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A rotating rake mode measurement system was designed to measure acoustic duct modes generated by a fan stage. After analysis of the measured data, the mode coefficient amplitudes and phases were quantified. Early studies using this system found that mode power levels computed from rotating rake measured data would agree with the far-field power levels. However, this agreement required that the sound from the noise sources within the duct propagated outward from the duct exit without reflection and previous studies suggested conditions could exist where significant reflections could occur. This paper shows that mounting a second rake to the rotating system, with an offset in both the axial and the azimuthal directions, measures the data necessary to determine the modes propagating in both directions within a duct. The rotating rake data analysis technique was extended to include the data measured by the second rake. The analysis resulted in a set of circumferential mode coefficients at each of the two rake microphone locations. Radial basis functions were then least-squares fit to this data to obtain the radial mode coefficients for the modes propagating in both directions within the duct while accounting for the presence of evanescent modes. The validation of the dual-rotating-rake measurements was conducted using data from a combination of experiments and numerical calculations to compute reflection coefficients and other mode coefficient ratios. Compared to results from analytical and numerical computations, the results from dual-rotating-rake measured data followed the expected trends when frequency, mode number, and duct termination geometry were changed.

The NASA Broadband Aeroacoustic Stator Simulation code was used to compute the acoustic field for higher-order modes in a circular duct geometry. To test the accuracy of the results computed by the code, the duct was terminated by an open end with an infinite flange or no flange. Both open end conditions have a theoretical solution that was used to compare with the computed results. Excellent comparison for reflection matrix values was achieved after suitable refinement of the grid at the open end. The study also revealed issues with the level of the mode amplitude introduced into the acoustic held from the source boundary and the amount of reflection that occurred at the source boundary when a general nonreflecting boundary condition was applied.

The Rotating Rake mode measurement system was designed to measure acoustic duct modes generated by a fan stage. Initially, the mode amplitudes and phases were quantified from a single rake measurement at one axial location. To directly measure the modes propagating in both directions within a duct, a second rake was mounted to the rotating system with an offset in both the axial and the azimuthal directions. The rotating rake data analysis technique was then extended to include the data measured by the second rake. The analysis resulted in a set of circumferential mode levels at each of the two rake microphone locations. Radial basis functions were then least-squares fit to this data to obtain the radial mode amplitudes for the modes propagating in both directions within the duct. Validation experiments have been conducted using artificial acoustic sources. Results are shown for the measurement of the standing waves in the duct from sound generated by one and two acoustic sources that are separated into the component modes propagating in both directions within the duct. Measured reflection coefficients from the open end of the duct are compared to analytical predictions.

A code for predicting supersonic jet broadband shock-associated noise was assessed using a database containing noise measurements of a jet issuing from a convergent nozzle. The jet was operated at 24 conditions covering six fully expanded Mach numbers with four total temperature ratios. To enable comparisons of the predicted shock-associated noise component spectra with data, the measured total jet noise spectra were separated into mixing noise and shock-associated noise component spectra. Comparisons between predicted and measured shock-associated noise component spectra were used to identify deficiencies in the prediction model. Proposed revisions to the model, based on a study of the overall sound pressure levels for the shock-associated noise component of the measured data, a sensitivity analysis of the model parameters with emphasis on the definition of the convection velocity parameter, and a least-squares fit of the predicted to the measured shock-associated noise component spectra, resulted in a new definition for the source strength spectrum in the model. An error analysis showed that the average error in the predicted spectra was reduced by as much as 3.5 dB for the revised model relative to the average error for the original model.

Empirical mode decomposition is an adaptive signal processing method that when applied to a broadband signal, such as that generated by turbulence, acts as a set of band-pass filters. This process was applied to data from time-resolved, particle image velocimetry measurements of subsonic jets prior to computing the second-order, two-point, space-time correlations from which turbulent phase velocities and length and time scales could be determined. The application of this method to large sets of simultaneous time histories is new. In this initial study, the results are relevant to acoustic analogy source models for jet noise prediction. The high frequency portion of the results could provide the turbulent values for subgrid scale models for noise that is missed in large-eddy simulations. The results are also used to infer that the cross-correlations between different components of the decomposed signals at two points in space, neglected in this initial study, are important.

