investigation of the mechanisms of jet-engine core noise...
TRANSCRIPT
Investigation of the mechanisms of
jet-engine core noise using large-eddy simulation
Jeff O’Brien∗, Jeonglae Kim†, and Matthias Ihme‡
Stanford University, Stanford, California 94305
As further reductions in aircraft engine noise are realized, the relative importance of
reducing engine-core noise increases. In this work, a representative engine flowpath is
studied to examine the mechanisms by which direct and indirect core noise propagate
through the engine and affect the far-field sound radiation. The flowpath consists of a
model combustor, a single-stage turbine, a converging nozzle, a near-field jet, and far-field
acoustic radiation. A combination of high-fidelity simulations and low-order semi-analytic
models is used to represent the generation and propagation of disturbances through the
flowpath. Particular details are provided for LES calculations of combustion chamber,
nozzle exhaust flow, and jet noise radiation. A one-way coupling procedure is employed
for propagating disturbances from one stage of the calculations to the next, and the results
show substantial changes in the far-field sound directivity and frequency spectra due to
fluctuations generated by the upstream engine core.
I. Introduction
Core noise is one of the important sources of noise generated by modern gas-turbine engines. As jet
noise and fan noise have been progressively reduced, the relative importance of core noise has increased. Its
generation is often associated with combustion and the propagation of temperature inhomogeneities through
the turbine stages.1, 2 Understanding the fundamental mechanisms of core-noise generation and propagation
is an essential step toward further reducing the overall noise from gas-turbine engines. It is also important
to understand how core noise interacts with the engine components, since its generation and propagation
can be closely linked with thermo-acoustic instabilities in the combustor.
The complex mechanisms of core noise pose significant challenges to prediction. Due to excessive compu-
tational costs, modeling assumptions or theoretical tools are often employed. However, due to the subtlety
of noise generation and propagation, it is desired that high-speed turbulent flows within the flowpath of
gas-turbine engines are simulated using consistently high-fidelity simulation tools.
∗Graduate Research Assistant, Department of Mechanical Engineering. Member AIAA.†Post-Doctoral Fellow, Center for Turbulence Research. Member AIAA.‡Assistant Professor, Department of Mechanical Engineering. Member AIAA.
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54th AIAA Aerospace Sciences Meeting
4-8 January 2016, San Diego, California, USA
AIAA 2016-0761
Copyright © 2015 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
AIAA SciTech
Large-eddy simulation (LES) has proven viable in modeling high-speed, high-temperature turbulent flows
with chemical reactions. Although its industrial application is not widespread as of yet, modern computing
power has reached a point where the complex turbulent reacting flows within realistic gas-turbine engines
can be simulated with LES in their entirety without needing to resort to low-order models. The fidelity of the
LES-based approach depends critically upon an accurate description of the complex geometry often found
in practical gas-turbine engines. Thus, LES based upon unstructured-grid technology appears essential to
satisfy such requirements and has proven suitable for massively parallel computing platforms by providing
good scalability.
In this study, we investigate fundamental core-noise mechanisms in a model gas-turbine flowpath that
contains essential components of a commercial jet engine at a high-altitude cruise condition. By applying
LES to the combustor, nozzle and jet stages of the flowpath, this study captures both the generation of direct
core-noise within the combustion chamber as well as the development of turbulent and thermal fluctuations
that lead to indirect noise downstream. Using a one-way coupling procedure, the combustor output will
inform an inflow boundary condition for a single stage, high pressure turbine. The turbine stage will be
modeled using a low-order modeling technique, and the amplification of direct noise as well as the conversion
of upstream fluctuations into indirect noise in the turbine stage. Lastly, the turbine output will be used to
form an inflow boundary condition for a simulation of a subsonic heated jet and nozzle, an environment in
which the impact of core-noise has not been studied as extensively. The thermodynamic state and modeling
approach for each stage of the flow path are shown in Figure 1.
Combustor
Compressible
Single-StageTurbine
Actuator DiskTheory
Nozzle& Jet
CompressibleLESLES
Far field
Ffowcs Williams
and Hawkings
T0 = 215K
p0 = 4.5atm
M0 = 0.06
T1 = 1010K
p1 = 4.4atm
M1 = 0.15
T2 = 895K
p2 = 1.5atm
M2 = 0.48
T3 = 805K
p3 = 1.0atm
M3 = 0.90
Figure 1. Summary of the component models and thermodynamic states for the flowpath of the representative gas-turbine engine.
II. Direct core noise generation in the combustor stage
The combustor stage is modeled using the in-house code Chris, an LES-solver that has previously been
validated in similar applications.3 Chris is a tool that solves the fully compressible Navier–Stokes equations
on unstructured grids. The code is explicit and second-order accurate in time and space on arbitrary grids.
