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Jet Noise Analysis of a Mixed Turbofan Engine
Jens TRÜMNER1; Christian MUNDT2
1,2 Institute for Thermodynamics, UniBw München, Germany
ABSTRACT
Due to constantly increasing flight traffic the aircraft industry is faced with major challenges. Essentially
these are reduction of fuel consumption and noise emission. The latter plays an outstanding role in the
vicinity of airports where residents are subjected to increased noise disturbance. Strict regulations protect
these citizens and force airlines to decrease the noise emission of their fleet to stay cost efficient.
Noise is generated by diverse mechanisms at several parts of the aircraft. During take-off jet noise is the most
important source since the engines operate at maximum thrust condition. The development of turbofan
engines drastically reduced jet velocities and thus sound emission. A further improvement could be achieved
by adding forced mixers and expanding both, bypass and core flow through a common nozzle. These mixers
increase the energy transport from hot to cold flow and thereby further decrease the maximum jet velocity.
In this work such a mixer is aeroacoustically studied using a hybrid approach to determine the noise level at
distant observer points.
Keywords: Jet noise, DES, Ffowcs-Williams & Hawkings Analogy
1. INTRODUCTION
With the development of civil jet engines in the early 50th
the importance of aerodynamically
generated noise became obvious. The work of Lighthill(1,2) laid the foundation for a new field of
research known as aeroacoustics.
Lighthill derived an exact formulation resembling wave equations from classical acoustical problems
with a source term depending on the flow field. From these findings he could show that the sound
intensity scales with the 8th
power of the jet velocity. Lighthill's analogy was later extended to shear
flows by Lilley(3), solid objects in the source region by Curle(4) and objects in motion by
Ffowcs-Williams and Hawkings (FW-H)(5). Initially acoustic analogies helped to better understand
the fundamental mechanisms of sound generation while engineering problems were investigated
experimentally. With increasing computational resources it became possible to numerically integrate
the wave equation with its sources and thereby determine the sound pressure level (SPL) at arbitrary
observer points.
Experiments by Seiner et al.(6) show that noise generation is not only determined by the jet velocity,
but also by temperature gradients. Lighthill's 8th
-power law fails on hot jets because he neglected the
dipole term for density fluctuations. Tam et al.(7) proved analytically that temperature gradients also
increase the instability of Kelvin-Helmholtz waves and thus the growth of turbulent shear layers. The
latter finding does not directly affect the source terms in acoustic analogies but leads to an under
prediction of Reynolds stresses in most turbulence models and therefore indirectly of Lighthill's stress
tensor.
To determine the noise level of aircraft engine jets at certain observer locations different approaches
are used. Empirical and semi-empirical models such as ISVR/Purdue by Tester et al.(8) are very well
validated with scale and full-scale exhaust systems.
Theoretically one could directly compute the transient jet and the wave propagation to the observer in
a single simulation. However, this would lead to a huge computational domain and by far exceed
arguable calculating capacity. Even a transient simulation of a domain which only covers the free jet
is not practicable today. Therefore different alternatives have been developed.
Tam et al.(9) proposed an adjoint approach to determine the spectral density of the sound pressure field
1 jens.truemner@unibw.de 2 christian.mundt@unibw.de
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at a certain observer point. This model directly processes mean flow and turbulence quantities from
steady RANS simulations which drastically reduces the computational cost for the flow field
simulation. They extended the model to hot jets and achieved very good agreements with experimental
data. Ewert(10) formulated a model to synthesize an unsteady pressure field from steady RANS data.
In a second step the linearized Euler equations are solved to obtain the unsteady pressure distribution
on a surface surrounding the source region. This surface can then be processed by a FW-H solver to
calculate the SPL at an observer’s location.
A considerable more complex approach is to determine the unsteady pressure field from transient flow
simulations. In high Reynolds number flows occurring in jet engines this can be done by unsteady
RANS or detached eddy simulations (DES). Traub et al.(11) could reproduce the tendencies of the
ISVR/Purdue model by using a classical DES in combination with a FW-H surface.
In this work the stress blended eddy simulation (SBES) by Menter(12) was used to calculate the
unsteady flow field of a mixed nozzle. Afterwards the noise level at different observer points was
determined using acoustic analogies.
2. NUMERCAL MODEL
2.1 Flow Simulation
Flow Solver 2.1.1The commercial CFD code ANSYS Fluent was utilized in this study. To account for compressibility
effects a pressure-based algorithm solves the Favre averaged Navier Stokes equations in a coupled
manner. An implicit second order time discretization with a time step of 2*10-6
s was applied. Likewise
spatial discretization of the flow equations was second order. Heat capacity was set to 1007J/kgK and
the Sutherland law defines the viscosity as a function of the temperature .
