On the Development of Semi-Empirical Noise Models for the Prediction of the Noise from Jets with Forced Mixers

10th AIAA/CEAS Aeroacoustics Conference AIAA 2004-2898 On the Development of Semi-Empirical Noise Models for the Prediction of the Noise from Jets with Forced Mixers L. A. Garrison * Purdue University, West Lafayette, IN, 47905 W. N. Dalton Rolls-Royce Corporation, Indianapolis, IN, 46206-0420 A. S. Lyrintzis and G. A. Blaisdell Purdue University, West Lafayette, IN, 47905 In recent years there has been a significant interest in the development of jet noise prediction models due to increased restrictions on aircraft noise near airports. However, currently there are no industry tools that can be used to predict the noise from the complex flows of modern jet engines that include internal forced mixers. The four-source method is a noise prediction tool applicable to simple coplanar, coaxial jets. In this study the fundamental components of the four-source model are used as the building blocks for a noise prediction method which would be applicable to coaxial jets with internal forced mixers. First, the four-source model is applied to an internally mixed jet with a confluent or axisymmetric mixer. A two-source noise model is then proposed to predict the noise for cases with an internal forced mixer. Three variable parameters in this two-source model are optimized to match the forced mixer experimental noise data. It is shown that the twosource noise model is capable of accurately modeling the noise spectra of internally mixed jets with forced mixers. NPR λ V T D H SPL θ f F U F D db α T St E w Nomenclature = nozzle pressure ratio = velocity ratio = jet velocity = jet total temperature = jet diameter = lobe penetration height = Sound Pressure Level = far-field observer angle (referenced from the upstream or intake axis) = frequency = upstream source filter function = downstream source filter function = source strength reduction / augmentation = ratio of peak turbulence intensities = Strouhal number = error weighting function * Graduate Research Assistant, School of Aeronautics and Astronautics, Student Member AIAA. Manager, Mechanical Methods and Acoustics, Member AIAA. Professor, School of Aeronautics and Astronautics, Associate Fellow AIAA. Associate Professor, School of Aeronautics and Astronautics, Senior Member AIAA. 1 Copyright 2004 by the authors. Published by the, Inc., with permission.

I. Introduction N recent decades there have been increased restrictions imposed on aircraft noise during take-off and landing. Jet I noise is a major component of the overall aircraft noise during take-off. However, currently there are no industry design tools for the prediction of the jet noise resulting from complex jet flows. As a result, the noise levels of modern turbofan jet engines can only be determined by expensive experimental testing after they have been designed and built. Traditionally, turbulent mixing is thought to be the primary source of jet noise. This notion suggests that to be able to predict the noise from a jet in the most general case, one must first have information describing the turbulence. Following this assumption, a number of methods, such as those based on the acoustic analogy, have been developed that use Reynolds averaged Navier-Stokes (RANS) solutions with a k-ε turbulence model as the input to a noise prediction method. 1 However, most current noise prediction methods, such as the acoustic analogy approaches (e.g. MGB 2-4 ) have only been applied to simple axisymmetric single or co-flowing jets. In addition, these methods require a model for the two-point space-time cross correlations of turbulent sources. 1,5 Measurement of these statistics is difficult at best and has been completed for only a small number of flow fields. Based on the data that is available, a number of closure models have been developed but none have proven universally acceptable. As a result, the predictive methods requiring detailed descriptions of the turbulence are not of sufficient accuracy at this time to use for engine design purposes. Furthermore, it has been seen that previous attempts to apply MGB to lobed mixer jets by using circumferential averaging have also proven unsuccessful. 6 Another approach for predicting jet noise currently being investigated involves the use of Large Eddy Simulations (LES) to determine the unsteady pressure fluctuations generated by the turbulent noise sources. The time history of the unsteady pressure fluctuations on a surface that encloses the noise source mechanisms can then be extended to the far field by the use of Kirchoff s method or the Ffowcs Williams-Hawkins method to determine the far-field noise characteristics. 7-9 However, even with the use of the most advanced supercomputers, presently it is not practical to perform LES calculations for Reynolds numbers that are consistent with modern jet engines. In addition, current LES simulations only model the jet plume and not the full complex geometry of the internal nozzle and mixer. Consequently, it is not feasible at this time to use LES as a design tool for the application at hand. An alternate approach to predicting the noise from a coaxial jet has been previously formulated by Fisher et al. 10,11 In this method the total jet noise is found by adding the contributions of four representative sources that are modeled as single stream jets. Although, the four-source method is dependent on the magnitude of the turbulent fluctuations in the jet, it uses experimental far field measurements of single stream jets to determine the noise spectra. Therefore, this method is not dependent on assumptions made about correlations of the turbulent statistics. As a result, the four-source method has been shown to provide accurate predictions of the noise spectra of coaxial jets. The objective of the current study, which is a continuation of previous work 12, is to develop a semi-empirical jet noise model, based on the fundamental concepts of the four-source method, that would be applicable to internally forced mixed jets. First, the four-source coaxial jet prediction method is applied to the case of a jet with an internal confluent or axisymmetric mixer. Then, an alternate noise prediction model, based on two single jet noise sources, is applied to predict the noise for cases with an internal forced mixer. Three variable parameters in this two-source model are then optimized to match the forced mixer experimental noise data at a range of operating conditions. These optimized parameters are then correlated to differences in the mixer geometries. The work summarized in this paper has been performed in parallel with B. Tester and M. Fisher at the ISVR, Southampton, UK, whose work is summarized in Ref. 13. The primary differences between the work summarized here and that of Ref. 13 are the optimization process for matching the two-source models to the experimental data and the method used to make the single jet noise predictions. All of the single jet noise predictions used in this study are calculated based on SAE s ARP876C standards for jet engine exhaust noise predictions. 14 A. Four-Source Method Overview The four-source jet noise prediction method is fundamentally different from approaches based on the acoustic analogy. This method is based on the observation that distinct regions can be identified in coaxial jets that exhibit similarity relationships that are identical to those observed in simple single stream jets. Rather than attempting to model the details of the correlations of turbulence statistics, as is required for the application of the acoustic analogy, the noise of a simple coaxial jet is represented 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 a given 2

