JET NOISE MODELS FOR FORCED MIXER NOISE PREDICTIONS. A Thesis. Submitted to the Faculty. Purdue University. Loren A. Garrison

Transcription

1 JET NOISE MODELS FOR FORCED MIXER NOISE PREDICTIONS A Thesis Submitted to the Faculty of Purdue University by Loren A. Garrison In Partial Fulfillment of the Requirements for the Degree of Masters of Science in Aeronautics and Astronautics December 2003

2 ii ACKNOWLEDGMENTS I would like to thank Professor Tasos Lyrintzis and Professor Greg Blasidell for giving me the opportunity to work on this project and for their leadership and guidance. The work summarized in this thesis is part of a joint effort with the Rolls-Royce Corporation, Indianapolis and has been sponsored by the Indiana 21st Century Research and Technology Fund. I would also like to thank Bill Dalton at the Rolls-Royce Corporation, Indianapolis for his many valuable discussions and for providing the technical data and the experimental acoustic data used in this research. I would like to thank Professor Stuart Bolton for serving on my advisory committee. I would like to thank Dr. Rod Self, Dr. Brian Tester, and Prof. Mike Fisher at the Institute of Sound and Vibration Research for both their guidance while I studied there, and for their valuable advice and suggestions throughout my research. I would like to thank my colleague Ali Uzun for his help and assistance.

3 iii TABLE OF CONTENTS Page LIST OF TABLES... v LIST OF FIGURES... vi NOMENCLATURE... x ABBREVIATIONS... xii ABSTRACT... xiii 1 Introduction Background Current Jet Noise Prediction Models Goals of the Present Research Coaxial Jet Noise Prediction Four-Source Model Practical Jet Configurations Acoustic Data Current Jet Noise Model Comparisons Single Jet Noise Predictions Four-Source Single Jet Characteristic Parameters Confluent Mixer Comparisons Forced Mixer Noise Predictions Forced Mixer Jet Noise Two-Source Forced Mixer Noise Models Two-Source Model Parameter Optimization Two-Source Model Results Model 1 Results Model 2 Results... 55

4 iv Page Parameter Correlations Two-Source Model Performance Conclusions LIST OF REFERENCES... 96

5 v LIST OF TABLES Table Page 3.1 Non-Dimensional Lobed Mixer Penetration Data Test Conditions Dual Flow Aerodynamic Test Conditions ARP876C Input Parameters Model 1 Optimized Parameters for the Low Penetration Mixer Model 1 Optimized Parameters for the Intermediate Penetration Mixer Model 1 Optimized Parameters for the High Penetration Mixer Model 2 Optimized Parameters for the Low Penetration Mixer Model 2 Optimized Parameters for the Intermediate Penetration Mixer Model 2 Optimized Parameters for the High Penetration Mixer Final Optimized Parameters for Model Coefficients from the Linear Curve-fit of the Results from Model Final Optimized Parameters for Model Coefficients from the Linear Curve-fit of the Results from Model Average Weighted Errors in db for Model Average Errors in db for Model Maximum Errors in db for Model Average Weighted Errors in db for Model Average Errors in db for Model Maximum Errors in db for Model

6 vi LIST OF FIGURES Figure Page 2.1 Coaxial Jet Structure Single Stream Source Distribution Function for f c = 1000 Hz F U and F D Functions for f c = 1000 Hz Spectral Filter Functions for f c = 1000 Hz Effective Jet Source Reduction Function Dual Flow Configurations (a) Coplanar, Coaxial Jet (b) Internally Mixed Jet with a Confluent Mixer (c) Internally Mixed Jet Configuration with a Forced Mixer Internally Mixed Jet Configuration with a Forced Mixer Typical Lobed Mixer Geometry Lobed Mixer Vortex Strutcure NASA Glenn Aero-Acoustic Propulsion Laboratory Confluent and 12-Lobe Mixer Data at Set Point Confluent and 12-Lobe Mixer Data at Set Point Confluent and 12-Lobe Mixer Data at Set Point OASPL Dependence on the Fully Expanded Mean Jet Velocity OASPL Directivity Dependence on the Fully Expanded Mean Jet Velocity SPL Dependence on the Jet Total Temperature at 90 degrees SPL Dependence on the Jet Total Temperature at 150 degrees Confluent Mixer Predictions for Set Point Confluent Mixer Predictions for Set Point Confluent Mixer Predictions for Set Point Forced Mixer Penetration... 37

7 vii Figure Page 5.2 Model 1 Parameter Optimization Error Results for the Low Penetration Mixer at Set Point Model 1 Parameter Optimization Non-Dimensional Error Results for the Low Penetration Mixer at Set Point Model 1 Parameter Optimization Results for the Low Penetration Mixer at Set Point Model 1 Optimized Predictions for the Low Penetration Mixer at Set Point Model 1 Parameter Optimization Non-Dimensional Error Results for the Low Penetration Mixer at Set Point Model 1 Parameter Optimization Results for the Low Penetration Mixer at Set Point Model 1 Parameter Optimization Non-Dimensional Error Results for the Low Penetration Mixer at Set Point Model 1 Parameter Optimization Results for the Low Penetration Mixer at Set Point Model 1 Parameter Optimization Average Weighted Error Results for the Low Penetration Mixer at Set Points 1, 2 and Model 1 Parameter Optimization Results for the Low Penetration Mixer at Set Points 1, 2 and Model 1 Parameter Optimization Average Weighted Error Results for the Intermediate Penetration Mixer at Set Points 1, 2 and Model 1 Parameter Optimization Results for the Intermediate Penetration Mixer at Set Points 1, 2 and Model 1 Parameter Optimization Average Weighted Error Results for the High Penetration Mixer at Set Points 1, 2 and Model 1 Parameter Optimization Results for the High Penetration Mixer at Set Points 1, 2 and Model 2 Parameter Optimization Average Weighted Error Results for the Low Penetration Mixer at Set Points 1, 2 and Model 2 Parameter Optimization Results for the Low Penetration Mixer at Set Points 1, 2 and Model 2 Parameter Optimization Average Weighted Error Results for the Intermediate Penetration Mixer at Set Points 1, 2 and

