Aero-Acoustic Analyses and Experimental Validation

Computational Analyses in Support of Sub-scale Diffuser Testing for the A-3 Facility – Part 3: Aero-Acoustic Analyses and Experimental Validation

Authors:

Daniel C. Allgood, Aerospace Technologist, EA33, NASA Stennis Space Center, Stennis Space Center, MS, 39529.

Jody L. Woods, A-3 Chief Engineer, EA00, NASA Stennis Space Center, Stennis Space Center, MS, 39529.

Jason S. Graham, CFD Engineer, Jacobs Technology Inc. Test operations Group, Stennis Space Center, MS, 39529.

Greg P. McVay, Supervisor, Jacobs Technology Inc. Test operations Group, Stennis Space Center, MS, 39529.

Lester L. Langford, Electrical Engineer, Jacobs Technology Inc. Test operations Group, Stennis Space Center, MS, 39529.

Abstract

A unique assessment of acoustic similarity scaling laws and acoustic analogy methodologies in predicting the far-field acoustic signature from a sub-scale altitude rocket test faci¬¬lity at the NASA Stennis Space Center was performed. Point-source and distributed-source similarity analyses were implemented for predicting the acoustic far-field. In these approaches, experimental acoustic data obtained from “similar” rocket engine tests were appropriately scaled using key geometric and dynamic parameters. The accuracy of these engineering-level methods are discussed by comparing the predictions with acoustic far-field measurements obtained. In addition, a CFD solver was coupled with a Lilley’s acoustic analogy formulation to determine the improvement of using a physics-based methodology over an empirical correlation approach. In the current work, steady-state Reynolds-Averaged Navier-Stokes (RANS) calculations were used to model the internal flow of the rocket engine and altitude diffuser. These internal flow simulations provided the necessary realistic input conditions for external plume simulations. The CFD plume simulations were then used to provide the spatial turbulent noise source distributions in the acoustic analogy calculations.

Nomenclature

CFD+LAA =  computational fluid dynamics (CFD) + Lilley’s acoustic analogy (LAA) model
D       =  exit diameter of subscale altitude facility
DSM     =  empirical distributed-source acoustic model
f       =  frequency
OASPL   =  overall sound pressure level
p’      =  pressure fluctuation
PSM     =  empirical point-source acoustic model
r       =  radial distance from facility exit
St      =  Strouhal Number
U       =  exit velocity
$\theta$       =  directivity angle measured from nozzle exit and relative to primary exhaust flow direction

Introduction

Figure1: Conceptual Rendering of the New A-3 Test Facility at NASA Stennis Space Center.

This paper is the third paper in a three-part series on an engineering analysis that has been performed at NASA Stennis Space Center in support of the new A-3 rocket-engine test facility, shown in Figure 1. The A-3 test facility consists of a large test cell that is evacuated and pumped down to a simulated altitude of 100,000 ft (0.16 psia) by a two-stage steam-ejector system. The primary purpose of A-3 is to provide a long-duration, altitude test-bed for the upcoming J-2X engine. The J-2X engine is a liquid hydrogen-oxygen engine that is currently slated to be used on the ARES I and ARES V vehicles for the NASA Constellation exploration program. For a more detailed description of this NASA program and the A-3 test facility, the reader is referred to the first paper in this series.

Due to the orientation and close proximity of the new A-3 facility’s exhaust flow to populated areas and highways, it was imperative that NASA-SSC have a complete understanding of the expected far-field acoustic signature from the A-3 test facility. However, after reviewing the available acoustic data from large-scale rocket testing, there was little to no information for test facilities of this type. Furthermore, the rocket acoustic modeling tools which were available had not been formally validated for the steam-loaded and relatively slower A-3 exhaust plume. This possible deficiency and uncertainty in modeling led to the current effort of performing a combined experimental and computational study of the aero-acoustics from a dynamically-similar sub-scale altitude test facility. The primary objective was to develop a validated methodology for characterizing the far-field acoustic signature from an altitude rocket test facility of this type. Evaluation of the validity of the acoustic models was achieved by measuring the acoustic signature from a 1/17^th sub-scale A-3 facility and comparing the experimental data to the model predictions. The 1/17^th subscale test facility was recently constructed and tested at NASA-SSC as part of a risk mitigation effort for the new A-3 facility. Ultimately, the insights gained from this study would provide NASA-SSC engineers a higher confidence level in their acoustic analyses of the full-scale A-3 facility and provide guidance on noise mitigation efforts that might need to be implemented.

