[american institute of aeronautics and astronautics 15th aiaa/ceas aeroacoustics conference (30th...

American Institute of Aeronautics and Astronautics

1

Improved Hybrid Prediction of Fan Noise

Keisuke Tanigawa1 and Nobuhiko Yamasaki2 Kyushu University, Fukuoka, 819-0395, Japan

and

Tsutomu Ooishi3 IHI Corporation, Nishitama-gun, Tokyo, 190-1297, Japan

To predict fan noise level, the hybrid scheme, i.e., the combinational approach of a numerical simulation based on the three-dimensional unsteady Reynolds-averaged Navier-Stokes (URANS) equations and an analytical calculation based on the three-dimensional linear singularity theory, is to be improved. It takes into account the acoustic effects on the unsteady loading on the rotor blades as well as the stator vanes. The calculated noise level is compared more favorably with the experimental data, and the superiority of the improved hybrid scheme is confirmed.

Nomenclature CaR = mean axial chord length of the rotor blade CaS = mean axial chord length of the stator vane G = distance between the rotor and the stator centers divided by the average axial chord length FP = mode pressure amplitude h = hub/casing ratio i = imaginary number k = eigenvalue of radial eigenfunction K = sub-matrix including kernel functions Ma = axial Mach number n = circumferential mode number NR = number of rotor blades NS = number of stator vanes p = disturbance pressure PR = unsteady loading on the rotor surface PS = unsteady loading on the stator surface R = radial eigenfunction (span mode function) RT = radius of the casing (r, θ, z) = absolute (cylindrical) coordinate system fixed to the duct t = time W = upwash on the stator vane Wa = mean axial flow velocity ν = the order of blade passing frequency (BPF) µ = arbitrary integer number Ω = angular velocity of the rotor rotation normalized by Wa / RT

1 Graduate student, Department of Aeronautics and Astoronautics, 744 Motooka Nishi-ku, Fukuoka. 2 Professor, Department of Aeronautics and Astoronautics, 744 Motooka Nishi-ku, Fukuoka, Senior Member AIAA 3 Manager, Noise, Emission & System Engineering Group, Advanced Technology Department, Research & Engineering Division, Aero Engine & Space Operation, 229, Tonogaya, Mizuho-machi, Nishitama-gun, Tokyo.

15th AIAA/CEAS Aeroacoustics Conference (30th AIAA Aeroacoustics Conference)11 - 13 May 2009, Miami, Florida

AIAA 2009-3341

Copyright © 2009 by Keisuke Tanigawa and Nobuhiko Yamasaki. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.


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I. Introduction n recent years, jet engines have been developed under the stringent environmental regulations. It is essential, therefore, to establish the method of numerically predicting the noise generated from jet engines with a high

degree of accuracy and low cost at the development phase. Large parts of the noises generated from the jet engines are fan and jet noises. The jet noise has been reduced greatly in the current use of high bypass turbo-fan engines. The fan noise, on the other hand, is mainly caused by the rotor-stator interaction and closely related to the energy exchange between flows and blades, and the notably effective methods for reducing it have not been developed yet. The fan noise, i.e., the rotor-stator interaction noise, has two generating mechanisms. One is the noise caused by the interaction of the downstream blade rows with the wake of the upstream blade rows (wake interaction) and the other is the potential interaction caused by the relative unsteady movement of rotor blade and stator vane rows. The prediction of fan noise has been investigated using various kinds of approaches including CFD (Computational Fluid Dynamics), CAA (Computational Aeroacoustics), analytical methods and so forth1, 2. Among the prospective methods of predicting the fan noise is the hybrid scheme3, 4, which is the combinational approach of the numerical simulation based on the three-dimensional unsteady Reynolds-averaged Navier-Stokes (URANS) equations to obtain the unsteady loading on the downstream stator vanes generated by the rotor-stator interaction, and the analytical acoustic calculation method based on the three-dimensional linear singularity theory5, 6 to estimate the cut-on fan noise from the unsteady loading on the downstream stator vane calculated the URANS calculation. In that hybrid prediction, the acoustic effects of the unsteady loading on the upstream rotor blades generated by the potential interaction are not taken into account due to the assumption of the original singularity method. Figure 1 a) shows the analysis flow of the conventional hybrid scheme. In this study, the hybrid scheme is improved to take into account the acoustic (potential) effects of the unsteady loading on the upstream rotor blades. In this improved hybrid scheme, the URANS calculation is carried out to obtain the unsteady loading on the stator vanes as was in the conventional hybrid scheme, and the three-dimensional linear singularity theory is applied to the unsteady loading on the downstream stator vanes to determine the unsteady loading on the upstream rotor blades on the assumption of the three-dimensional singularity theory. The cut-on noises propagating through the fan annular duct forward and aft are finally determined from the calculated results of unsteady loading on the rotor blades and stator vanes. Figure 1 b) shows the analysis flow of the improved hybrid scheme.

