RANS-Based Noise Predictions of Jets with Internal Forced Mixers *

Transcription

1 12th AIAA/CEAS Aeroacoustics Conference (27th AIAA Aeroacoustics Conference) 8-10 May 2006, Cambridge, Massachusetts AIAA RANS-Based Noise Predictions of Jets with Internal Forced Mixers * L.A. Garrison, A. S. Lyrintzis, G. A. Blaisdell Purdue University, West Lafayette, IN, Internal forced mixers are used in a number of jet engine designs to mix the core and bypass flows inside of a common nozzle. However, currently there are no existing industry design tools that can predict the far-field noise generated in the plumes of jet configurations with internal forced mixers. The work presented in this paper is part of an ongoing effort to develop a stand-alone jet noise prediction methodology for jets with internal mixers. In the current study the performance of two noise models are evaluated for the prediction of the noise from jets with internal forced mixers. The basic components of both noise models consist of portions of single stream jet noise spectra. In the first model, the plume is divided into two regions. The noise from each region is modeled as a modified fully mixed single stream jet. The single stream jet spectra are filtered and modified based on the turbulence levels from a RANS calculation. In the second model, the upstream portion of the plume is divided into a small number of additional sections, each being modeled as a single stream jet. In the second model the single stream jet characteristic velocity and temperature scales are determined from a RANS calculation. These single jet spectra are also filtered and modified based on the turbulence levels in the RANS calculations. The results from both models show an under-prediction in the high frequency portion of the far-field sound pressure level spectra. This under-prediction appears to be due to under-predictions of the CFD calculations of the enhancement of the turbulence levels in the forced mixer jet plumes. Nomenclature Roman Symbols A Jet area D Jet diameter f Frequency Fm Turbulence enhancement F D Downstream spectral filter function F U Upstream spectral filter function H Lobe penetration height k Turbulence kinetic energy L EnJ Length of the enhanced upstream region L s Scallop depth R Radial coordinate T Jet temperature V Jet velocity X Axial coordinate Greek Symbols α Peak turbulence intensity α o Single jet peak turbulence intensity θ Far-field observer location * AIAA presented at the 12 th AIAA/CEAS Aeroacoustics Conference, Cambridge, MA, May Graduate Research Assistant, School of Aeronautics and Astronautics, Student Member AIAA. Professor, School of Aeronautics and Astronautics, Associate Fellow AIAA. Associate Professor, School of Aeronautics and Astronautics, Senior Member AIAA. 1 of 21 Copyright 2006 by the authors. Published by the, Inc., with permission.

