folie Oberflächenladungen. Vorteile von PVDF-Detektoren sind die hohe Effizient der Detektion, die Detektion von neutralen Atomen und Molekülen (eine Ionisierung der zu detektierenden Teilchen ist nicht notwendig), ein einfaches und leicht anzupassendes Detektordesign und außerdem eine schnelle Antwortzeit (im Mikrosekundenbereich). Da nur Ladungen im Bereich von wenigen Pikocoulomb generiert werden, sind verschiedene Verstärker getestet worden. Zur Analyse und Beschreibung des detektierten Signals wird der piezoelektrische Anteil durch ein Materialmodell in Verbindung mit einem schwingenden System, nämlich der erzwungenen Schwingung einer gedämpften Kreismembran, beschrieben. Der pyroelektrische Anteil wird durch einen Energieaustausch beschrieben. Durch die Ausnutzung des pyroelektrischen sowie des piezoelektrischen Effektes können zusätzliche wichtige Informationen wie zum Beispiel der Restitutionskoeffizient oder der Energieakkommodationkoeffizient experimentell erhalten werden. Zur Demonstration der Anwendungsmöglichkeiten sind Detektoren in verschiedenen Größen zur Messung von unterschiedlichen Strahleigenschaften verwendet worden. Untersucht wurde dabei die Strahlgeschwindigkeit von verschiedenen Edelgasen über einen großen Stagnationsdruck- und Stagnationstemperaturbereich. Außerdem wurden Strahlprofile zur Bestimmung der Strahldichte gemessen und mathematisch beschrieben. Zusätzlich wird eine Methode zur Bestimmung der Strahltemperatur mit Hilfe der Strahldichte und der Strahlgeschwindigkeit vorgestellt. / In this study, different particle detectors with a foil of polyvinylidene difluoride have been designed and built for use in a pulsed supersonic molecular jet experiment. Here, the molecular jet collides with the sensitive detector area and generates a charge. This generated charge is caused by the piezo- and the pyroelectric effect. Advantages of polyvinylidene difluoride detectors are a high detection efficiency, the detection of neutral atoms or molecules --- no ionization is required, a simple setup which can be easily incorporated in an existing experiment, an easy adjustment of the detector design because the shape and size can be changed easily, and a fast response-time in the sub-microsecond regime. Because the amount of charges generated is in the order of some picocoulomb, different amplifiers are used. In this analysis of the detected signal, the piezoelectric contribution is defined by the constitutive equations of piezoelectricity, which are used in combination with the concept of a driven damped circular membrane in order to obtain an analytic solution. The pyroelectric contribution is described via the exchanged energy. Because both the piezo- and the pyroelectric effects can be exploited, valuable additional information such as the coefficient of energy accommodation or the coefficient of restitution can be determined experimentally. In order to demonstrate the application possibilities of polyvinylidene difluoride detectors, detectors of different sizes are used as a local jet probe to determine different jet properties. The mean velocities of different rare gases for a wide range of source conditions are determined. Density profiles of various supersonic jets are measured and described mathematically in detail. In addition, both quantities, the velocity and the density, are used to determine the temperature of the supersonic jet.

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No description available.