characteristic velocity, diameter, and temperature. 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. 10-11 The structure of a simple coaxial jet is shown in Fig. 1. The coaxial jet plume is divided into three regions, the initial region, the interaction region, and the mixed flow region. In the initial region there are two noise producing elements, the secondary-ambient shear layer and the primary-secondary shear layer. The basis of the four-source method relies on the fact that a simple coaxial jet can be broken down into regions whose mean flow and turbulent properties resemble a single stream jet. In particular, in the initial region the secondary-ambient noise source is characterized by the secondary velocity (V s ), diameter (D s ), and temperature (T s ). The noise from the primary-secondary shear layer is usually neglected since the turbulence intensities in this region are much less than those in other parts of the jet plume for the velocity ratios of interest. In the mixed flow region the mixed jet noise source is characterized by the fully mixed velocity (V m ), diameter (D m ), and temperature (T m ), which are found by conserving mass, momentum and energy. The noise produced in the interaction region is represented by the effective jet noise source, which is characterized by the primary velocity (V p ), primary temperature (T p ), and the effective diameter (D e ). The effective diameter corresponds to the diameter of a jet with the primary velocity that would provide the same thrust as that of the original coaxial configuration. The individual noise source regions are corrected to account for source overlap and any deviations from single jet characteristics. Specifically, a low frequency filter is applied to the secondary-ambient noise source to eliminate any contributions from sources that are downstream of the secondary potential core. Similarly, a high frequency filter is applied to the mixed jet noise source to eliminate any contributions from sources upstream of the primary potential core. These corrections are applied to avoid any double accounting between various noise source regions. Finally, the effective jet noise source levels are reduced to account for lower peak turbulence intensities that are observed in the effective jet region of the coaxial jet as compared to a single jet. The overall coaxial jet noise is ultimately found by adding the uncorrelated contributions from the three major noise source regions. In the present study, all of the single jet predictions are made based on the SAE ARP876C guidelines for predicting single stream jet noise. 14 It should be noted that in general these predictions are only accurate to within approximately 3 db. Secondary / Ambient Shear Layer V s Primary / Secondary Shear Layer V p V s Initial Region Interaction Region Mixed Flow Region Figure 1: Structure of a simple coaxial jet. 3

