COMPUTATION OF ENGINE NOISE PROPAGATION AND

SCATTERING OFF AN AIRCRAFT

J. Xu∗, D. Stanescu∗, M.Y. Hussaini∗, and F. Farassat†∗School of Computational Science and Information Technology, Florida State University

Tallahassee, Florida 32306-4120† NASA Langley Research Center, Hampton, Virginia 23681-0001

Abstract

The paper presents a comparison of experimentalnoise data measured in flight on a two-engine busi-ness jet aircraft with Kulite microphones placed onthe suction surface of the wing with computationalresults. Both a time-domain discontinuous Galerkinspectral method and a frequency-domain spectral el-ement method are used to simulate the radiation ofthe dominant spinning mode from the engine andits reflection and scattering by the fuselage and thewing. Both methods are implemented in computercodes that use the distributed memory model tomake use of large parallel architectures. The resultsshow that trends of the noise field are well predictedby both methods.

INTRODUCTION

The fan inlet and exhaust noise represents oneof the major components of the noise signa-ture of an aircraft at take-off and landing. Thenoise radiated to the far field by the engineof an aircraft is largely influenced both by theflow around the wing and fuselage and by thescattering from various other aircraft surfaces.In principle, it is possible to reduce the air-craft noise footprint by taking advantage of en-gine and wing location and manipulating theflow around the aircraft. Experimental inves-tigations of these phenomena are difficult toperform and extremely expensive. Numericalsimulations offer a relatively inexpensive alter-native, and such simulations are becoming in-creasingly attractive due to the recent advances

in both computer architecture and computa-tional methods. To date, most measurementsand modeling of engine noise are confined toisolated engines [1, 2, 3]. However, Stanescu,Hussaini, and Farassat [4] have recently com-puted the engine noise propagation and scat-tering for a generic aircraft configuration by nu-merically solving the Euler equations by a dis-continuous Galerkin spectral element method.The recent popularity of such methods in aero-dynamic applications stems from the fact thatthey require relatively fewer points per wave-length, they have low dispersion and dissipationerrors [5, 6, 7], they have geometric flexibility,and they are compact, robust and inherentlyparallelizable [4, 8]. In a more recent work [9],the same authors presented a simultaneous re-search initiative consisting in the developmentof a spectral element method for the solution,in the frequency domain, of the acoustic poten-tial equation in the presence of a non-uniformflow field. The two methods are believed to becomplementary tools useful for prediction of thetonal sound field in the near field of the engine.

The purpose of the present effort is to in-vestigate the feasibility of large-scale aircraftnoise simulations, and validate them with theavailable experimental data. To that end, weemploy the aforementioned numerical method-ology in the investigation of engine noise prop-agation and scattering off an actual two-enginejet aircraft. After a brief discussion of the twomethods in the next section, we present the nu-

Copyright c©2003 by D. Stanescu. Published by the American Institute of Aeronautics and Astronautics, Inc. with

permission.

1American Institute of Aeronautics and Astronautics

41st Aerospace Sciences Meeting and Exhibit6-9 January 2003, Reno, Nevada

AIAA 2003-542

Copyright © 2003 by D. Stanescu. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

merical results obtained for several flight condi-tions and compare them with the available ex-perimental data. Although the modal composi-tion of the source could not be obtained exper-imentally and the actual flight conditions couldnot be replicated exactly in the computationspresented here, results show that the noise sig-nature obtained from computations matches thetrend of the experimental data.

