validation of caa prediction of noise radi- ated from turbofan intakes

VALIDATION OF CAA PREDICTION OF NOISE RADI- 

ATED FROM TURBOFAN INTAKES 

Jeremy Astley, Iansteel Achunche and Rie Sugimoto 

ISVR, University of Southampton, Southampton, SO17 1BJ, United Kingdom 

Prediction codes based on Computational Aero-Acoustics (CAA) have been developed over the 

last decade to the point where they can model quite accurately the physics of noise propagation 

in turbofan ducts at acceptable computational cost. This is certainly true in the intake where the 

boundary layers on the inner surface of the nacelle are small and where the mean flow is largely 

irrotational. Linearised Euler methods based on the acoustic velocity potential are able to deal 

with such problems at frequencies of practical interest, certainly for cases where the geometry 

and liner configuration can be assumed to be axisymmetric. The correct characterisation of the 

fan sources is however critical in exploiting this technology. In this paper, numerical studies are 

presented in which fan sources are represented as a summation of tones and multiple uncorrelated 

modes. A Finite/Infinite element approach is used to perform noise predictions for a turbofan 

intake. By inferring the relative strength of tone and multimode source components from 

hard-walled test data, the far field SPL and directivity for lined configurations can be predicted. 

Corrections for nonlinear acoustic behaviour close to the fan are included and lead to significant 

improvements in the correlation between measured and predicted data. 

1. Introduction 

The evolution of aero-engines from the turbojets of the 1960s to modern turbofans has led to a 

large reduction in jet mixing noise, highlighting the importance of other noise sources such as the 

fan. The fan is a major noise source both at approach and take-off. It propagates to the forward arc 

through the intake and to the rear arc through the bypass duct. This paper addresses the issue of predicting 

noise levels in the forward arc due to the fan (see Fig.1). 

In order to predict radiated fan noise, it is important to accurately model both source and 

propagation effects. The source spectrum of the fan consists of tone peaks superposed on a broadband 

noise floor. The strongest tones are generated by rotating pressure patterns ‘locked’ to the shaft 

rotation frequency Ω. These have a strong angular periodicity equal to the angular blade spacing, 

and generate a discrete spectrum at frequencies which are integer multiples of the number of blades, 

B, multiplied by the shaft rotation frequency Ω. The first of these corresponds to the blade passing 

frequency (BPF) at a radian frequency of 1 × BΩ, and subsequent tones are generated at higher 

harmonics: 2×BPF, 3×BPF and so on. These BPF tones propagate strongly when the fan tip speed is 

supersonic. Other tones which are not locked to the shaft rotation are also generated by rotor-stator 

interaction at the same frequencies. Broadband noise is also generated by the fan at all frequencies. 

The source mechanisms of broadband noise are more complex since they involve turbulent unsteady 

flow in the boundary layers and wakes of the fan blades and its interaction with the fan casing 

boundary layer and with the Outlet Guide Vanes (OGV). 

ICSV16, Kraków, Poland, 5-9 July 2009 1

16 th International Congress on Sound and Vibration, Kraków, Poland, 5–9 July 2009 

As fan noise propagates through the intake, it is attenuated by acoustic liners in the nacelle 

and scattered by the intake geometry, by liner discontinuities and by the non-uniform mean flow. 

Scattering effects are most pronounced in the tones. Numerical predictions of the far-field Sound 

Pressure Level (SPL) field shapes for a given source distribution are computationally challenging. 

The acoustic wavelengths are generally an order of magnitude smaller than the geometric scales, 

and methods are needed which exhibit low dispersion and low dissipation. Conventional low order 

CFD is unsuitable on both counts. Methods that have been applied to this problem include; Boundary 

Element (BE) methods 1 , Finite and Infinite Element (FE/IE) models 2 and Computational 

Aeroacoustics (CAA) methods based on the solution of the full or Linearised Euler Equations 

