1

Computation and Aircraft Noise

Philip J. MorrisBoeing/ A.D. Welliver Professor of Aerospace

EngineeringPenn State University

ICS SeminarApril 6th 2009

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OutlineSome background

Jet engine basicsBasics of aircraft noise

Sources of aircraft noise Jet noise simulations

IssuesStrategiesSolutions

Fan noise predictionsIssuesStrategiesSolutions

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Core Engine

Compressor

Burner orCombustor

Turbine

Credits: NASA Glenn Research Center

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Turbojet Engine

Credits: NASA Glenn Research Center

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Turbojet Engine

P&W F135 engine for F35 (JSF)

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Turbofan Engine

Credits: NASA Glenn Research Center

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Turbofan Engine

GE90-(76 – 115)

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Sir Frank Whittle (1907 – 1996)

Power Jets (1936)First Engine: Whittle Unit (1937)

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Aircraft Noise Reduction Trend

Credits – Dennis Huff (2004), “TECHNOLOGIES FOR TURBOFAN NOISE REDUCTION

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Jet Noise Spectrum (Subsonic)

0.51, / 1.0, 171j r o jM T T U= = = m/s

45oθ = 25oθ =

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Jet Noise Spectrum (Supersonic)

1.5, 1.0, 120 oj dM M θ= = =

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Jet Noise Simulation

Issues:Broadband frequency contentAcoustic fluctuation levels orders of magnitude smaller than turbulent fluctuations and mean propertiesAcoustics are non-dissipative and dispersiveRadiation generally occurs into “infinite” domainsSound is generated by turbulence

Turbulence modeling

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Direct Numerical Simulation

Freund (2001) Mach 1.92 unheated jet

APS Gallery of Fluid Motion

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Direct Numerical Simulation

Freund (2001) Mach 1.92 unheated jet

APS Gallery of Fluid Motion

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Jet Noise Simulation Strategies

Geometry and GridsStructured vs. unstructured grids?

DiscretizationHigh or low order?

Turbulence modelingSelection of turbulence model

Noise predictionPropagation of sound from jet to observer

Linear or nonlinear?

16

Grid Generation

Unstructured gridsConform to complicate geometriesHigh-order accuracy difficult to achieveGenerally poor dispersion characteristicsCoding is more complicated

Structured gridsDifficult to conform to complicated geometriesHigh-order accuracy easy to achieveGenerally good dispersion characteristicsCoding is straightforward

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Structured Grids

Can result in wasted grid resolution

C. Bogey, C. Bailly, and D. Juve, “Noise Investigation of a High Subsonic, Moderate Reynolds Number Jet Using a Compressible Large Eddy Simulation,” Theoret. Comput. Fluid Dynamics (2003) 16: 273–297

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Structured Multiblock Grids

Yongle Du, PhD candidate aerospace engineering

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Mesh Singularities

Use of natural coordinates (polar for circular jets) introduces a centerline mesh singularityOvercome with multiblock structure -

Frame 001Created with Tecplo t 10.0-3-66

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Triggering the Turbulence

It is not possible to resolve the details of the boundary layer turbulence at the nozzle exit“Excitation” strategies

Exclude the nozzle from the calculationInput mean flow profile from RANS calculationAdd artificial excitation at nozzle exit

Random excitation How random? New noise source?

Include the nozzle in the calculationUnsteady RANS in the nozzle

Artificial excitation

No excitation but resolution of flow in nozzle lip region

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Absolute Wake Instability

Nozzle lip

•Wake downstream of the nozzle lip exhibits an “absolute instability.”•This triggers unsteadiness that drives the turbulence in the jet shear layer.

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Spatial Discretization

Unstructured gridsFinite elementDiscontinuous Galerkin

Structured gridsTaylor series-based finite differencesCompact finite difference schemes

High-order of accuracyRequire solution of diagonal matrix equation

More difficult to parallelize

Dispersion-Relation-Preserving finite difference methodsSpecifically designed for computational aeroacoustic problems

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Dispersion Relation Preserving Schemes

=

1 ( )M

jj N

f a f x jhx h −

∂⎛ ⎞ +⎜ ⎟∂⎝ ⎠∑

Introduced by Tam and Webb, J. Comp. Phys., 107 (1993) 262-281.

=

1( ) = ( )M

ij hj

j N

i f a e fh

αα α α−

⎧ ⎫⎨ ⎬⎩ ⎭∑

Fourier transform in space

=

=M

ij hj

j N

i a eh

αα−

− ∑

Thus the effective numerical wavenumber is given by,

Coefficients are chosen to minimize the difference between the numerical and physical wavenumbers over a user-defined wavenumber range – e.g.