PROBLEM FORMULATION AND

SOLUTION TECHNIQUE

Computational model

We assume that the engine noise source isknown and consider noise propagation and scat-tering in the left half space implicitly assumingsymmetry of the problem about the y = 0 planewhich is chosen to bisect the aircraft along thefuselage. For the computational purpose, thehalf space is truncated into a computational do-main comprised of a bounded physical domainwith a damping layer surrounding it. The lat-ter is used to ensure the physical domain re-mains uncontaminated by reflections. The sur-face that separates the computational domainfrom the surrounding medium is denoted byΓ∞. This governing equations are solved in non-dimensional form. The reference quantities fornon-dimensionalization are: ρ∞ for the density,c∞ for the velocity components, ρ∞c

2∞ for the

pressure, the radius R of the noise-source diskfor distance, and R

c∞for time. The total domain

of computation (including the damping layers)is defined in the non-dimensional Cartesian co-ordinates as 21.4 ≤ x ≤ 40.0, −12.0 ≤ y ≤ 0.0and −1.8 ≤ z ≤ 11.2. The computational do-main with the embedded aircraft is depicted inFig. 2. As the propagation distance is rela-tively small, viscous effects are neglected andthe problem is assumed to be governed by in-viscid compressible flow equations.

The computational domain is covered by agrid of non-overlapping general hexahedral ele-ments that can have curved boundaries. TheICEMCFD Hexa commercial package is usedto generate the unstructured hexahedral grid

around the aircraft configuration. Once an un-structured grid of hexahedra is generated, anattractive new feature of this package allows forthe generation of points along each of the edgesof the hexahedral mesh, which can be either aLegendre-Lobatto or a Chebyshev-Lobatto dis-tribution for a specified polynomial of degree N .Fig. 3 shows the hexahedral representation ofthe underlying geometry with Gauss-Legendrepoint distribution, where N = 5. All the neces-sary point coordinates can then be computed byinterpolation based on the spectral interpolantsalong the edges (to obtain coordinates at theGauss points from the Lobatto points on theedges) followed by three-dimensional transfiniteinterpolation [10] on the faces and inside the el-ements.

Boundary conditions

A zero normal velocity boundary condition isimposed on the symmetry surface y = 0 (thissupposes that the engines are symmetricallyplaced on either side of the fuselage and rotatein opposite sense) as well as on the fuselage,nacelle and wing surfaces. The boundary condi-tions on the other sides of the computational do-main that make up Γ∞ are treated by a damp-ing layer method [11]. The damping layer isabout 3.5 wide in the x−, y− and z−directions.Waves incident on this layer are damped andreflections into the physical domain of interestare minimized. This is obtained by modifyingthe governing equations through the addition ofa damping term in the form

∂Q

∂t+ ∇ · F = −σ(x)Q (1)

where the damping parameter is made to varyfrom 0 at the interior limit of the damping layerto a maximum value on Γ∞ according to a powerlaw

σ(x) = σM

∑

i

(

xi − xinti

xexti − xint

i

)β

(2)

with xinti and xext

i the coordinates of the interiorand exterior limits of the absorbing layer, limitsthat lie along planes on which one coordinate is

2American Institute of Aeronautics and Astronautics

constant.

The engine tone noise source is specified asa combination of spinning modes on a surfaceΓf conveniently situated inside the nacelle. Fora single spinning mode with azimuthal order sand radial order d, usually denoted as (s, d),the perturbation of the flow variables from themean flow quantities (denoted by bars) is givenby [11, 12]:

p− pρ− ρvx − vx

vr − vr

vθ − vθ

= A

Em(kmdr) cos Θ1

c2· Em(kmdr) cos Θ

kx

ωr ρ· Em(kmdr) cos Θ

kxd

ωr ρ· E′

m(kmdr) sinΘm

rωr·Em(ksdr) cos Θ

,

(3)where Θ = kxx + mθ − ωrt, kmd =√

(ωr/c)2 − kx2, and ωr = ω·R

c∞. The function

Em(kmdr) = Jm(kmdr)+ qYm(kmdr) is the ducteigenfunction with Jm and Ym denoting theBessel functions of the first and second kind,respectively. The noise source is specified onthe circular disk centered at (34.7, 4.6, 5.3).