8 viii Figure Page 5.19 Model 2 Parameter Optimization Results for the Intermediate Penetration Mixer at Set Points 1, 2 and Model 2 Parameter Optimization Average Weighted Error Results for the High Penetration Mixer at Set Points 1, 2 and Model 2 Parameter Optimization Results for the High Penetration Mixer at Set Points 1, 2 and Model 1 Optimized Parameter Correlation of the Source Strengths Model 1 Optimized Parameter Correlation of the Cut-off Strouhal Number Model 2 Optimized Parameter Correlation of the Source Strengths Model 2 Optimized Parameter Correlation of the Cut-off Strouhal Number Model 1 Predictions for the Low Penetration Mixer at Set Point Model 1 Predictions for the Low Penetration Mixer at Set Point Model 1 Predictions for the Low Penetration Mixer at Set Point Model 1 Predictions for the Intermediate Penetration Mixer at Set Point Model 1 Predictions for the Intermediate Penetration Mixer at Set Point Model 1 Predictions for the Intermediate Penetration Mixer at Set Point Model 1 Predictions for the High Penetration Mixer at Set Point Model 1 Predictions for the High Penetration Mixer at Set Point Model 1 Predictions for the High Penetration Mixer at Set Point Model 2 Predictions for the Low Penetration Mixer at Set Point Model 2 Predictions for the Low Penetration Mixer at Set Point Model 2 Predictions for the Low Penetration Mixer at Set Point Model 2 Predictions for the Intermediate Penetration Mixer at Set Point Model 2 Predictions for the Intermediate Penetration Mixer at Set Point

9 ix Figure Page 5.40 Model 2 Predictions for the Intermediate Penetration Mixer at Set Point Model 2 Predictions for the High Penetration Mixer at Set Point Model 2 Predictions for the High Penetration Mixer at Set Point Model 2 Predictions for the High Penetration Mixer at Set Point

10 x NOMENCLATURE V T P ρ D A f θ r β λ δ τ F U F D db St E w α F turb I d I q T ij Velocity Total Temperature Total Pressure Density Diameter Area frequency Far-Field Angle (Referenced from the Inlet Axis) Far-Field Radius Area Ratio A s /A p Velocity Ratio V s /V p Density Ratio ρ s /ρ p Temperature Ratio T J /T o Upstream Spectral Filter Function Downstream Spectral Filter Function Source Strength Augmentation Strouhal Number Error Weighting Function Ratio of Turbulence Intensities Ratio of Turbulence Intensities Dipole Source Intensity Quadrupole Source Intensity Lighthill Stress Tensor

11 xi Subscripts e m p s n o J Effective Jet Mixed Jet Primary Jet Secondary Jet Nozzle Exhaust Condition Ambient Condition Jet Condition

12 xii ABBREVIATIONS FAA ISVR SAE ESDU LES RANS AAPL NPR NTR OASPL SPL Federal Aviation Administration Institute of Sound and Vibration Society of Automotive Engineers Engineering Sciences Data Unit Large Eddy Simulation Reynolds Averaged Navier-Stokes Aero-Acoustic Propulsion Laboratory Nozzle Pressure Ratio Nozzle Temperature Ratio Overall Sound Pressure Level Sound Pressure Level

13 xiii ABSTRACT Garrison, Loren A. MSAE, Purdue University, December, Jet Noise Models for Forced Mixer Noise Predictions. Major Professor: Anastasios S. Lyrintzis and Gregory A. Blaisdell. The Four-Source method is a recently developed noise prediction tool applicable to simple coaxial jets. Extensions to this noise prediction model are investigated with the goal of developing a semi-empirical jet noise prediction method that would be applicable to jet configurations with internal forced mixers. In the following study, the noise signals resulting from an internally mixed jet are compared to both a coplanar, coaxial and single jet prediction. It is shown that the current Four-Source coaxial jet noise prediction method predicts with reasonable accuracy the noise from an internally mixed jet for the case with a confluent mixer. However, the standard Four-Source model does not have the capability to model the differences in the noise spectrum that result from changes in the mixer geometry. It is shown that these spectra can be modeled using a modified Two-Source model that has three variable parameters. These parameters are optimized to best match the experimental data, and they are then correlated back to the changes in the mixer geometry to yield a jet noise prediction method for a specific family of forced mixers.