B. Internally Mixed Jets The geometry of modern jet engines can greatly deviate from that of a simple coaxial jet. This fact is particularly true for the case of engines with internal flow mixers. For these configurations the flow will be influenced by both the presence of a center body or tail cone and the nozzle wall contour. A schematic of a simple coplanar, coaxial jet and the internally mixed dual flow configurations examined in this study is shown in Fig. 2. The introduction of a forced, or lobed, mixer, shown in Fig. 3, increases the mixing in a turbulent jet through a number of mechanisms. First, the convolution of the forced mixer increases the initial interface area between the primary and secondary flows as compared to a confluent splitter plate. A second mechanism that creates increased mixing is the introduction of streamwise vortices. These vortices assist the mixing process in two ways. First, they further increase the interface area due to the roll up of the counter rotating vortices. Second, the cross stream convection associated with the streamwise vortices sharpens the interface gradients. 15 In addition to the enhancement of the mixing process, the introduction of the streamwise vortices substantially alters the flow field as compared to the simple coaxial configuration. The structure of lobed mixer flows, which is summarized in the subsequent text, is shown in Fig. 4. In a lobed mixer, each lobe produces a pair of counter rotating vortices. These vortices twist the hot core flow and cold bypass flow in a helical manner. As the vortices evolve downstream they grow due to turbulent diffusion and eventually begin to interact with both their paring vortex and vortices produced by adjacent lobes. Secondary Flow (a) Primary Flow (b) Secondary Flow Primary Flow Secondary Flow Primary Flow (c) Figure 2: Dual flow configurations (a) coplanar, coaxial (b) internally mixed (c) internally forced mixed. 4

Vortex Pair Interactions Vortex Interaction with Cold Bypass Flow Vortex Interactions with Hot Core Flow Vortex Interactions of Adjacent Lobes Figure 3: Typical forced mixer geometry. Figure 4: Forced mixer flow structure. II. Data The experimental acoustic data for the mixers evaluated in this study was taken in Aeroacoustic Propulsion Laboratory at NASA Glenn during the spring of 2003. 16 The jet noise data was acquired in the acoustic far field at a radius of approximately 80 jet diameters. The acoustic data is supplied in the form of one foot lossless 1/3 Octave Sound Pressure Levels at angles ranging from 50 to 165 to the intake axis in 5 increments. Three operating set points are evaluated in this study. The primary and secondary nozzle pressure ratios and the velocity ratios for these set points are shown in Table I. Table I: data set point operating conditions. Set Point NPR primary NPR secondary λ 110 1.39 1.44 0.68 210 1.54 1.61 0.64 310 1.74 1.82 0.62 III. Confluent Mixer Predictions Before applying the four-source method to an internally mixed jet it is important to note that the four-source method was derived for a coplanar, coaxial jet. As a result, to properly apply the four-source method an Equivalent Coplanar Coaxial jet has been defined by Tester and Fisher 13, where the primary and secondary flow properties are defined at the final nozzle exit. In this study, the final nozzle exit primary and secondary flow properties are determined based on the nozzle exit area and measurements of the mass flow and total pressure and temperature in both the primary and secondary streams. Using the Equivalent Coplanar Coaxial jet primary and secondary flow properties, the four-source method is used to predict the noise of the internally mixed configuration with a confluent mixer. The noise spectra for the four- 5

source method prediction and for a fully mixed single prediction are shown in Figures 5 and 6 for set point 110 and 210, respectively. From these comparisons it can be seen that the four-source noise predictions agree well with the experimental data. Slight deviations in the four-source prediction occur at angles close to the jet axis where the foursource method somewhat under-predicts the noise near the spectral peak. The errors between the model predictions and the experimental data are evaluated at each of the 27 1/3 octave bands over a range of angles from 90 to 160 from the intake axis, in 5 increments. This process results in approximately 400 error values. Three metrics are used to evaluate the errors between the noise predictions and the experimental data. These metrics are the maximum error, the average error, and the average weighted error. The average weighted error is calculated by first weighting the errors at each angular location using the weighting function E w ( θ f) i 0.1( SPL exp ( θi, f) SPL exp ( θi, f) max ) = (1), 10 which is based on the experimental data spectrum. This weighting function has a value of 1 at the peak of the experimental data, and approaches 0 as the differences between a given experimental Sound Pressure Level value and peak Sound Pressure Level in the experimental data spectrum become large. This weighting, which is similar to the one implicit in the calculation of the Overall Sound Pressure Level, will weigh the errors in the predicted Sound Pressure Level that are closer to the peak in the experimental data more heavily. The weighted errors at all angular locations are then averaged to determine the average weighted error. The maximum error, average error, and average weighted errors between the various noise predictions and the experimental data for the confluent mixer are given in Table II. It is seen that the four-source prediction average weighted error is approximately half that of the single jet prediction average weighted error. These error values can be used as a baseline for evaluating the performance of the forced mixer noise model predictions. Set Point 110 210 Table II: Confluent mixer prediction errors. Prediction Maximum Error [db] Average Error [db] Weighted Error Four-Source 14.94 1.96 0.37 Single Jet 14.24 2.29 0.73 Four-Source 10.66 1.83 0.49 Single Jet 11.01 2.44 0.90 6