Time domain formulation

For the time domain formulation, the governingequations are considered the Euler equations inCartesian conservation form,

∂Q

∂t+

3∑

d=1

∂Fd

∂xd

= 0. (4)

where the state vector Q and the flux vector Fd

are given by

Q =

ρρv1ρv2ρv3ρE

, Fd =

ρvd

ρv1vd + pδ1d

ρv2vd + pδ2d

ρv3vd + pδ3d

(ρE + p)vd

, (5)

with ρ the fluid density, E the internal energy,p the pressure, and vd(d = 1, 2, 3) the velocitycomponents.

Each element of the grid is mapped onto themaster element ΩM = [−1, 1]3 with an isopara-metric transformation for the expediency of

representing the solution in each element byspectral basis functions defined on the interval[−1, 1]. Under the mapping, Eq. (4) becomes

∂Q

∂t+

3∑

d=1

∂Fd

∂ξd= 0, (6)

where Q and F are the transformed componentsof the state and flux vectors

Q = JQ, Fd = J3∑

m=1

∂ξd∂xm

Fm, (7)

and J is the Jacobian of the transformation.The computational space coordinates are de-noted by either (ξ1, ξ2, ξ3) or (ξ, η, ζ) hereafterfor convenience.

Let the space of polynomials of degree N inξ ∈ [−1, 1] be denoted by PN . A basis for thisspace can be constructed using the Lagrangeinterpolating polynomials hj , j = 0, 1, . . . , N ,through the N +1 Gauss-Legendre [13] quadra-ture nodes ξi, i = 0, 1, . . . , N . A discontinuousGalerkin approximation is obtained by requir-ing

(Qt, φijk) + (∇ξ · F, φijk) = 0 (8)

where (·, ·) represents the usual L2 inner prod-uct, and φijk = hi(ξ)hj(η)hk(ζ) are the basisfunctions of P 3

N .

Using the divergence theorem and Gaussquadrature, expanding the boundary integraland performing some algebraic manipulation,the final discrete form of the equations govern-ing each variable at the Legendre-Gauss pointsare given by

dQijk

dt= −

[

Dξ +Dη +Dζ]

F, (9)

where the right-hand side is a sum of discretedifferential operators acting on the flux valuesof an element, which include values on the ele-ment faces. Here, the differential operator DξF ,for example, is defined as

DξF =1

wi

[F ∗1 (1, ηj , ζk)hi(1)−

F ∗1 (−1, ηj , ζk)hi(−1) − dξF

]

,(10)

3American Institute of Aeronautics and Astronautics

where F ∗ denotes a common face flux, whichcan be computed directly from the readily avail-able values of the state vector. DηF and DζFfollow by obvious permutations.

As the solution is approximated by a poly-nomial that passes through interpolation nodesdistributed within the elements, a mismatch en-sues when the interpolants are evaluated at el-ement interfaces. This mismatch in the solu-tion at element boundaries is resolved by solv-ing the Riemann problem for the flux there (justas in the finite volume method) [14, 15]. Thisleads to a semidiscrete form of Euler equations,which is simply an ordinary differential equa-tion (ODE) system. The resulting ODE sys-tem is integrated in time using a low-storageRunge-Kutta scheme optimized for wave prop-agation [16]. Acoustic perturbations are ob-tained at each time step by subtracting themean flow from the total flow variables, andthe RMS pressure is obtained by integrating intime the acoustic pressure. This integration isonly performed after sufficient time is allowedfor the acoustic signal from the source to prop-agate through the computational domain andestablish a periodic acoustic field.