Experimental Facility

Subscale Altitude Test Facility

Figure 2: Subscale Altitude Test Facility.

To help minimize risk of failure and cost of the new A-3 altitude test facility, a subscale altitude facility was designed and constructed to perform a series of verification tests. These verification tests could potentially pinpoint design and/or operational issues with the A-3 test stand prior to its construction. The subscale test facility, shown in Figure 2, is approximately 1/17^th scale of the A-3 test facility. A subscale J-2X engine has also been constructed and installed in the test facility. The area ratios, combustion chamber pressure and mixture fractions of the J-2X have been maintained in the subscale engine. As a result, the subscale engine plume entering the diffuser closely resembles that of the J-2X. The mass flow rates of the 1^st and 2^nd steam ejectors have also been appropriately scaled to ensure the same gas dynamic processes are occurring inside the subscale diffuser flow path. The subscale diffuser has been instrumented with an array of high-speed pressure transducers and thermal couples to assess the facility operation behavior and efficiency. The high-speed diffuser data in conjunction with IR outer wall surface temperature measurements also provided experimental data to assess the capability of the CFD simulations in capturing the locally averaged flow and heat transfer characteristics throughout the diffuser flow path.

Acoustic Measurements and Data Collection

In order to anchor far-field acoustic models that were being using to estimate the A-3 test facility acoustic signature, a detailed acoustic mapping of the subscale test facility during its operation was performed. A radial arc of seven free-field microphones (B&K ½” Type 4191) were placed in what was perceived a priori to be the acoustic far-field of the subscale facility. Figure 3 shows that the seven microphones were placed at approximately 228 nozzle exit diameters away. Two additional microphones were placed at approximately half that distance on 45 and 90 degree nozzle aft directivity angles. The microphones had a reported accuracy of +/- 0.2dB for frequencies between 10 and 4000 Hz. The microphone data was sampled at a rate of 43kHz and then filtered using a band-pass, 3^rd order, Butterworth filter with cutoff frequencies of 1Hz and 20kHz.

Figure 3: Placement of Microphone Sensors for Far-field Acoustic Mapping.

Predictive Methodologies

Three aero-acoustic (or jet-noise) models were implemented in this study. The lowest fidelity model was a directional, point-source empirical-acoustic model used frequently by NASA-SSC for far-field rocket engine acoustic environment predictions. This model served as a base-line model for comparison to two distributed-source acoustic models. The first distributed-source model used was an engineering standard for near-field acoustic environment predictions for rockets on test stands and/or launch pads. In this model, the noise-source characteristics and their distribution were derived using an empirical-based scaling approach. The second distributed source model was an acoustic analogy model which used Reynolds-Averaged Navier-Stokes solutions from a CFD model to provide the turbulent noise source distribution in the altitude diffuser exhaust plume. Since, this model is the most physically-based model, it was anticipated that it would result in the best predictions of the diffuser acoustics. However, due to the simplicity and timely manner of implementing the experimental-based models, these models could have significant engineering value if they were deemed to perform adequately for acoustical environmental surveys at rocket test complexes. The following sections will discuss each of these models in more detail.

Empirical Point-Source Acoustic Model

Figure 4: Examples of Rocket-Engine Acoustic Spectra from the Empirical Point-Source Model Database.