14 xiv

15 1 1. Introduction 1.1 Background The subject of jet noise has been a topic of interest ever since the introduction of the commercial jet aircraft in the early 1950 s. The problem of jet noise is still prevalent today; a reality that is reinforced by the increased restrictions on aircraft noise during take-off and landing that have been imposed by the Federal Aviation Administration (FAA) in recent decades. Jet 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. 1.2 Current Jet Noise Prediction Models Single Jet Models The far-field noise spectrum of a simple, single stream jet is determined by three characteristic parameters, the jet velocity, jet temperature, and jet diameter. Given these parameters a similarity spectrum for the relative sound pressure level can be determined for a given jet velocity and temperature ratio at a specified angular location in the far field. These similarity spectra are functions of Strouhal number, where the frequency is non-dimensionalized by the fully expanded jet velocity and diameter. In addition, a similarity spectrum for the overall sound-pressure level (OASPL) is determined based on the velocity of the jet. The single stream jet noise is then found by appropriately scaling the similarity spectra using the jet area, observer radius, and ambient pressure. This method for predicting single stream jet

16 2 noise is outlined in the Society of Automotive Engineers (SAE) standard ARP876: Gas Turbine Jet Exhaust Noise Prediction [1]. A similar approach is used by the Engineering Sciences Data Unit (ESDU) in their single stream jet noise prediction code, ESDU [2]. The jet noise prediction method used in the ESDU code uses an experimental database with a test matrix of various jet velocities and temperatures. The database of jet noise spectra are normalized based on the jet area, observer distance, and ambient pressure, and then interpolated/extrapolated based on the jet velocity and temperature at each far-field angular location. These values are then scaled appropriately to yield a single jet noise prediction. Coaxial Jet Models Although the aerodynamic process that leads to the generation of sound in a coaxial jet is the same as that of a single stream jet, the aerodynamic structure of a coaxial jet is greatly different. In addition, the coaxial jet structure is dependent on a number of additional variables such as the velocity, temperature, and area ratios between the two streams. Furthermore, the effects of various parameters are not always separable. These additional complexities make it difficult to develop a noise prediction method that is based solely on the interpolation of an experimental database. Even so, there are a few coaxial jet noise prediction methods that are based on interpolating an experimental database. In particular, the SAE standard, AIR1905: Gas Turbine Coaxial Exhaust Flow Noise Prediction [3], and the ESDU program ESDU [4], provide coaxial jet noise predictions based the interpolation of an experimental database. However, there are two main limitations to these methods. First, they require the interpolation over a multi-dimensional matrix of experimental data. Second, the predictions are only valid within the bounds of the matrix of jet conditions, thereby limiting the range of jet conditions which can be predicted.

17 3 An alternative approach to predicting the noise from a coaxial jet, named the Four-Source method, has recently been developed by Fisher et al. [5,6]. This method is based on the observation that distinct regions can be identified in coaxial jets which exhibit similarity relationships that are identical to those observed in simple single stream jets. Based on this fact, it is then proposed that the noise of a simple coaxial jets 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 and length scales. This allows existing experimental databases of single stream jet noise spectra to be used as a foundation for determining the noise from a coaxial jet. A detailed description of the Four-Source method is given in Chapter 2. RANS Based Models Traditionally, the noise resulting from the turbulent mixing in the shear layer of a jet, referred to as jet mixing noise, is known to be the primary source of noise in subsonic jets. Lightihill [7, 8] first derived an equation to describe the generation of this type of aerodynamically generated noise by rearranging the Navier-Stokes equations. His approach for modeling the noise generated by turbulent flow is now referred to as the acoustic analogy. In particular, Lighthill derived the acoustic analogy by combining the continuity and momentum equations. He then formed a wave equation on the left hand side and moved all other terms to the right hand side resulting in the following form where the Lighthill stress tensor, T ij, given as 2 ρ t 2 c2 o 2 ρ = 2 y i y j T ij (1.1) T ij = ρu i u j + ( p c 2 oρ ) δ ij (1.2) contains all of the source terms responsible for the generation of the noise.

18 4 However, both the strength and the weakness of the acoustic analogy theory lies in the simplicity of the model. For the case of a turbulent jet, to appropriately model the sources in the Lighthill stress tensor it is necessary to have information regarding the turbulence statistics. In particular, this method requires a model for the twopoint space-time cross correlation of turbulent sources [9, 10]. 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, this predictive method, which requires a detailed description of the turbulence, is not of sufficient accuracy at this time to use for engine design purposes. Further developments have been made to the standard acoustic analogy developed by Lighthill to account for noise sources that are embedded in a mean flow. An acoustic analogy was derived by Lilley [11, 12] in which the the governing equation is linearized about a parallel sheared mean flow, which is representative of the mean flow in a jet. An added benefit of this approach is that it accounts for the refraction of sound waves by the jet s mean flow. Despite the drawbacks of the acoustic analogy approach, a number of jet noise prediction methods have been developed based on this method. The most current acoustic analogy based jet noise prediction methods commonly use a Reynolds averaged Navier-Stokes (RANS) solution with a two-equation turbulence model to obtain information about the turbulence in the jet [9]. The most common of these methods is referred to as MGBK [13 15]. In this method the length and time scales of the turbulence in each volume element are used in conjunction the Acoustic Analogy theory to determine the characteristic frequency, spectrum and acoustic intensity of each volume element. The total noise from the jet is then found by summing the uncorrelated contributions from each volume element. A Similar method based on the Acoustic Analogy has also been recently developed by Self [16]. In addition, an Acoustic Analogy based noise prediction method currently being developed by NASA [17] has been applied to full three-dimensional, non-axisymmetric flow fields.