2 Subscripts ( ) D Downstream region property ( ) i Upstream section property ( ) m Fully mixed jet property ( ) PC ( ) U Upstream region property Abbreviations CFD Computational Fluid Dynamics PIV Particle Image Velocimetry RANS Reynolds Averaged Navier-Stokes SPL Sound Pressure Level I. Introduction he prediction of jet noise from complex configurations continues to be a problem for industry despite over a half T century of research in flow generated noise. The lack of accurate noise prediction methods for the complex geometries applicable to modern jet engines force engine companies to design, build, and perform relatively expensive experimental tests of new nozzle and mixer designs to determine whether they will meet FAA noise requirements. In addition, the lack of an accurate noise prediction method prevents engine companies from factoring noise into the design of new mixer geometries. Despite recent advances in the application of direct numerical simulations (DNS) and large eddy simulations (LES) to the prediction of jet noise 1-3, these methods remain too computationally expensive for high Reynolds number applications. Consequently, many researchers have worked to develop jet noise prediction methodologies that rely on the flow field information obtained from a solution to the Reynolds averaged Navier-Stokes (RANS) equations with an appropriate turbulence model. The most common of these methods typically adopt some form of the acoustic analogy to determine the far-field noise contribution from each elemental volume of turbulent fluid in the jet plume. The acoustic analogy was originally developed by Lighthill 4-5, which represented aerodynamically generated noise as a distribution of quadrupole sources embedded in a stationary ambient fluid. This approach was extended by Lilley 6 to account for sources embedded in a parallel shear flow. One of the first general applications of the acoustic analogy theory, commonly referred to as MGB, was developed by Mani, Gliebe, and Balsa The MGB methodology was latter extended by Khavaran to use the mean flow and turbulence properties determined from a RANS solution with a two-equation turbulence model. A number of researchers since then have worked to develop and refine jet noise prediction methodologies that use the acoustic analogy. Despite much work on the development of acoustic solvers that use a RANS-based acoustic analogy framework, a robust RANS-based implementation has not yet been developed. In particular, two key inhibiting features are the need to determine calibrated model constants and the need to model the source terms in the acoustic analogy based on two-point correlations of the turbulence statistics. One recent approach to modeling the noise for the complex configuration of a jet with an internal forced mixer has been developed which uses modified single jet noise spectra to build a noise prediction This two-source noise prediction method, which is a modification of the four-source method for predicting coaxial jets developed by Fisher et al , uses a combination of two single jet predictions which are filtered and shifted by empirically derived source strength terms. This type of noise model has been previously shown to be capable of accurately matching experimental noise data for a family of 12-lobe forced mixers. In this study, far-field noise predictions from a two-source model using input parameters determined from a RANS solution are compared to experimental acoustic data. In addition, a more robust extension to the two-source noise model is developed. Results from the new model, which also uses inputs from a RANS calculation, are also compared to the experimental data. II. CFD Analysis In the current study three 12-lobe mixers and two 20-lobe mixers are evaluated. A typical internal lobed mixer configuration is shown in Figure 1. The geometries of all five forced mixers evaluated in this study are shown in Figure 2. The 12-lobe mixers all have similar designs, with the primary difference being the lobe penetration height (H), which is defined in Figure 3. In addition to the 12-lobe mixers, both a scalloped and an unscalloped 20-lobe high penetration mixer were evaluated. The properties of the forced mixers are given in Table 1. These forced mixer geometries have been extensively tested in the NASA Glenn Aeroacoustic Propulsion Laboratory. 24 The 2 of 21

3 experimental program consisted of both far-field acoustic measurements and particle image velocimetry (PIV) measurements in the jet plume. The far-field acoustic measurements are used in the comparisons of the noise predictions in Section IV. The PIV measurements have been used to validate the computational fluid dynamics (CFD) analysis of the jet plume flow fields. 18,21 The CFD analysis of the steady-state jet plume flow fields is performed using the WIND code, which solves the Reynolds averaged Navier-Stokes (RANS) equations. 25 The two-equation shear stress transport (SST) turbulence model is used in all of the CFD simulations. 26 A complete description of the CFD analysis and validation with experimental PIV data is given in References 18 and 21. III. Noise Model Formulations The initial investigation of using a two-source model for the prediction of the noise from jets with internal lobed mixers was performed as part a previous research effort The most recent developments using this approach have been performed as part of a joint project with Dr. Brian Tester and Dr. Michael Fisher funded by the Aeroacoustics Research Consortium The results from the previous research showed that the far-field Sound Pressure Level (SPL) spectra of a jet with an internal forced mixer can be modeled by empirically fitting the sum of two modified single stream jet spectra. The initial motivation for this noise modeling approach was based on the success of the four-source noise model developed by Fisher et al , which showed that the far-field noise from a coaxial jet could be modeled using the sum of four modified single stream jet spectra. The four-source method is based on the observation that in coaxial jets distinct regions can be identified which exhibit similarity relationships that are identical to those observed in simple single stream jets. Based on this fact, it was then proposed that the noise of a simple coaxial jet can be described as the combination of four noise producing regions each of whose contribution to the total far field noise levels is the same as that produced by a single stream jet with the appropriate characteristic velocity, temperature, and length scales. This approach allows existing experimental databases of single stream jet noise spectra to be used as a foundation for determining the noise from a coaxial jet. For coaxial jets the four noise source regions are the secondary-ambient shear layer, the primarysecondary shear layer, the interaction region where the secondary-ambient shear layer and primary-secondary shear layer merge, and finally the fully mixed region. Following a similar approach as the four-source method, the previous research work on semi-empirical noise models led to the development of a two-source model formulation for forced mixer applications This formulation, which was based on both observations of the changes in the forced mixer experimental noise data and the aerodynamic structure of the forced mixer jet plumes, uses the sum of two modified single stream jet noise spectra. It was observed that the velocities of the flow exiting the nozzle of a jet with an internal forced mixer were often close to the fully mixed jet velocity scale. In addition, it was observed that the forced mixers produce turbulent streamwise vortices which eventually impact the main jet shear layer causing a local enhancement of the turbulence intensity. The enhancement of the shear layer turbulence intensity increases as the lobe mixer penetration height increases. It is, therefore, proposed that the increase in high frequency noise that occurs in jets with forced mixers is due to the enhanced turbulence levels that are produced in the jet plume from the interaction of the main jet shear layer and the turbulent streamwise vorticies. In the current study the performance of two noise models are evaluated. The basic components of both noise models consist of portions of single stream jet noise spectra. In the first model, the plume is divided into two regions. The noise from each region is modeled as a modified fully mixed single stream jet. The single stream jet spectra are filtered and modified based on the turbulence levels from the RANS calculations. In the second model, the upstream portion of the plume is divided into a number of additional sections, each being modeled as a single stream jet. In this model the single stream jet characteristic velocity and temperature scales are determined from a RANS calculation. These single jet spectra are also filtered and modified based on the turbulence levels in the RANS calculations. A. Two-Source Noise Model In the two-source model approach the jet plume is divided into two regions, as shown in Figure 4. The noise that is generated in the upstream region of the jet plume is modeled as an enhanced, fully mixed, single stream jet. The noise from this source region is modeled using the far-field spectra of a single stream jet that has been filtered to remove the low frequency portion (corresponding to sources in the downstream region of the plume) and enhanced to represent the effects of higher turbulence levels in the jet shear layer that result from the interaction of the streamwise vorticies generated by the forced mixer. The noise from the upstream region, SPL U, is then given as 3 of 21

