AN INVESTIGATION OF THE EXTENSION OF THE FOURSOURCE 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.
Introduction
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 spacetime 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
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
AIAA Paper 2003-3165, Presented at the 9th AIAA/CEAS
Aeroacoustics Conference, Hilton Head, SC, May 2003
*
Graduate Research Assistant, Student Member AIAA
Manager, Mechanical Methods and Acoustics
‡ Professor, Associate Fellow AIAA
§
Associate Professor, Senior Member AIAA
†
1
American Institute of Aeronautics and Astronautics
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.
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 secondaryambient 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 (V m),
diameter (Dm), 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 (Vp), primary temperature (T p), and
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-
Secondary / Ambient
Shear Layer
Primary / Secondary
Shear Layer
Vs
Vp
Vs
Initial
Region
Interaction
Region
Figure 1: Structure of a Simple Coaxial Jet
2
American Institute of Aeronautics and Astronautics
Mixed Flow
Region
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.
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.
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 3: Typical Lobed Mixer Geometry
3
American Institute of Aeronautics and Astronautics
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
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
4
American Institute of Aeronautics and Astronautics
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.
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 LevenbergMarquardt 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.
The results of the four-source parameter
optimization show that the mixer data is matched
reasonably well by using modified forms of the mixed
jet source and the secondary jet source. With this
combination, only three variable parameters are needed
to match the experimental data. These three parameters
are the secondary jet source augmentation (dBs),
mixed jet source reduction (dBm), and a common cutoff frequency (fc = fs = fm).
The optimized prediction for the low penetration
mixer is shown in Figure 9 for three far field angles.
The average error between the optimized prediction and
the experimental data is 1.2 dB, the maximum error is
3.7 dB.
These errors are calculated using the
predictions from 13 different angles (90 o to 150o in 5o
increments). The primary differences between the
optimized prediction and the experimental data occur at
angles close to 90o in the low frequency range of the
spectrum.
The optimized prediction for the high penetration
mixer is shown in Figure 10. The average error for this
case is 1.1 dB and the maximum error is 4.7 dB.
Similar to the low penetration case, the primary
difference in the optimized prediction and the
experimental data occur at angles close to 90o in the
low frequency range of the spectrum.
The optimized parameters for the low and high
penetration mixers are shown in Table I. The standard
four-source parameters for the corresponding case are
dBs = 0, dBm = 0, fc = 1000. For both of the high
and low penetration mixers the secondary jet source is
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
SPL s ( , f )  SPL(Vs , Ts , D s , , f )
 10log 10 FU ( f s , f )  dB s
SPL m ( , f )  SPL(Vm , Tm , D m , , f )
 10log 10 FD ( f m , f )  dB m
SPL e ( , f )  SPL(Vp , Tp , D e , , f )
 10log 10 FD ( f e , f )  dB e
(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,
5
American Institute of Aeronautics and Astronautics
increased, the mixed jet source is decreased, and the
cut-off frequency is increased.
noise source are the presence of the turbulent fluid
produced by the mixer in the upstream portion of the
plume, the interactions of this turbulence with the
downstream portions of the jet plume, and the
interaction of the mixer turbulence with the nozzle
walls.
The sound pressure level spectrum of a jet with an
internal forced mixer can be matched using a modified
version of the four-source method that includes two
single jet sources, the mixed jet and the secondary jet.
Three variable parameters are used to match the data in
this formulation.
The work summarized in this paper represents a
preliminary effort in developing a robust method for
predicting the noise from jets with internal forced
mixers. Future work will focus on determining
empirical relationships between the three variable
parameters in the modified method and the geometric
and aerodynamic properties of a given configuration.
Table I: Optimized Four-Source Parameters
Mixer Type
dBs
dBm
fc
Low Penetration
7.85
-3.52
19020
High Penetration
9.92
-5.74
4982
The increase of the secondary jet source reflects
the differences between the secondary-ambient shear
layer of a coplanar, coaxial jet, and the nozzle exit
flow-ambient shear layer for the case of an internally
mixed jet with a convergent nozzle. As previously
stated, the jet from the nozzle exhaust will have a
higher velocity than the secondary flow, therefore one
would expect higher noise levels from this source.