Unsteady Loading on the Stator Surfaceby Rotor-Stator Interaction

Unsteady CFD

3D Singularity Theory

Unsteady Loading on the Rotor Surfaceby Potential Interaction

Acoustic Waves


a) Conventional hybrid scheme b) Improved hybrid scheme

Fig. 1 Two different kinds of analysis flow: a) conventional hybrid scheme and b) improved hybrid scheme

II. Calculation Methods and Conditions As the CFD code, the Turbo version of Unified Platform for Aerospace Computational Simulation (UPACS)

developed by Japan Aerospace Exploration Agency (JAXA) is used in this study. The finite volume method of cell-center type is used for the spatial discretization. The Roe scheme is applied to the convection terms and the 2nd-order central difference scheme is applied to the viscous terms. The Crank-Nicolson scheme with the Newton sub-iterations is used for the implicit time marching in favor of the default choice of the Matrix-Free Gauss Seidel (MFGS) method. The turbulent viscosity is determined by the Spalart-Allmalas model.

I

Unsteady Loading on the Stator Surfaceby Rotor-Stator Interaction

Unsteady CFD

Acoustic Waves



3

The single-stage low speed fan model7 developed by IHI Corporation is adopted to validate the predicted noise level. Figure 2 shows the fan model which is composed of 20 rotor blades and 30 stator vane blades. The design parameters of the fan are summarized in Table 1, and the computational grid is shown in Fig. 3. The computational domain is 1/10 sector of the annulus with 2 rotor blades and 3 stator vanes and divided into 7 computational blocks, i.e., 2 for the rotor passage, 3 for the stator passage and other 2 for the connecting domain between the rotor and stator blocks. The total number of grid points is 1.5 million. Table 1 Fan design parameters

Fig. 2 Fan model

Computational domain divided into 7 blocks

Mid-span plane of computational domain Meridian plane of computational domain

Fig. 3 Computational grid

Number of Rotor Blade (NR) 20 Number of Stator Vane (NS) 30

Hub to Tip Ratio (h) 0.54Axial Inflow Mach Number (Ma) 0.26

R.P.M of 60% Design point 16028


4

A noise test for the fan model is conducted at the anechoic fan noise test facility of the IHI Mizuho plant. The sound pressure level (SPL) of the fan noise is measured by the pressure sensors mounted on the casing surface of the fan duct inlet and the downstream of the stator vanes. The pressure sensors are fixed at about 2.5RT upstream and 3.5RT downstream from the mid-span position of the rotor blade. The noise spectrums measured at two pressure sensors of the upstream and the downstream positions are shown in Fig. 4.

0 4000 8000 12000 16000 20000

SPL

[dB

]

Frequency [Hz]

10 dB

0 4000 8000 12000 16000 20000SP

L [d

B]

Frequency [Hz]

10 dB

a) Upstream position b) Downstream position

Fig. 4 Noise spectrum of the fan model operating Table 1 condition

In order to calculate the acoustic waves analytically, there are some assumptions in modeling in 3D linear singularity theory. The fluid is assumed as an isentropic flow of a perfect gas. The main time-averaged flow is assumed to have a constant density, pressure and axial Mach number. Furthermore, the rotor blade is assumed to be a helical plate (zero thickness and zero camber) and the stator vane is assumed to be a straight plate (zero thickness and zero camber) so that the steady loadings on the rotor blades and stator vanes are ignored. The blades and vanes have a constant chord, and the fan duct is assumed to be an annular duct with an infinite length. The calculation model used for the 3D linear singularity theory is shown in Fig. 5. The distance between the rotor blade and the stator vane centers in this model is normalized by the average axial chord length of the rotor blade and the stator vane. The input fan geometry parameters used for the 3D linear singularity theory are shown in Table 2.

