AN INVESTIGATION OF THE EXTENSION OF THE FOUR-SOURCE METHOD FOR PREDICTING THE NOISE FROM JETS WITH INTERNAL FORCED MIXERS
L. A. Garrison*
School of Aeronautics and Astronautics
Purdue University, West Lafayette, IN, USA
W. N. Dalton†
Rolls-Royce Corporation, Indianapolis, IN, USA
A.S. Lyrintzis‡, and G.A. Blaisdell§
School of Aeronautics and Astronautics
Purdue University, West Lafayette, IN, USA
Abstract
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 signal resulting from an internally forced 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 does not accurately predict the noise from an internally forced mixed jet. However, it is shown that for a given mixer and nozzle geometry, the internally forced mixed jet noise data can be matched by optimizing three parameters of a modified version of the four-source method that uses the partial noise spectrum of two single stream jets.
1
American Institute of Aeronautics and Astronautics
Introduction
In recent decades the FAA has been imposing increased restrictions on aircraft noise during take-off and landing. 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 a modern turbofan jet engine can only be determined by expensive experimental testing after it has 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- 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. MGB2,3,4), 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.
Another approach 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 Ffowcs Williams-Hawkins method to determine the far-field noise characteristics.6-8 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. 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.9,10 In this method the total jet noise is found from 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, the method is not dependent on assumptions made about 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 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 configurations considered in this study. Once it is shown that the current prediction method does not accurately predict the noise from a jet with an internal forced mixer, modifications to the standard method are investigated to provide an improved prediction.
Four-Source Method Overview
The four-source jet noise prediction method is fundamentally different from approaches based on the acoustic analogy. The method is based on the observation that distinct regions can be identified in co-axial jets which exhibit similarity relationships which are identical to those observed in simple single stream jets. Rather than attempting to model the details of the turbulence statistics as is required for the application of the acoustic analogy, it is proposed that the noise of a simple co-axial 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 same 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.
The structure of a simple coaxial jet is shown in Figure 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.11 Using this information, the individual noise source regions are modeled as single stream jets with a specified characteristic velocity, diameter and temperature.
In particular, in the initial region the secondary-ambient noise source is characterized by the secondary velocity (Vs), diameter (Ds), and temperature (Ts). Likewise, in the mixed flow region the mixed jet noise source is characterized by the mixed velocity (Vm), diameter (Dm), and temperature (Tm), 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 (Vp), primary temperature (Tp), and the effective diameter (De). 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 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 noise source regions. In the present study all of the single jet predictions are made based on the SAE ARP876C guidelines for predicting jet noise.12 It should be noted that these predictions are only accurate to within approximately 3 dB. In addition, the atmospheric attenuation model developed by Bass et al13 is used in all single jet predictions.
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 contours. A schematic of the mixed dual flow exhaust configuration examined in this study is shown in Figure 2.
The introduction of a lobed mixer, shown in Figure 3, 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 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.14
Figure 2: Mixer-Nozzle Geometry and Flow Structure for an Internally Forced Mixed Configuration
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 Figure 4. In a lobed mixer, each lobe produces 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 evolve downstream they grow due to turbulent diffusion and eventually begin to interact with both their pairing vortex and a vortex produced by the adjacent lobe.
Figure 3: Typical Lobed Mixer Geometry
Figure 4: Lobed Mixer Flow Structure
Experimental Data
The experimental acoustic data of the mixers used in this study was taken in Aeroacoustic Propulsion Laboratory at NASA Glenn during the winter/spring of 2003. The jet noise data was taken in the acoustic far field at a radius of approximately 80 jet diameters.
For all the cases in this study the velocity and static temperatures of the primary flow, bypass flow, and at the nozzle exit are determined based on the total pressures and total temperatures using isentropic flow assumptions. These properties are therefore ideal 1-D approximations of the flow at the specified locations.
Lobed Mixer Comparisons
The noise from two different lobed mixers is compared to predictions of both a coaxial jet and a single jet with the characteristic velocity, diameter, and temperature of the nozzle exit. The two 12-lobed mixers used in this study have different amounts of penetration; they will be referred to as the low penetration mixer and the high penetration mixer. The penetration of a mixer (H), or lobe height, is defined as the difference in the radius at the peak from the radius at the trough (at the end of the splitter plate) as shown in Figure 5.
