[american institute of aeronautics and astronautics 11th aiaa/ceas aeroacoustics conference -...

_________________________________* Engineer/Scientist, Aeroacoustics and Fluid Mechanics, Member AIAA

1American Institute of Aeronautics and Astronautics

Acoustic Propagation and Radiation of Fan Noise Sources inTreated Ducts

Y.A. Abdelhamid*The Boeing Company, Seattle, WA, 98124

Duct propagation and far field radiation from fan noise sources with the presence of walltreatment at low to moderate frequencies is investigated using two different codes. The firstone is the Eversman radiation code and the second one is a modified version of theEversman code that includes compressibility effects and with a different terminationnonreflecting boundary condition. The modified Eversman code was developed to investigatethe modal reflection and scattering inside the duct due to geometrical variations, mean flowfield, and acoustic treatment boundary condition. The two codes are based on the velocitypotential formulation and solved numerically using the standard Galerkin FE technique.The modified Eversman code is used in the inlet and fan exit ducts. Source propagationinside the duct as well as radiation outside the duct will be considered. The soft wallboundary effect on mode cut-on cut-off or cut-off cut-on transitions are included and theeffect of the inlet lip on the far field directivity pattern is also investigated.

Nomenclature

c∞ = reference speedCo = mean flow local speed of soundE = mean flow Bernoulli constantm = circumferential modal orderM = Mach numberMf = fan face mach numbern = radial modal order

pp,~ = unsteady pressure and acoustic perturbation component

ρ, ρo = unsteady density and mean flow density componentφφ ,, oΦ = unsteady, mean flow, and acoustic perturbation velocity potential

ν~ = unsteady velocity vectorρ∞ = reference densityR = duct inner nacelle radius at source plane, reference lengthx, r, t = axial, radial, and time coordinatesxt = axial location of mode cut-on cut-off or cut-off cut-on transition

Xr

= position vectorZ = specific acoustic impedanceγ = specific heat ratioω = reduced frequency, Helmholtz number, nondimensional frequency

I. Introduction

Fan noise radiation in the forward and aft arc is a significant portion of the total aircraft engine noise,particularly for high bypass ratio turbofan engines. Fan noise sources are comprised of discrete tones superimposedon a broadband component. The generated fan noise spinning and radial modes create a certain directivity patternwhich is unique for each spinning and radial mode at each frequency. Also, the duct geometry and mean flowconditions have a significant effect on the far field directivity. The complexity of the problem increases at higher

11th AIAA/CEAS Aeroacoustics Conference (26th AIAA Aeroacoustics Conference)23 - 25 May 2005, Monterey, California

AIAA 2005-3021

Copyright © 2005 by The Boeing Company. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.


frequencies where several radial modes are able to propagate along the duct, depending on the spinning ordernumber and hub to tip ratio. Cut-on cut-off and/or cut-off cut-on modal transitions could also occur in the inlet andaft fan duct.

Nayfeh, et al.1 presented an extensive review on acoustic propagation inside aircraft engine duct systems, up to1975. In the last three decades the acoustic propagation inside ducts has been exhaustively studied. A more recentreview was given by Eversman2, published in 1991. Syed, et al.3 derived an analytical solution of sound propagationin a straight annular fan exhaust duct with axially segmented treatment for the uniform flow and the radially shearedflow cases. Nayfeh, et al.4 used the method of multiple scales for sound propagation in a slowly variable area duct.Eversman5 developed a FE model for duct propagation and radiation for axially symmetric duct in non-uniformflows. More recently, Richards, et al.6 used the linearized Euler equations (LEE) to determine the near fieldpropagation using a higher order temporal and spatial scheme. Far field directivity is predicted using an integralsolution of the FW-H equations.