Furthermore, it is seen that the high penetration mixer
requires a higher shift in the secondary jet source. This
difference is likely due to the increased turbulence
levels that are generated by the high penetration mixer
as compared to the low penetration case.
The decrease in the mixed jet source most likely
reflects the effects of the turbulent mixing layer with
embedded streamwise vortices on the downstream
development of the jet plume. Furthermore, it is seen
that the high penetration mixer requires a larger
reduction in this source. Similar to the secondary jet
source, this difference is also likely due to the
differences in the turbulence levels produced by the two
different mixers, due to their differing amounts of
penetration.
The location of the cut-off frequency for the source
spectral filters will likely be related to the position at
which the turbulent mixing layer from the lobed mixer
intersects the nozzle exhaust-ambient mixing layer.
This location will depend on both the amount of
penetration in the mixer and the nozzle geometry.
Acknowledgements
This work is a joint effort with Rolls-Royce,
Indianapolis and is sponsored by the Indiana 21 st
Century Research and Technology Fund. The first
author is also supported by a Rolls-Royce Fellowship.
References
1.
2.
3.
Concluding Remarks
4.
In summary, it has been shown that the current
coplanar, coaxial jet prediction method does not
accurately predict the noise from a jet with an internal
forced mixer. In addition, it is seen that a single jet
prediction using the nozzle exit conditions as the
characteristic properties agrees relatively well with the
experimental data for a jet with an internal lobed mixer
with low penetration. For the case of the high
penetration mixer there appears to be an additional
noise source producing a contribution in the high
frequency range. Possible causes for this additional
5.
6.
7.
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.
Balsa, T.E., and Gliebe, P.R., “Aerodynamics
and Noise from Fine-Scale Turbulence,” AIAA
Journal, Vol. 15, No. 11, 1977, pp. 1550-1558.
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.
Khavaran, A., “Role of Anisotropy in Turbulent
Mixing Noise,” AIAA Journal, Vol. 37, No. 7,
1999, pp. 832-841.
Tam, C.K.W., and Auriault, L., “Jet Mixing
Noise from Fine-Scale Turbulence,” AIAA
Journal, Vol. 37, No. 2, 1999, pp. 145-153.
Uzun, A., Blaisdell, G.A. and Lyrintzis, A.S., “3D Large Eddy Simulation for Jet Aeroacoustics,”
AIAA Paper 2003-3322 , May 2003.
Zhao, W., Frankel, S.H., and Mongeau, L.,
“Large Eddy Simulations of Sound Radiated
6
American Institute of Aeronautics and Astronautics
8.
9.
10.
11.
12.
13.
14.
from Subsonic Turbulent Jets,” AIAA Journal,
Vol. 39, No. 8, 2001, pp. 1469-1477.
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.
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.
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.
Ko, N.W.M. and Kwan, A.S.H., “The Initial
Region of Subsonic Co-axial Jets,” Journal of
Fluid Mechanics, Vol. 73, 1976, pp. 305-332.
“ARP876C: Gas Turbine Jet Exhaust Noise
Prediction,” Society of Automotive Engineers,
Inc, November 1985.
Bass, H.E., Sutherland, L.C., Zuckerwar, A.J.,
Blackstock,
D.T.,
and
Hester,
D.M.,
“Atmospheric Absorption of Sound: Further
Developments,” Journal of the Acoustical Society
of America, Vol. 97 (1), 1995, pp. 680-683.
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.
7
American Institute of Aeronautics and Astronautics
Figure 6: Low Penetration Mixer Comparisons
Figure 7: High Penetration Mixer Comparisons
8
American Institute of Aeronautics and Astronautics
Figure 8: Comparison of the Low and High
Penetration Experimental Data
9
American Institute of Aeronautics and Astronautics
Figure 9: Optimized Four-Source Solution for the
Low Penetration Lobed Mixer
Figure 10: Optimized Four-Source Solution for
the High Penetration Lobed Mixer
10
American Institute of Aeronautics and Astronautics