The chemical source term is modeled by the flamelet progress variable approach4 using a three-dimensional
chemistry table based on tabulated chemistry for methane–air diffusion flames. The filtered momentum
equation is closed using the Vreman model,5 and the turbulent scalar fluxes are closed using a constant
turbulent Schmidt number assumption. The resulting set of governing equations is
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∂ρ
∂t+∂ρuj∂xj
= 0 (1a)
∂ρui∂t
+∂ρuiuj∂xj
= −∂p
∂xi+
∂
∂xj
[(µ+ µt)
(∂ui∂xj
+∂uj∂xi
−2
3δij∂uk∂xk
)−
2
3ρkδij
](1b)
∂ρE
∂t+∂ρujE
∂xj=
∂
∂xj
[(λ
cp+
µt
Prt
)∂h
∂xj
]+
∂
∂xj(−uj p+ uiτij) (1c)
∂ρZ
∂t+∂ρujZ
∂xj=
∂
∂xj
[(ρD +
µt
Sct
)∂Z
∂xj
](1d)
∂ρC
∂t+∂ρujC
∂xj=
∂
∂xj
[(ρD +
µt
Sct
)∂C
∂xj
]+ ¯ωc
(Z, Z ′′2, C
)(1e)
∂ρQ
∂t+∂ρujQ
∂xj=
∂
∂xj
[(ρD +
µt
Sct
)∂Q
∂xj
]−
[2ρD
∂Z
∂xj
∂Z
∂xj+ ρCQZ
′′2µt
Sct∆2
](1f)
where Z is the mixture fraction, C is the progress variable, Q is the mixture fraction variance and CQ is an
empirical constant set to 40. The combustor design chosen for the flowpath is the dual-swirler gas turbine
model combustor (GTMC) configuration originally studied by Meier et al.6, 7 The combustor geometry is
represented using a block-structured hexagonal mesh of roughly 5 million control volumes. The operating
condition has been scaled up from the high-power “A” condition in Meier’s work to achieve thermodynamic
consistency with the downstream components of the flowpath as well as a specific heat release consistent
with aviation engines. In spite of this change in operating condition, the chamber dynamics are quite similar
to those observed in Meier’s high-power “A” case, as can be seen in the time-averaged flow fields shown
in Figure 2. It can be seen that the flame exhibits the same “V” configuration observed by Meier at high
power, and that the flow field is dominated by the presence of a precessing vortex core (PVC) and strong
recirculation zone in the center of the chamber.
Acoustic measurements are taken near the exit of the combustion chamber at the plane x = 31 cm. To
reduce the potential for spurious reflection, the combustor mesh is then stretched over an additional 3 chimney
diameters and characteristic non-reflecting boundary conditions are applied at the outflow boundary of the
domain. Figure 3 displays the planar-averaged spectrum taken at the combustor exhaust. The OASPL in this
plane is 155 dB, which is consistent with limited experimental data available at this location.8 Additionally,
the noise peaks at low frequencies (f < 1kHz) which is characteristic for direct combustion noise. The
spectrum exhibits several features which are indicative of the flame dynamics.
To establish the link between the flame behavior and the acoustic signature emerging from the flame, the
dynamics of the precessing vortex core are analyzed in detail. Since a connection to frequency is desired,
dynamic mode decomposition (DMD),9 is applied to examine the temporal dynamics of the flame. Specif-
ically, the sparsity promoting DMD method10 is applied to help isolate key dynamics and improve mode
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Figure 2. Time-averaged flow fields in GTMC combustor: a) pressure, b) axial velocity and c) temperature
Frequency [Hz]10 2 10 3 10 4 10 5
SP
L [d
B]
115
120
125
130
135
140
145
150
155
160
Figure 3. Averaged pressure spectra at combustor exit
orthogonality. Figure 4 plots the spectral coherence of the PVC’s pressure modes as a function of frequency.
The plot indicates significant mode amplitudes at 2900, 3600, and 5500 Hz. The first mode is a Helmholtz
or volumetric mode and can clearly be observed in the combustor exit spectra at this fundamental frequency
(2900 Hz) as well as its first (5800 Hz) and second harmonics (8700 Hz). The second PVC mode, at 3600
Hz, corresponds to a spinning mode in the PVC. This spinning can be observed at twice the frequency (7200
Hz) at the combustor chimney plane. While there is no peak at 7200 Hz in Figure 3 (there is a local dip in
SPL), individual microphone measurements taken in this plane exhibit strong tones at 7200 Hz as can be
seen in Figure 5. This is because phase averaging hides the presence of circumferential modes in Figure 3,
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Frequency [Hz]0 2000 4000 6000 8000 10000
Ene
rgy
Coh
eren
ce10 4
10 5
10 6
10 7
10 8 Pressure
Figure 4. DMD mode spectra of combustor PVC, showing mode coherence vs. frequency
Frequency [Hz]10 2 10 3 10 4 10 5
SP
L [d
B]
135
140
145
150
155
160
165
170
Figure 5. Pressure spectra taken from a single probe at the radial location r = 30 mm, x = 29 cm.
and the SPL deficit near 7200 Hz suggests that some of the available broadband energy is absorbed in the
mean flow. Lastly, the third prominent mode in the PVC is another Helmholtz mode, which can also be
observed in Figure 2. Clearly, the acoustic signature emerging from the chimney has strong links to the
in-chamber dynamics.
III. Turbine stage
The turbine stage in the flowpath consists of a single rotor and stator with a nominal pressure ratio of
2.4, allowing for a relatively large enthalpy extraction over a compact computational domain. The turbine
design is taken from Stabe et al.11 The turbine stage inflow is decomposed into three quantities:
φ(r, t) = ¯φ+ φ(r) + ψ(t)φ(r), (2)
where ¯φ is the nominal inflow operating condition of the device, φ(r) is the spatially varying, time-averaged
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mean which allows the combustor’s mean flow structures to be retained, and the product ψ(t)φ(r) represents
the time and space varying fluctuations measured at the combustor exit.