90 90 Data Single Jet Prediction Coaxial Jet Prediction FS Sources Data Single Jet Prediction Coaxial Jet Prediction FS Sources 120 Data Single Jet Prediction Coaxial Jet Prediction FS Sources 150 Data Single Jet Prediction Coaxial Jet Prediction FS Sources 120 Data Single Jet Prediction Coaxial Jet Prediction FS Sources 150 Data Single Jet Prediction Coaxial Jet Prediction FS Sources Figure 5: Confluent Mixer Predictions at Set Point 110. Figure 6: Confluent Mixer Predictions at Set Point 210. 7

IV. Forced Mixer Noise Predictions A. Forced Mixer Jet Noise In addition to the confluent mixer, three different forced mixers are evaluated in this study. All three forced mixers have the same number of lobes, and are of similar designs. The primary difference between them is their lobe height, or penetration height (H). The penetration height of a forced mixer is defined as the difference between the maximum and minimum radii at the end of the mixer, as shown in Fig. 7. The lobe penetration height values nondimensionalized by the final nozzle diameter (H/D) for the three forced mixers (Low, Mid, and High) are given in Table III. The effects of the differences in lobe penetration on the experimental far-field noise spectra at set point 110 are shown in Fig. 8. Here it is seen that as the forced mixer penetration increases, the low frequency part of the spectrum decreases, while the high frequency part of the spectrum increases. Based on the experimental data shown in Fig. 8, it is clear that additional noise generating mechanisms will need to be accounted for in a forced mixer noise prediction method. H H Figure 7: Definition of lobe mixer penetration height. Table III: Forced mixer non-dimensional lobe penetration heights. Forced Mixer Mixer ID H/D Low 12CL 0.199 Mid 12UM 0.260 High 12UH 0.280 B. Forced Mixer Noise Model Based on observations of the changes in the forced mixer experimental noise data, an alternate noise prediction model is proposed which uses portions of two corrected single stream jet noise spectra. The low frequency region of the noise spectrum is modeled using a reduced, filtered, fully mixed jet, given as SPL ( θ, f) = SPL(V,T,D, θ, f) + 10log F ( f, f) + db (2) md m m m 10 D m md where SPL md refers to the noise from the downstream fully mixed jet source and SPL refers to a single jet prediction using the fully mixed jet values, V m, T m, and D m. In addition, the spectral filter, F D, filters out the high frequency part of the spectrum, which corresponds to sources in the upstream portion of the fully mixed single stream jet. This filter is a function of the filter cut-off frequency, f m. The form of this filter, as given in Ref. 10, is 8