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Numerical Wavenumber

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Dispersion Relation Preserving Schemes

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Temporal Discretization

Explicit vs. ImplicitLimitations on time stepParallelization

Explicit schemesRunge-Kutta

Compact and non-compactDispersion Relation Preserving

Multi-step methods

Dual Time-SteppingImplicit “real” time discretization, with explicit sub-iterations

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Boundary Conditions

Characteristics-based schemesDetermine direction of information flowSpecify conditions based on one-sided differences or boundary conditions

Asymptotic boundary conditionsReplace equations of motion with equations that apply far from the “source” region

Buffer zonesAdd fictitious damping region

Perfectly Matched Layer (PML)Buffer zone with smooth transfer of solution across buffer/physical domain interface

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Turbulence Modeling

Reynolds-averaged Navier-Stokes (U/RANS)Unable to provide frequency resolution

Requires additional modeling of turbulent statistics

Direct Numerical Simulation (DNS)No modeling (only discretization)Limited to low Reynolds numbers

Large Eddy SimulationResolves larger scales of turbulenceModels unresolved scales (sub grid scale model)

Detached Eddy Simulation (DES)Hybrid RANS/LESAutomatic transition from URANS to LES depending on grid resolution and distance to nearest surface

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Far Field Noise Prediction

Direct calculationComputationally expensiveNecessary for nonlinear propagation?

Linearized Euler Equations (LEE)Navier-Stokes for turbulent flow field and LEE for propagationComputationally expensive

Wave Extrapolation MethodsKirchhoff Integral Method

Only applicable of the wave equation holds outside the integration surface

Ffowcs Williams-Hawkings Acoustic AnalogyBased on the Navier-Stokes Equations

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0.008 0.009 0.010 0.011 0.012-50

-25

0

25

50

p′, Pa

FW-H

t, sec

j=1 (r = 0.5D)j=62 (r ≈ 1.5D)j=70 (r ≈ 2.5D)j=80 (r ≈ 5.1D)

0.008 0.009 0.010 0.011 0.012

-300

-200

-100

0

100

p′, Pa

Kirchhoff

t, sec

Kirchhoff Formulation Fails When Wake Passes Through Surface

Vorticity field from CFD

r = 5.1Dr = 2.5Dr = 1.5D

D

Brentner and Farassat, “Analytical Comparison of the Acoustic Analogy and Kirchhoff Formulation for Moving Surfaces,” AIAA Journal, 36(8), 1379-1386

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Jet Noise Predictions

Non-Circular JetsCircular Beveled Noise

U. Paliath (Ph.D. 2006)

Fan Noise PropagationY. Zhao and Steve Miller (Ph.D. candidate)

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Outline (Simulations)

Problem FormulationAveraged equations & turbulence model

Numerical ApproachFlow simulationNoise radiation

ResultsRound nozzles

Comparisons with experimentBeveled nozzles

Comparison with experimentEffect of initial excitation

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Present Methodology

Hybrid RANS/LES formulationDetached Eddy Simulation

URANS for attached flowSmagorinsky-like LES for separated flow

Short time averaging and Favre averaging of NS equations – alternatively standard spatial averagesEddy viscosity for unresolved stresses and turbulent Prandtl number for turbulent heat fluxPolar grid and generalized coordinates for grid stretchingSpectral discretization [Constantinescu and Lele(2004)] for azimuthal discretization

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Spalart-Allmaras Turbulence Model

Evolution of eddy viscosityDesigned for attached boundary layer flows –external aerodynamics

( ) ( ){ }1

22

1 1 2

ˆ

ˆ ˆ 1ˆˆ ˆ ˆ ˆ

T v

b w w b

μ ρν f

Dν νc Sν c f ν ν ν c νDt d σ

=

⎛ ⎞ ⎡ ⎤= − + ∇ ⋅ + ∇ + ∇⎜ ⎟ ⎣ ⎦⎝ ⎠

ProductionDestruction

Diffusion

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Detached Eddy Simulation

Parameter d set by minimum of distance to wall and grid size

In absence of transport the S-A model reduces to

Could also use two-equation turbulence model

( ) SCASdA DESˆˆ~ˆ 222 Δ==ν

( )min , DESd d C= Δ

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Boundary Conditions

Spectral method used in the azimuthal direction at centerlineBuffer zone method by J.B. Freund at exit boundariesWall functions used to avoid the use of full turbulent grid in nozzle internal and external boundary layersRigid wall boundary condition for nozzleUniform flow interior to nozzle with slip boundary – no slip implemented to begin boundary layer growthRandom excitation downstream of nozzle exit

Gaussian distribution centered on lip lineBinary decision on excitation

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Results

Calculations have been performed for two nozzle geometries with plane exits: an axisymmetric and a nearly square nozzle. Calculations also performed for a beveled nozzle. The computational domain is divided into at least two blocks, with the nozzle being along part of the boundary of the inner blockA rigid cylindrical boundary is used to represent the jet exhaust nozzle (Very crude model – being upgraded)The nozzle length is taken as 5L, the flow field is calculated up to x = 30L from the nozzle exit and r = 10L