4 = θ + + ( ) SPL ( θ, f ) SPL( V, T, D,, f ) 10log F ( f, f ) 40log10 Fm U m m 10 U c, (1) where SPL refers to a single stream jet noise prediction using the final nozzle diameter, D, and the fully mixed velocity, V m, and temperature, T m. In the current study the single jet noise predictions are made using the ESDU database. 27 The fully mixed jet properties (V m, T m, A m ) provide the same mass, momentum and energy as the unmixed coaxial jet flow. In addition, the term 10log 10 (F U ) represents the spectral filter which eliminates the low frequency portion of the spectra. 22 This spectral filter is a function of the cut-off frequency, f c, given as f c V D X ( ) = m D P C, (2) m L EnJ X where L EnJ is the length of the enhanced upstream region and ( D ) PC is the axial location of the end of the potential core, which usually occurs at approximately 5 diameters downstream of the nozzle exit for a single stream jet. The formulation of the cut-off frequency given in Equation 2 is consistent with the assumption that a Strouhal number of 1 is associated with noise sources near the end of the potential core. In Equation 1 the single jet enhancement level, Fm, is defined as Fm = α, (3) α o where α is the peak turbulence intensity in the upstream portion of the actual jet plume and α o is the peak turbulence intensity in a single stream jet. In this study the turbulence intensities are defined as k α =, (4) V where V J is the characteristic jet velocity and k is the turbulence kinetic energy, which is determined from a RANS calculation. In a similar fashion, the downstream region of the jet is modeled as a fully mixed single stream jet that is filtered to eliminate the high frequency portion of the noise spectra. The noise from this source region, SPL D, is then given as D m m m 10 D J SPL ( θ, f ) = SPL( V, T, D, θ, f ) + 10log F ( f, f ), (5) where 10log 10 (F D ) is the filter function which eliminates the high frequency portion of the single stream jet spectra. The total noise prediction is then found by adding the uncorrelated contributions from the two source regions. B. Multi-Source Noise Model The basic approach in the multi-source noise model is similar to the two-source model. However, the formulation of the multi-source model has two primary differences. First, the characteristic jet velocities and temperatures for the upstream sections are determined directly from a RANS calculation. Second, the upstream portion of the jet plume is divided into a small number of additional sections, as shown in Figure 5. The impact of determining the representative single jet properties directly from a RANS solution, as opposed to using the fully mixed jet values, is evaluated by using one section in the upstream region. The multi-source model approach should provide more robust predictions for a wider range of geometric configurations since it has a more general formulation that does not assume that the fully mixed velocity scale characterizes the entire upstream region. In the multi-source model formulation the noise from the downstream region is modeled in the same fashion as the two-source model using Equation 5. The noise from each of the upstream sections, SPL i, is modeled as c 4 of 21