The Rotating Rake mode measurement system was designed to measure acoustic duct modes generated by a fan stage. After analysis of the measured data, the mode amplitudes and phases were quantified. For low-speed fans within axisymmetric ducts, mode power levels computed from rotating rake measured data would agree with the far-field power levels on a tone by tone basis. However, this agreement required that the sound from the noise sources within the duct propagated outward from the duct exit without reflection at the exit and previous studies suggested conditions could exist where significant reflections could occur. To directly measure the modes propagating in both directions within a duct, a second rake was mounted to the rotating system with an offset in both the axial and the azimuthal directions. The rotating rake data analysis technique was extended to include the data measured by the second rake. The analysis resulted in a set of circumferential mode levels at each of the two rake microphone locations. Radial basis functions were then least-squares fit to this data to obtain the radial mode amplitudes for the modes propagating in both directions within the duct. The fit equations were also modified to allow evanescent mode amplitudes to be computed. This extension of the rotating rake data analysis technique was tested using simulated data, numerical code produced data, and preliminary in-duct measured data.

A goal of NASA s Fundamental Aeronautics Program is the improvement of aircraft noise prediction. This document provides an assessment, conducted from 2006 to 2009, on the current state of the art for aircraft noise prediction by carefully analyzing the results from prediction tools and from the experimental databases to determine errors and uncertainties and compare results to validate the predictions. The error analysis is included for both the predictions and the experimental data and helps identify where improvements are required. This study is restricted to prediction methods and databases developed or sponsored by NASA, although in many cases they represent the current state of the art for industry. The present document begins with an introduction giving a general background for and a discussion on the process of this assessment followed by eight chapters covering topics at both the system and the component levels. The topic areas, each with multiple contributors, are aircraft system noise, engine system noise, airframe noise, fan noise, liner physics, duct acoustics, jet noise, and propulsion airframe aeroacoustics.

Empirical mode decomposition is an adaptive signal processing method that when applied to a broadband signal, such as that generated by turbulence, acts as a set of band-pass filters. This process was applied to data from time-resolved, particle image velocimetry measurements of subsonic jets prior to computing the second-order, two-point, space-time correlations from which turbulent phase velocities and length and time scales could be determined. The application of this method to large sets of simultaneous time histories is new. In this initial study, the results are relevant to acoustic analogy source models for jet noise prediction. The high frequency portion of the results could provide the turbulent values for subgrid scale models for noise that is missed in large-eddy simulations. The results are also used to infer that the cross-correlations between different components of the decomposed signals at two points in space, neglected in this initial study, are important.

In an earlier study, a prediction model for jet noise in dual stream jets was proposed that is founded on velocity scaling laws in single stream jets and similarity features of the mean velocity and turbulent kinetic energy in dual stream flows. The model forms a composite spectrum from four component single-stream jets each believed to represent noise-generation from a distinct region in the actual flow. While the methodology worked effectively at conditions considered earlier, recent examination of acoustic data at some unconventional conditions indicate that further improvements are necessary in order to expand the range of applicability of the model. The present work demonstrates how these predictions compare with experimental data gathered by NASA and industry for the purpose of examining the aerodynamic and acoustic performance of such nozzles for a wide range of core and fan stream conditions. Of particular interest are jets with inverted velocity and temperature profiles and the appearance of a second spectral peak at small aft angles to the jet under such conditions. It is shown that a four-component spectrum succeeds in modeling the second peak when the aft angle refraction effects are properly incorporated into the model. A tradeoff of noise emission takes place between two turbulent regions identified as transition and fully mixed regions as the fan stream velocity exceeds that of the core stream. The effect of nozzle discharge coefficients will also be discussed.