For computational efficiency, the perturbations are imposed via a modal representation. Specifically,
Proper Orthogonal Decomposition (POD) is applied to the combustor outflow data, allowing for an efficient
representation of the mode shapes. Since the POD procedure can only be applied to a single quantity and
it is desired that each of the fluctuating quantities be represented by the same basis, the L2-norm of the
non-dimensional fluctuations is used:
ξ =p′
γp0+s′
cp+v′
c0(3)
where p0 represents the mean pressure, cp the specific heat of the gas, and c0 the sound speed at the combustor
exit, is chosen as the metric for the procedure, as it applies roughly equal weighting to the acoustic, vortical
and entropic perturbations. The efficiency of the POD-procedure in capturing the fluctuating fields is shown
in Figure 6 and indicates that while this metric does not perfectly capture all three fluctuating quantities
in the first few modes, it does provide an adequate representation of the fields efficiently. At this time, only
the first (largest amplitude) POD mode is imposed at the turbine inlet, and examining the effect of this
simplification is an area for further research. The fundamental mode shapes for each quantity are shown in
Figure 7.
Mode0 5 10 15 20
Mod
e A
mpl
itude
0.014
0.016
0.018
0.02
0.022
0.024
0.026
0.028
0.03
0.032
(a)
Mode0 5 10 15 20
Mod
e A
mpl
itude
0.014
0.016
0.018
0.02
0.022
0.024
0.026
0.028
0.03
0.032
(b)
Mode0 5 10 15 20
Mod
e A
mpl
itude
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
(c)
Figure 6. RMS of fluctuation amplitude for a)pressure, b) axial velocity and c) entropy vs. POD mode number.
The effect of the turbine stage is modeled using Actuator Disk Theory (ADT), a low-order analytical
method based on a linearization of conservation equations applied across a turbine stage, specifically the
conservation of momentum, energy, and entropy as well as the Kutta condition. ADT is best suited for
acoustically compact disturbances in which the characteristic length scale is much greater than the chord
lengths of the turbine blades. Because of its linearity, the method cannot take into account for the “chopping”
effect of the turbine blade-passing frequency which can map moderate frequency disturbances to higher
frequencies due to blade rotation. However, this effect is not expected to be significant at the low frequencies
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r\R [-]0 0.2 0.4 0.6 0.8 1
φp
-0.22
-0.21
-0.2
-0.19
-0.18
-0.17
(a)
r/R [-]0 0.2 0.4 0.6 0.8 1
φv
-0.35
-0.3
-0.25
-0.2
-0.15
-0.1
(b)
r/R [-]0 0.2 0.4 0.6 0.8 1
φs
0.12
0.14
0.16
0.18
0.2
0.22
0.24
0.26
(c)
Figure 7. Fundamental POD-mode shapes from combustor exhaust: a) pressure, b) axial velocity and c) entropy.
associated with core noise. The method was first presented by Cumptsy and Marble,12 and has been
validated against higher fidelity methods and found to perform satisfactorily for the frequencies of interest
in this study.13, 14 The set of linearized equations is given as:
s′1 = s′2 (4a)
p′1 +w′
1
Ma1− θ′1tan(θ1) = p′2 +
w′2
Ma2− θ′2tan(θ2) (4b)
1
1 + 12(γ − 1)Ma21
(p′1 +
1
γ − 1s′1 +Ma1w
′1
)=
1
1 + 12(γ − 1)Ma22
(p′2 +
1
γ − 1s′2 +Ma2w
′2
)(4c)
θ′2 = 0 (4d)
ADT is derived from jump conditions of conserved quantities over each blade row and has been shown
to be successful at predicting the amplification of direct noise and generation of indirect core-noise at low
frequencies in multiple applications.15, 16 Figure 8 demonstrates the increase in noise (attributable to both
direct and indirect noise) across the turbine.
IV. Responses of an Mach 0.9 heated jet to the turbine-stage fluctuations
In the modeled engine flowpath, fluctuations from the turbine stage propagate downstream to an exhaust
nozzle. While propagating, some of the fluctuations decay or disperse depending on frequency, amplitude,
geometry, and so forth, and some of them convect or amplify.17 As they reach the nozzle exit, they interact
with a turbulent jet developing downstream of the nozzle.
It is well known that jet flows in general respond to external disturbances.18 Mechanisms by which
jet flows respond are complicated and sometimes not described by a simple linear theory even for small-
amplitude excitation. One of the important outcomes of such responses is a change in acoustic radiation.
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r/R0 0.2 0.4 0.6 0.8 1
SP
L [d
B]
150
155
160
165
170
175
180Combustor ExitTurbine Exit
Figure 8. Pointwise OASPL increase over the turbine.
Radiated sound takes only a tiny portion of fluctuation energy of high-speed turbulent jet19 and thus, even
small-amplitude disturbances can have significant impacts on sound.
The acoustic responses of high-speed turbulent jets are often examined under conditions subject to
excitation at well-defined discrete frequencies. However, in realistic operating conditions of aircraft engine,
post-turbine fluctuations are typically broadbanded. Considering complexities of jet responses to external
excitation, turbulent jet noise subject to realistic turbine-stage fluctuations can be drastically different from
acoustics of isolated, laboratory-scale jet.