19 5 An alternative RANS based noise model has been developed by Tam [10]. This approach explicitly models the noise sources based on a modeled space-time correlation function. The sound from these sources is then propagated to the far-field through the use of the linearized Euler equations. The implementation of this method is similar to the Acoustic Analogy models in that the turbulent flow field is determined from a RANS solution with a two-equation turbulence model. The turbulence information from the two-equation model is used as inputs to the space-time correlation function. An important limitation of the RANS based noise models is the fact that good quality RANS solutions are required to obtain accurate noise predictions. As a result, for jets with complex geometries and flow fields, an accurate solution must first be obtained before running the acoustic solver. For the application of the current study, the jet has a strongly rotating flow field due to presence of stream-wise vorticies produced by the forced mixers. Consequently, it may be fairly difficult to obtain a reliable solution of the turbulent flow field using traditional two-equation turbulence models. LES/DNS Based Models The use of Direct Numerical Simulation (DNS) has recently been used to find the far-field noise of a low Reynolds number jet [18,19]. Through this approach the time history of the flow field is determined from a DNS simulation. Direct Numerical Simulation solves the time dependent Navier-Stokes equations and resolves all of the relevant length scales in the turbulent flow field. The flow field data is then post-processed using Lighthill s acoustic analogy to determine the far-field sound. The advantage of this approach is that no turbulence models are required for the application of the acoustic analogy, since the entire turbulent flow field is known. However, DNS simulations are limited to relatively low Reynolds numbers, on the

20 6 order of 3,000-4,000, due to the large range of length and time scales in a turbulent flow. As a result, this approach is not feasible for the application at hand. Another noise prediction approach currently being investigated involves the use of a Large Eddy Simulation (LES). A Large Eddy Simulation also solves the time dependent Navier-Stokes equations, however, a spatial filter is applied to remove the small scales that are not resolved by the grid. Using this method, the large scale motion is calculated directly, and a subgrid-scale model is used to model the effects of the small scales. The LES solution provides the time history of the unsteady pressure fluctuations on a surface that encloses the noise source mechanisms. These pressure fluctuations are then extended to the far field by the use of Kirchoff s method or Ffowcs Williams-Hawkins method to determine the far-field noise characteristics [20 22]. 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, especially if the internal mixed flow region is included. Consequently, it is not feasible at this time to use DNS or LES as a design tool for the application at hand. 1.3 Goals of the Present Research The objective of the current study is to extend the Four-Source coaxial jet prediction method to predict the noise from a jet with an internal forced mixer. First, the Four-Source method formulation for coplanar, coaxial jets is evaluated for the practical confluent mixer configuration considered in this study. Then a modified Two-Source model is described in which the noise from an internally forced mixed jet is matched using a combination of two modified single jet noise predictions. Three free parameters in the Two-Source model are optimized to match the forced mixer experimental data. These optimized parameters are then correlated to the changes in the mixer geometry to yield a semi-empirical noise model for a given family of forced mixers.

21 7 2. Coaxial Jet Noise Prediction 2.1 Four-Source Model An novel approach to predicting the noise from a coaxial jet, referred to as the Four-Source method, has been previously formulated by Fisher et al. [5, 6]. In this method the total jet noise is found by adding the contributions of four representative sources that are modeled as single stream jets. An experimental database of single stream jet noise spectra is then used as a foundation for determining the noise from a coaxial jet. 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 the nature 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 structure of a simple coaxial jet is shown in Figure 2.1. 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 heart 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. These properties of a simple coaxial jet were concluded based on the analysis of the experimental coaxial jet data of Ko [23]. The experimental data of Ko illustrates that the mean velocity and turbulent intensity profiles of the secondary-ambient shear layer resemble that of a single jet characterized by the secondary diameter and exit velocity. The noise in this region will therefore be modeled as that from a single jet based on the secondary velocity,

22 8 Secondary / Ambient Shear Layer V s Primary / Secondary Shear Layer V p V s Initial Region Interaction Region Mixed Flow Region Figure 2.1. Coaxial Jet Structure

23 9 temperature, and diameter. However, only the portion of the shear layer upstream of the end of the secondary potential core is modeled in the initial region. Since the shear layer generally produces high frequency noise in the upstream portion and low frequency noise in the portions downstream of the potential core, a low frequency spectral filter is applied to the noise of the single stream jet that models this source. The remainder of the secondary-ambient shear layer interacts with the primary-secondary shear layer in the interaction region. The model for the spectral filter is based on the single stream jet source distribution given by ( ) mx S(x) =x m 1 exp (2.1) where S(x) is the source strength per unit length, x is the position on the jet axis downstream of the nozzle exit, x c, which is a function of frequency, determines the centroid of the distribution, and m is a shape parameter, which has a typical value of 4. The fraction of energy, F U, that is radiated from upstream of a given position x 1, is then given by x c F U (x 1 )= x x c S(x)dx S(x)dx (2.2) For the case when the shape parameter m is equal to 4, the fraction of energy that is radiated from upstream of x 1 can then be written as ( ) [ mx F U (x 1 )=1 exp 1+ mx ( ) mx1 2 ( ) ] 1 mx1 3 + (2.3) x c 2 6 This relation can then be formulated in terms of frequency, f, by assuming the centroid positions varies inversely with frequency. Using this assumption, the fraction of energy radiated from upstream of x 1 can be written as ( ) mf F U (x 1,f)=1 exp 1+ mf + 1 ( ) 2 mf + 1 ( ) 3 mf (2.4) f f 1 where f 1 is the frequency that corresponds to the position x 1. In addition, the fraction of energy, F D radiated downstream of a given position x 1 is given by, f 1 x c F D =1 F U (2.5) f 1 x c