2 3 f f 1 f 1 f FD = exp 4 1+ 4 + 4 + 4 fc fc 2 fc 6 f c (3) where f c is the filter cut-off frequency. The source reduction term, db md, shifts the fully mixed jet noise spectra down. This term can be related to differences in the turbulence intensities of a simple single stream jet and of those which occur in the downstream portion of the actual jet plume. This relationship, as given in Ref. 10, is ( α ) db= 40log (4) where α T is the ratio of peak turbulence intensities in the actual jet plume to the peak turbulence intensities in a simple single stream jet. In this study, the source strength parameter, db, is a free parameter whose value is determined empirically through the parameter optimization process. Consequently, the resulting α T values will be theoretical estimates of the magnitude of the turbulence intensities in the actual jet plume. If this turbulence information is known, then it can be compared to the optimized values to provide a measurement of the validity of the assumptions made in this model. Two models are evaluated for the prediction of the high frequency region of forced mixer noise spectra, which corresponds to the upstream portion of the actual jet plume. The first model (Model 1) uses an augmented, filtered, fully mixed jet, given as 10 T SPL ( θ, f) = SPL(V,T,D, θ, f) + 10log F ( f, f) + db mu m m m 10 U m mu (5) where SPL mu refers to the noise from the upstream fully mixed jet source and SPL refers to a single jet prediction using the fully mixed jet values, V m, T m, and D m. The spectral filter, F U, filters out the low frequency part of the single jet noise prediction, which corresponds to sources in the downstream region of the jet plume. From Ref. 10, this filter is given as F = 1 - F U D (6) The source augmentation term, db mu, shifts the fully mixed jet noise spectra up. This term is analogous to the differences that are seen in a single stream jet whose turbulence intensities are increased. The second model (Model 2) for predicting the high frequency part of the forced mixer noise spectrum uses an augmented, filtered, secondary jet, given as SPL ( θ, f) = SPL(V,T,D, θ, f) + 10log F ( f, f) + db (7) su s s s 10 U s su where SPL su refers to the noise from the upstream secondary jet source and SPL refers to a single jet prediction based on the secondary flow values, V s, T s, and D s. Similar to the previous source model, a spectral filter is applied to eliminate the low frequency part of the single jet prediction, and the overall source levels are augmented by the source strength term db su. For simplicity, it is assumed that the cut-off Strouhal numbers of the low frequency and high frequency sources are equal. The cut-off frequency, f c, can be calculated from the cut-off Strouhal number, St c, through the relation V f (8) c = St c D where V and D are the jet characteristic velocity and diameter, respectively. 9

C. Parameter Optimization The proposed two-source model has three variable parameters, the low frequency source reduction, db md, the high frequency source augmentation, db mu or db su, and the common cut-off Strouhal number, St c. The optimum values of these variable parameters for a given mixer and nozzle geometry are determined empirically through the use of a non-linear least squares optimization method. In this method the best set of variable parameters are found which minimize the average of the weighted errors between the model prediction and the experimental data. This process essentially curve-fits the experimental data using the two-source model. The non-linear least squares optimization is performed using MATLAB s lsqnonlin function. This routine uses a Levenberg-Marquardt method for minimizing the errors between the model prediction and the experimental data. This non-linear least squares optimization routine is used to find the optimum source strength parameters for a given cut-off Strouhal number. This process is repeated for a range of cut-off Strouhal numbers to find the set of optimized parameters which yield the lowest averaged weighted error. This exhaustive type of approach for determining the optimum cut-off Strouhal number is necessary because of the non-linear nature of the filter functions and the averaged weighted error criterion, which cause difficulties due to both solution non-uniqueness and the presence of local mimina. This process is repeated for three set point operating conditions for each mixer design. The optimization information from all three set points is then combined to determine the single set of optimized model parameters for a given mixer geometry. The final optimized parameters from all three forced mixers can then be correlated with the changes in the mixer geometry, namely the mixer penetration height. D. Model 1 Results The final optimized parameters for each mixer design that result from using the reduced, filtered, fully mixed jet and the augmented, filtered, fully mixed jet model (Model 1) are shown in Table IV. The peak turbulence intensity ratios that are consistent with the optimized db source strength terms calculated using Eqn. 4 are also given in Table IV. As expected the upstream source strength term increases with increasing penetration. Likewise, the downstream source strength decreases with increasing penetration. In addition, there is a relatively small variation in the Strouhal number for the three mixer designs. The typical range of Strouhal numbers in the experimental SPL spectra range from 0.1 to 50. The final parameters for each mixer design are plotted in Figures 9 and 10. The source strength terms are correlated to the non-dimensional mixer penetration height with a linear relation. The cut-off Strouhal number is assumed constant in this model and is found by averaging the three values. The Sound Pressure Level spectra predictions using the final parameter correlations for the low and high penetration mixers at set point 110 are shown in Figures 11 and 12, respectively. In addition, the final spectra predictions for the low and high penetration mixers at set point 210 are shown in Figures 13 and 14, respectively. The maximum, average, and average weighted errors that result from the model 1 predictions with the final optimized parameters at set points 110 and 210 are given in Table V. The two-source prediction average error and average weighted error values for all three mixer designs are comparable to the error values between the four-source prediction and the confluent mixer experimental data. This fact suggests that a two-source prediction is capable of accurately modeling the noise from an internally mixed jet with a forced mixer. Mixer Penetration Table IV: Model 1 final parameter optimization results. db mu db md St c (α T ) mu (α T ) md Low 4.91-0.12 5.45 1.33 0.99 Mid 6.91-0.71 4.25 1.49 0.96 High 7.96-1.96 4.33 1.58 0.89 10