(LEE). BE and FE/IE models solve a convected wave equation in the frequency domain. They are 

applicable only when the mean flow is irrotational. More general CAA methods which are applied 

to the LEE do not suffer from this limitation. They are applied most effectively in the time-domain 

but this brings additional challenges such as controlling non-physical shear instablities and modelling 

the impedance of acoustic liners in the time-domain. The assumption of irrotational flow is 

however not a major limitation in the intake given that the mean flow originates in a region of uniform 

flow upstream of the nacelle and that the boundary layers on the inner surfaces of the nacelle 

are relatively small on a wavelength scale. FE/IE methods are therefore an attractive option for 

intake predictions and are widely used for this purpose. In the case of axisymmetric problems (such 

as those presented in this paper) FE/IE predictions of intake noise can be computed for an acceptable 

frequency range and for a complete set of sources in times which are acceptable for industrial 

application (minutes or hours rather than days or weeks of serial rather than parallel computation). 

One major limitation both of Helmholtz FE/IE methods and of more general CAA methods based 

on LEE is that they are unable to deal with non-linear propagation effects which can be significant 

close to the fan when the blade tip speed is supersonic. In the current article these will be dealt separately 

using a different technique. 

In this paper, predictions are made by using ACTRAN/TM 3 , a commercial code developed 

by Free Field Technologies SA. ACTRAN/TM uses a Finite/Infinite Element approach 5,2 . In the 

current application, it is executed within a shell programme ANPRORAD, developed at ISVR 

within a collaborative partnership with IHI Corporation. Tone predictions are presented at BPF for 

realistic hard-walled and lined intakes, and compared to data from a fan test rig. Broadband noise 

predictions have also been made, but these results are not presented here. 

The BPF tone source levels used in the prediction are calibrated by using in-duct mode detection 

measurements. At supersonic fan tip speeds a non-linear propagation code ‘Frequency Domain 

Numerical Solution’ (FDNS) developed by McAlpine and Fisher 4 is used as a correction to the linear 

ANPRORAD/ACTRAN predictions. 

2 

Forward arc noise 

Intake liner 

Non-linear decay of 

rotor-locked tones 

Fan 

Scattering by liners, internal geometry 

and non uniform mean flow 

OGV 

Figure 1. Propagation of fan noise through the intake and radiation into the far-field.


Baffle 

Duct intake 

Spinner 

2. The Prediction Scheme 

ANPRORAD is a shell program that generates and executes a sequence of ACTRAN/TM 

computations for an axisymmetric turbofan intake with subsonic mean flow. ANPRORAD reads 

key geometric data, mean flow data and frequency data and generates a sequence of finite element 

(FE) meshes for the intake and a surrounding near field region, each with an appropriate resolution 

for a given frequency range of interest. Fan source data is defined on the fan plane in terms of prescribed 

set of incident modal intensities for hard-walled annular duct modes and anechoic conditions 

are assumed for noise propagating back into the fan. Prior to the acoustic computation, the 

compressible Euler equations are solved within ANPRORAD to define the mean flow in the intake 

and in the surrounding region. A coarse version of the acoustic mesh is used and the results are interpolated 

onto the acoustic mesh for a sequence of ACTRAN/TM acoustic analyses at prescribed 

frequency intervals. A coarse low-frequency ANPRORAD FE mesh is shown in Fig. 2 for the rig 

geometry shown in Fig. 3. The ACTRAN model contains a conical baffle which is treated as an 

extended nacelle lip. The FE mesh itself is extended to the back of what would be the nacelle in a 

flight configuration, to model the anechoic nature of the chamber into which the test rig protrudes. 

The inner domain shown in Fig. 2 is discretised by quadratic elements giving fourth order accuracy 

in the usual sense. The outer region is modelled by a single layer of high order infinite elements 

which are compatibly matched to the FE mesh at the FE/IE interface. The acoustic pressure within 

each infinite element is modelled by an n th order multipole expansion. The order of the multipole 

expansion used for the results presented here is typically 15. The treatment of acoustic liners 

within ACTRAN/TM is based on a slip condition at the wall and continuity of pressure and particle 

displacement over an infinitely thin vortex sheet above the impedance surface. This is modelled by 

Eversman’s implementation of the Myers 6 boundary condition. In the far-field, acoustic pressure 

amplitude is computed on an arc with its centre point on the duct axis. This defines a field shape 

for the sound pressure level (SPL) which can be compared with measured SPL data. 