24 10 A spectral filter can be formulated based on the radiated energy by simply taking ten times the base ten logarithm of the fraction of the radiated energy. A plot of the single stream jet source distribution as a function of frequency for a centroid frequency (f c ) of 1000 Hz is shown in Figure 2.2. In addition, the corresponding F U and F D functions and the resulting spectral filters for this sample case, with cut-off frequency f c = 1000 Hz, are shown in Figure 2.3 and 2.4 respectively S(x) Source Distribution Function Figure 2.2. Single Stream Source Distribution Function for f c = 1000 Hz The noise from the secondary-ambient shear layer, SPL s, as a function of observer angle, θ, and frequency, f, is given by, SPL s (θ, f) =SPL(V s,t s,d s,θ,f) + 10 log 10 F U (f s,f) (2.6) where SPL denotes a single jet prediction using the characteristic jet properties V s, T s, and D s, which are the secondary exit velocity, temperature, and diameter respectively. In addition, f s is the spectral filter cut off frequency defined by f s = V s D s (2.7)

25 F U : Upstream Radiated Energy F D : Downstream Radiated Energy F U and F D Figure 2.3. F U and F D Functions for f c = 1000 Hz Spectral Filter [db] log 10 (F U ) 10log 10 (F D ) Figure 2.4. Spectral Filter Functions for f c = 1000 Hz

26 12 The second noise producing area within the initial region is the primary-secondary shear layer. It is observed from the experimental results of Ko that turbulence intensities in this shear layer are much less than those in the other regions of the jet. It is therefore determined that this component can be neglected since its noise levels will have little effect on the overall noise of the jet. The mixed flow region in the coaxial jet is modeled as a fully mixed jet. The velocity, temperature and diameter of the fully mixed jet are based on conserving mass, momentum and energy and are given by ( 1+λ 2 ) βδ V m = V p 1+λβδ D m = D p ( (1 + λβ)(1 + λβδ) 1+λ 2 βδ T m = T p 1+λβ (1 + λβδ) ) 1 2 (2.8) (2.9) (2.10) where V m, D m, and T m are the mixed jet velocity, diameter, and temperature respectively, and λ, β, and δ are the secondary to primary ratios of velocity, geometric area, and density respectively. In addition, V p, D p, and T p are the primary flow velocity, diameter, and temperature respectively. Similar to the secondary-ambient shear layer source region, a high frequency spectral filter is applied to the single stream jet data which models the mixed flow source region. This spectral filter is necessary due to the fact that only the downstream portion of the mixed jet is present in the mixed flow region and this is where the low frequency part of the noise is produced. The fraction of energy that is radiated from the region of the jet downstream of position x 1 is given by Equation 2.5. The noise from the mixed jet region, SPL m, is then given by SPL m (θ, f) =SPL(V m,t m,d m,θ,f) + 10 log 10 F D (f 1,f) (2.11) where, V m, D m, and T m are mixed jet velocity, temperature, and diameter respectively, and f 1 is the spectral filter cut off frequency defined by f 1 = V m D m (2.12)

27 13 In the interaction region there are no obvious flow characteristics by which to model a single stream jet. It is noted from the work of Ko, however, that the interaction region contains the largest volume of highly turbulent flow and it exhibits characteristics of a single jet. It is determined through noise scaling analysis based on experimental data that the noise from the interaction region scales with the primary velocity to the eighth power. Therefore, the velocity of the effective jet, which models the noise noise from the interaction region, is taken to be equal to the primary jet. The diameter of the effective jet is determined by finding the diameter of a jet with the given effective velocity that would provide the same amount of thrust as the original coaxial jet configuration. Based on this model, the diameter of the effective single jet whose noise will model that of the interaction region is found from D e = D p ( 1+λ 2 β ) 1/2 (2.13) where D e is the diameter of the effective jet and λ and β are the previously defined velocity and area ratios. In order to account for differences in the quadrupole noise sources due to turbulence intensity levels in noise producing regions which differ from those of a single stream jet, a scaling analysis of the turbulence intensity is performed based on Lighthill s solution to the far-field pressure fluctuations at 90 to the jet axis. The results of this analysis show that the far field pressure fluctuations scale as p 2 (r o ) α 4 ρ2 ou 8 j D 2 r 2 oc 4 o (2.14) where p 2 (r o ) is the far-field mean square pressure, r o is the distance from the source to the observer, U J and D are the jet velocity and diameter, ρ o and c o are the ambient density and speed of sound, and α is the turbulence intensity defined as α u U J (2.15)

28 14 where u is the magnitude of the velocity fluctuations and U J is the jet velocity. As a result of Equation 2.14, a variation in the turbulence level in a noise producing region of the coaxial cold jet will result in an attenuation effect given by ( ) α db = 40 log αo (2.16) where α is the peak turbulence intensity in the interaction region of the coaxial jet and α o is the peak turbulence intensity of a single stream jet, which is approximately equal to 15%. However, for a heated jet the attenuation effect is slightly more complicated due to the addition of a dipole source resulting from the mixing process of fluids of different densities. A scaling law for the intensity of the quadrupoles, I q, was derived based on the expression for the far field pressure fluctuations given in equation This scaling law is given by I q α4 ρ 2 sujd 8 2 (2.17) ρ o c 5 oro 2 where ρ s is the density in the dominant source region and α is the turbulence intensity. Similarly, a scaling law for the dipoles source intensity, I d, is given as I d α2 (ρ s ρ o ) 2 U 6 JD 2 ρ o c 3 or 2 o (2.18) which is derived based on the dipole source strength given by Morfey [24]. It is seen from these scaling laws that the quadrupole sources scale with the fourth power of the turbulence intensity, while the dipole sources scale with the second power of the turbulence intensity. Using this information the attenuation of a heated jet is then given by, ( r 2 I d + r 4 ) I q db = 10 log 10 (2.19) I d + I q where r is the ratio of turbulence intensities (α/α o ). As a result, for a single jet peak turbulence intensity, α o, of 15% and an interaction region peak turbulence intensity, α, of 10%, if the quadrupole sources were dominant, then an attenuation of 7 db of the single stream jet noise would occur. Similarly, if the dipole sources were dominant, then an attenuation of only 3.5 db would occur.