In this section, responses of a subsonic heated jet to the turbine-stage fluctuations are discussed. The
post-turbine fluctuations are imposed at the nozzle inlet as a unsteady boundary condition. The nominal
nozzle-exit condition is thermodynamically consistent with the upstream combustor and turbine stages.
The spectrum of the imposed fluctuations is broadbanded, and their magnitudes are close to the level of
fluctuations found at a realistic jet-engine’s nominal operating condition. However, the magnitudes are not
large enough to modify the mean flow and thus, the fluctuations are still considered as perturbations to the
base flow. The flow and computational conditions are first described, and the results for the baseline unforced
and forced jets are presented. Comparisons between the unforced and forced jets show that engine-core noise
has significant impacts on radiated sound of high-speed turbulent jet at high exhaust temperature.
IV.A. Simulation set-up
The high-fidelity, computational fluid dynamics code, CharLES†, is used to solve the fully compressible
Navier–Stokes equations. Ideal gas is assumed with γ = cp/cv = 1.4, where cp and cv are the specific
heats at a constant pressure and volume, respectively. Molecular viscosity is assumed to be a function of
temperature only and to follow the power-law relation, µ/µ∞ = (T/T∞)n where n = 0.76. The Prandtl
† http://www.cascadetechnologies.com/pdf/CHARLES.pdf
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number is assumed constant at Pr = 0.7. The subgrid-scale model of Vreman5 is used with the model
constant c = 0.07 and a constant turbulent Prandtl number of Prt = 0.9. Turbulent jet simulations are
performed using LES under a similar condition as that of O’Brien et al.20
The governing equations are discretized in space using a cell-based finite volume formulation. Solutions
are time advanced using the standard third-order Runge–Kutta method at a constant time-step size of
∆trJ/c∞ = 0.00125, which results in the CFL number of approximately 1.0. The spatial discretization
is non-dissipative and formally second-order accurate on arbitrary unstructured grids. In addition, the
convective fluxes are combined, depending on local grid quality (for example, element skewness), with fluxes
computed by an HLLC-upwind discretization. Khalighi et al.21 provide more detailed discussions on the
spatial discretization.
High-temperature gas from the turbine stage flows into a straight pipe shown in Figure 9(a), after which
it is discharged into the ambient air at rest through an axisymmetric nozzle. The nozzle is strictly converging
and its geometry is generated to meet the ASME-standards, as can be seen in Figure 9(b). The nozzle-exit
radius is rJ = DJ/2 = 1 in. The nozzle cross-sectional area decreases over 2.5rJ in the axial direction, and
the area contraction ratio is 4.73. The straight pipe connected to the ASME-nozzle has a radius of 2.17rJ
and a length of 15rJ .
(a)
-2.0 -1.0 0.0
-4.0
-2.0
0.0
2.0
4.0
x/rJ
y/r J
(b)
Figure 9. (a) Three-dimensional geometry of the jet exhaust system. (b) Cross-section of the ASME-standard con-verging nozzle.
The nozzle-exit condition is obtained based upon the outflow condition of the turbine stage, the same as
the nominal nozzle-exit condition of the test-point number 49 of Tanna.22 The non-dimensional velocity at
the nozzle exit with respect to the ambient speed of sound is uJ/c∞ = 1.48, and the nozzle-exit temperature
relative to the ambient temperature is TJ/T∞ = 2.857. The nozzle-exit Mach number isMJ = uJ/cJ = 0.876,
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and the Reynolds number based on the nozzle-exit condition is ReJ = ρJuJDJ/µJ = 2.3×105. This Reynolds
number is lower than the critical Reynolds number 4 × 105 above which low Reynolds number effects on
far-field sound become less significant.23
The physical domain extends 40rJ downstream of the nozzle exit and 40rJ in the radial direction. The
center of the nozzle exit is (x, r =√y2 + z2) = (0, 0), which is also the reference point to define far-field
locations using the distance d and the radiation angle ϕ, where ϕ = 0◦ corresponds to the downstream jet
axis, as illustrated in Figure 10.
x/rJ
y/r J
T/T∞
dϕ
Figure 10. Part of computational domain on the x-y plane. The contours represent instantaneous static temperaturenormalized by the ambient temperature.
At the nozzle inlet, the total pressure of p0/p∞ = 1.621 and the total temperature of T0/T∞ = 3.229
are prescribed following the test-point number 49 of Tanna.22 At the outflow, an absorbing buffer zone is
used. The nozzle wall is modeled as a no-slip, isothermal boundary at Twall = T∞. The rest of the domain
boundaries are modeled to have the ambient total pressure and the ambient total temperature. There is no
co-flow in this flow configuration.
A base-grid having 0.8 million unstructured control volumes is generated and subsequently refined using
Adapt, the grid-adapting tool in the CharLES suite of codes. For computational accuracy and efficiency,
only hexahedral elements are used. The total number of control volumes for the adapted grid is 25.3 million.
Neither turbulent statistics nor sound prediction exhibited sensitivity upon additional mesh refinement. A
cross-section of the computational grid on the z = 0 plane is shown in Figure 11(a).