3. Experimental Set-up 

FE/IE interface 

Fan plane 

Figure 2. An example of a low-frequency ANPRORAD FE mesh for a fan rig intake incorporating the baffle 

as an extension of the nacelle intake geometry. 

Noise measurements were taken on the 1/3-scale model fan rig, shown in Fig. 3. The rig was 

mounted so that the intake radiated into an Anechoic Test Cell . The configuration tested had a cylindrical 

intake barrel, and a 24-bladed fan. The general set up is shown in Fig. 3. A ring of pressure 

transducers is located at the entrance the lined intake barrel. Two intake configurations are 

considered: a hard-walled intake barrel with a hard-walled fan case, and a lined intake barrel with a 

lined fan case. Far field SPL measurements were taken at an array of far-field microphones located 

at the rig centreline height, between 0 and 120 degrees relative to the intake axis with a 5 degrees 

spacing. 

3


4 

TCS 

Baffle 

Figure 3. Intake of 1/3 scale model fan rig with acoustic baffle and Turbulence Control Screen (TCS). 

4. Mode Detection Data 

Transducers ring Intake barrel 

Transition casing 

Fan case 

Cylindrical section 

The measured data obtained from the pressure transducers mounted in the mode detection ring 

are converted to wall sound pressure levels of the circumferential duct modes using the method dedescribed 

by Rademaker et al. 7 . 

5. Tone Predictions at the Blade Passing Frequency (BPF) 

Spinner 

Predictions at BPF were performed for the fan rig described above. Predictions of the far-field 

sound pressure level (SPL) were made for hard-walled and lined configurations at a number of fan 

speeds. The source is assumed to consist of a multimodal base and a single BPF tone at higher fan 

speeds. The distribution of acoustic power in the multimode source is modelled by assuming equal 

power per mode for all cut-on modes. When the fan tip speed is supersonic, an additional rotorlocked 

component is included which corresponds to the first radial BPF tone for which (in this 

case) m = 24. All of the cut-on modes which are included in the mutimodal content, as well as the 

'm = 24' mode, are assumed to be uncorrelated. At subsonic tip speeds (50% to 70% fan speed), the 

‘m = 24’ mode is cut-off and the source model then consists only of the multimodal, equal power, 

component. Above 80% fan speed however, the ‘m = 24’ mode is cut-on and the fan source contains 

both contributions. In all cases and at all frequencies, far-field directivities are computed for 

each of the modes present at the fan plane, and these are summed in the far field as contributions 

from uncorrelated sources. The sound pressure level is then calculated as; 

p 1 

SPL = 20. log10 

. , (1) 

2 pref 

where p 2 is the root mean square pressure and Pref is a reference pressure, 2.10 -5 Pa. 

Measured data are taken for the case of a hard (i.e. no liners) and a lined intake. The hardwalled 

case is used to calibrate the source model. Fig. 4 shows mode detection data for a hardwalled 

intake taken from the ring of transducers close to the outlet flare (see Fig. 3). The measured 

SPL on the wall is sampled at a frequency which corresponds, at each fan operating speed, to an 

'Engine Order' (EO) of 24, corresponding to BPF for a 24 bladed fan. At each fan speed the measured 

data is decomposed into components corresponding to each circumferential mode number m. 

Fan


The results are shown as a contour plot for SPL versus circumferential order and fan speed. For fan 

speeds less than about 80% , the modal SPL is distributed fairly evenly over an expanding range of 

azimuthal orders corresponding to the modes which are cut on at that condition. However, for fan 

speeds greater than 80% , the ‘m = 24’ mode can be seen to be strongly cut-on (in the upper 1/3 of 

the figure). Fig. 5 shows a typical prediction at 80% fan speed of the overall far-field field shape 

plotted against angle from the forward axis of the engine. Contributions from the 'equal energy' portion 

of the source and from the m=24 tone are plotted separately and combined. Absolute levels of 

both contributions are obtained from the calibration procedure described in the following section. 

Figure 4. Mode detection plot at 1 BPF showing the variation of sound pressure level with circumferential 

mode number and fan speed. 