Engineering applications for aircraft noise prediction contain models for physical phenomenon that enable solutions to be computed quickly. These models contain parameters that have an uncertainty not accounted for in the solution. To include uncertainty in the solution, nondeterministic computational methods are applied. Using prediction models for supersonic jet broadband shock-associated noise, fixed model parameters are replaced by probability distributions to illustrate one of these methods. The results show the impact of using nondeterministic parameters both on estimating the model output uncertainty and on the model spectral level prediction. In addition, a global sensitivity analysis is used to determine the influence of the model parameters on the output, and to identify the parameters with the least influence on model output.

Codes for predicting supersonic jet mixing and broadband shock-associated noise were assessed using a database containing noise measurements of a jet issuing from a convergent nozzle. Two types of codes were used to make predictions. Fast running codes containing empirical models were used to compute both the mixing noise component and the shock-associated noise component of the jet noise spectrum. One Reynolds-averaged, Navier-Stokes-based code was used to compute only the shock-associated noise. To enable the comparisons of the predicted component spectra with data, the measured total jet noise spectra were separated into mixing noise and shock-associated noise components. Comparisons were made for 1/3-octave spectra and some power spectral densities using data from jets operating at 24 conditions covering essentially 6 fully expanded Mach numbers with 4 total temperature ratios.

An acoustic assessment is being conducted by NASA that has been designed to assess the current state of the art in NASA s capability to predict aircraft related noise and to establish baselines for gauging future progress in the field. The process for determining NASA s current capabilities includes quantifying the differences between noise predictions and measurements of noise from experimental tests. The computed noise predictions are being obtained from semi-empirical, analytical, statistical, and numerical codes. In addition, errors and uncertainties are being identified and quantified both in the predictions and in the measured data to further enhance the credibility of the assessment. The content of this paper contains preliminary results, since the assessment project has not been fully completed, based on the contributions of many researchers and shows a select sample of the types of results obtained regarding the prediction of aircraft noise at both the system and component levels. The system level results are for engines and aircraft. The component level results are for fan broadband noise, for jet noise from a variety of nozzles, and for airframe noise from flaps and landing gear parts. There are also sample results for sound attenuation in lined ducts with flow and the behavior of acoustic lining in ducts.

The acoustic assessment task for both the Subsonic Fixed Wing and the Supersonic projects under NASA s Fundamental Aeronautics Program was designed to assess the current state-of-the-art in noise prediction capability and to establish baselines for gauging future progress. The documentation of our current capabilities included quantifying the differences between predictions of noise from computer codes and measurements of noise from experimental tests. Quantifying the accuracy of both the computed and experimental results further enhanced the credibility of the assessment. This presentation gives sample results from codes representative of NASA s capabilities in aircraft noise prediction at the system level and at the component level. These include semi-empirical, statistical, analytical, and numerical codes. An example of system level results is shown for an aircraft. Component level results are shown for airframe flaps and landing gear, for jet noise from a variety of nozzles, and for broadband fan noise. Additional results are shown for modeling of the acoustic behavior of duct acoustic lining and the attenuation of sound in lined ducts with flow.

The acoustic assessment task for both the Subsonic Fixed Wing and the Supersonic projects under NASA s Fundamental Aeronautics Program was designed to assess the current state-of-the-art in noise prediction capability and to establish baselines for gauging future progress. The documentation of our current capabilities included quantifying the differences between predictions of noise from computer codes and measurements of noise from experimental tests. Quantifying the accuracy of both the computed and experimental results further enhanced the credibility of the assessment. This presentation gives sample results from codes representative of NASA s capabilities in aircraft noise prediction both for systems and components. These include semi-empirical, statistical, analytical, and numerical codes. System level results are shown for both aircraft and engines. Component level results are shown for a landing gear prototype, for fan broadband noise, for jet noise from a subsonic round nozzle, and for propulsion airframe aeroacoustic interactions. Additional results are shown for modeling of the acoustic behavior of duct acoustic lining and the attenuation of sound in lined ducts with flow.