29 15 In general, to evaluate the expression for the attenuation due to varying turbulence intensities, information regarding the relative contributions of the quadrupole and dipole source is determined based on their jet properties. The result of this analysis is I d I q = K ( TJ T o T s )( Ts T o ) M 2 J (2.20) where K is a constant determined from a master spectra to have a value of 7, and M J is the jet mach number defined by jet velocity divided by the ambient speed of sound (U J /c o ). In addition, the temperature in the source region, T s, is defined as T s = T o (T J T o ) (2.21) Equations 2.19 and 2.20 are then combined to yield the final representation of the effective jet source reduction, given as ( 7r 2 y + r 4 ) db = 10 log 10 (2.22) 7y +1 where r is the previously defined ratio of the turbulence intensities and y is defined as (τ 1) 2 y = (τ 1) M J 2 (2.23) where τ is the jet temperature ratio (T J /T o ). A graph showing the effective jet source decibel reductions as a function of jet temperature ratio and Mach number is shown in Figure 2.5 Given the previously described attenuation factor, the noise spectra from the interaction region, SPL e, is determined from SPL e (θ, f) = SPL(V p, T p, D e,θ,f) + db (2.24) where V p and T p are the velocity and temperature of the primary jet, D e is the effective diameter from equation 2.13 and the attenuation factor, db, is determined from Equation The overall noise of the coaxial jet is then found by the incoherent sum the contributions from each of the three source regions. The results of this method

30 Effective Jet Noise Reduction [db] M J = 0.2 M J = 0.4 M J = 0.6 M J = 0.8 M J = 1.0 M J = Temperature Ratio (τ) Figure 2.5. Effective Jet Source Reduction Function

31 17 provide noise predictions that are within the order of ±1 db of experimental data for a wide range of angles of observation and for a wide range of jet operating conditions, including primary jet temperatures up to 980 F (800 K). 2.2 Practical Jet Configurations Dual Flow Configurations 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. Schematics of a simple coplanar, coaxial jet and the internally mixed, dual flow configurations examined in this study are shown in Figure 2.6. In addition, a 3-D rendering of the forced mixer configuration is shown in Figure 2.7. Forced Mixers The introduction of a forced, or lobed mixer, shown in Figure 2.8, increases the mixing in a turbulent jet through a number of mechanisms. First, the convolution of the lobed 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 stream-wise 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 stream-wise vortices sharpens the interface gradients [25]. In addition to the enhancement of the mixing process, the introduction of the stream-wise 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 Figure 2.9. In a lobed mixer, each lobe produces

32 Figure 2.6. Dual Flow Configurations (a) Coplanar, Coaxial Jet (b) Internally Mixed Jet with a Confluent Mixer (c) Internally Mixed Jet Configuration with a Forced Mixer 18

33 19 Figure 2.7. Internally Mixed Jet Configuration with a Forced Mixer Figure 2.8. Typical Lobed Mixer Geometry

34 20 a pair of counter rotating vortices. As these vortices evolve they effectively twist the hot core flow and cold bypass flow in a helical manner. As the vortices move downstream they grow due to turbulent diffusion and eventually begin to interact with their pairing vortex, the vortex produced by the adjacent lobe, and possibly the nozzle wall. Figure 2.9. Lobed Mixer Vortex Strutcure

35 21 3. Acoustic Data The experimental acoustic data of the mixers used in this study was taken in the Aero-Acoustic Propulsion Laboratory (AAPL) at NASA Glenn during the spring of The Aero-Acoustic Propulsion Laboratory, shown in Figure 3.1, is an anechoic geodesic dome, which is 130 feet in diameter and 65 feet high. This facility houses the Nozzle Acoustic Test Rig (NATR), which is a 53 inch diameter free-jet acoustic wind tunnel. This rig is capable of producing jet flows in simulated flight conditions up to Mach The NATR rig is fed by the High Flow Jet Exit Rig (HFJER). This rig can provide nozzle exit conditions up to 1425 F (1050 K) with a nozzle pressure ratio (NPR) of 4.5. In addition, it has the capability to provide dual flow configurations with independent primary and secondary flow temperature and pressure ratios. The AAPL facility has two far field microphone arrays located at approximately 50 feet from a test model in the Nozzle Acoustic Test Rig. far-field jet noise data was obtained for the four mixer configurations that are evaluated in this study. These mixer configurations are the confluent mixer (CFM), the low penetration 12-lobe mixer (12CL), the intermediate penetration 12-lobe mixer (12UM), and the high penetration 12-lobe mixer (12UH). The amount of penetration in the three lobed mixers is shown in Table 3.1. The acoustic data for the four mixers considered was evaluated at three different operating points. The nozzle total pressure ratios (NPR) and total temperature ratios (NTR) of these operating points is shown in Table 3.2. In addition, the corresponding velocity and temperature ratios between the two coaxial streams are shown in Table 3.3. Furthermore, all of experimental jet noise data used in this study was taken in the acoustic far field at a radius of approximately 80 jet diameters. The aerodynamic properties of the flow were recorded at each data point. These properties include the primary and secondary flow charging station total temper-

36 22 Figure 3.1. NASA Glenn Aero-Acoustic Propulsion Laboratory Table 3.1 Non-Dimensional Lobed Mixer Penetration Mixer Name Mixer ID (Penetration/Nozzle Diameter) Low Penetration 12CL Inetermediate Penetration 12UM High Penetration 12UH Table 3.2 Data Test Conditions Operating Point NPR primary NPR secondary NTR primary NTR secondary