The aim of this paper is to accomplish three main objectives. The first objective is to validate the far fieldradiation code and compare prediction against available experimental data for both hard wall and acousticallytreated configurations. The reason for this validation is to check the implementation of the acoustic treatmentboundary condition which is based on the full Myers7 boundary condition. The second objective is to carry out acomprehensive study to investigate modal scattering inside the duct and its impact on the far field directivity. Thework by Ovenden, Eversman and Rienstra8 will be extended to include the soft wall boundary effect on mode cut-oncut-off or cut-off cut-on transitions. The third objective is to investigate the important parameters that affect the farfield directivity patterns such as inlet lip thickness. Acoustic measured data and numerical results obtained by otherinvestigators will be used whenever possible to validate numerical results.

II. Problem Formulation

A. Governing equations

For an inviscid, non-heat conducting compressible, isentropic flow, the governing equations in non dimensionalform can be written as

Continuity: ( ) 0~~~

=•∇+∂∂ νρρ

t(1)

Momentum: 0~~~~

~ =∇+

∇•+∂∂

pt

νννρ (2)

Equation of State: γργ ~~ =p (3)

The problem is non-dimensionalised using the duct radius at the fan face R, as a reference length, the free streamdensity, ρ∞, and speed of sound, c∞. For a potential flow, the velocity can be written in terms of a velocity potentialas follows:

( ) ( )tXtX ,,~ rrΦ∇=ν (4)

The governing equations are solved by splitting the velocity potential into a first order perturbation acousticvelocity potential superimposed on a steady velocity potential field, so that

),()(),( tXXtXrrr

o φφ +=Φ (5)

and

),()(),(~ tXXtXrrr

o ρρρ += (6)

where the o subscript denotes the mean flow field variables and the unsubscripted ones represent the acousticperturbation variables. By substitution of Eqs. (4) – (6) into Eqs. (1) – (3), yields


Steady Flow:

( ) 0=∇•∇ oo φρ (7)

EC =−

+∇12

1 22

γφo (8)

12 −= γρooC (9)

Acoustic Perturbation:

( ) ( ) ( )0

2=

∇•∇+∇•∇+−∇•∇

oC

ii

φφωφωρφρ (10)

( )φφωρ ∇•∇+−= ip (11)

ρ2oCp = (12)

where the harmonic dependence of the acoustic quantities are defined in terms of ω, the non dimensional frequencyof the acoustic source. Because the acoustic perturbation equations are dependent on the mean flow variables, the setof Eqs. (7) – (9) must be solved first to obtain the mean flow before starting solving the acoustic perturbationproblem. The same mesh used for obtaining the mean flow is used for the acoustic calculations. The Eversman’sradiation code solves Eq. (7) for the velocity potential, assuming a constant density field while the modified codesolves the compressible set of Eqs. (7) – (9) using an iterative scheme.

B. Boundary conditions

1. The radiation code

The computational domain used in the Eversman’s radiation code is shown in Fig. 1a. The computational meshis divided into three regions. The first region is contained inside the inlet and extends up to the highlight circle. Thesecond region extends from outside the inlet to a certain boundary, B, from the inlet, where the flow is nearlyuniform. The third region extends from B to the outer boundary. Regions I and II use a conventional finite elementswhereas region III uses mapped infinite wave envelope elements. For the mean flow calculations, the normalvelocity component vanishes at the center body and at the outer wall. The mean flow is defined completely by thefan face and the free stream Mach numbers, Mf and M∞; respectively. Using a mass flux balance between the inflowand outer flow the complete set of equations can be solved by forcing the velocity potential to a constant value at asingle point inside the domain. For the acoustic perturbation problem, Eqs. (10)-(12), the normal component of theparticle velocity vanishes at the center body and at the outer wall for hard wall surfaces and the full Meyersboundary condition is used for treated boundaries9. The source is assumed to propagate from left to right. For theinlet duct, the sound wave propagate against the mean flow whereas in the fan exit the wave propagates with themean flow. For a specific spinning mode number, the complex modal amplitudes of the right running incident wavesare specified at the source plane. The left running reflected waves are calculated as part of the solution. Theradiation code uses mapped infinite wave envelope elements at far field which allow propagation in only onedirection simulating a non reflection radiation condition. More details about the boundary conditions implemented inthe radiation code is given in Ref. 10.