Far-field SPL / dB 

10 dB 

Rotor-alone (m=24) contribution 

Multimodal contribution 

Total prediction 

0 20 40 60 80 100 120 

Angle from intake axis / degrees 

Figure 5. Typical prediction of the overall far-field SPL field shape at 80% fan speed for a hard-walled intake. 

5.1 Calibrating Predictions to obtain Absolute Levels 

In order to compare the predictions with measured data, the predicted levels for the multimodal 

content and the ‘m = 24’ content are calibrated individually from mode detection measurements. 

The calibration is performed by computing an SPL prediction for each propagating mode at a grid 

point on the FE mesh which coincides with the location of the mode detection ring on the rig. 

5


In the case where only a multimodal contribution is present, at 50% of maximum fan speed for 

example, the far-field SPL predictions are calibrated by using the difference between the predicted 

value of SPL at the grid point and the measured value of SPL at the same point. The measured 

value is obtained by adding the contributions from all the circumferential modes incoherently (see 

Fig. 6(a)). 

When tones are present, above 80% of the maximum fan speed, the far-field SPL prediction 

is calibrated by using the difference between the predicted wall SPL and the in-duct SPL measurement 

for the ‘m = 24’ mode as shown in Fig. 6(b). However, due to the high sound energy level in 

the rotor-locked ‘m = 24’ mode and the limited dynamic range (18 dB) of the mode detection ring, 

the measured multimodal content of the source at these speeds is unreliable and hence could not be 

used to calibrate the predictions. An approximate approach was used to obtain absolute levels by 

adjusting the predicted far-field SPL directivity curves to match the measurements between 0 to 20 

degrees, where the multimodal content dominates over the ‘m = 24’ mode. 

6 

In-duct SPL / dB 

50% fan speed 

10 dB 

-80 -60 -40 -20 0 20 40 60 80 

Circumferential mode number, m 

Measurements 

In-duct SPL / dB 

80% fan speed 

-80 -60 -40 -20 0 20 40 60 80 

Circumferential mode number, m 

(a) (b) 

Figure 6 Mode detection plots at 50% and 80% fan speeds at BPF. 

10 dB 

Measurements 

5.2 Comparing BPF tone Predictions with Measurements 

The BPF tone predictions at 50%, 60%, 70%, 80% and 90% fan speeds are shown in Fig. 7(a) 

to 7(e). Results are shown for the hard-walled and lined cases. The source strength obtained from 

hard-walled data, is used for both predictions. These comparisons generally show good agreement 

between measured and predicted data for fan speeds up to 80%. However at 90% fan speed (Fig. 

7(e)), ANPRORAD over-predicts the overall attenuation due to the liner. This results from an overprediction 

by ANPRORAD of the attenuation of the ‘m = 24’ mode. It is quite possible that a similar 

over-predicted has occurred for the ‘m = 24’ mode at 80% fan speed, but in this case the overall 

directivity is dominated by the multimode component and any over-prediction of the tone attenuation 

is lost below the 'floor' set by the multimode source. At 90% fan speed, however, the ‘m = 24’ 

mode is less attenuated and dominates in the measurements over the multimodal contribution at 

some angles in the measured data (Fig. 7(e)). An over-prediction of the attenuation of the ‘m = 24’ 

mode therefore shows as a discrepancy with the measured data. 

5.3 The Effect of Non-linear Propagation and the presence of a Boundary Layer on 

the Attenuation of EO modes 

A non-linear Frequency Domain Numerical Solution (FDNS) model for EO tones, has been developed 

by McAlpine and Fisher 4 . This can be used to estimate the non-linear propagation of the rotor-alone 

pressure field in hard-walled and lined intake ducts. The basis of the FDNS approach is 

to model the rotor-alone pressure approximately by a one-dimensional irregular sawtooth pressure 

waveform and to include non-linear effects in this simple model. In this paper, decay rates for the 

1 st and 2 nd radial modes of the rotor-locked ‘m=24’ tones have been obtained by using FDNS .