A fundamental assumption in the point-source acoustic model is that the observer location of interest is sufficiently far from the exhaust jet that its noise sources can be treated as an equivalent acoustic “point-source”. The theoretical basis for the point-source model is to correlate experimental far-field acoustic data from a wide variety of rocket engine tests and from that correlation determine a dimensionless acoustic power spectrum and directivity index. In general, the model appropriately scales these dimensionless functions based on key dynamic and geometric parameters for the particular scenario being modeled. The key parameters are the mechanical power of the rocket exhaust (thrust and velocity), effective exit diameter, and acoustic efficiency of the jet. This scaling approach has been shown to be valid for single and multi-nozzle engine configurations under non-deflected and deflected test configurations. A sample set of rocket engine acoustic spectra from the model’s database is shown in Figure 4. Note this figure presents normalized acoustic spectra data for hydrogen and hydro-carbon fueled engines in both single and multi-engine configurations. In addition, the point-source model can account for molecular attenuation by an assumed homogeneous atmosphere. For a more detailed description of the theoretical framework of this modeling approach, the reader is referred to references 3 and 4.

Empirical Distributed-Source Acoustic Model

Figure 5: Axial Location of Apparent Sources as a Function of Strouhal Number for Chemical Rockets [Reproduced from Ref. 5].

The empirical-based distributed-source model is a direct implementation of the NASA SP-8072 standard “method 1” for computing near-field acoustic environments for rocket engines. Its is very similar to the point-source method except for the fact that it allows the rocket exhaust to be modeled as a distribution of noise sources. The distribution is derived from an understanding that the noise sources appear to be “distributed” along the axis of the plume and its distribution is frequency dependent. The “apparent” noise source locations for each frequency band is effectively determined by the model through scaling experimental data that has been fitted to an inverse-square loss curve and extrapolated to zero distance. The normalized source distribution curve from NASA SP-8072 has been shown in Figure 5.

CFD+Acoustic Analogy Model

The third method of modeling the sub-scale diffuser exhaust acoustics was via the acoustic analogy formulation. Specifically, a modified version of the NASA MGBK code was used. In the original MGBK code, Lilley’s equation is solved were the self-noise and shear-noise terms are modeled. The far-field noise is obtained by volumetrically integrating the noise source region in which the source convection and mean-flow refraction effects are properly accounted for. A more detailed description of the methodology may be found in reference 7.

In the current study, there is one distinct difference in the original MGBK code and that which was used here. Our initial predictions for the diffuser using the original form of the MGBK code showed significant discrepancies compared to the acoustic experimental data. Further analysis revealed that the shear noise being predicted was inconsistent with existing acoustic data for rocket engines. An improvement was found by using the proposed scaling by Ribner of shear noise based on self noise. Ribner had proposed this scaling to improve the basic Lilley equation predictions. The shear-noise scaling term proposed is shown in equation 1 below. When this correction was applied, the agreement between experimental and predicted acoustic levels significantly improved in both overall levels and spectra. The results presented in this paper are those obtained using this Ribner shear noise relation.

Equation 1: Ribner shear-noise scaling term.

The mean and turbulent flow properties of the diffuser exhaust plume required for this type of analysis were generated by modeling the diffuser exhaust flow using the CRUNCH CFD code. In a separate work, the complete diffuser flow path was modeled using the compressible, turbulent Reynolds-Averaged Navier-Stokes equations and assuming ideal gas properties. This diffuser flow-path model was successfully validated with experimental data, and a detailed description of this modeling effort has been provided in the companion paper. However, for the current acoustic modeling effort, a CFD model of the diffuser exhaust plume was required. The exhaust conditions predicted by the validated diffuser flow-path model provided the inflow conditions for the axi-symmetric exhaust plume model shown in Figure 6. In the current study, the explicit-algebraic stress turbulence model (EASM) form of the k-epsilon equations was used, which has been demonstrated in previous jet-noise modeling efforts to perform well due to the model’s ability of capturing anisotropic turbulence. The simulations showed an over-expanded plume which separated from the diverging exhaust duct creating a detached shock-laden turbulent jet. The location of flow separation predicted using the compressible EASM turbulence formulation was verified from the test data by wall pressure taps and “corrosion” rings which typically form near hot-steam laden separation points. The turbulent flow-field shown in Figure 6 was the input provided to the modified MGBK acoustic analogy code.