2. The modified propagation code

The computational domain used in the modified code is shown in Fig. 1b. The boundary conditions at the fanface, inner nacelle, and center body surfaces are the same as the radiation code. The mean flow velocity potentialtakes a constant value at the termination boundary8. For the acoustic perturbation equations, a non reflectingtermination boundary condition is used which allows only right propagating waves and the left running waves areforced to vanish at that boundary.


III. Numerical Solution

Both the steady flow and the acoustic perturbation equations are solved using the standard Galerkin FEformulation. The computational domain is divided into a finite mesh which contains at least 5 quadratic elements pereffective wavelength. The effect of the mean flow on the acoustic wavelength is taken into consideration. The samegrid is used for both mean flow calculations and acoustic solution. Although the far field radiation problem containsthe duct as part of the solution it was decided, for computational efficiency to develop a modified propagation codewith a non reflecting termination boundary to study the modal scattering inside the duct due to geometry, steadyflow and the acoustic treatment boundaries. Both the inner nacelle and center body surfaces could be treated. Thesource boundary allows reflected waves from inside the duct. The right running incident waves are input at thesource plane while the left running reflecting waves are obtained as part of the solution.

IV. Results and Discussion

The Eversman radiation code is first validated against measured far field data for both hard wall and treatedinlets. The JT15D11 nacelle, used in the validation case, is shown in Fig. 2. Both hard wall and treated nacelleconfigurations are shown. The acoustic source is generated by inlet flow distortion rotor interaction. The flowdistortion is created by the wakes of 41 rods in the inlet. The number of fan blades is 28. At a non dimensionalfrequency of 15.4 only one radial mode, (-13,1), first radial, is propagating. Predicted and measured directivitypattern of that mode for the hard wall case is shown in Fig. 3a. Good agreement between prediction andmeasurement is noticed. For the treated case, the specific acoustic impedance is Z = 2.272 + 0.5i, which is the samevalue reported in Ref. 11. The validation between predicted and measured directivity for treated nacelle is still ingood agreement. There is about 1-2 dB discrepancy in the peak sound pressure level. This could be attributed to theuncertainty in the given value of the impedance. The sound pressure level contours for the JT15D inlet for both hardand treated nacelles are shown in Fig. 4, which shows the attenuated levels with the presence of the acoustictreatment.

Table 1. The four cases considered in the inlet modal scattering.

Case No. Acoustic Source Duct Boundary Inlet Mean Flow1 m = 21, n = 4, ω = 41.0 Hard Wall No Flow2 m = 21, n = 4, ω = 41.0 Hard Wall Mf = 0.53 m = 21, n = 4, ω = 41.0 Treated Wall No Flow4 m = 21, n = 4, ω = 41.0 Treated Wall Mf = 0.5

The modified propagation code is used next for inlet and fan exit modal scattering due to duct geometry, meanflow field, and acoustic treatment boundaries. For the inlet modal scattering problem, four cases are considered asgiven in Table 1. The computational domains for the four inlet configurations are shown in Fig. 5. The firstconfiguration is hard wall inlet with no mean flow. The second configuration is hard wall inlet with Mf = 0.5. Thethird configuration is treated inlet wall with no mean flow. The fourth configuration is treated inlet wall withMf=0.5. Streamlines and Mach number contours for the inlet with Mf = 0.5 are given in Fig. 6. Notice that the flowgoes from right to left, i.e. inlet flow. The acoustic source used in this case is the same as the one used in Ref. 8, m =21, n = 4, and ω = 41.0. This case was chosen for comparison with the results obtained from Ref. 8. The soundpressure level contours for the four different cases are shown in Fig. 7. Case 1 shows the (21,4) mode will encountercut-on cut-off at about xt = 1.5 similar to Ref. 8. Case 2 shows that adding an inlet flow with Mf = 0.5 to the hardwall inlet will eliminate the cut-on cut-off inside the duct and the (21,4) mode will continue to propagate inside theduct and radiates to the far field. Case 3 shows some modal scattering and sound pressure level attenuation insidethe duct. Although the (21,4) mode will continue to cut-off at about the same station as the hard wall case, theacoustic treatment will scatter the mode to other radial orders as shown in Fig. 7c. Case 4 shows that by adding aninlet flow with Mf = 0.5 to the treated duct, the (21,4) mode will continue to propagate but with more attenuatedlevels than case 2.