Turbulence Model 2.1.2As mentioned in the introduction the SBES model was used for turbulence modelling. This
formulation explicitly switches between a RANS and a LES model, whereas classical DES approaches
increase the turbulent dissipation of existing RANS models depending on the local cell size. The
effective eddy viscosity is calculated using a shielding function fs:
𝜇𝑡𝑆𝐵𝐸𝑆 = 𝑓𝑠 ∗ 𝜇𝑡
𝑅𝐴𝑁𝑆 + (1 − 𝑓𝑠) ∗ 𝜇𝑡𝐿𝐸𝑆. (1)
In this work the k-ω-SST model(13) was applied in wall near and the WALE model(14) in bulk
regions. Thereby the free jet is completely covered by the LES model.
Mesh 2.1.3A block-structured mesh was created in ANSYS ICEM-CFD. An attempt was made to create wall
near cells with y+=1 to properly resolve the boundary layer. Due to high Reynolds numbers this led to
very high aspect ratios, so that in the final mesh y+<=3. The LES region was created to fulfill the
following requirement:
∆𝑚𝑎𝑥≤ 0.1 (𝑘32
𝜀)𝑅𝐴𝑁𝑆
. (2)
Since this leads to a very high grid resolution the computational domain had to be drastically
diminish to limit computational costs. This was achieved in two ways. First periodic boundary
conditions were applied. For the considered geometry this reduces the amount of cells by a factor of
14-1
. Second the free jet was only simulated two nozzle diameters downstream of the nozzle exit. The
shortcomings of these simplifications will be discussed later on.
Boundary Conditions 2.1.4In this work a cruise operation point at Ma=0.8 was studied. Non-reflecting pressure inlet
conditions with turbulence profiles from preliminary 2D simulations were employed. Non-reflecting
versions were also used for far field and outlet boundaries. All walls were adiabatic.
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2.2 Acoustic Analysis
Ffowcs-Williams & Hawkings Method 2.2.1Formula (3) represents the differential form of the Ffowcs-Williams & Hawkings equation with a
control surface at rest. As mentioned in the introduction it consists of a part describing the wave
propagation (LHS) and source terms depending on the transient flow field (RHS). The function f(x,y,z)
is less than zero in the source region, zero on the control surface and greater than zero in the exterior
flow. H(f) and δ(f) are Heaviside and Dirac functions. p’ is the sound pressure, a0 is the speed of sound
in the far field, Tij and Pij are Lighthill’s and compressive stress tensor, ni is the unit normal vector
pointing toward the exterior region, ρ is density and ui and un are velocity and control surface normal
velocity.
1
𝑎02
𝜕2𝑝′
𝜕𝑡2− ∇2𝑝′ =
𝜕2
𝜕𝑥𝑖𝜕𝑥𝑗{𝑇𝑖𝑗𝐻(𝑓)} −
𝜕
𝜕𝑥𝑖{[𝑃𝑖𝑗𝑛𝑗 + 𝜌𝑢𝑖𝑢𝑛]𝛿(𝑓)} +
𝜕
𝜕𝑡{[𝜌𝑢𝑛]𝛿(𝑓)} (3)
This inhomogeneous wave equation can be integrated by means of the retarded Green’s function.
Thereby the first term results in a volume integral over the Lighthill stress tensor and represents
quadrupole sources. This part corresponds to the source in Lighthill's original formulation. The second
and third term contain surface integrals and represent dipole and monopole sources on a control
surface. If the control surface surrounds all volume sources, the first term drops due to the Heaviside
function and equation (3) needs only to be integrated over the control surface. The latter is depicted in
Figure 1.
Figure 1: Nozzle with FW-H surface
Far Field Noise Analysis 2.2.2
As for the flow calculation a jet parallel free flow at Ma=0.8 was assumed. The pressure
distribution on the FW-H surface was recorded at every 10th
time-step for 0.03s. According to the
Nyquist theorem this gives a maximum frequency of 25kHz to be found. The Fast Fourier Transform
was then performed using Hamming windowing with a bandwidth of 125Hz. 12 fixed observer
locations were evaluated in the x-z plane as shown in Figure 2. In this study only the FW-H-surface
from Figure 1 instead of a 360° surface was used which leads to a reduction of the SPL.
Figure 2: Observer locations
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3. Results
3.1 Flow Field
Since the RANS model only operates in a thin wall attached region, a very quick transition to
turbulent structures is predicted by the SBES model. In Figure 3 this becomes obvious at the high
temperature surface (red) starting on the lower side of the mixer. Small Kelvin-Helmholtz instabilities
occur close to the mixer’s trailing edge and turn into larger turbulent structures soon. This makes the
exhaust jet fully turbulent at a very early stage and therefore has an important influence on the fine
scale turbulence noise sources.
Figure 3: Temperature on iso-vorticity surface (𝜔 =6000s-1
)
One further observation in Figure 3 is a diminishment of turbulent structures in the middle region.