Using the same computational code CharLES, Bres et al.24 simulated a Mach 0.9 isothermal jet and its
acoustics. Their BL16M WM is compared for space–time resolution with the current simulation. It should
be noted that the nozzle geometry and nozzle-exit condition differ between Bres et al.24 (convergent–straight
nozzle and Mach 0.9 isothermal jet) and the current set-up (converging nozzle and Mach 0.9 heated jet), and
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thus the comparison is qualitative. However, it can provide a useful guideline to assess whether the current
resolution is reasonable.
To investigate the impacts of turbulent boundary layer on sound radiation, Bres et al.24 selectively
refined the near-wall regions of the straight nozzle, while, in the current study, the entire region within the
nozzle is refined to resolve the fluctuations from the turbine stage (see Figure 11(b)). For the same reason,
the grid within the potential core is refined. When the nozzle interior and the potential core are not refined,
the total number of control volumes is approximately 18 million, which is comparable to Bres et al.24 In
addition, The nozzle-exit velocity of the current simulation is 1.64 times faster due to the higher temperature
ratio (TJ/T∞ = 2.857 compared to TJ/T∞ = 1.0 of Bres et al.24). As a result, the nozzle-exit boundary
layer becomes thinner for the current simulation Also, the strictly converging ASME-type nozzle suppresses
turbulent fluctuations within the incoming boundary layer, thus making the boundary layer thinner at the
nozzle exit. Overall, the resolution requirement for the current simulation appears to be higher than Bres et
al.24 This explains the choice of a smaller time-step size (∆trJ/c∞ = 0.00125 compared to ∆trJ/c∞ = 0.002
of Bres et al.24).
x/rJ
y/r J
(a)
x/rJ
y/r J
(b)
Figure 11. Cross-sections of the computational grid on the x-y plane for (a) downstream of the nozzle and (b) thenozzle interior. The dashed line in Figure 11(a) represents a part of the integral surface for the Ffowcs Williams andHawkings method.
Sound radiation at acoustic far-field locations is computed using the Ffowcs Williams and Hawkings
method.25 Additional details on the formulation and some practical guidelines for using the Ffowcs Williams
and Hawkings method are found elsewhere.26, 27 The integral surface is located within the grid-refined zones,
as illustrated in Figure 11(a). Its minimum radius is 2.9rJ near the nozzle exit and the maximum radius is
8.9rJ at the downstream end at x/rJ = 40. It was confirmed that the acoustic prediction is insensitive to
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the radial location of the integral surface. Following Shur et al.,28 the end caps are used to accurately close
the Ffowcs Williams and Hawkings surface downstream. Sixteen end caps are used for 30 ≤ x/rJ ≤ 40. The
upstream end is closed by the nozzle wall and thus no end caps are required. Solutions are sampled on the
integral surface at a rate of StD ≈ 10.8. The maximum resolved frequency is estimated as StG ≈ 1.54 by
computing the grid Strouhal number29, 30
IV.B. Baseline clean-nozzle simulation
The simulation is time-averaged for 10 nominal acoustic flow-through times. Figure 12 shows the comparisons
of time-averaged axial velocity and fluctuating axial velocity rms with the particle image velocimetry (PIV)
measurement31 along the jet centerline and the nozzle lipline, respectively. The “consensus” dataset (i.e. a
weighted average of the as-measured PIV data to account for uncertainties) is compared with the current
LES prediction. Also shown in Figure 12(a) is the measurement data obtained for the Acoustic Research
Nozzle (ARN) 2. The ARN2 nozzle is a converging nozzle with the same exit diameter as the current
ASME-standard nozzle. Its contracting section is three times longer and the area contraction ratio is two
times larger than the current nozzle. Also, the nozzle internal contour is slightly different. Agreement with
both PIV-datasets is good along the jet centerline and the nozzle lipline. Flow within a strictly converging
nozzle undergoes a strong acceleration and the nozzle-exit boundary layer is likely to be relaminarized (see,
for example, Mi et al.32). This is also the case for the ARN-type nozzles,31 which can presumably explain
its slightly better agreement than the consensus dataset in Figure 12(a). As a result, velocity fluctuations at
the current nozzle exit are much lower (0.32% of uJ) compared to the experiment, as shown in Figure 12(a).
This causes the nozzle-exit boundary layer to undergo rapid transition to turbulence, substantiated by an
initial peak in u′x,rms near the nozzle exit in Figure 12(b). Artificial inflow turbulence based upon the digital
filtering technique33 was tested to increase the fluctuation levels at the nozzle exit; however, due to the strong
contraction of the current nozzle, even unrealistically strong fluctuations showed negligible improvement.
Radial profiles of streamwise velocity at several streamwise locations compare well with the consensus
PIV-measurement, as shown in Figures 13(a) and 13(b). At the nozzle exit, the time-averaged velocity has
a nearly top-hat profile. The computed 99% boundary-layer thickness is 0.0475DJ which is resolved by 20
points. The momentum thickness is 0.0024DJ where two points are used. The shape factor is computed
as 2.2, indicating that the nozzle-exit boundary layer is nominally laminar. As shown in Figure 13(b),
fluctuation levels are very low near the center of the nozzle exit and their maximum value is less than 13%
of uJ near the nozzle wall.