Frequency domain formulation

The equation governing the acoustic field is inthis case obtained by considering the flow irrota-tional, so that the continuity equation becomes

∂ρ

∂t+ ∇ · (ρ∇Φ) = 0 (11)

where ρ is the fluid density, and Φ is the to-tal velocity potential, related to the velocity byV = ∇Φ. Under the isentropic assumption, themomentum equation is reduced to an algebraicrelation relating the density to the velocity po-tential as

ρ =

[

1 − (γ − 1)

(

∂Φ

∂t+

(∇Φ)2 −M2∞

2

)]

1

γ − 1

(12)where M∞ is the far field Mach number andγ the specific heats ratio. Consider the un-

steady flow field resulting from the superposi-tion of small acoustic perturbations, denoted bya prime, on a steady mean flow denoted by anoverbar: ρ = ρ + ρ′ and Φ = Φ + Φ′. The par-tial differential equation governing the acousticperturbations is

∂ρ′

∂t+ ∇ · (ρ∇Φ′ + ρ′∇Φ) = 0 (13)

with the following relation relating the acousticdensity to the acoustic velocity potential, ob-tained by linearization of equation (12):

ρ′ = −ρ

c2

[

∂Φ′

∂t+ ∇Φ · ∇Φ′

]

. (14)

For a frequency domain approach, the acousticpotential is considered to be of the form Φ′ =φ(x, y, z) exp(iωt). In view of a weak formula-tion, the governing equation (13) is multipliedby a test function Ψ′ = ψ(x, y, z) exp(−iωt) andintegrated using the divergence theorem to yield

∫

Ω

ψ∂ρ′

∂trdΩ −

∫

Ω

∇ψ · (ρ∇φ+ ρ′∇φ)rdΩ+

∫

Γf

ψ(ρ∇φ+ ρ′∇φ) · nrds = 0

(15)On the aircraft surface both the mean flow andthe acoustic normal velocity component are sup-posed to be zero, so the surface integrand can-cels there. Furthermore, the integrand is set tozero artificially on the Γ∞ surface, which doesnot sensibly affect the computed solution sincethe acoustic field is strongly damped in the ab-sorbing layer.

Let Z denote the complex vector space offunctions that are continuous on Ω, whose re-strictions to an element are polynomials of de-gree at most N in each variable, where N isa specified integer, and ZΓf

⊂ Z the subsetof functions that satisfy the Dirichlet boundarycondition on the source surface Γf . Substitutingthe expression of the density from the linearizedmomentum equation, the following variational

4American Institute of Aeronautics and Astronautics

problem is obtained: find φ ∈ ZD such that

∫

Ω

ρ

c2

[

ω2φψ + iωu (φψx − ψφx) +

iωv (φψy − ψφy) + iωw (φψz − ψφz)+

(

u2 − c2)

φxψx +(

v2 − c2)

φyψy+

(

w2 − c2)

φzψz + uv (φxψy + φyψx)+

uw (φxψz + φzψx) + vw (φyψz + φzψy)−

ψσ (iωφ+ uφx + vφy + wφz)] dΩ = 0(16)

holds for any ψ ∈ ZΓf.

The previous equation is discretized by aChebyshev spectral element method. To thisend, a basis for Z is constructed using tensorproducts of the Lagrange interpolants throughthe Chebyshev-Gauss-Lobatto points in the ele-ment. Upon evaluating the integrals, a complexlinear algebra problem of the form A φ = bis obtained, where φ is the vector of pointvalues of the complex-valued acoustic potentialφ. The solution of this system is obtained us-ing a Schur complement domain decompositionmethod implemented using the Message Pass-ing Interface (MPI) standard. The matrix isstored in sparse mode (i.e. only the non-zeroesare stored), with each processor only storing anumber of lines in the matrix. Let us denote byP the total number of processors, the computa-tional domain Ω is subdivided in as many parti-tions, and the unknowns situated on the surfaceB which separates the partitions are numberedlast in the system. For every processor p, therewill be a number of unknown φ values locatedon B. The vector of unknowns is partitioned as

φ =

φ1I . . . φ

PI φB

(17)

where φpI denotes all the unknowns in subpar-

tition p not located on B. The right-hand sidevector b is partitioned accordingly. The ma-

trix A can then be written in the form

A =

A1II 0 . . . A1

IB

0 A2II . . . A2

IB

. . . .A1

BI A2BI . . . ABB

(18)

and straightforward elimination of the terms be-low the main diagonal leads to

A1II 0 . . . A1

IB

0 A2II . . . A2

IB

. . . .0 0 . . . S

φ1I

φ2I

.φB

=

b1Ib2I.bS

(19)

where bS = bB−∑

p

ApBI(A

pII)