A technique is presented for the analysis of measured data obtained from a rotating microphone rake system. The system is designed to measure the interaction modes of ducted fans. A Fourier analysis of the data from the rotating system results in a set of circumferential mode levels at each radial location of a microphone inside the duct. Radial basis functions are then least-squares fit to this data to obtain the radial mode amplitudes. For ducts with soft walls and mean flow, the radial basis functions must be numerically computed. The linear companion matrix method is used to obtain both the eigenvalues of interest, without an initial guess, and the radial basis functions. The governing equations allow for the mean flow to have a boundary layer at the wall. In addition, a nonlinear least-squares method is used to adjust the wall impedance to best fit the data in an attempt to use the rotating system as an in-duct wall impedance measurement tool. Simulated and measured data are used to show the effects of wall impedance and mean flow on the computed results.

The field of computational aeroacoustics (CAA) encompasses numerical techniques for calculating all aspects of sound generation and propagation in air directly from fundamental governing equations. Aeroacoustic problems typically involve flow-generated noise, with and without the presence of a solid surface, and the propagation of the sound to a receiver far away from the noise source. It is a challenge to obtain accurate numerical solutions to these problems. The NASA Glenn Research Center has been at the forefront in developing and promoting the development of CAA techniques and methodologies for computing the noise generated by aircraft propulsion systems. To assess the technological advancement of CAA, Glenn, in cooperation with the Ohio Aerospace Institute and the AeroAcoustics Research Consortium, organized and hosted the Fourth CAA Workshop on Benchmark Problems. Participants from industry and academia from both the United States and abroad joined to present and discuss solutions to benchmark problems. These demonstrated technical progress ranging from the basic challenges to accurate CAA calculations to the solution of CAA problems of increasing complexity and difficulty. The results are documented in the proceedings of the workshop. Problems were solved in five categories. In three of the five categories, exact solutions were available for comparison with CAA results. A fourth category of problems representing sound generation from either a single airfoil or a blade row interacting with a gust (i.e., problems relevant to fan noise) had approximate analytical or completely numerical solutions. The fifth category of problems involved sound generation in a viscous flow. In this case, the CAA results were compared with experimental data.

This publication contains the proceedings of the Fourth Computational Aeroacoustics (CAA) Workshop on Benchmark Problems. In this workshop, as in previous workshops, the problems were devised to gauge the technological advancement of computational techniques to calculate all aspects of sound generation and propagation in air directly from the fundamental governing equations. A variety of benchmark problems have been previously solved ranging from simple geometries with idealized acoustic conditions to test the accuracy and effectiveness of computational algorithms and numerical boundary conditions; to sound radiation from a duct; to gust interaction with a cascade of airfoils; to the sound generated by a separating, turbulent viscous flow. By solving these and similar problems, workshop participants have shown the technical progress from the basic challenges to accurate CAA calculations to the solution of CAA problems of increasing complexity and difficulty. The fourth CAA workshop emphasized the application of CAA methods to the solution of realistic problems. The workshop was held at the Ohio Aerospace Institute in Cleveland, Ohio, on October 20 to 22, 2003. At that time, workshop participants presented their solutions to problems in one or more of five categories. Their solutions are presented in this proceedings along with the comparisons of their solutions to the benchmark solutions or experimental data. The five categories for the benchmark problems were as follows: Category 1:Basic Methods. The numerical computation of sound is affected by, among other issues, the choice of grid used and by the boundary conditions. Category 2:Complex Geometry. The ability to compute the sound in the presence of complex geometric surfaces is important in practical applications of CAA. Category 3:Sound Generation by Interacting With a Gust. The practical application of CAA for computing noise generated by turbomachinery involves the modeling of the noise source mechanism as a vortical gust interacting with an airfoil. Category 4:Sound Transmission and Radiation. Category 5:Sound Generation in Viscous Problems. Sound is generated under certain conditions by a viscous flow as the flow passes an object or a cavity.

An approximate technique is presented for the prediction of the large-scale turbulent structure sound source in a supersonic jet. A linearized Euler equations code is used to solve for the flow disturbances within and near a jet with a given mean flow. Assuming a normal mode composition for the wave-like disturbances, the linear radial profiles are used in an integration of the Navier-Stokes equations. This results in a set of ordinary differential equations representing the weakly nonlinear self-interactions of the modes along with their interaction with the mean flow. Solutions are then used to correct the amplitude of the disturbances that represent the source of large-scale turbulent structure sound in the jet.