Rotor Blades(Helical Plate)

Stator Vanes(Straight Plate)

Flow

Rotate

Fig. 5 Calculation model of the singularity method


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Table 2 Input parameters of the fan geometry

Axial Chord Length of the Rotor Blade Normalized by RT CaR 0.28 Axial Chord Length of the Stator Vane Normalized by RT CaS 0.30

Distance between the Two Rows Normalized by RT (CaR + CaS) / 2 G 1.6

III. Improved Hybrid Scheme In the acoustic calculation method for the present hybrid scheme, the unsteady loading on the stator vanes PS fed

by the CFD results is used as the input for the three-dimensional singularity theory to determine the unsteady loading on the rotor blades PR which is consistent in the acoustic calculation. The relation between PR and PS is given by

⎥⎦

⎤⎢⎣

⎡−

=⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡WP

PKKKK

S

R

SSRS

SRRR 0 (1)

where KRR, KSR, KRS and KSS denote the sub-matrix including the kernel functions, i.e., the effect of unsteady loading of upstream rotor blades on the upwash of the upstream rotor blades etc. Here W denotes the upwash on the downstream stator vanes, whereas the upwash on the upstream rotor blades is zero. Since the unsteady loading on the downstream stator vanes can be expressed as the sum of the effects of the wake and the potential interactions, PS

w and PS p, respectively,

PS = PS w + PS

p (2)

and the unsteady loading due to the wake interaction on the downstream stator vanes can be expressed as

WPK wSSS −= , (3)

then

⎥⎦

⎤⎢⎣

⎡−=⎥

⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡0

0 SSRp

S

R

SSRS

RR PKPP

KKK

. (4)

Here PS is given by the CFD calculation as stated earlier. Once unsteady loadings on the rotor blades and the stator vanes are determined, acoustic waves in the duct are calculated easily from them. The pressure disturbances of acoustic waves at the upstream and downstream positions in the duct are expressed by

( ) ( ) ( )lnFPrRzzM

MNiezrp

l

nl

nl

a

aR

intNi R ,)(1

exp),,(0

2

2

±

∞

−∞=

∞

=

∞

−∞=

+Ω± ∑ ∑∑

⎭⎬⎫

⎩⎨⎧

Λ−

Ω=ν µ

θν νθ m (5)

where n denotes the circumferential mode order expressed by Eq. (6) and Λ is expressed by Eqs. (7) and (8). Rl(n)

denotes the radial eigenfunction (span mode function) and k denotes its eigenvalue.

n = νNR +µNS (6)

( )

( )( )( )oncut

offcut0:sgn0:

−−

⎩⎨⎧

<Ω>

=ΛBNiBB

R

nl ν

(7)

( )( ) ( )⎭⎬⎫

⎩⎨⎧

−Ω−

−= 2

222

2 111

a

aR

nl

a MM

NkM

B ν (8)


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Here FP denotes the mode pressure amplitude determined from all of unsteady loadings PR and PS. The frequencies of acoustic waves generated by the fan rotor-stator interaction are expressed by NRΩ and its higher harmonics νNRΩ (ν=1, 2,…).

IV. Validation of UPACS Before conducting the fan noise prediction, the UPACS code in use is to be validated. Two models used for the

validation is the single-stage turbine. One is the transonic speed turbine model8 and the other is the low speed turbine model9. Figure 6 shows the pressure on the stator and rotor blades surfaces normalized by the total pressure on the inlet plane and the experimental data8. The present UPACS results are given by three-dimensional Euler calculation, and compared favorably with the experimental data both on the stator and rotor blades. Figure 7 shows the pressure coefficient by the present UPACS results and the experimental data9. The UPACS results are given by RANS calculation, and compared favorably with the experimental data both on the stator and rotor blades. Thus the UPACS codes are validated.

0 0.25 0.5 0.75 1Dis tance Along C hord

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

3D E uler ( UPACS )3D E uler ( S axer )

P / P

t,inl


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

3D E uler ( UPACS )3D E uler ( S axer )

P / P

t,inl

a) Stator surface b) Rotor surface

Fig. 6 Pressure distribution around stator and rotor surfaces of single-stage turbine (Euler calculation)

0 0.25 0.5 0.75 1Distance Alog Chord

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Cp

UPACSExperimental Data


-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Cp

UPACSE xperimental Data

a) Stator surface b) Rotor surface

Fig. 7 Pressure distribution around stator and rotor surfaces of single-stage turbine (RANS calculation)


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V. Results and Discussion Figure 8 shows the instantaneous total pressure contours on the mid-span plane for the model single-stage fan.