The outer wall sound pressure level for the same mode is shown in Fig. 8 for the four cases. Case 1 shows astrong standing wave pattern inside the inlet duct due to the interaction between incident and reflected acousticmodes. Again the (21,4) mode is cut off for x ≥ 1.5 and the sound pressure level rises just before the mode cuts-offand then decays rapidly in the duct. Introducing an inlet flow, the (21,4) mode will continue to propagate. As


mentioned previously, the acoustic treatment will enhance modal scattering in the duct and will attenuate the soundpressure level during the propagation phase of the mode. Due to modal scattering, other modes will continue topropagate in the duct contributing to the total acoustic pressure. Adding an inlet flow with the treated duct will againreduce the standing wave pattern in the duct as in case 4. The far field sound pressure level directivity for the fourcases are obtained from the radiation codes and shown in Fig. 9. The directivity patterns show that both the meanflow and the acoustic treatment have significant effect on the far field sound pressure levels.

Table 2. The four cases considered in the fan exit modal scattering.

Case No. Acoustic Source Duct Boundary Fan Exit Mean Flow1 m = 20, n = 6, ω = 52.0 Hard Wall No Flow2 m = 20, n = 6, ω = 52.0 Hard Wall Mf = 0.53 m = 20, n = 6, ω = 52.0 Treated Wall No Flow4 m = 20, n = 6, ω = 52.0 Treated Wall Mf = 0.5

In the fan exit propagation problem, the sound waves propagate with the flow. Similar to the inlet, four cases areconsidered as given in Table 2. The computational domains for the four cases are shown in Fig. 10. The mean flowstreamlines and Mach number contours are shown in Fig. 11 for Mf = 0.5. Due to the duct axial variation, the meanflow expands to higher Mach numbers than in the inlet case. The acoustic source selected is m = 20, n = 6, and ω =52.0. The sound pressure level contours for the (20,6) mode for the four cases are given in Fig. 12. The (20,6) mode,which is propagating mode at the source plane, will encounter cut-on cut-off transition at xt = 0.9. Case 2 shows thatby adding fan exit flow the mode will continue to propagate but with reduced levels than in case 1. Case 3 showsthat the acoustic treatment will attenuate the sound pressure levels inside the duct and the axial station of the cut-oncut-off transition is slightly moved upstream of the hard wall case. Adding fan flow, Mf = 0.5, to the treated ductwill increase the sound pressure levels inside the duct but the (20,6) mode will continue to cut-off. The outer wallsound pressure levels of the (20,6) mode, for the four cases, are shown in Fig. 13. As we noticed in the inlet cases,the standing wave pattern generated in the duct due to the interaction between incident and reflected waves arereduced by the presence of the flow. Also, the acoustic treatment attenuates the sound pressure levels inside the duct.It is interesting to note that the sound pressure level for case 2 is nearly flat.

Table 3. The three cases considered in the inlet lip study.

Case No. Acoustic Mode Frequency Cut-off Ratio1 m = 1, n = 1 ω = 5.0 3.352 m = -13, n = 1 ω = 15.4 1.033 m = -13, n = 1 ω = 25.0 1.67

During static engine tests, a bell mouth inlet is used to simulate the flight conditions around the lip region. Theinlet lips used with those inlets are usually different from those of the flight inlet lips. The acquired static enginedata are extrapolated to flight conditions for noise certification purposes. One of the objectives of the current studyis to investigate the effect of inlet lip on noise radiation .