An analysis of the nonlinear development of the large-scale structures or instability waves in compressible round jets was conducted using the integral energy method. The equations of motion were decomposed into two sets of equations; one set governing the mean flow motion and the other set governing the large-scale structure motion. The equations in each set were then combined to derive kinetic energy equations that were integrated in the radial direction across the jet after the boundary-layer approximations were applied. Following the application of further assumptions regarding the radial shape of the mean flow and the large structures, equations were derived that govern the nonlinear, streamwise development of the large structures. Using numerically generated mean flows, calculations show the energy exchanges and the effects of the initial amplitude on the coherent structure development in the jet.

This paper provides preliminary results of the study of the acoustic radiation from the source model representing spatially-growing instability waves in a round jet at high speeds. The source model is briefly discussed first followed by the analysis of the produced acoustic directivity pattern. Two integral surface techniques are discussed and compared for prediction of the jet acoustic radiation field.

A thin free shear layer containing an inflection point in the mean velocity profile is inherently unstable. Disturbances in the flow field can excite the unstable behavior of a shear layer, if the appropriate combination of frequencies and shear layer thicknesses exists, causing instability waves to grow. For other combinations of frequencies and thicknesses, these instability waves remain neutral in amplitude or decay in the downstream direction. A growing instability wave radiates noise when its phase velocity becomes supersonic relative to the ambient speed of sound. This occurs primarily when the mean jet flow velocity is supersonic. Thus, the small disturbances in the flow, which themselves may generate noise, have generated an additional noise source. It is the purpose of this problem to test the ability of CAA to compute this additional source of noise. The problem is idealized such that the exciting disturbance is a fixed known acoustic source pulsating at a single frequency. The source is placed inside of a 2D jet with parallel flow; hence, the shear layer thickness is constant. With the source amplitude small enough, the problem is governed by the following set of linear equations given in dimensional form.

An acoustic source inside of a 2-D jet excites an instability wave in the shear layer resulting in sound radiating away from the shear layer. Solve the linearized Euler equations to predict the sound radiation outside of the jet. The jet static pressure is assumed to be constant. The jet flow is parallel and symmetric about the x-axis. Use a symmetry boundary condition along the x-axis.

The proceedings of the Third Computational Aeroacoustics (CAA) Workshop on Benchmark Problems cosponsored by the Ohio Aerospace Institute and the NASA Glenn Research Center are the subject of this report. Fan noise was the chosen theme for this workshop with representative problems encompassing four of the six benchmark problem categories. The other two categories were related to jet noise and cavity noise. For the first time in this series of workshops, the computational results for the cavity noise problem were compared to experimental data. All the other problems had exact solutions, which are included in this report. The Workshop included a panel discussion by representatives of industry. The participants gave their views on the status of applying computational aeroacoustics to solve practical industry related problems and what issues need to be addressed to make CAA a robust design tool.

The noise from perfectly expanded coaxial jets was measured in an anechoic chamber for different operating conditions with the same total thrust, mass flow, and exit area. The shape of the measured noise spectrum at different angles to the jet axis was found to agree with spectral shapes for single, axisymmetric jets. Based on these spectra, the sound was characterized as being generated by large turbulent structures or fine-scale turbulence. Modeling the large scale structures as instability waves, a stability analysis was conducted for the coaxial jets to identify the growing and decaying instability waves in each shear layer and predict their noise radiation pattern outside the jet. When compared to measured directivity, the analysis identified the region downstream of the outer potential core, where the two shear layers were merging, as the source of the peak radiated noise where instability waves, with their origin in the inner shear layer, reach their maximum amplitude. Numerical computations were also performed using a linearized Euler equation solver. Those results were compared to both the results from the instability wave analysis and to measured data.