5 ( ) SPLi( θ, f ) = SPL( Vi, Ti, D, θ, f ) + 10log 10 Fi( fi, f ) + 40log10 Fmi, (6) where V i, and T i are the characteristic jet properties in a given section (CFD-based), Fm i is the single jet enhancement level based on the peak turbulence intensities in a given section (CFD-based), and F i is the filter function for a given section. The filter functions for the upstream sections are formulated in same process that Fisher et al. 22 used to develop the four-source model spectral filters. In this process the fraction of the total energy radiated between two axial locations in the plume, F i, is found by integrating a model source distribution function. Using this approach, the filter functions are calculated as F i X 2 X1 = 0 S( X) dx S( X) dx, (7) where S(X) is a model source distribution function. For the current analysis, the model source distribution function, which is a function of frequency, is defined as 3 4XD m S( X) = X exp f XPC Vm, (8) where X PC is the location of the end of the potential core. In Equation 8 it is assumed that the source distribution centroid location is inversely proportional Strouhal number and that for a Strouhal number of 1 the centroid location occurs at the end of the potential core. An example of the spectral filter function values for a sample case with 4 equally spaced upstream sections between the nozzle exit (X/D=0) and X/D=5 is shown in Figure 6. IV. CFD-Based Noise Predictions In this section the predictions of the two noise models previously described are compared to experimental acoustic data. The noise predictions presented here do not use any empirical constants that are dependent on the lobed mixer design. Instead all lobed mixer dependent model parameters are determined based on data from the RANS calculations of the jet plume flow fields. In all of the following noise predictions the far-field sound pressure level spectra for the basic single stream jet components, SPL(V,T,D,θ,f), are determined using the ESDU prediction method. 27 A. Two-Source Noise Model In the two-source model predictions the upstream region enhancement level, Fm, is calculated based on the peak turbulence intensities in the jet plume of a RANS calculation. The axial variation of the peak turbulence intensity is shown in Figure 7 for the five lobed mixers. Also included for reference in Figure 7 is the peak turbulence intensities of a single stream jet. For the lobed mixer flow fields, at a given axial location in the upstream portion of the jet plume the peak turbulence intensity typically occurs along the lip-line in the lobe peak azimuthal plane. It is seen in Figure 7 that for the 12-lobe mixers the magnitude of the peak turbulence intensity increases with increasing lobe penetration height. In addition, the location of the peak turbulence intensity moves upstream with increasing lobe penetration height. The upstream region enhancement levels for each lobed mixer design are calculated using the peak values in Figure 7 along with Equation 3. These CFD derived model parameters are given in Table 2, along with the empirically derived two-source model parameters. The empirically derived parameters are determined by fitting a two-source model to the acoustic data using three variable model parameters. The three empirical model parameters are the upstream region enhancement level, Fm, the downstream region enhancement level, Fm D, and the length of the enhanced region, L EnJ. Additional details concerning the determination of the empirical model parameters can be found in References 15 and 16. The data for the length of the enhanced region, L EnJ, in Table 2 is calculated based on a potential core length of 5 diameters. It is seen that the empirical value for the downstream region enhancement level has a value of approximately 1 for all lobed mixer designs. However, it is noted that this parameter does decrease slightly as the lobed mixer penetration height increases. This trend suggests that for the higher penetration mixers the turbulence levels in the downstream region of the jet plume are slightly less then those in the downstream region of a single stream jet. Since the differences in the empirical values for this 5 of 21