Set Point 110 Table V: Model 1 prediction errors at set points 110 and 210. Mixer Penetration Maximum Error [db] Average Error [db] Weighted Error Low 7.74 1.58 0.46 Mid 7.94 1.34 0.36 High 5.61 1.36 0.44 Low 5.65 1.41 0.39 210 Mid 6.17 1.35 0.40 High 7.13 1.23 0.39 E. Model 2 Results The final optimized parameters for each mixer design that result from using the reduced, filtered, fully mixed jet and the augmented, filtered, secondary jet model (Model 2) are shown in Table VI. The peak turbulence intensity ratios that are consistent with the optimized db source strength terms calculated using Eqn. 4 are also given in Table VI. Similar to the results from Model 1, it is seen that the upstream source strength term increases with increasing penetration. Likewise, the downstream source strength decreases with increasing penetration. In addition, once again there is a relatively small variation in the Strouhal number for the three mixer designs. The final parameters for each mixer design are plotted in Figures 15 and 16. Once again, the source strength terms are correlated to the non-dimensional mixer penetration height with a linear relation and the cut-off Strouhal number is assumed constant in this model. The Sound Pressure Level spectra predictions using the final parameter correlations for the low and high penetration mixers at set point 110 are shown in Figures 17 and 18, respectively. In addition, the final spectra predictions for the low and high penetration mixers at set point 210 are shown in Figures 19 and 20, respectively. The maximum, average, and average weighted errors that result from the model 2 predictions with the final optimized parameters at set points 110 and 210 are given in Table VII. Again, the two-source prediction average error and average weighted error values for all three mixer designs are comparable to the error values between the four-source prediction and the confluent mixer experimental data. This fact suggests that this two-source model is also capable of accurately modeling the noise from an internally mixed jet with a forced mixer. Mixer Penetration Table VI: Model 2 final parameter optimization results. db su db md St c (α T ) su (α T ) md Low 8.66-0.06 6.86 1.65 1.00 Mid 10.06-0.70 4.25 1.78 0.96 High 11.04-1.99 4.25 1.89 0.89 11

Table VII: Model 2 prediction errors at set points 110 and 210. Set Point 110 Mixer Penetration Maximum Error [db] Average Error [db] Weighted Error Low 5.22 1.77 0.49 Mid 5.34 1.43 0.35 High 4.48 1.27 0.40 Low 5.48 1.64 0.41 210 Mid 5.69 1.40 0.41 High 7.10 1.20 0.40 V. Conclusion The results of the preceding study demonstrate that the noise from a jet with an internal forced mixer can be matched using a two-source model. The single jet sources in this model are filtered and their source strengths are modified. The optimum source strength and filter cut-off Strouhal numbers are determined empirically. These values can be correlated to the mixer penetration to yield a predictive tool that will be able to model the noise from this family of forced mixers. Future work in this area will focus on developing a correlation between the model source strength terms and the turbulent properties in the actual jet plume. Acknowledgments This work has been a joint effort between Purdue University and Rolls-Royce, Indianapolis and has been sponsored by the Indiana 21 st Century Research and Technology Fund. Additional guidance has been provided by Dr. Brian Tester and Dr. Mike Fisher from the ISVR, Southampton, United Kingdom. In addition, the experimental data used in this study has been provided by Dr. James Bridges at NASA Glenn. References 1 Morris, P. J., and Farassat, F., Acoustic Analogy and Alternative Theories for Jet Noise Prediction, AIAA Journal, Vol. 40, No. 4, 2002, pp. 671-680. 2 Balsa, T.E., and Gliebe, P.R., Aerodynamics and Noise from Fine-Scale Turbulence, AIAA Journal, Vol. 15, No. 11, 1977, pp. 1550-1558. 3 Khavaran, A., Krejsa, E.A., and Kim, C.M., Computation of Supersonic Jet Mixing Noise for an Axisymmetric Convergent Divergent Nozzle, Journal of Aircraft, Vol. 31, No. 3, 1994, pp. 603-609. 4 Khavaran, A., Role of Anisotropy in Turbulent Mixing Noise, AIAA Journal, Vol. 37, No. 7, 1999, pp. 832-841. 5 Tam, C.K.W., and Auriault, L., Jet Mixing Noise from Fine-Scale Turbulence, AIAA Journal, Vol. 37, No. 2, 1999, pp. 145-153. 6 Barber, T.J., Chiappetta, L.M., and Zysman, S.H., An Assessment of Jet Noise Analysis Codes for Mulitstream Axisymmetric & Forced Mixer Nozzles, AIAA Paper 1996-0750. 7 Uzun, A., Blaisdell, G.A. and Lyrintzis, A.S., 3-D Large Eddy Simulation for Jet Aeroacoustics, AIAA Paper 2003-3322, May 2003. 8 Zhao, W., Frankel, S.H., and Mongeau, L., Large Eddy Simulations of Sound Radiated from Subsonic Turbulent Jets, AIAA Journal, Vol. 39, No. 8, 2001, pp. 1469-1477. 9 Bogey, C., Bailly, C., and Juve, D., Computation of the Sound Radiated by a 3-D Jet Using Large Eddy Simulation, AIAA Paper No. 2000-2009, June 2000. 10 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, Vol. 209, No. 3, 1998, pp. 385-403. 11 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, Vol. 209, No. 3, 1998, pp. 405-417. 12 Garrison, L.A., Dalton, W.N., Lyrintzis, A.S., and Blaisdell, G.A., An Investigation of the Extension of the Four-Source Method for Predicting the Noise from Jets with Internal Forced Mixers, AIAA Paper No. 2003-3165, May 2003. 13 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 2004-2897, May 2004. 14 ARP876C: Gas Turbine Jet Exhaust Noise Prediction, Society of Automotive Engineers, Inc, November 1985. 12