Two different inlets are considered as shown in Fig. 14. Both inlets have the same duct length and radius. Theonly difference between the two inlets is the lip thickness, inlet 1 has a thicker lip than inlet 2. The radiation code isused in this problem. Three different cases are considered as given in Table 3. The first case is m = 1, n = 1, ω = 5.0,the mode is well above cut-on mode. The second case is m = -13, n = 1, ω = 15.4, the mode is barely cut-on mode.The third case is m = -13, n = 1, ω = 25.0, the mode is above cut-on. Those three cases are selected to representacoustic sources at low, mid, and high frequencies with different cut-off ratios. The fan face Mach number, Mf, is0.175. The far field directivity patterns for all cases and for the two inlets, are shown in Fig. 15. The directivitypatterns of the (1,1) mode at ω = 5.0 are given in Fig. 15a. There is a slight difference between the two patterns atdirectivity angles above 50o, the directivity angle is measured from the forward arc center line. The directivitypatterns of the (-13,1) mode at ω = 15.4 are shown in Fig. 15b. Since this mode is barely cut-on, there is a significantdifference between the directivity patterns of the two inlets. Also there is a shift in the peak directivity angle. Thepeak angle of the thin lip is about 55o, while for the thick lip is 50o. The directivity patterns of the (-13,1) mode at ω= 25.0 are given in Fig. 15c. Since the (-13,1) mode at ω = 25.0 is well cut-on, there is a slight difference betweenthe two lips at lower angles but there is appreciable difference at larger angles. The sound pressure level contours


for the two inlets, for the (-13,1) mode at ω = 15.4, are given in Fig. 16. The inlet with thinner lip direct the soundwaves to higher directivity angles and the peak angle shifts to larger angle.

V. Conclusions

The Eversman radiation code has been validated with measured data for both hard wall and treated ducts. Thecomparison between predicted and measured data shows good agreement. A modified version of the Eversman’scode has been used to study the cut-on cut-off and cut-off cut-on modal transition inside the duct. The work ofOvenden, et al. has been extended to include the acoustic treatment and flow for inlets and fan exhausts. The floweffect in the inlet noise propagation is to delay the cut-on cut-off transition. Adding mean flow to the duct reducesthe standing wave pattern generated due to the interaction between incident and reflected waves. The acoustictreatment enhances the modal scattering inside the duct and attenuate the sound pressure levels of propagatingmodes. The optimal acoustic nacelle design is to maximize the cut-on cut-off occurrence in both inlet and fan ducts. The noise directivity from static inlet lip could be different from flight inlet lip for modes which are close to cut-on.The prediction could be used to provide correction factors for static-to-flight extrapolation process.

References

1A.H. Nayfeh, J.E. Kaiser, and D.P. Telionis, “Acoustics of aircraft engine duct systems,” AIAA J., Vol. 13, no. 2, 1975, pp.130-153.

2 W. Eversman, “Aeroacoustics of flight vehicles: Theory and practice,” Vol. 2: Noise control, pp. 101-163, NASA referencepublication 1258, 1991.

3A.A. Syed, R.E. Motsinger, G.H. Fiske, M.C. Joshi, R.E. Kraft, “ Turbofan aft duct suppressor study,” NASA CR 175067,July, 1983.

4A.H. Nayfeh, J.E. Kaiser, R.L. Marshall and C.J. Hurst, “A comparison of experiment and theory for sound propagation invariable area ducts,” Journal of Sound and Vibration, 1980, 71(2), 241-259.

5W. Eversman and I. Danda Roy, “Ducted fan acoustic radiation including the effects of nonuniform mean flow and acoustictreatment,” 15th AIAA Aeroacoustics Conference, AIAA 93-4424.

6S.K. Richards, X. Zhang and X.X. Chen, “Acoustic radiation computation from an engine inlet with aerodynamic flowfield,” 42nd AIAA Aerospace Sciences Meeting and Exhibit, AIAA 2004-0848.