Figure 14(a) shows sound directivity at 72DJ from the nozzle exit. Also shown are the measurement
data of Tanna22 and Brown & Bridges.34 Agreement is good within 2 dB over the angles considered in this
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0 10 20 30 400.0
0.2
0.4
0.6
0.8
1.0
1.2
0.0
0.1
0.2
0.3
0.4
x/rJ
ux/uJ
u′ x,rms/uJ
PIV31 (consensus)PIV31 (ARN2)
(a)
0 10 20 30 400.0
0.1
0.2
0.3
0.4
0.5
0.6
0.0
0.1
0.2
0.3
0.4
x/rJ
ux/uJ
u′ x,rms/uJ
PIV31 (consensus)
(b)
Figure 12. Streamwise variation of time-averaged axial velocity and fluctuating axial velocity rms along (a) the centerline(r = 0) and (b) the nozzle lipline (r/rJ = 1).
-3 -2 -1 0 1 2 30.0
0.2
0.4
0.6
0.8
1.0
y/rJ
ux/uJ
(a)
-3 -2 -1 0 1 2 30.00
0.05
0.10
0.15
0.20
y/rJ
u′ x,rms/uJ
(b)
Figure 13. Radial profiles of (a) time-averaged axial velocity and (b) fluctuating axial velocity rms at several axiallocations on the x-y plane: x/D = 0, solid; x/DJ = 4, dashed; x/DJ = 8, dashed-dot; x/DJ = 12, dashed-dot-dot;x/DJ = 16, dotted; symbols, PIV31 (consensus).
study. At sideline and upstream angles (ϕ & 90◦), the measurement of Tanna22 shows overprediction by 2
to 3 dB, which is attributed to its very large (≈ 36) area contraction ratio of the nozzle.35 Figure 14(b)
shows sound pressure levels (SPL) at the aft and sideline angles. At ϕ = 30◦, SPL is well predicted over
the computed frequency range. At the sideline angle, sound at StD & 1.0 is overpredicted by 2 to 5 dB. At
both angles, the computed sound matches well up to the estimated grid cut-off frequency StG = 1.54, shown
as a dotted line in Figure 14(b). It was confirmed that varying the radial location of Ffowcs Williams and
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Hawkings surface gives no improvement in Figures 14(a) and 14(b).
20 40 60 80 100 120 140
85
90
95
100
105
110
ϕ (◦)
OASPL(dB)
CurrentTanna22
Brown & Bridges34
(a)
10-2 10-1 100
90
100
110
120
130
StD
SPL(dB)
ϕ = 30◦
ϕ = 90◦
(b)
Figure 14. (a) Sound directivity and (b) sound pressure levels at ϕ = 30◦ and 90◦. Measurement is made at d/DJ = 72.
Regarding the 2 to 5 dB overprediction at StD & 1.0 at ϕ = 90◦ in Figure 14(b), it is worthwhile
mentioning the work of Viswanathan & Clark,36 who studied the effects of nozzle internal contour on radiated
sound. Their finding was that among three different converging nozzles, having the same nozzle-exit diameter
and the same operating condition, the ASME-standard nozzle (also used in this study) generates more sound.
They observed an increased SPL (≈ 3 dB) at the sideline and upstream radiation angles, especially at higher
frequencies than the spectral peaks. This trend becomes more pronounced as jet temperature increases. They
argued that different nozzle internal contours produce distinctly different boundary-layer characteristics at
the nozzle exit, thereby affecting the early development of the mixing layer and turbulence. Their Figure 12
shows similar 2 to 3 dB more sound at StD & 0.5 at the sideline angle as the current jet. Similar studies
were done by Zaman37 and Bogey & Marsden.38 Since the grid cut-off frequency is StG = 1.54, there could
be some contribution from unresolved fluctuations at StG & 1.54 on the integral surface. Nevertheless, the
overprediction seems consistent with the previous studies using the ASME-standard nozzle.
IV.C. Forced jet simulation
The baseline jet is perturbed using the fluctuations from the turbine stage. The fluctuations are prescribed
as a reference state for the inlet buffer zone having a streamwise lengh of DJ . Instantaneous temperature
contours for the baseline clean-nozzle and forced jet simulations are shown in Figures 15(a) and 15(b),
respectively. The prescribed fluctuations convect downstream through the nozzle and interact with the
turbulent jet. Jet spreading and large-scale structures do not show strong sensitivity to the upstream
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fluctuations, at least qualitatively.
x/rJ
y/r J
T/T∞
(a)
x/rJ
y/r J
T/T∞
(b)
Figure 15. Instantaneous temperature contours on the x-y plane (a) without and (b) with the turbine-stage fluctuations.
Figures 16(a) through 16(c) show fluctuation amplitudes along the centerline. For the forced jet, the
maximum amplitude of the streamwise velocity fluctuation within the nozzle is 0.018uJ , corresponding to
10 m/s. The temperature fluctuation is less than 20 K and pressure fluctuation less than 165 dB. The
fluctuations do not decay significantly in the axial direction as they convect.
In Figure 17(a), streamwise velocity at r = 0 for unforced and forced jets is plotted. At the nozzle exit,
fluctuation increases from 0.32% (unforced jet) to 1.8% (forced jet) of uJ (a sufficiently large amplitude to
enter the nonlinear regime for the forced case), and time-averaged velocity increases by 0.024uJ . Due to
the increased level of upstream fluctuation, forced jet decays faster and its centerline fluctuation saturates
slightly earlier than that of unforced jet. At the nozzle lipline, the initial u′x,rms peak discussed in Figure 12(b)
persists for the forced jet, though its amplitude is slightly reduced due to the increased upstream fluctuation.