15 Waitz, I.A., Qiu, Y.J., Manning, T.A., Fung, A.K.S., Elliot, J.K., Kerwin, J.M., Krasnodebski, J.K., O Sullivan, M.N., Tew, D.E., Greitzer, E.M., Marble, F.E., Tan, C.S., and Tillman, T.G., Enhanced Mixing with Streamwise Vorticity, Progress in Aerospace Sciences, 1997, Vol. 33, pp. 323-351. 16 Bridges, J., and Wernet, M.P., Cross-stream PIV Measurements of Jets with Internal Lobed Mixers, AIAA Paper 2004-2896, May 2004. 13

90 CFM 12CL 12UM 12UH 120 CFM 12CL 12UM 12UH 150 CFM 12CL 12UM 12UH Figure 8: Comparison of the confluent and forced mixer experimental data for set point 110. 14

Source Strength db [db] 8 7 6 5 4 3 2 1 0 1 Upstream Jet Downstream Jet 2 0.18 0.2 0.22 0.24 0.26 0.28 0.3 Lobe Penetration / Nozzle Diameter Figure 9: Model 1 optimized parameter correlations for the source strength terms. Cut Off Strouhal Number 10 1 10 0 10 1 0.18 0.2 0.22 0.24 0.26 0.28 0.3 Lobe Penetration / Nozzle Diameter Figure 10: Model 1 optimized parameter correlations for the cut-off Strouhal number. 15

90 90 120 150 120 150 Figure 11: Model 1 prediction for the low penetration mixer at set point 110. Figure 12: Model 1 prediction for the high penetration mixer at set point 110. 16

90 90 120 150 120 150 Figure 13: Model 1 prediction for the low penetration mixer at set point 210. Figure 14: Model 1 prediction for the high penetration mixer at set point 210. 17

15 Upstream Jet Downstream Jet Source Strength db [db] 10 5 0 5 0.18 0.2 0.22 0.24 0.26 0.28 0.3 Lobe Penetration / Nozzle Diameter Figure 15: Model 2 optimized parameter correlations for the source strength terms. Cut Off Strouhal Number 10 1 10 0 10 1 0.18 0.2 0.22 0.24 0.26 0.28 0.3 Lobe Penetration / Nozzle Diameter Figure 16: Model 2 optimized parameter correlations for the cut-off Strouhal number. 18

90 90 120 150 120 150 Figure 17: Model 2 prediction for the low penetration mixer at set point 110. Figure 18: Model 2 prediction for the high penetration mixer at set point 110. 19

90 90 120 150 120 150 Figure 19: Model 2 prediction for the low penetration mixer at set point 210. Figure 20: Model 2 prediction for the high penetration mixer at set point 210. 20