Figure 6: CFD Predicted Plume Conditions (a) Mach Number (b) Temperature and (c) Turbulent Kinetic Energy (TKE).

Results

Experimental Far-field Acoustic Data

The microphone data were processed using a Lab-View based Fast Fourier Transform (FFT) acoustic code that was developed in-house and has been used previously on other NASA Stennis test programs. The Lab-View code could provide time-averaged or transient one-octave, 1/3 octave or narrow-band spectra for each microphone. The results in this paper all show the one-octave averaged spectra over the 3 second rocket hot-fire test duration. The acoustic data acquired during steam ejector startup and shutdown have been removed from the time data in order to capture only the nominal 100% power-level facility operation. Several acoustic tests were conducted for the 100% power-level condition which showed repeatability in the measurements to with +/- 0.5 dB.

Figure 7: One-Octave Microphone Acoustic Spectra at r/D=228.

Figure 7 are the one-octave microphone spectra for the r/D=228 radial arc location. The data shows that the dominant acoustic levels are concentrated along a 45 degree angle with a peak frequency of 500 Hz at this radial location. The one exception is the microphone which is located directly downstream in the path of the plume. This microphone picked up a significant amount of low-frequency energy. One potential cause for this is the well known fact that low frequencies (or large-wavelengths) are not refracted as much by the plume because their wavelengths are much larger in comparison to the width of the shear layer. Also, Mach number and convection effects are more dominant on the low frequencies. Lastly, some wind loading on the microphone could be possible since it is in the far but direct path of the steam laden plume. However, wind-screens were installed on the microphone to help minimize contamination of the signals.

One beneficial way to visualize these spectra is by normalizing the frequency based on the facility exit diameter and average exit velocity. In this case the average exit velocity was estimated from the CFD calculations. The resulting normalized spectra, given in Figure 8, indicated a preferred Strouhal frequency of 0.1 to 0.2 at this radial location. Since this is a subscale system of A-3, we would expect the A-3 spectra to have a similar preferred Strouhal frequency range at this normalized radial location. It should be also noted that the preferred Strouhal frequency in the acoustic spectra is also a function of radial distance from the noise source. Figure 9 provides two 45 degree directivity spectra at different radial locations. The data show that as you move further away from the noise source the higher frequencies attenuate faster in the atmospheric environment resulting in the dominant frequency of the acoustic spectra shifting to lower values.

Figure 8: Normalized One-Octave Microphone Acoustic Spectra at r/D=228.

Figure 9: One-Octave Microphone Acoustic Spectra at 45 degree Directivity Angle (relative to the plume flow direction).

Assessment of the Acoustic Modeling Methodologies

Figure 10: Comparison of OSPL Directivity Measurements and Acoustic Model Predictions at the Two Radial Arc Locations (r/D=109 and r/D=228).

Figures 10a and 10b show a comparison between the experimental and predicted overall sound pressure level directivities for the subscale facility. The circle symbols on the directivity polar plots indicate experimental data and the line contours or triangle symbols indicate model predictions. The flow direction is oriented vertically upward (0 deg.) in the figures as depicted by the vector located at the origin of the graphs. It was observed that while there was qualitative consistency between the models, none of the methodologies performed adequately for the nearest observer locations (r/D=109) as shown in Figure 10a. This was likely due to the fact that these microphones were technically not in the acoustic far-field and non-linear effects were still prevalent.