This implies that the nozzle-exit boundary layer is still nominally laminar.
Figure 18(a) shows the comparisons of radial profiles of streamwise velocity at several axial locations
for unforced and forced jets. At the nozzle exit, the impacts of the upstream fluctuations are significant.
The 99% boundary-layer thickness of the forced jet is 0.305DJ , nearly 6.4 times larger than that of the
unforced jet. In addition, the momentum thickness increases four times due to the upstream fluctuations.
Boundary-layer shape factors for unforced and forced jets are 2.2 and 1.28, respectively. However, the shape
factor of the forced jet does not necessarily indicate that its nozzle-exit boundary layer is fully turbulent.
Rather, this appears to be caused by large-scale thermal fluctuations that modify the velocity profiles.
A comparison of the sound directivity at d/DJ = 72 is shown in Figure 19(a) for unforced and forced jets.
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-15 -10 -5 0 5 100.00
0.02
0.04
0.06
x/rJ
u′ x,rms/uJ
Unforced jetForced jet
(a)
-15 -10 -5 0 5 100
10
20
30
40
50
60
70
x/rJ
T′(K
)
Unforced jetForced jet
(b)
-15 -10 -5 0 5 10120
130
140
150
160
170
x/rJ
p′(dB)
Unforced jetForced jet
(c)
Figure 16. Centerline fluctuation amplitudes of (a) streamwise velocity, (b) temperature, and (c) pressure.
Depending on the radiation angle ϕ, the incoming turbine-stage fluctuations have two distinct effects on the
radiated sound. At lower radiation angles, OASPL is decreased with its maximum reduction of 1.2 dB at
ϕ = 50◦. In the sideline and forward directions, sound is consistently amplified. The maximum amplification
is 3.1 dB at ϕ = 85◦.
In Figure 19(b), frequency spectrum at ϕ = 30◦ is plotted. At lower frequencies (StD . 0.05 or 500 Hz), a
consistent increase by ≈ 5 dB is observed. This is often associated with the direct contribution of engine-core
noise. Pressure fluctuations produced by combustion processes are characterized by frequencies at O(102) Hz.
Their wavelengths are typically much longer than the geometric length scales of engine components. Some
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0 10 20 30 400.0
0.2
0.4
0.6
0.8
1.0
1.2
0.0
0.1
0.2
0.3
0.4
x/rJ
ux/uJ
u′ x,rms/uJ
Unforced jetForced jet
(a)
0 10 20 30 400.0
0.1
0.2
0.3
0.4
0.5
0.6
0.0
0.1
0.2
0.3
0.4
x/rJ
ux/uJ
u′ x,rms/uJ
Unforced jetForced jet
(b)
Figure 17. Streamwise variation of time-averaged axial velocity and fluctuating axial velocity rms for unforced andforced jets along (a) the centerline (r = 0) and (b) the nozzle lipline (r/rJ = 1).
-3 -2 -1 0 1 2 30.0
0.2
0.4
0.6
0.8
1.0
y/rJ
ux/uJ
(a)
-3 -2 -1 0 1 2 30.00
0.05
0.10
0.15
0.20
y/rJ
u′ x,rms/uJ
(b)
Figure 18. Radial profiles of (a) time-averaged axial velocity and (b) fluctuating axial velocity rms at several axiallocations on the x-y plane: x/D = 0, solid; x/DJ = 4, dashed; x/DJ = 8, dashed-dot; x/DJ = 12, dashed-dot-dot;x/DJ = 16, dotted. Lines with symbols represent forced-jet results.
of the pressure fluctuations are able to directly propagate through the engine flowpath through the exhaust
nozzle and acoustic far field. In addition, the indirect process generates additional pressure fluctuations at
the combustor nozzle exit and turbine stages, some of which can propagate to the acoustic far field.1 The
observed noise amplification at StD . 0.05 shows the core-noise propagation unambiguously contributes to
far-field sound of jet engines.
At frequencies higher than StD ≈ 0.05 in Figure 19(b), radiated sound is suppressed. The noise reduction
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is approximately uniform over frequencies as ≈ 5 dB. Also, several predominant tones are found at discrete
frequencies. This observation is consistent with the broadband jet-noise reduction.39, 40 When jet flows
are perturbed using acoustic excitation, radiated sound is often reduced over a range of frequencies where
jet noise is dominant. The acoustic excitation triggers the most unstable (fundamental) shear-layer mode
at 0.01 ≤ Stθ = f0θ/uJ ≤ 0.02. As its amplitude grows and saturates downstream, energy is gradually
transferred to subharmonic motions. This is demonstrated as pronounced peaks at subharmonic frequencies
of f0 and successive vortex pairing in the jet shear layer. Hence, shear-layer dynamics becomes more regular
and broadband turbulence is suppressed, which leads to the broadband reduction of radiated noise. Due to
the tonal amplification at f0 and its subharmonics, far-field sound shows strong peaks at the corresponding
frequencies.
20 40 60 80 100 120 140
90
95
100
105
110
ϕ (◦)
OASPL(dB)
Unforced jetForced jet
(a)
10-2 10-1 100
10-4 10-3 10-2
80
90
100
110
120
130
StD
SPL(dB)
Stθ
Unforced jetForced jet
f0
f0/2
(b)
Figure 19. (a) Sound directivity and (b) sound pressure levels at ϕ = 30◦ for unforced and forced jets. Measurementis made at d/DJ = 72.