6 model parameter are small, as a first approximation a value of 1 is used in the CFD-based predictions for all lobed mixer designs. In addition, it is seen in Table 2 that there is also a small variation in the empirical values of the length of the enhanced jet, L EnJ, (and the corresponding cut-off Strouhal number) for all of the lobed mixer designs. A variation of the length of the enhanced region from 1.0D to 2.0D corresponds to a difference in the cut-off frequency of less than 3 one-third octave band numbers for typical set point 110 fully mixed jet conditions. As a result, for the CFD-based predictions a constant value of 1.5D is used for the enhanced region length for all lobed mixer designs. Comparisons between the CFD-based two-source model predictions and the experimental acoustic data are shown for each lobed mixer design in Figures Also included in these comparisons are the two-source model predictions using the empirically derived model parameters. It is seen in Figure 8 that the agreement of the CFDbased prediction is comparable to the predictions using the empirical model parameters for the 12CL mixer. However, a noticeable under-prediction of the high frequency region is seen for the other forced mixers. This under-prediction of the high frequency portion of the far-field noise spectra implies that the CFD predicted peak turbulence intensities are too low. In general it is seen from comparisons between the CFD results 18,21 and PIV data 24 that the CFD analysis typically over-predicts the turbulence levels, which is contradictory to what one would infer from the CFD-based and empirically derived two-source noise model parameters. Upon further review it has been determined that the CFD calculations actually under-predict the enhancement of the turbulence intensities in the shear layer for the forced mixer configurations (i.e. the ratio of forced mixer peak turbulence levels to those in a single stream jet). A comparison of the CFD and PIV peak turbulence intensities in the shear layer of a static (no flight stream) single stream jet is given in Figure 13. In this figure it is observed that the CFD analysis over-predicts the turbulence levels with a peak value of approximately 16.4%, compared to the PIV data peak value of about 15.4% (traditional scaling laws based on other experimental data suggest a peak value of about 15%). The peak values in the azimuthally averaged turbulence intensities for the 12UM and 12UH forced mixer configurations are shown in Figure 14 for both CFD predictions and the PIV data at set point 312. In this figure it is also observed that the CFD analysis over-predicts the peak turbulence levels in the jet plume. However, in Figure 15 the ratio of the forced mixer peak turbulence levels (Figure 14) to the single jet peak turbulence levels (Figure 13) is shown. Here it is observed that although the CFD analysis over-predicts the absolute turbulence intensities, it actually under-predicts the enhancement of the turbulence levels due to the interaction of the turbulent streamwise vorticies with the main jet shear layer. It should be noted that in the data plotted in Figure 15 the numerator of the ratio (forced mixer peak turbulence levels) correspond to a set point with a Mach 0.2 flight stream, however the data in the denominator of the ratio (single jet peak turbulence level) corresponds to a static condition (no flight stream). As a result, the forced mixer peak turbulence levels reflect a reduction due to the presence of the flight stream. If static forced mixer data were used, then the result would be consistent with an azimuthally averaged turbulence enhancement parameter, Fm. However, PIV data was only acquired at set point 312 for these configurations so a complete CFD to PIV comparison can not be made for a static condition. B. Multi-Source Noise Model The multi-source noise model has been developed by applying two modifications to the standard two-source model. First, the characteristic jet properties (velocity and temperature) for each upstream section are determined from a RANS calculation rather than being assumed equal to the values for a fully mixed jet. Second, the upstream region is divided into a small number of additional subsections. The effects of these two modifications are tested independently. First, a noise prediction is made using just one upstream section with a characteristic jet velocity and temperature that is determined from a RANS solution. These results are compared to a noise prediction with the standard two-source model (using the fully mixed velocity and temperature scale for the upstream region). Second, the effect of dividing the upstream region in to several subsections is studied. The CFD-based single stream jet characteristic properties in each section are determined by analyzing the mean velocity profiles in a RANS solution. In this process each radial grid line at a given axial location in the jet plume is analyzed to find the location of the inside edge of the shear layer. In this study this location is defined by finding the first radial point in the jet plume between the jet lip-line and the centerline where the mean velocity gradient (dv/dr) drops below a specified fraction of the velocity gradient at the lip-line (R/D=0.5). This process is shown graphically in Figure 16 for an example threshold fraction of Once the shear layer edge location is identified, the velocity and temperature values at this location are stored. The characteristic jet velocity and temperatures are then determined by averaging the shear layer inside edge values at all axial locations in a given section of the plume. In Figure 17 sample velocity profiles are shown for the 12CL mixer at four downstream locations. In Figure 17 the locations of the inside edge of the shear layer are marked with a circle. The axial variation of the shear layer inside 6 of 21