Improvement in the accuracy of the predictions was obtained at the larger radial arc of r/D=228. Figure 10b shows fairly good quantitative agreement in the overall sound pressure level directivity using the empirical distributed-source model (DSM) and the CFD+LAA methodology. Most of the OSPL directivity estimates where within +/- 2dB, which is within reason for this simplified scaling approach. The only significant deviations between these two models and the experimental data occurred at the high intensity lobe region of 45 degrees. The point source model (PSM) performed relatively poorly in predicting the directivity of the acoustics especially at the low and high directivity angles. Comparison of the spectra had shown the point-source model performed poorly in predicting the low frequency contribution of the signals which explained its deficiency in predicting the OSPL at the low directivity angles. Since the results indicated that it was necessary at these radial locations to account for the distribution of noise sources in the plume, the remaining portion of this work focuses only on evaluating the performance of the empirical distributed source model and the CFD+LAA model.

Band-centered one-octave directivity polar plots are shown in Figures 11a through 11h. The array of polar plots depict how the preferred directivity angle shifts with frequency. The experimental data indicates that the low frequency (<125Hz) content or large-wavelengths of the jet noise are directed downstream with the plume. This behavior has been attributed in jet noise theory to the fact that the larger wavelength cannot be refracted radially outward as easily as the smaller acoustic wavelengths. The CFD+LAA model appeared to capture this phenomenon reasonably well, while the empirical distributed source model (DSM) was significantly off (~10dB maximum error). For smaller wave lengths (125-2000Hz), the noise gets refracted to a preferential direction of approximately 45 degrees, which is characteristic of the diffuser exhaust plume geometry and exit conditions. All models successfully indicated this preferred direction within this frequency range, with the CFD+LAA model performing the best. However, none of the models quite captured the peak intensity decibel level accurately. Once the frequency reaches above 2000 Hz, the acoustics are nearly omni-directional with no preferential direction. Generally, both models were qualitatively accurate in this higher frequency range for all directivity angles.

Further insight into the performance of the models was obtained by comparing their predicted acoustic spectra at discrete points corresponding to microphone locations. Figure 12 shows the comparison of one-octave acoustic spectra for the two distributed source models and the experimental data at directivity angles of 30 and 60 degrees. Overall, the figures show that the CFD+LAA model predicted the octave-band levels more effectively than the empirical distributed-source model. However, neither model captured the preferred frequencies at these locations. Also, the spectrum level “roll-off” from the preferred frequency was more rapid in the data than in either model. From an engineering survey perspective though, both models did consistently provide conservative predictions which is desirable in practice.

Figure 11: Sound Pressure Level Directivities at One-Octave Band Centered Frequencies of (a) 63, (b) 125, (c) 250, (d) 500, (e) 1000, (f) 2000, (g) 4000, and (h) 8000 Hz.

Figure 12: One-Octave Spectra Comparisons for Directivity Angles of (a) 30 and (b) 60 degrees.

Conclusions

Three aero-acoustic jet-noise models were evaluated for predicting the far-field acoustics emitted by the jet plume of a 100,000ft simulated-altitude rocket-engine test facility. The first model evaluated was a directional point source acoustic model. While it adequately predicted the overall acoustic levels from the facility exhaust plume, it was deficient in predicting the directivity and the acoustic emissions within an acceptable level for acoustical environmental surveys within 200 diameters of the exhaust. In these localities, the distribution of noise sources in the exhaust plume was deemed significant. The other two models investigated were distributed source acoustic models. The first distributed-source model was an empirical-based model that has been widely accepted for near-field acoustic environment predictions for rocket-engines. The second distributed-source model was a more physics-based methodology which combined CFD and Lilley’s acoustic analogy (CFD+LAA model) to predict the acoustic environment. Both of these models performed adequately in that they predicted the overall acoustic levels, the general directivity and the preferred frequencies. However, the CFD+LAA model was much more successful in predicting the low to mid-frequency directivity contributions. The results from this study lead to the general conclusion that the empirical-based distributed source model was an adequate “engineering” model for fast and reasonably conservative acoustic surveys of altitude test facilities, but where higher fidelity was required, the acoustic analogy method would be more reliable. Furthermore, it is expected that as improvements in the acoustic analogy methodology continue, the CFD+LAA modeling approach will become even more competitive.