The interactions between the rotor wake and the stator vanes are captured clearly. Figure 9 shows the instantaneous entropy contours on the leading edge plane of the stator vanes. The wake profile on the leading edge plane of the stator vanes is captured in detail. Each of the wakes inflowing the stator vane row intersects with 3 stator vanes at the leading edge at one time.

Fig. 8 Instantaneous total pressure contours on the mid-span and the exit boundary planes

Rotor Blade Rotation

Fig. 9 Instantaneous entropy contours on the leading edge plane of the stator vanes


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Figure 10 shows the BPF (Blade Passing Frequency), 2BPF (2nd BPF) and 3BPF (3rd BPF) components of the unsteady loading distribution on the downstream stator vane surfaces, which are calculated by the Fourier Transform of the unsteady pressure difference between the upper and lower surfaces of the stator vanes. The left side of the figures shows the amplitude of unsteady loading, and the middle and right sides of the figures show real and imaginary parts of unsteady loading. It is confirmed that high loading areas are distributed not only near the leading edge but also at many positions on the stator vane surface. The amplitude of unsteady loading of BPF component is highest of all, and the amplitude of unsteady loading of 2BPF component is second highest of all. As far as the BPF component is concerned, two pairs of positive and negative values around the leading are observed, which indicate the stator leading edge intersects with the upstream rotor wake twice along the span on average.

Amplitude Real-Part Imaginary-Part

BPF Component


2BPF Component


3BPF Component

Fig. 10 Unsteady loading distribution on the stator surface calculated by CFD


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Figure 11 shows the BPF, 2BPF and 3BPF components of the unsteady loading distribution on the upstream rotor blade surfaces, which are calculated by 3D linear singularity theory from unsteady loading on the stator vane surfaces fed by CFD. The number of grid points is 7, i.e., the number of truncated series, for both the span-wise and chord-wise directions on the rotor blade and stator vanes surfaces. It is confirmed that high amplitude areas are generated at multiple number of positions on the rotor blade surface. The amplitude of unsteady loading of 2BPF component is highest of all, and the amplitude of unsteady loading of 3BPF component is second highest of all.


BPF Component


2BPF Component


3BPF Component

Fig. 11 Unsteady loading distribution on the rotor surface calculated by 3D linear singularity theory


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Figure 12 shows the sound pressure level (SPL) of each acoustic mode. Acoustic modes are denoted the in terms of the circumferential mode n and radial mode l. The circumferential modes are decomposed by using Eq. (6) as stated earlier. Only cut-on acoustic modes are shown in the figure, which are propagating with no attenuation in the fan duct. The number of cut-on acoustic modes increases as the order of BPF does. In the singularity theory, the radial modes are calculated up to 1st to 7th order. In most acoustic modes, the SPL of the aft propagation waves are higher than that of the forward propagation waves.

BPF Component

2BPF Component

3BPF Component a) Forward Propagation b) Aft Propagation

Fig. 12 Comparison of sound pressure level of each acoustic mode between forward and aft propagations


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Figure 13 shows the comparisons of SPL (Sound Pressure Level) among the conventional hybrid scheme3, 4, the present improved hybrid scheme and the validation experimental data. The present prediction of the BPF component of the forward propagation wave is greatly improved compared with the conventional hybrid scheme, but the 2BPF component of the forward propagation wave is apparently overestimated. The BPF component of aft propagation waves in the improved hybrid scheme is nearly equal to that in the conventional hybrid scheme, but the prediction accuracy of the 2BPF and 3BPF components of the aft propagation waves is somewhat improved. It is confirmed that in both forward and aft propagation waves, the overall accuracy of the prediction is greatly enhanced. By comparing the forward propagation waves to the aft propagation waves, it is clear that the acoustic effect of the unsteady loading on the upstream rotor blades, which is taken into account in this improved hybrid scheme, greatly contributes to estimate the forward propagation. As far as the forward propagation waves are concerned, it is confirmed that the qualitative characteristics of the fan noise can be captured in the present improved hybrid scheme, which indicates that the SPL of the 2BPF component is highest of all.