7 edge velocities for the five lobed mixers calculated using their respective RANS solutions are shown in Figure 18. In addition, the corresponding shear layer edge locations are shown in Figure 19. A jump in the shear layer edge velocities is seen in Figures 18 and 19 at an axial location of approximately 5 diameters downstream. This jump corresponds to the point when the algorithm begins to identify the centerline as the shear layer inside edge, which generally occurs shortly after the location of the end of the potential core of the unmixed core flow. The impact of extracting the characteristic jet velocity and temperature from the forced mixer RANS solutions is first examined by making a noise prediction with one section in the upstream region. The upstream region characteristic jet properties are determined by averaging the shear layer edge properties from the nozzle exit to approximately 5 diameters downstream. The results from this process for each lobed mixer design are given in Table 3. In Figure 20 noise predictions using the CFD-based single stream jet properties for the upstream region are compared to the standard two-source model predictions (which use the fully mixed velocity and temperature scales for the upstream region single jet prediction). It is seen in Figure 20 that the noise predictions using the CFD-based velocity scale are almost identical to the standard two-source model predictions, which is expected since the average velocity scales in the upstream region for all of the lobe mixer design are within 5% of the fully mixed velocity scale. In the multi-source model formulation the upstream region is divided into several subsections. The locations of the subdivisions are determined based on the axial variation of the shear layer edge velocity for each lobed mixer. These divisions are chosen at points where there are sharp changes in the axial variation of the shear layer edge velocity. The average shear layer edge velocity and the peak turbulence enhancement level for these sections as determined from the RANS CFD solutions are shown in Figures 21 and 22, respectively. Multi-source noise model predictions using these values are shown in Figures It is seen in Figures 23 and 24 that the multi-source model predictions for the 12CL and 12UM mixer are in better agreement with the experimental data when compared to the standard two-source model predictions. However, it is noted that for the high penetration 12UH mixer the multi-source model predictions show an increase in the under-prediction of the high frequency portion of the spectrum. This additional under-prediction is likely due to the fact that the multi-source model predictions are dependent on the details of the axial variation of the turbulence intensities in the plume. Although this aspect of the model should provide for more robust noise predictions for a wider range of geometries, it does amplify any deficiencies in the CFD predictions of the turbulence levels in the jet plume. The trends in the experimental SPL data at 90º for various mixer designs are shown in Figure 28. Similar plots of CFD-based two-source model and multi-source model noise predictions are shown in Figures 29 and 30, respectively. It is seen in these Figures that the trends in the high frequency enhancement for various mixer designs are well predicted by the CFD-based two-source model predictions. In particular, for the 12-lobed mixers the high frequency enhancement increases with increasing lobe penetration height. In addition, the 20UH enhancement falls between the 12CL and 12UM values and the 20DH enhancement is comparable to the 12CL value. V. Conclusion In the current study two CFD-based noise prediction methodologies have been presented and their performance has been compared to experimental data. In the first methodology a two-source model prediction is made using fully mixed single stream jet components that are filtered and modified based on the turbulence levels in a RANS CFD solution. This model shows reasonable agreement for low penetration mixer design; however, it under-predicts the high frequency portion of the spectrum for the other mixers. Despite the under-prediction in the absolute noise levels it is noted that the trends in the RANS-based enhancement levels are in agreement with the empirical values for the 12CL, 12UM, 12UH, and 20UH mixers. In the second methodology the standard two-source model prediction method is modified in two ways. First, the upstream section characteristic jet properties are determined directly from the RANS CFD solution. Second, the upstream section is divided into several subsections. The results from this methodology show an improvement in the predictions for the less aggressive mixers. However, predictions for the high penetration mixers show additional under-predictions in the high frequency portion of the spectrum. The under-prediction of the high frequencies that is seen in both noise models is due to an under-prediction of the enhancement of the turbulence intensities in the shear layer for the forced mixer configurations. Acknowledgments The two-source model development work has been performed with Dr. Brian Tester and Dr. Michael Fisher under a grant from the Aeroacoustics Research Consortium (AARC). The first author is also supported by the Purdue Research Foundation. All WIND calculations were performed using 10 CPUs on the School of Aeronautics 7 of 21