Figure 19(b) shows that the broadband jet-noise radiation is suppressed at StD & 0.05 and tonal am-
plification is observed at the shear-layer instability frequencies denoted by f0 and subharmonic f0/2. The
excitation of the most unstable shear-layer mode and its subharmonics is evidenced by examining near-field
pressure spectra. As illustrated in Figure 20(a), pressure amplitudes at several axial locations along the
nozzle lipline are computed. Figure 20(b) shows pressure spectra for unforced and forced jets at x/rJ = 3.
For the unforced jet, spectra are broadbanded and distinct peaks are not observed. In contrast, for the
forced jet, two strong peaks exist near f0, which correspond to StD ≈ 1.0 (Stθ ≈ 0.01). The stronger peak
at StD = 0.46 (Stθ = 0.0046) represents the subharmonic mode. At x/rJ = 7, the subharmonic becomes
predominant and the fundamental mode decays to the level of broadband turbulent fluctuations, as can be
seen in Figure 20(c). In Figure 20(d), farther downstream at x/rJ = 11, fluctuation peaks at StD = 0.28.
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Spectrum becomes more broadbanded and similar with that of the unforced jet.
x/rJ
y/r J
T/T∞
(a)
10-2 10-1 100 101
10-4 10-3 10-2
10-4
10-3
10-2
StD
PSD
Stθ
Unforced jetForced jet
f0f0/2
(b)
10-2 10-1 100 101
10-4 10-3 10-2
10-4
10-3
10-2
StD
PSD
Stθ
Unforced jetForced jet f0/2
(c)
10-2 10-1 100 101
10-4 10-3 10-2
10-4
10-3
10-2
StD
PSD
Stθ
Unforced jetForced jet
(d)
Figure 20. (a) Pressure-measured locations denoted by circles. (b-d) Lipline pressure spectra at x/rJ = 3, 7, and 11,respectively, for unforced and forced jets.
V. Summary and future work
A hybrid modeling approach to predict engine core noise from a modeled gas-turbine engine and assess
its receptivity to nozzle upstream fluctuations is proposed. The modeled core-noise system consists of a
combustor, single-stage turbine, converging nozzle, and free-field radiation to the acoustic far field. The
computational strategy for the generation and propagation of turbulent fluctuations from the combustor to
the nozzle exhaust is developed.
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Compressible reacting LES is performed for flows within the modeled gas-turbine combustor. Fluctuation
data are recorded at the combustor exit. A modal analysis of the combustor’s in-chamber behavior is
performed, and a clear link between the precessing vortex core and combustor exit acoustics is established.
POD is then applied to decompose the signals coming from the combustor for an efficient downstream
coupling with the turbine stage. Effects of the turbine stage on the fluctuating fields, in turn, are simulated
using the semi-analytic ADT technique to estimate the fluctuations that would be seen at the exhaust-nozzle
entrance. These fluctuations are then used to forced a subsonic heated jet and to assess the changes induced
by the upstream perturbations on acoustic radiation.
High-fidelity simulations of the high-temperature jet exhaust flow are conducted using the combined
LES and acoustic analogy based upon the Ffowcs Williams and Hawkings formulation. Good agreement is
obtained for jet turbulence and sound radiation. Some discrepancies remain for the upstream propagating
sound at higher frequencies.
The baseline jet is then perturbed by fluctuations generated by the POD–ADT technique modeling the
effects of the turbine stage. Fluctuation levels at the nozzle exit are comparable with the experiment and the
forced jet decays slightly faster than the baseline jet. Far-field sound is found to decrease slightly over shallow
downstream angles (≈ 1 dB) while the upstream directivity is amplified (≈ 3 dB). The sound spectra show
that the prescribed forcing has two main effects on downstream radiation: low frequency sound is amplified
while high frequency sound is reduced and exhibits clear tones. The increase in low frequency noise suggests
that the upstream combustion noise passes through the nozzle and jet largely unimpeded and radiates at
all angles. The high frequency effects are likely attributable to an increase in vortex pairing at the nozzle
lip resulting in decreased turbulence in the shear layer and pronounced tones indicative of the characteristic
eddy size.
Future work will focus on more detailed analysis of the effects of upstream perturbations on downstream
noise, including attempts to assess the relative importance of direct and indirect core noise. More sophisti-
cated coupling techniques and a higher fidelity model for the turbine stage will also be pursued.
Acknowledgments
The authors acknowledge the following award for providing computing and visualization resources that
have contributed to the research results reported within this paper: MRI-R2: Acquisition of a Hybrid
CPU/GPU and Visualization Cluster for Multidisciplinary Studies in Transport Physics with Uncertainty
Quantification (http://www.nsf.gov/awardsearch/showAward.do?AwardNumber=0960306). This award is
funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). Additional comput-
ing resources are provided by the Argonne National Laboratory through the ASCR Leadership Computing
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Challenge.
The first author acknowledges the Stanford Graduate Fellowship program for continued support of this
work. The authors are grateful to Prof. Sanjiva Lele for useful discussions. The authors also thank Dr. James
Bridges at the NASA Glenn Research Center for sharing the PIV and acoustic measurement data for vali-
dation.
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