−1bpI . The problem

has thus been reduced to solving a reduced sys-

tem with matrix S = ABB−∑

p

ApBI(A

pII)

−1ApIB

for the points on B only, followed by a solutionon each domain of the interior problem. Thematrix S is much denser than the original ma-trix A and its direct computation and storage isnot efficient or even possible. However, for aniterative method, only the action of S on a vec-tor is needed, and once the sparse, distributed,matrix ABB is formed, this action can be com-puted by matrix-vector multiplications and so-lutions with Ap

II which are local operations onprocessor p and do not require communications,followed by accumulation in the global vectorφB . All computations can be conveniently im-plemented by use of the high level primitives inthe PETSc [17] package for efficient solution ofpartial differential equations.

RESULTS AND DISCUSSION

Experimental data

The data available for comparison was collectedin M∞ = 0.3 flight at 500 foot above groundlevel. The average Mach number at the sourcedisk based on the mass flux through the engineis approximately Mf = 0.53. The Blade Pass-ing Frequency (BPF) tone was measured us-ing several Kulite microphones located on thewing suction side at different angles from the

5American Institute of Aeronautics and Astronautics

nacelle axis as shown in Fig. 1, at a relativelyhigh power setting of the engine. Modal com-position of the signal could not be satisfactorilyestablished, however there were indications thatthe dominating mode is the spinning mode withazimuthal order m = 22, and m = 18 is also ex-pected to have a large contribution. The datais presented as Sound Pressure Level (SPL) val-ues, normalized such that the value at 20 de-grees corresponds to zero SPL.

Time domain results

Propagation of both modes was simulated inthe time domain with a quiescent medium sur-rounding the aircraft in a first attempt to de-termine the dominating mode and conduct afirst test of the method on this geometry. TheBPF tone corresponds to a reduced frequencyωr = 26.3. Propagation and radiation of modes(18, 0) and (22, 0) was computed separately us-ing an unstructured grid with 103, 105 elements.The solution is approximated by a sixth-orderLegendre polynomial in each element, raisingthe number of Gauss-Legendre discretizationpoints to 22, 270, 680 in the computational do-main that includes the damping layers. Thecomputations used one node (32 processors run-ning at 1.1GHz) of an IBM Regatta-type SP4machine and each one lasted about 10 days. Anarbitrary value has been used for the ampli-tude of the incoming mode, which is not knownfrom the experiments. Therefore, for the pur-pose of data comparison, computational datawas matched with experimental data at the 60degree microphone location, where the peak inSPL was noticed experimentally.

Fig. 4 shows a snapshot of the acoustic pres-sure contours on the surface of the aircraft atnon-dimensional time t = 44, immediately be-fore starting integration for the RMS pressurecomputation, for spinning mode (18, 0). Thecomputation indicates that radiation of mode(22, 0) has a pattern that is completely differ-ent from the experimental data, presented inFig. 5. However, mode (18, 0) seems to pro-duce a SPL distribution on the wing with thesame characteristics as the experiments, Fig. 6.

The quantitative difference in levels may stemfrom the mean flow effect. Indeed, increasingthe mean flow Mach number in the duct fromits zero value used for the present results willdetermine the mode to be more cut-on, with animmediate effect that the main radiation lobewill hit the wing at a lower angle location. Thus,SPL levels at angles lower than 60 degrees areexpected to increase, while decreasing at 70 de-grees. The effect of the mean flow, on the otherhand, is expected to be in the opposite sense,but not as strong. It must also be consideredthat other sources of noise, not modeled in thiscomputation (i.e. airframe noise) will increasethe value of the measured SPL data, and thiseffect will become more important at larger dis-tances from the engine (lower angles in the fig-ures).

