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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