8 and Astronautics 104-processor LINUX cluster acquired by a Defense University Research Instrumentation Program (DURIP) grant sponsored by ARO. References 1 Freund, J.B., Lele, S.K., and Moin, P., Direct Numerical Simulation of a Mach 1.92 Turbulent Jet and its Sound Field, AIAA Journal, 38(11): , Freund, J.B., Noise Sources in a Low-Reynolds Number Turbulent Jet at Mach 0.9, Journal of Fluid Mechanics, 438: , Uzun, A., 3-D Large Eddy Simulation for Jet Aeroacoustics, PhD Thesis, School of Aeronautics and Astronautics, Purdue University, West Lafayette, IN, December Lighthill, M.J., On the Sound Generated Aerodynamically: I, General Theory, Proc. Royal Soc. London A, 211: , Lighthill, M.J., On the Sound Generated Aerodynamically: II, Turbulence as a Source of Sound, Proc. Royal Soc. London A, 222:1-32, Lilley, G.M., The Generation and Radiation of Supersonic Jet Noise, Part IV: Theory of turbulence generated jet noise, noise radiation from upstream sources and combustion noise, AFAPL-TR Volume IV, Mani, R., The Influence of Jet Flow on Jet Noise, Journal of Fluid Mechanics, 74(5): , Balsa, T.F., The Acoustic Field of Sources in Shear Flow with Application to Jet Noise: Convective Amplification, Journal of Fluid Mechanics, 79(1):33-47, Balsa, T.F., Gliebe, P.R., Aerodynamics and Noise of Coaxial Jets, AIAA Journal, 15(11): , Gliebe, P.R., T.F. Balsa Aeroacoustics of Axisymmetric Single- and Dual-Flow Exhaust Nozzles, Journal of Aircraft, 15(11): , Khavaran, A. Krejsa, E.A., and Kim, C.M. Computation of Supersonic Jet Mixing Noise for an Axisymmetric Convergent Divergent Nozzle, Journal of Aircraft, 31(3): , Khavaran, A., Role of Anisotropy in Turbulent Mixing Noise, AIAA Journal, 37(7): , Garrison, L.A., Dalton, W.N., Lyrintzis, A.S., and Blaisdell, G.A., An Investigation of the extension of the Four-Source Method for the Prediction of the Noise from Jets with Internal Forced Mixers, AIAA Paper , 9 th AIAA/CEAS Aeroacoustics Conference, Hilton Head, SC, May Tester, B., and Fisher, M.J., 21 st Century Jet Noise Test Data Appraisal, ISVR Consultancy Ref:6920-Final Report, November Garrison, L.A., Jet Noise Models for Forced Mixer Noise Predictions, Master s Thesis, School of Aeronautics and Astronautics, Purdue University, West Lafayette, IN, December Garrison, L.A., Dalton, W.N., Lyrintzis, A.S., and Blaisdell, G.A., On the Development of Semi-Empirical Noise Models for the Prediction of the Noise from Jets with Forced Mixers, AIAA Paper , 10 th AIAA/CEAS Aeroacoustics Conference, Manchester, UK, May Tester, B., Fisher, M.J., and Dalton, W.N., A Contribution to the Understanding and Prediction of Jet Noise Generation in Forced Mixers, AIAA Paper , 10 th AIAA/CEAS Aeroacoustics Conference, Manchester, UK, May Garrison, L.A., Lyrintzis, A.S., Blaisdell, G.A., and W.N. Dalton, Computational Fluid Dynamics Analysis of Jets with Internal Forced Mixers, AIAA Paper , 11 th AIAA/CEAS Aeroacoustics Conference, Monterey, CA, May Tester, B., Fisher, M.J., A Contribution to the Understanding and Prediction of Jet Noise Generation in Forced Mixers: Part II Flight Effects, AIAA Paper , 11 th AIAA/CEAS Aeroacoustics Conference, Monterey, CA, May Tester, B., Fisher, M.J., Garrison, L.A, Lyrintzis, A.S., Blaisdell, G.A., Understanding and Prediction of Lobed Mixer Jet Noise, Final Report submitted to the Aeroacoustics Research Consortium, October Garrison, L.A., Computational Fluid Dynamics and Noise Modeling of Jets with Internal Forced Mixers, PhD Thesis, Purdue University, West Lafayette, IN, May Fisher, M.J., Preston, G.A., and Bryce, W.D., A Modeling of the Noise from Simple Coaxial Jets, Part I: With Unheated Primary Flow, Journal of Sound and Vibration, 209(3): , Fisher, M.J., Preston, G.A., and Mead, C.J.., A Modeling of the Noise from Simple Coaxial Jets, Part II: With Heated Primary Flow, Journal of Sound and Vibration, 209(3): , Bridges, J., and Wernet, M.P., Cross-stream PIV Measurements of Jets with Internal Lobed Mixers, AIAA Paper , 10 th AIAA/CEAS Aeroacoustics Conference, Manchester, UK, May WIND User s Guide, NPARC Alliance, NASA Glenn Research Center, May Menter, F.R., Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications, AIAA Journal, 32(8): , Engineering Science Data Unit (ESDU), Computer-based estimation procedure for single-stream jet noise: Including farfield, static jet mixing noise database for circular nozzles, ESDU: 98019, of 21