37 23 Table 3.3 Dual Flow Aerodynamic Test Conditions Operating Velocity Ratio Temperature Ratio Point λ δ atures, total pressures, and static pressures. The charging station is located just upstream of the mixer or splitter plate. In addition, the primary and secondary flow mass flow rates are measured, along with the ambient conditions. This information is later used to determine the characteristic properties of the flows (velocities, temperatures and diameters) that are used in the single jet noise predictions. The acoustic data is supplied in the form of 1/3 octave Sound Pressure Level (SPL) spectra. These SPL spectra cover a frequency range of Hz to Hz (1/3 octave bands 22 to 49), at angles from 55 to 165 in 5 deg increments, as referenced from the intake axis. The acoustic data is recorded for frequencies up to 80kHz because the mixer/nozzle model is 1/4 scale. The 80kHz frequency limit for the model scale data corresponds to 20kHz at full scale, which is the approximate upper frequency limit of human hearing. The acoustic data is normalized to a 50 ft arc, which results in a far-field observer radius to jet diameter ratio of The acoustic data is corrected for microphone response and referenced to an acoustic standard day (T amb = K, P amb = kpa, 70% relative humidity). A sample of the acoustic data for all four mixers at the lower power setting is shown in Figure 3.2. In addition, the acoustic data at the operating points 2 and 3 is shown in Figures 3.3 and 3.4, respectively.

38 db CFM 12CL 12UM 12UH db CFM 12CL 12UM 12UH db CFM 12CL 12UM 12UH Figure 3.2. Confluent and 12-Lobe Mixer Data at Set Point 1

39 db CFM 12CL 12UM 12UH db CFM 12CL 12UM 12UH db CFM 12CL 12UM 12UH Figure 3.3. Confluent and 12-Lobe Mixer Data at Set Point 2

40 db CFM 12CL 12UM 12UH db CFM 12CL 12UM 12UH db CFM 12CL 12UM 12UH Figure 3.4. Confluent and 12-Lobe Mixer Data at Set Point 3

41 27 4. Current Jet Noise Model Comparisons In this chapter the ARP876C single jet prediction method and the influence of this prediction method s input parameters are discussed. In addition, the derivation of the Four-Source single jet characteristc parameters are described. Finally, the experimental data for the confluent mixer is compared to a single jet and a coaxial jet noise prediction. The fully mixed flow conditions at the final nozzle exit are used in the single jet prediction and the Four-Source method, as applied to an internally mixed configuration, is used to make the coaxial jet prediction. 4.1 Single Jet Noise Predictions In the present study all of the single jet predictions are made based on the SAE ARP876C guidelines for predicting jet noise [1]. It should be noted that the SPL spectra of these predictions are, in general, accurate to within approximately ±3 db. The ARP876C guidelines outline a method for predicting the noise from a simple single stream jet. These guidelines are based on experimental data of jet engine noise. The necessary input parameters that are used in the prediction are shown in Table 4.1 The fully expanded mean jet velocity, V J has the most influence on the single jet noise prediction. This parameter scales the Overall Sound Pressure Level (OASPL) and determines the shape of the OASPL spectrum as shown in Figures 4.1 and 4.2. In these figures lines with square markers indicate the maximum and minimum velocity scales for the low power setting. The maximum velocity scale is the primary velocity and the minimum velocity scale is the secondary velocity. The velocity of the mixed jet will be somewhere between these two limiting velocities. Likewise the lines with circle markers in Figures 4.1 and 4.2 indicate the maximum and minimum

42 28 Table 4.1 ARP876C Input Parameters Parameter V J T J D J A J γ T o P o RH r Description Fully Expanded Mean Jet Velocity Jet Total Temperature Exhaust Nozzle Diameter Cross Sectional Area of the Exhaust Nozzle Ratio of Specific Heats Ambient Total Temperature Ambient Total Pressure Ambient Relative Humidity Radial Distance from Nozzle Exit to Observer velocity scales for the high power settting. The jet velocity is also used to determine the jet density exponent, ω, which also scales the OASPL spectrum. Furthermore, at shallow angles to the jet axis the jet velocity influences the relative SPL spectrum shape. Finally, the jet velocity is used to scale the relative SPL spectrum frequencies. The jet total temperature, T J, influences the relative SPL spectrum. An example of this parameter s influence is seen in Figures 4.3 and 4.4. The jet diameter, D J, scales the frequencies of the relative SPL spectrum. The remaining parameters, the jet exit area, A J, the far-field radius, r, and the ambient total pressure, P o, all scale the OASPL spectrum. The ARP876C method produces noise predictions that correspond to a lossless acoustic arena. As a result, to be consistent with the experimental data, an atmospheric absorption correction is applied to the ARP876C noise prediction. In this study the absorption model developed by Bass et. al [26] is used to correct for atmospheric absorption. This model uses the ambient pressure, P o, temperature, T o, and relative humidty, RH.