Frequency domain results

The effect of the mean flow has not yet beenattested with the time domain formulation, asour efforts concentrated lately on the develop-ment of the frequency domain code. The latterincorporates a solver for the mean flow aroundthe given configuration (at this time based on anincompressibility assumption to avoid nonlineariteration). The frequency domain code howeverhas far larger memory requirements. To date,our largest computation with this code was doneon the same mesh with 103, 105 elements butwith quartic elements. There are thus a totalof 6, 746, 736 discretization points in the mesh,which would generate a complex matrix with atotal of 1.4 billion non-zeroes whose only stor-age in sparse mode necessitates approximately20GB memory. This resolution does not allowus to handle the exact experimental conditions,in particular at larger distances from the na-celle where the mesh becomes coarser and thenecessary number of points per wavelength isnot reached. Therefore, we considered a testcase in which the mean flow around the aircraftwas modeled based on a far field Mach num-ber M∞ = 0.1 and a fan face Mach numberMf = 0.2. The problem was run on 192 pro-cessors of the same IBM machine, and conver-

6American Institute of Aeronautics and Astronautics

gence more than three orders of magnitude wasachieved after 2.5 days. This clearly demon-strates the need for a better multi-level precon-ditioner for the reduced matrix S. We mustpoint out, however, that to our knowledge this isthe largest problem of this type reported in theliterature. Moreover, solving the complex linearalgebra problem associated with discretizationof Helmholtz-type equations is a well-known is-sue in the numerical analysis and parallel com-puting community and no satisfactory solutionhas, to our knowledge, been found as of now.Results obtained from this simulation for mode(18, 0) are presented in Fig. 7, which shows thatthe presence of the mean flow has the antici-pated effects as discussed above.

ACKNOWLEDGEMENTS

The authors want to thank D. Weir and T.Wolownik for their help with the experimentaldata. The support of D. Stanescu by NASAgrant NAG-1-01031 is gratefully acknowledged.

References

[1] A.V. Parrett, and W. Eversman, “WaveEnvelope and Finite Element Approxi-mations for Turbofan Noise Radiation inFlight,” AIAA Journal, Vol. 24, No. 5,1986, pp.753-760.

[2] M. Nallasamy, “Computation of Noise Ra-diation from Fan Inlet and Aft Ducts,”Journal of Aircraft, Vol. 34, No. 3, 1997,pp.387-393.

[3] Y. Ozyoruk and L. N. Long, “Computa-tion of Sound Radiating from Engine In-lets,” AIAA Journal, Vol. 34, 1996, No. 5,pp.894-901.

[4] D. Stanescu, M.Y. Hussaini and F. Faras-sat, “Aircraft Engine Noise Scattering -A Discontinuous Spectral Element Ap-proach,” AIAA Paper 2002-0800, Reno,NV.

[5] F.Q. Hu, M.Y. Hussaini and P. Rase-tarinera, “An Analysis of the Discontinu-ous Galerkin Method for Wave Propaga-tion Problems.”Journal of Computational

Physics Vol. 151, 1999, pp.921-946.

[6] D. Stanescu, D.A. Kopriva and M.Y. Hus-saini. “Dispersion Analysis for Discontinu-ous Spectral Element Methods.” Journal of

Scientific Computing Vol. 15, 2000, pp.149-171.

[7] P. Rasetarinera, M.Y. Hussaini and F.Q.Hu, in Discontinuous Galerkin Meth-

ods, Lecture Notes in Computational Sci-ence and Engineering 11 407-412. Berlin:Springer-Verlag, 2000.

[8] S. Rebay, “Efficient Unstructured MeshGeneration by Means of Delaunay Trian-gulation and Bowyer-Watson Algorithm.”Journal of Computational Physics Vol.106, 1993, pp.125-138.