This follows from the assumption of periodicity which forces resolved turbulence to be zero on the
axis of rotation and is therefore non-physical. On the one hand this area represents only a small
fraction of the total mass flow, on the other hand it contains the highest temperatures and thus
velocities, as it rarely comes in touch with the cold bypass flow. These effects were studied in detail in
(15).
Another problem becomes obvious in Figure 4 looking at an instantaneous pressure field on the
outlet boundary. A short-wave pattern with relatively high amplitudes is visible. These structures
developed after a longer simulation time and reached even higher amplitudes inside the nozzle. Since
no physical explanation could be found, they are assumed to be resonances artificially introduced by
the periodic boundaries. With a wave length of approximately λ≈2cm and a speed of sound of
a0≈300m/s they appear at a frequency of f≈15kHz in the noise spectra.
Figure 4: Pressure pattern on outlet boundary
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3.2 Acoustic
During the evaluation of the far field noise spectra two problems identifiable in Figure 5 became
obvious. The first one corresponds to the pressure patterns observed in the flow field analysis. In the
noise spectrum they create an increased SPL between 8kHz and 25kHz with a maximum at about 15kHz.
Although these frequencies are usually neglected since they are strongly damped by the atmosphere, it
is a difficult task to determine where their sphere ends and if other resonances exist which influence
the low-frequency part of the spectrum.
The second problem concerns the Fast Fourier Transformation where the setup, in particular the
window size, had a distinct influence on the noise spectrum. In Figure 5 two different window sizes are
compared. The shift becomes apparent between 1kHz and 2kHz where a smaller window size (150Hz)
predicts the local minimum and the following local maximum at about 200Hz higher in comparison to
a larger window size. The same effect was observed with the Hann window function.
Figure 5: Comparison of FFT window size
As stated in the previous paragraph the main focus in jet noise analysis is usually on lower
frequencies. In this work the spectra up to 2kHz are discussed. In Figure 6 and Figure 7 each graph
corresponds to one angle of φ with three distances respectively.
In Figure 6 on the left side the spectra for φ=30° show relative low SPLs. A local minimum is
located at 1kHz followed by two weak maxima at 1.1kHz and 1.8kHz. As the FW-H-surface is inclined
itself, the effective angle is very acute in this case, which explains the low noise level.
For φ=60° in the low-frequency region all values move up by about 9dB. Since the shifting reduces
towards higher frequencies, steeper gradients arise. Especially for the 15m-curve the afore mentioned
local maxima become more distinct and enclose a local minimum at 1.5kHz.
Figure 6: Noise spectra at 30° and 60°
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Looking at a 90° observer angle the Sound Pressure Level is again shifted up by about 8dB at low
frequencies. The gradients also become steeper than those of the 60° cases and form a very concise
minimum at 1kHz. The absolute values at this point are even lower than those in Figure 6, whereas the
following local maximum at 1.2kHz is higher and therefore appears much more distinct.
Moving upstream of the nozzle exit to the 120° locations all maxima only slightly increase. The
lowest local maxima become more apparent and the minimum at 1kHz moves up for the 50m and 100m
positions.
Figure 7: Noise spectra at 90° and 120°
4. Conclusion
The purpose of this work was the buildup of a numerical model for the investigation of the far field
noise level caused by the exhaust jet of a mixed turbofan engine. The main focus was on a qualitative
determination of important influencing variables and not on the precise definition of noise levels for a
specific engine at a relevant condition.
A hybrid model was used to determine the transient pressure field of the exhaust jet and to evaluate
the noise level at distant observer points.
The application of the SBES model allowed for high resolved turbulent structures on the one hand
but on the other hand determined a very limited computational domain in size due to high requirements
on the grid resolution. These limitations have several shortcomings. First only two nozzle diameters
downstream the nozzle exit were regarded, whereas Neifeld et al.(16) found approximately 30 nozzle
diameters to be sufficient for far field noise predictions. Secondly the assumption of periodicity has
three negative effects, namely the creation of unphysical pressure patterns, decreasing eddy size
towards the axis of rotation and a FW-H-surface covering only 360°/14=25.7° of the jet. The last
problem can be solved by rebuilding a 360° surface from the periodic part, which in turn could
introduce unwanted interference effects.
The far field analysis showed the expected tendencies concerning spectral distributions and noise
levels. It became apparent that acute angles to the control surface lead to lower SPLs at distant points.
This can also be an advantage as only a certain angle of the afore mentioned 360° surface contributes
to the noise at an observer’s point.
In a next step the domain will be stepwise enlarged circumferentially to better understand the
mechanisms behind the unwanted pressure patterns and to find a sufficient sector for the FW-H
analysis. An examination of further operational conditions such as take-off and side-line is also
planned.
Concerning the FFT additional investigations are necessary to better understand the effect of
window functions, window size and requirements on the time period to be recorded.
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ACKNOWLEDGEMENTS
This work was conducted within the scope of a Munich Aerospace scholarship. Furthermore the
authors like to thank the MTU Aero Engines AG and Dr. Ramm for the technical support.
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