43 29 OA OASPL for a Various Values of V J /a o Angle from the Inlet Axis [deg] Figure 4.1. OASPL Dependence on the Fully Expanded Mean Jet Velocity OA OASPL OASPL(90 ) for a Various Values of V J /a o Angle from the Inlet Axis [deg] Figure 4.2. OASPL Directivity Dependence on the Fully Expanded Mean Jet Velocity

44 SPLrel at 90 for Various Values of T J /T o SPLrel log 10 (Strouhal Number) Figure 4.3. SPL Dependence on the Jet Total Temperature at 90 degrees SPLrel at 160 for Various Values of T J /T o SPLrel log (Strouhal Number) 10 Figure 4.4. SPL Dependence on the Jet Total Temperature at 150 degrees

45 Four-Source Single Jet Characteristic Parameters The Four-Source jet noise prediction method was developed to predict the noise from simple coplanar, coaxial jets. An application of this method for the case of a jet with a recessed, or buried, primary flow involves defining the equivalent primary and secondary flow single jet properties at the final nozzle exit. The following describes a method for determining these single jet properties based on flow properties measured upstream of the coaxial flow splitter plate. Jet Velocity (V J ) The ARP876C noise prediction method is based on the fully expanded mean jet velocity, calculated as V J = 2 γ γ 1 RT J 1 ( Po P J ) γ 1 γ (4.1) where R is the ideal gas constant, γ is the ratio of specific heats, T J is the jet total temperature, P J is the jet total pressure, and P o is the ambient total pressure. If it is assumed that the flow from the charging station (upstream of the splitter plate where the total pressure and total temperature measurements are taken) to the final nozzle exit is isentropic, then the total pressure and total temperature at the final nozzle exit will be the same as the total pressure and total temperature at the charging station. Therefore, the primary and secondary fully expanded mean velocities at the final nozzle are calculated with Equation 4.1 using the ambient pressure measurement and the total temperature and total pressure measurements taken at the charging station. Jet Temperature (T J ) The ARP876C noise prediction method is based on the jet total temperature. If it is assumed that the flow from the charging station to the final nozzle is isen-

46 32 tropic, then the total temperature at the final nozzle will be the same as the total temperature at the charging station. Jet Area (A J ) Given the areas of the ducts at the charging station, the final nozzle exit primary and secondary areas are found by assuming that the flow is isentropic inside the nozzle, the primary and secondary flows do not mix inside the nozzle, and that the static pressures of the two flows at the nozzle exit are equal. The resulting problem is then solved in an iterative manner using the following steps: 1. Guess a value for the primary flow area at the final nozzle exit (A p ) 2. Calculate the secondary flow area (A s ) using the equation A s = A n A p (4.2) 3. Calculate the actual Mach number at the final nozzle exit for both the primary and secondary flows using the isentropic area relation [ A exit A = M 1+ γ 1 M exit 2 M 2 exit ] γ+1 2(γ 1) [ 1+ γ 1 M ] γ (γ 1) (4.3) where, for a given flow stream, A is the charging station area, M is the charging station Mach number, A exit is the final nozzle area, and M exit is the unknown final nozzle Mach number. 4. Calculate the static pressures of the two flows based on the calculated Mach numbers using the isentropic relation ( P J = 1+ γ 1 P static 2 M 2 exit ) γ γ 1 5. Adjust the core flow area until the static pressure of the two flows are equal. (4.4) A method for determining the charging station area for this particular application is given in Appendix A.

47 33 Jet Diameter (D J ) The diameter of the secondary flow, D s, at the final nozzle will be equal to the diameter of the final nozzle, D n. The diameter of the primary flow, D p at the final nozzle is calculated based on the primary flow area, A p at the final nozzle using the geometric relation D p =2 Ap π (4.5) 4.3 Confluent Mixer Comparisons Using the primary and secondary flow properties at the final nozzle exit, which were previously described, the standard Four-Source method is used to predict the noise of the internally mixed configuration with a confluent mixer. In these predictions a constant effective jet reduction of -7 db is used. It was determined by Mike Fisher [27] that based on previous experience this value of the effective jet reduction generally provides more accurate predictions for heated jets. The results of the confluent mixer predictions are shown for the low power operating point in Figure 4.5. In addition, comparisons at operating points 2 and 3 are given in Figure 4.6 and Figure 4.7 respectively. From these comparisons it can be seen that the Four- Source noise predictions agree well with the experimental data at angles close to 90. However, the predictions near the spectral peaks at angles near the jet axis are slightly under-predicted by the Four-Source method. Furthermore, it is seen from Figures that the Four-Source predictions are more accurate than the single jet predictions. This fact is particularly true at angles close the jet axis.

48 db Data Single Jet Prediction Coaxial Jet Prediction FS Sources db Data Single Jet Prediction Coaxial Jet Prediction FS Sources db Data Single Jet Prediction Coaxial Jet Prediction FS Sources Figure 4.5. Confluent Mixer Predictions for Set Point 1

49 db Data Single Jet Prediction Coaxial Jet Prediction FS Sources db Data Single Jet Prediction Coaxial Jet Prediction FS Sources db Data Single Jet Prediction Coaxial Jet Prediction FS Sources Figure 4.6. Confluent Mixer Predictions for Set Point 2

50 db Data Single Jet Prediction Coaxial Jet Prediction FS Sources db Data Single Jet Prediction Coaxial Jet Prediction FS Sources db Data Single Jet Prediction Coaxial Jet Prediction FS Sources Figure 4.7. Confluent Mixer Predictions for Set Point 3

51 37 5. Forced Mixer Noise Predictions 5.1 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 heights, or penetration (H). The penetration of a forced mixer is defined as the difference between the maximum and minimum radii at the end of the mixer, as shown in Figure 5.1. H Figure 5.1. Forced Mixer Penetration The effects of the differences in lobe penetration on the experimental far-field noise were shown in Figures 3.2, 3.3, and 3.4. From these figures 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 these figures, it is clear that additional noise generating mechanisms will need to be accounted for in a forced mixer noise prediction method.