While strictly speaking, FDNS assumes that only the first radial order is present, decay rates for 

the 1 st and 2 nd radial modes have been used in the current instance to obtain the FDNS estimate for 

the liner attenuation of the ‘m=24’ mode. It is assumed that the 1 st and 2 nd radial modes have equal 

acoustic power. Fig. 8 shows the original over-prediction of liner attenuation, and that obtained 

when FDNS is used to adjust for non-linear effects. This significantly improves the general level of 

agreement between the measured and predicted data. The difference in field shapes is not completely 

removed however, which may be due to the fact that the interaction between the first and 

second radial modes is not modelled in either the linear ANPRORAD/ACTRAN solution nor the 

non-linear FDNS solution. 


5.4 Author names and affiliations 


10 dB 

Measured: Hardwall 

Predicted: Hardwall 

Measured: Lined 

Predicted: Lined 

0 20 40 60 80 100 120 


10 dB 

(a) 1 BPF, 50% fan speed 

Measured: Hard-walled 

Predicted: Hard-walled 



0 20 40 60 80 100 120 



10 dB 



10 dB 





0 20 40 60 80 100 120 


10 dB 





0 20 40 60 80 100 120 


(b) 1 BPF, 60% fan speed 





0 20 40 60 80 100 120 


(c) 1 BPF, 70% fan speed (d) 1 BPF, 80% fan speed 

(e) 1 BPF, 90% fan speed 

Figure 7. Comparisons of measured and predicted far-field sound pressure levels for hard-walled and lined 

configurations. 

7


6. Conclusions 

The authors draw the following conclusions from this study. 

• That accurate absolute predictions of far field SPL and field shapes due to BPF tones are possible 

for realistic intake geometries and flows in the absence of liners provided that the source 

modal content is correctly specified. 

• That the prediction of attenuated tone field shapes for lined intakes requires accurate impedance 

data and the inclusion at supersonic fan tip speeds of adjustments to account for non-linear 

propagation close to the fan. 

7. Acknowledgements 

This work is supported by Rolls-Royce plc and undertaken within the Rolls-Royce University 

Technology Centre in Gas Turbine Noise at the University of Southampton (UoS). The second author 

is supported also by the Engineering and Physical Sciences Research Council (EPSRC) within 

the Engineering Doctorate programme at the UoS. The authors are indebted to Dr. Alan McAlpine 

who provided modal decay rates for use in the FDNS calculation. 

REFERENCES 

1 S. Lidoine, H.T.S. Batard and A. Delnevo. “Acoustic radiation modelling of aeroengine Intake, 

comparison between analytical and numerical methods,” AIAA paper 2001-2140, 2001. 

2 W. Eversman, “Mapped infinite wave envelope elements for acoustic radiation in a uniformly 

moving medium”, J. Sound Vib., Vol. 224, 1999, pp. 665 – 87. 

3 ACTRAN 2006 User’s Manual, Free Field Technologies, Louvain-la-Neuve, Belgium, 2006. 

4 A. McAlpine and M.J. Fisher. On the prediction of “buzz-saw” noise in acoustically lined aeroengine 

inlet ducts. J. Sound Vib., 265(1):175-200, 2003. 

5 

R. J. Astley, G. J. Macaulay, J-P Coyette and L. Cremers. "Three-dimensional wave-envelope 

elements of variable order for acoustic radiation and scattering. Part I. Formulation in the frequency 

domain". JASA, Vol 103(1) 1998, pp 49-63. 

6 

Myers, K.K., “On the acoustic boundary condition in the presence of flow,” J. Sound Vib., Vol. 

71, 1980, pp. 429 – 434. 

7 

E.R. Rademaker, P. Sijtsma, B.J. Tester. “Mode detection with an optimised array in model turbofan 

engine intake at varying shaft speeds”, AIAA paper 2001-2181, NLR-TP-2001-132, 2001. 

8 


10 dB 





Predicted: Lined, N.L. effects + 4% B.L. 

0 20 40 60 80 100 120 


Figure 8. Comparisons of measured and predicted far-field sound pressure levels for hard-walled and lined 

configurations showing the effect of a boundary layer and non-linear propagation on the attenuation of EO 

modes at 1BPF at 90% fan speed.


9

validation of caa prediction of noise radi- ated from turbofan intakes

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