[9] D. Stanescu, M.Y. Hussaini and F. Faras-sat, “Large Scale Frequency Domain Nu-merical Simulation of Aircraft Engine ToneNoise Radiation and Scattering”, AIAAPaper 2002-2586, 8th AIAA/CEAS Aeroa-coustics Conference, Breckenridge, CO.

[10] W.J. Gordon and C.A. Hall, “Construc-tion of curvilinear co-ordinate systems andapplications to mesh generation.” Interna-

tional Journal for Numerical Methods in

Engineering Vol. 7, 1973, pp.461-477.

[11] D. Stanescu, D. Ait-Ali-Yahia, W. G.Habashi, and M. Robichaud, “Multido-main Spectral Computations of Sound Ra-diation from Ducted Fans,” AIAA Journal,Vol. 37, 1999, pp.296-302.

[12] J. M. Tyler and T. G. Sofrin, “Axial FlowCompressor Noise Studies.” SAE Transac-

tions Vol. 70, 1962, pp.308-332.

[13] C. Canuto, M.Y. Hussaini, A. Quarteroni,and T.A. Zang, Spectral Methods in Fluid

Dynamics, Springer-Verlag (1988).

7American Institute of Aeronautics and Astronautics

[14] P.L. Roe, “Approximate Riemann Solvers,Parameter Vectors, and DifferenceSchemes.” Journal of Computational

Physics Vol. 43, 1981, pp.357-372.

[15] C. Hirsch Numerical Computation of Inter-

nal and External Flows. Volume 2: Com-

putational Methods for Inviscid and Vis-

cous Flows, John Wiley & Sons (1990).

[16] D. Stanescu and W.G. Habashi, “2N-storage Low Dissipation and Disper-sion Runge-Kutta Schemes for Computa-tional Acoustics.” Journal of Computa-

tional Physics Vol. 143, 1998, pp.674-681.

[17] Balay, S., Gropp, W.D., McInnes, L.C.and Smith, B.F., “PETSc Users Manual”,ANL-95/11 Revision 2.1.1, Argonne Na-tional Laboratory, 2001.

Fig. 1: Location of microphones on the wing and corresponding experimental data.

8American Institute of Aeronautics and Astronautics

XY

Z

Fig. 2: Computational domain.

Fig. 3: Mesh on the aircraft surface for N = 5 (quintic elements).

9American Institute of Aeronautics and Astronautics

Fig. 4: Acoustic pressure contours on the aircraft surface. Mode (18,0) radiated at ωr = 26.3.

-15

-10

-5

0

5

10

15

20

25

30

20 25 30 35 40 45 50 55 60 65 70

SP

L n

orm

aliz

ed

to

20

de

g.

me

asu

red

va

lue

Angle from inlet axis, degrees

SPL variation on the wing suction side

Measured, M=0.3Computed, (22,0), M=0

Fig. 5: SPL levels on the wing surface for mode (22,0) radiated at ωr = 26.3 in a quiescent medium.

10American Institute of Aeronautics and Astronautics

-15

-10

-5

0

5

10

15

20

20 25 30 35 40 45 50 55 60 65 70

SP

L n

orm

aliz

ed

to

20

de

g.

me

asu

red

va

lue

Angle from inlet axis, degrees

SPL variation on the wing suction side

Measured, M=0.3Computed, (18,0), M=0

Fig. 6: SPL levels on the wing surface for mode (18,0) radiated at ωr = 26.3 in a quiescent medium.

-5

0

5

10

15

20

20 25 30 35 40 45 50 55 60 65 70

SP

L n

orm

aliz

ed

to

20

de

g.

me

asu

red

va

lue

Angle from inlet axis, degrees

SPL variation on the wing suction side

Measured, M=0.3Computed, (18,0), M=0.1

Fig. 7: SPL levels on the wing surface for mode (18,0) radiated at ωr = 26.3 in the presence of mean flow.

11American Institute of Aeronautics and Astronautics