The pressure disturbances generated by an instability wave in the shear layer of a supersonic jet are studied for an axisymmetric jet inside a lined cylindrical duct. For the supersonic jet, locally linear stability analysis with duct wall boundary conditions is used to calculate the eigenvalues and the eigenfunctions. These values are used to determine the growth rates and phase velocities of the instability waves and the radial pressure disturbance patterns. The study is confined to the dominant Kelvin-Helmholtz instability mode and to the region just downstream of the nozzle exit where the shear layer is growing but is still small in size compared to the radius of the duct. Numerical results are used to study the effects of changes in the outer flow, growth in the shear layer thickness, wall distance, wall impedance, and frequency. Results indicate that the effects of the duct wall on shear layer growth rates diminish as the outer flow increases. Also, wall reflections cause variations in growth rates depending on wall height and Strouhal number. These variations are due to the phase relationship between the outgoing and the reflected incoming pressure disturbances at the shear layer. The growth rate variations can be reduced and the maximum growth rate minimized by keeping the imaginary part of the impedance negative.

Recent theories for supersonic jet noise have used an instability wave noise generation model to predict radiated noise. This model requires a known mean flow that has typically been described by simple analytic functions for single jet mean flows. The mean flow of supersonic coaxial jets is not described easily in terms of analytic functions. To provide these profiles at all axial locations, a numerical scheme is developed to calculate the mean flow properties of a coaxial jet. The Reynolds-averaged, compressible, parabolic boundary layer equations are solved using a mixing length turbulence model. Empirical correlations are developed to account for the effects of velocity and temperature ratios and Mach number on the shear layer spreading. Both normal velocity profile and inverted velocity profile coaxial jets are considered. The mixing length model is modified in each case to obtain reasonable results when the two stream jet merges into a single fully developed jet. The mean flow calculations show both good qualitative and quantitative agreement with measurements in single and coaxial jet flows.

The pressure disturbances generated by an instability wave in the shear layer of a supersonic jet are studied for an axisymmetric jet inside a lined circular duct. For the supersonic jet, locally linear stability analysis with duct wall boundary conditions is used to calculate the eigenvalues and the eigenfunctions at each axial location. These values are used to determine the growth rates and phase velocities of the instability waves and the near field pressure disturbance patterns. The study is confined to the dominant Kelvin-Helmholtz instability mode and to the region just downstream of the nozzle exit where the shear layer is growing but is still small in size compared to the radius of the duct. Numerical results are used to study the effects of changes in the outer flow, growth in the shear layer thickness, wall distance, and wall impedance, and the effects of these changes on non-axisymmetric modes. The primary results indicate that the effects of the duct wall on stability characteristics diminish as the outer flow increases and as the jet azimuthal mode number increases. Also, wall reflections are reduced when using a finite impedance boundary condition at the wall; but in addition, reflections are reduced and growth rates diminished by keeping the imaginary part of the impedance negative when using the negative exponential for the harmonic dependence.

Predictions are made for the noise radiation from supersonic, coaxial jets. These predictions are based on the assumption that the noise radiation in the downstream direction of supersonic jets is dominated by sound generated by instability waves with supersonic phase velocities relative to ambient. Since the analysis requires a known mean flow and the coaxial jet mean flow is not described easily in terms of analytical functions, a numerical prediction is made for its development. The compressible, Reynolds averaged, boundary layer equations are solved with a modified mixing length turbulence model. The model has been calibrated to account for compressibility and temperature effects on the rate of mixing. Both normal and inverted velocity profile jets are considered. Predictions are made for the differences between the noise radiated by coaxial jets with difference operating conditions and a single reference jet with the same thrust, mass flow, and exit area. The effects of area ratio changes and simulated enhanced mixing on noise radiation are also considered.

In this paper, predictions are made of noise radiation from single, supersonic, axisymmetric jets. We examine the effects of changes in operating conditions and the effects of simulated enhanced mixing that would increase the spreading rate of the jet shear layer on radiated noise levels. The radiated noise in the downstream direction is dominated by mixing noise and it is well described by the instability wave noise radiation analysis. A numerical prediction scheme is used for the mean flow providing an efficient method to obtain the mean flow development for various operating conditions and to simulate the enhanced mixing. Using far field radiated noise measurements as a reference, the calculations predict that enhanced jet spreading results in a reduction of radiated noise.