Figure 5: Definition of Lobe Penetration, H
Referring to figure 6, it can be seen that the measured noise spectra for the low penetration mixer are well matched by predictions obtained from the method of reference 9 for a single stream jet. However predictions based on the four-source coaxial jet model over predict the noise levels by more than 5 dB near the spectrum peaks.
The comparison for the high penetration mixer, Figure 7, shows that once again the coaxial jet prediction over predicts the noise by more than 5 dB at the spectral peaks. In addition, the coaxial predictions under predict the noise levels in the high frequency region. Similar to the low penetration mixer, it is seen that the single jet prediction matches well with the experimental data in the low frequency region. However, it appears as if there is an additional high frequency noise source present in the high penetration mixer, as all of the model predictions under predict the noise levels in the high frequency region.
There are three possible mechanisms that are generating the additional high frequency noise source. First, the presence of the turbulence that is produced by the lobed mixer could possibly be acting as an additional noise source in the upstream region of the jet plume. It is likely that this noise source would behave similar to some portion of a single stream jet given the appropriate characteristic properties. Second, the turbulence produced by the mixer could be interacting with the jet plume in the downstream region of the jet thereby creating deviations from a single stream jet prediction. Finally, it is possible that the turbulence that is produced by the lobed mixer could be interacting with the nozzle wall to act as an additional noise source.
Two possible reasons that the coaxial jet prediction does not accurately predict the noise for the cases with an internal forced mixer are the effects of the convergent nozzle, and the effects of the streamwise vortices created by the mixer.
For cases with internal mixing with a convergent nozzle the characteristic properties of the secondary flow lose their physical relevance. In the original formulation of the four-source method the noise from the secondary-ambient shear layer is characterized by a portion of a single stream jet with the secondary velocity, temperature and diameter. However, for the case of an internally mixed jet with a convergent nozzle, the equivalent of the secondary-ambient shear layer should be represented by a portion of a single jet with the diameter, velocity, and temperature of the nozzle exit conditions. Due to the mixing of the secondary flow with the higher velocity primary stream within the nozzle and the presence of the convergent nozzle, the velocity at the nozzle exit will be greater than that of the secondary flow. Therefore the noise from this source would be greater than noise from the secondary jet source of the four-source method.
In addition, the over prediction in the low frequency spectrum of the coaxial jet prediction is likely due to interactions between the turbulent mixing layer with embedded streamwise vortices and the downstream regions of the jet plume.
An additional characteristic seen in the comparisons of the two lobed mixers is the apparent trade of low frequency noise with high frequency noise as shown in Figure 8. The case of the high penetration mixer exhibits reduced noise levels in the low frequency region as compared to the low penetration mixer. At the same time the high frequency noise levels of the high penetration mixer are greater than those of the low penetration mixer. It could be possible that the increased levels of turbulence in the upstream regions, which are characteristic of high frequency noise, are affecting the development of the turbulence in the downstream region in such a way that noise levels produced in the downstream region are reduced.
Four-Source Parameter Optimization
Possible extensions of the four-source method are investigated to see if the noise from a jet with an internal forced mixer can be represented by a combination of noise sources used in the four-source method. For these investigations the same characteristic properties of the jet noise sources are used (velocity, temperature, and diameter), however, the parameters describing the source strengths and lengths are varied. Taking this approach the following formulation of the four-source method is used
(1)
(2)
(3)
where SPL refers to the sound pressure level of a single jet prediction using the specified characteristic velocity, V, temperature, T, and diameter, D. In addition, FU and FD are the upstream and downstream spectral filters, and dB refers to the source strength reduction. Furthermore, the subscript s denotes the secondary jet source, the subscript m denotes the mixed jet source, and the subscript e denotes the effective jet source. In this formulation the variable parameters are the spectral filter cut off frequencies fs, fm, and fe, which effectively modify the lengths of the sources, and the source strength parameters dBs, dBm, and dBe.
The first approach to determining the best set of source parameters to match the experimental mixer data was to use standard nonlinear least-squares optimization techniques, such as the Levenberg-Marquardt method. However, due to the nonlinear nature of the formulation and the large number of variable parameters, the standard optimization packages were found to converge to local minima.
To overcome this difficulty a specific optimization algorithm was developed for the current problem to determine the combination of source parameters that provides the best agreement with the mixer acoustic data. This algorithm divides the total frequency domain into three sub-domains. Then, starting with the three uncorrected single jet predictions the error in each frequency sub domain is determined and the variable parameters that are relevant in each sub domain are adjusted. This process is then iterated upon until the method converges to a final solution.