9 Mixer ID Number of Lobes Table 1: Forced mixer geometric properties. H/D L s /D Description 12CL lobe, low penetration 12UM lobe, mid penetration 12UH lobe, high penetration 20UH lobe, high penetration 20DH lobe, high penetration, scalloped Table 2: Comparison of the empirical and CFD based two-source model parameters. Mixer ID Empirical Constants CFD-based Constants Fm Fm D L EnJ /D Fm Fm D L EnJ /D 12CL UM UH UH DH Table 3: CFD-based characteristic jet properties for the upstream region. Mixer ID V/V m T/T m 12CL UM UH UH DH of 21

10 Figure 1: Typical forced mixer geometry. (a) (b) (c) (d) (e) Figure 2: Forced mixer geometries: (a) 12CL, (b) 12UM, (c) 12UH, (d) 20UH, (e) 20DH. H H Figure 3: Definition of the forced mixer penetration height. 10 of 21

11 Figure 4: Two-source model source regions in the plume of a jet with an internal lobed mixer. Figure 5: Multi-source model source regions in the plume of a jet with an internal lobed mixer. 11 of 21

12 Figure 6: Example spectra filter functions for the multi-source model. Figure 7: Axial variation of the CFD predictions of the peak turbulence intensity (k 1/2 /V m ) for the five lobed mixers and a single stream jet. 12 of 21

13 Figure 8: Two-source model predictions for the 12CL mixer. Figure 9: Two-source model predictions for the 12UM mixer. 13 of 21

14 Figure 10: Two-source model predictions for the 12UH mixer. Figure 11: Two-source model predictions for the 20UH mixer. 14 of 21

15 Figure 13: Comparison of the CFD and PIV azimuthally averaged peak turbulence intensities in a single stream jet plume. Figure 14: Comparison of the CFD and PIV azimuthally averaged peak turbulence intensities in a forced mixer jet plume. Figure 12: Two-source model predictions for the 20DH mixer. Figure 15: Comparison of the ratio of the forced mixer peak turbulence intensities (Figure 14) to those of a single stream jet (Figure 13). 15 of 21

16 Figure 16: Example of the definition of the inside edge of the shear layer. Figure 18: Shear layer inside edge velocities for the lobed mixers. Figure 17: Sample velocity profiles in the 12CL mixer RANS solution; shear layer inside edge locations are marked with a circle. Figure 19: Shear layer inside edge locations for the lobed mixers. 16 of 21

17 (a) (b) (c) (d) (e) Figure 20: Two-source model and multi-source model noise predictions for the lobed mixers (a) 12CL, (b) 12UM, (c) 12UH, (d) 20UH, (e) 20DH. 17 of 21

18 Figure 21: Single jet characteristic velocity scale for the forced mixers. Figure 22: Single jet upstream section enhancement level for the forced mixers. 18 of 21

19 Figure 23: Multi-source model predictions for the 12CL mixer. Figure 24: Multi-source model predictions for the 12UM mixer. 19 of 21

20 Figure 25: Multi-source model predictions for the 12UH Mixer. Figure 26: Multi-source model predictions for the 20UH mixer. 20 of 21

21 Figure 28: Forced mixer experimental data at 90º. Figure 29: CFD-based two-source model predictions for the forced mixers at 90º. Figure 27: Multi-source model predictions for the 20DH mixer. Figure 30: CFD-based multi-source model predictions for the forced mixers at 90º. 21 of 21