Instability waves have been established as the dominant source of mixing noise radiating into the downstream arc of a supersonic jet when the waves have phase velocities that are supersonic relative to ambient conditions. Recent theories for supersonic jet noise have used the concepts of growing and decaying linear instability waves for predicting radiated noise. This analysis is extended to the prediction of noise radiation from supersonic coaxial jets. Since the analysis requires a known mean flow and the coaxial jet mean flow is not described easily in terms of analytic functions, a numerical prediction is made for its development. The Reynolds averaged, compressible, boundary layer equations are solved using a mixing length turbulence model. Empirical correlations are developed for the effects of velocity and temperature ratios and Mach number. Both normal and inverted velocity profile coaxial jets are considered. Comparisons with measurements for both single and coaxial jets show good agreement. The results from mean flow and stability calculations are used to predict the noise radiation from coaxial jets with different operating conditions. Comparisons are made between different coaxial jets and a single equivalent jet with the same total thrust, mass flow, and exit area. Results indicate that normal velocity profile jets can have noise reductions compared to the single equivalent jet. No noise reductions are found for inverted velocity profile jets operated at the minimum noise condition compared to the single equivalent jet. However, it is inferred that changes in area ratio may provide noise reduction benefits for inverted velocity profile jets.

In this paper predictions are made for the noise radiation from supersonic coaxial jets. The noise in the downstream arc of a supersonic jet is dominated by highly directional radiation from the supersonically convecting large scale structures in the jet mixing layer. Since the mean flow is not described easily in terms of simple analytic functions, a numerical prediction is made for its development. The compressible Reynolds-averaged boundary layer equations in cylindrical polar coordinates are solved. A mixing length turbulence model is used. Empirical correlations are developed the effects of velocity and temperature ratio and Mach number. Both normal and inverted velocity profiles are considered. Comparisons with measurements for both single and coaxial jets show good agreement. The large scale structures are modeled as instability waves. The noise radiation generated by the instability waves is determined by a matching between the inner instability wave solution and the outer acoustic solution. Predictions are made for the differences between the noise radiated by coaxial jets with different operating conditions and a single equivalent jet with the same exit area, thrust, and mass-flow.

The test section of the NASA Lewis 9- by 15-Foot Low Speed Wind Tunnel was acoustically treated to allow the measurement of acoustic sources located within the tunnel test section under simulated free field conditions. The treatment was designed for high sound absorption at frequencies above 250 Hz and to withstand tunnel airflow velocities up to 0.2 Mach. Evaluation tests with no tunnel airflow were conducted in the test section to assess the performance of the installed treatment. This performance would not be significantly affected by low speed airflow. Time delay spectrometry tests showed that interference ripples in the incident signal resulting from reflections occurring within the test section average from 1.7 dB to 3.2 dB wide over a 500 to 5150 Hz frequency range. Late reflections, from upstream and downstream of the test section, were found to be insignificant at the microphone measuring points. For acoustic sources with low directivity characteristics, decay with distance measurements in the test section showed that incident free field behavior can be measured on average with an accuracy of +/- 1.5 dB or better at source frequencies from 400 Hz to 10 kHz. The free field variations are typically much smaller with an omnidirectional source.

The test section of the NASA Lewis 9- by 15-Foot Low-Speed Wind Tunnel was acoustically treated to allow the measurement of sound under simulated free-field conditions. The treatment was designed for high sound absorption at frequencies above 250 Hz and for withstanding the environmental conditions in the test section. In order to achieve the design requirements, a fibrous, bulk-absorber material was packed into removable panel sections. Each section was divided into two equal-depth layers packed with material to different bulk densities. The lower density was next to the facing of the treatment. The facing consisted of a perforated plate and screening material layered together. Sample tests for normal-incidence acoustic absorption were also conducted in an impedance tube to provide data to aid in the treatment design. Tests with no airflow, involving the measurement of the absorptive properties of the treatment installed in the 9- by 15-foot wind tunnel test section, combined the use of time-delay spectrometry with a previously established free-field measurement method. This new application of time-delay spectrometry enabled these free-field measurements to be made in nonanechoic conditions. The results showed that the installed acoustic treatment had absorption coefficients greater than 0.95 over the frequency range 250 Hz to 4 kHz. The measurements in the wind tunnel were in good agreement with both the analytical prediction and the impedance tube test data.