7M.K. Myers, “On the acoustic boundary condition in the presence of flow,” J. of sound and vibration, 71, 429-434, 1980.8N.C. Ovenden, W. Eversman and S. W. Rienstra, “Cut-on cut-off transition in flow ducts: comparing multiple-scales and

finite-element solutions,” Paper 10th AIAA/CEAS Aeroacoustics Conference, AIAA 2004-2945.9W. Eversman, “The Boundary Condition at an Impedance Wall in a Nonuniform Duct With Compressible Potential Mean

Flow,” J. of Sound and Vibrations, 110, 2001, 41-47.10W. Eversman and O. Okunbor, “Aft Fan Duct Acoustic Radiation,” J. of Sound and Vibrations, 213, No. 2, 1998, 235-257.11K.J. Baumrister and S.J. Horowitz, “Finite element-integral simulation of static and flight fan noise radiation from the

JT15D turbofan engine,” NASA TM 82936.12C.L. Morfey, “Acoustic energy in non-uniform flows,” Journal of sound and Vibration, 1971, 14(2), 159-170.13E.C. Rice and M. F. Heidmann, “Modal propagation angles in a cylindrical duct with flow and their relation to sound

radiation,” 17th Aeroacoustics Meeting, 1079, Paper 79-0183.


(a) Domain of the radiation code (b) Domain of the modified code

Figure 1. Computational domains for both the radiation and the modified code.

(a) Hard wall nacelle (b) Treated wall nacelle

Figure 2. JT15D nacelle used in the validation case, both hard wall and acoustically treated duct areshown with the specific acoustic impedance given.


Figure 3. Far field directivity pattern of a single radial mode (-13,1) propagating in the JT15D inlet at ω =15.4, solid line is prediction and symbols are data.

American Institute of Aeronautics and Astronautics8


Figure 4. Sound pressure level contours for the JT15D inlet for hard and treated wall configurations.

Figure 5. Computational domain for four different inlet configurations a) Hard wall inlet, no flow b)Hard wall inlet, Mf = 0.5 c) Treated inlet, no flow d) Treated inlet, Mf = 0.5.

(a) Mean flow streamlines (b) Mach number contours

Figure 6. Mean flow streamlines and Mach number contours for the inlet case with Mf = 0.5.

(d) Treated Nacelle, Mf = 0.5(c) Treated Nacelle, no flow

(a) Hard wall, no flow (b) Hard wall, Mf = 0.5


Figure 8. Outer wall sound pressure level for m = 21, n = 4, ω = 41.0 a) Hard wall inlet, no flow b) Hardwall inlet, Mf = 0.5 c) Treated inlet, no flow d) Treated inlet, Mf = 0.5.

Figure 7. Sound pressure level contours for m = 21, n = 4, ω = 41.0 a) Hard wall inlet, no flow b) Hardwall inlet, Mf = 0.5 c) Treated inlet, no flow d) Treated inlet, Mf = 0.5.


(c) Treated wall, no flow (d) Treated wall, Mf = 0.5




Figure 9. Far field directivity patterns for the four inlet cases m = 21, n = 4, ω = 41.0.

Figure 10. Computational domain for four different fan duct configurations a) Hard wall fan duct, no flowb) Hard wall fan duct, Mf = 0.5 c) Treated fan duct, no flow d) Treated fan duct, Mf = 0.5.

(a) Mean flow streamlines (b) Mach number contours

Figure 11. Mean flow streamlines and Mach number contours for the fan exit case with Mf = 0.5.




Figure 12. Sound pressure level contours for m=20, n=6, ω=52.0 a) Hard wall fan duct, no flow b) Hardwall fan duct, Mf = 0.5 c) Treated fan duct, no flow d) Treated fan duct, Mf = 0.5.

Figure 13. Outer wall sound pressure levels for m=20, n=6, ω=52.0 a) Hard wall fan duct, no flow b)Hard wall fan duct, Mf = 0.5 c) Treated fan duct, no flow d) Treated fan duct, Mf = 0.5.







Figure 14. Inlet nacelle with two different lip thicknesses.

Figure 16. Sound pressure level contours for the two inlets m = -13, n = 1, ω = 15.4.

Figure 15. Far field directivity patterns for a single radial propagating mode for the two inlets, Mf = 0.175.

(a) m =1, n=1, ω = 5.0 (b) m = -13, n = 1, ω = 15.4 (c) m = -13, n = 1, ω = 25.0

(a) Thick Lip (b) Thin Lip

(a) Thick Lip (b) Thin Lip

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