60

80

100

120

140

160

180

BPF 2BPF 3BPF TOTAL

Conventional Hybrid SchemeImproved Hybrid SchemeExperimental Data

SPL

(dB

)

a) Forward Propagation

60

80

100

120

140

160

180

BPF 2BPF 3BPF TOTAL

Conventional Hybrid Scheme

Improved Hybrid Scheme

Experimental Data

SPL

(dB

)

b) Aft Propagation

Fig. 13 Comparison of sound pressure level with experimental data

VI. Conclusions The hybrid scheme is improved to take into account the acoustic effects of the unsteady loading on the rotor

blades. It is confirmed that the high amplitude areas are generated not only near the leading edge but also at a multiple number of positions on the rotor blade and stator vane surfaces.


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As a result of analyzing the acoustic field in the fan duct, it is confirmed that in both forward and aft propagation waves, the accuracy of the prediction is greatly enhanced in the present improved prediction method. By comparing the forward propagation waves to the aft propagation waves, it is clear that the acoustic effect of the unsteady loading on the upstream rotor blades greatly affects the forward propagation. As far as the forward propagation waves are concerned, it is confirmed that the qualitative characteristics of the fan noise can be captured in the present improved hybrid scheme.

Acknowledgments The experimental part in this study was carried out by IHI Corporation under the financial support from New

Energy and Industrial Technology Development Organization (NEDO) as a part of “Research and Development of Environmentally Compatible Engine for Small Aircraft” in the civil aircraft basic technology program of Ministry of Economy, Trade and Industry, Japan. The numerical computation was mainly carried out using the super-computer facilities at Research Institute for Information Technology, Kyushu University. The authors are indebted to Norimasa Iwasaki, the former graduate student of Aerospace Propulsion Laboratory, Kyushu University, for conducting validation calculations. The authors are also indebted to Professor Masanobu Namba who provided the authors with an original version of the acoustic calculation code, and Dr. Kazuomi Yamamoto, JAXA, who developed the original version of UPACS Turbo and provided the authors with much valuable information on it.

References 1Biedron, R.T., Rumsey, C.L., Podboy, G.G., and Dunn, M.H., “Predicting the Rotor-Stator Inter-action

Acoustics of a Ducted Fan Engine,” 39th AIAA Aerospace Sciences Meeting & Exhibit, AIAA Paper 2001-0664, Jan. 2001.

2Polacsec, C., Burguburu, S., Redonnet, S., and Terracol, M., “Numerical Simulations of Fan Interaction Noise Using a Hybrid Approach,” AIAA Journal, Vol. 44, No. 6, pp. 1188-1196, Jun. 2006.

3Tsuchiya, N., Nakamura, Y., Yamagata, A., and Kodama, H., “Fan Noise Prediction Using Unsteady CFD Analysis,” 8th AIAA/CEAS Aeroacoustics Conference, AIAA Paper 2002-2491, 2002.

4Tsuchiya, N., Nakamura, Y., Yamagata, A., and Kodama, H., “Investigation of Acoustic Modes Generated by Rotor-Stator Interaction,” 9th AIAA/CEAS Aeroacoustics Conference, AIAA Paper 2003-3136, 2003.

5Namba, M., “Lifting Surface Theory for a Rotating Subsonic or Transonic Blade Row,” Aeronautical Research Council Reports and Memoranda, No. 3740, Nov. 1972.

6Namba, M., “Three Dimensional Analysis of Blade Force and Sound Generation for Annular Cascade in Distorted Flows,” Journal of Sound and Vibration, Vol. 50, No. 4, pp. 479-508, Aug. 1976.

7Oba, Y., Ideta, T., and Ooishi, T., “Low Noise Research and Development in Japanese Environmentally Compatible Engine for Small Aircraft Project,” Proceedings of the International Gas Turbine Congress 2007 Tokyo, IGTC2007-TS-024, 2007.

8Saxer, A.P., and Giles, M.B., “Predictions of Three-Dimensional Steady and Unsteady Inviscid Transonic Stator/Rotor Interaction with Inlet Radial Temperature Nonuniformity,” Journal of Turbomachinery, Vol. 116, pp. 347-357, Jul. 1994.

9Dring, R.P., and Joslyn, H.D., Hardin, L.W., and Wagner, J.H., “Turbine Rotor-Stator Interaction,” Journal of Engineering for Power, Vol. 104, pp. 729 – 742, Oct. 1982.

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