The acoustic behavior of a flexible fibrous material was studied experimentally. The material consisted of cylindrically shaped fibers arranged in a batting with the fibers primarily aligned parallel to the face of the batting. This type of material was considered anisotropic, with the acoustic propagation constant depending on whether the direction of sound propagation was parallel or normal to the fiber arrangement. Normal incidence sound absorption measurements were taken for both fiber orientations over the frequency range 140 to 1500 Hz and with bulk densities ranging from 4.6 to 67 kg/cu m. When the sound propagated in a direction normal to the fiber alignment, the measured sound absorption showed the occurrence of a strong resonance, which increased absorption above that attributed to viscous and thermal effects. When the sound propagated in a direction parallel to the fiber alignment, indications of strong resonances in the data were not present. The resonance in the data for fibers normal to the direction of sound propagation is attributed to fiber motion. An analytical model was developed for the acoustic behavior of the material displaying the same fiber motion characteristics shown in the measurements.

A finite element model was developed to solve for the acoustic pressure and energy fields in a heterogeneous suppressor. The derivations from the governing equations assumed that the material properties could vary with position resulting in a heterogeneous variable property two-dimensional wave equation. This eliminated the necessity of finding the boundary conditions between different materials. For a two-media region consisting of part air and part bulk absorber, a model was used to describe the bulk absorber properties in two directions. Complex metallic structures inside the air duct are simulated by simply changing element properties from air to the structural material in a pattern to describe the desired shapes. To verify the numerical theory, experiments were conducted without flow in a rectangular duct with a single folded cavity mounted above the duct and absorbing material mounted inside a cavity. Changes in a nearly plane wave sound field were measured on the wall opposite the absorbing cavity. Fairly good agreement was found in the standing wave pattern upstream of the absorber and in the decay of pressure level opposite the absorber, as a function of distance along the duct. The finite element model provides a convenient method for evaluating the acoustic properties of bulk absorbers.

A finite element model was developed to solve for the acoustic pressure field in a nonhomogeneous region. The derivations from the governing equations assumed that the material properties could vary with position resulting in a nonhomogeneous variable property two-dimensional wave equation. This eliminated the necessity of finding the boundary conditions between the different materials. For a two media region consisting of part air (in the duct) and part bulk absorber (in the wall), a model was used to describe the bulk absorber properties in two directions. An experiment to verify the numerical theory was conducted in a rectangular duct with no flow and absorbing material mounted on one wall. Changes in the sound field, consisting of planar waves, was measured on the wall opposite the absorbing material. As a function of distance along the duct, fairly good agreement was found in the standing wave pattern upstream of the absorber and in the decay of pressure level opposite the absorber.

The acoustic behavior of a flexible fibrous material was studied experimentally. The material consisted of cylindrically shaped fibers arranged in a batting with the fibers primarily aligned parallel to the face of the batting. This type of material was considered anisotropic, with the acoustic propagation constant depending on whether the dirction of sound propagation was parallel or normal to the fiber arrangement. Normal incidence sound absorption measurements were taken for both fiber orientations over the frequency range 140 to 1500 Hz and with bulk densities ranging from 4.6 to 67 kg/cu m. When the sound propagated in a direction normal to the fiber alignment, the measured sound absorption showed the occurrence of a strong resonance, which increased absorption above that attributed to viscous and thermal effects. When the sound propagated in a direction parallel to the fiber alignment, indications of strong resonances in the data were not present. The resonance in the data for fibers normal to the direction of sound propagation is attributed to fiber motion. An analytical model was developed for the acoustic behavior of the material displaying the same fiber motion characteristics shown in the measurements.