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Circular and Nearly Square NozzlesAxisymmetric:

Inner block: Outer block:

2.4 million grid pointsSquare:

Inner block:Outer block:

3.3 million grid points

Grids

51 27 351r θ zn n n× × = × ×201 27 351r θ zn n n× × = × ×

51 37 351r θ zn n n× × = × ×201 37 351r θ zn n n× × = × ×

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-0.5 0 0.5X

-10 -5 0 5 10

Inner block Outer block

Grid for “Square” Nozzle

πθ 20100

305

<≤≤≤

≤≤−Hr

HzHExecution time: 200-300 hours on 24 2.4 GHz processors

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Centerline Mean Velocity

Nondimensional axial distance, x/D or x/h

Cen

terli

neax

ialv

eloc

ity,U

/Uj

0 10 20 300

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1CircularSquareLau et al. (1979)

5102Re

/308,9.0,02.0

×=

=== smUMmD jjj

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Nondimensional axial distance, x/D or x/h

RM

Sax

ialv

eloc

ityflu

ctua

tions

,<u'

u'>1/

2/U

cl

0 10 20 300

0.1

0.2

0.3

Centerline Axial Turbulence Intensity

CircularSquareArakeri et al. (2002)

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Permeable Surface Ffowcs Williams -Hawkings Method

Farassat formulation 1APermeable surface FW-H implemented in PSU-WOPWOP [Brès et al (2003)]No “quadrupole” termsOpen surface at upstream and downstream locations (corrections for missing surface contributions are being tested)

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FW-H surface at r=6D of length 25DSample time: 150, Resolved frequency range:

Resolution of grid (6 points per wavelength):

Noise Radiation

05.0=Δt

kHzfHz 154100100067.0

≤≤≤≤ St

kHz25:6.1 ≤≤St

5102Re

/308,9.0,02.0

×=

=== smUMmD jjj

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FW-H Surface Visualization

•Instantaneous pressure shown on FW-H surface•Note the fairly axisymmetric nature of the pressure field (noise field dominated by low order azimuthal modes)

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Spectral Density: Circular Jet

Frequency, Hz

Spe

ctra

lden

sity

,dB

re2

x10

-5N

/m2

10000 30000

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58

60

62

64

66

68

70

72

74

76

78

80

θ = 15θ = 30θ = 60θ = 90Experiment: θ = 30

•Note the expanded scale and the good agreement over the entire spectrum•Agreement at the highest frequencies is probably fortuitous

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Beveled Nozzle

Viswanathan: AIAA/CEAS 2004-2974/2975

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Deflection of Thrust Axis

Axial Distance, x/Dj

Rad

ialL

ocat

ion

ofM

axim

umM

ean

Axi

alV

eloc

ity,r

/Dj

0 10 20 300

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Nozzle with 45o bevel

8o∼

•Predicted deflection in close agreement with experiment 10o∼

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FW-H Surface Visualization

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Far Field Noise

145oχ =

Frequency, Hz

1/3-

Oct

ave

SP

L,dB

re2x

10-5

N/m

2

103 10465

70

75

80

85

90

95

φ=0o

φ=180o

Center Frequency, Hz

1/3-

Oct

ave

SP

L,dB

re2x

10-5

N/m

2

103 10465

70

75

80

85

90

95

φ=0o

φ=180o

Prediction Experiment

0.9, unheatedjM =

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Initial Excitation

Required to trigger more realistic development of turbulent shear layer?Various prescriptions have been suggestedWhen nozzle is included there is the possibility of non-physical scattering effects What happens when you turn the excitation off?

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Artificial Excitation

To trigger the unsteadiness in the flow, an artificial excitation is added at a distance of approximately one jet diameter from the nozzle exitRequired to trigger more realistic development of turbulent shear layer?What happens when you turn the excitation off?

X/D

U/U

e

10 20 30

0.3

0.4

0.5

0.6

0.7

0.8

0.9 with excitationwithout excitationLau et al.

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X

Y

3 .7 3 .8 3 .9 4 4 .1 4 .2 4 .30 .3

0 .35

0 .4

0 .45

0 .5

0 .55

0 .6

0 .65

0 .7

0 .75

0 .8

0 .85

0 .9

Self-Excitation at Nozzle Lip

•Absolute instability in finite thickness nozzle lip wake (This is equivalent to shedding in wake of circular cylinder)•Tests with finer resolution in the nozzle lip region confirm this interpretation

Nozzle wall

This indicated that the artificial excitation was not needed to sustain an unsteady flow, but, perhaps, to trigger the unsteadiness.

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X

Y

3.75 4 4.250.3

0.4

0.5

0.6

0.7

Nozzle lip thickness = 5 grid spacing

•Grid is finer and a third block is added •With a finer grid resolution in the nozzle lip region, the flow behaves like a wake region behind a bluff body. •This generates a self-excitation, such that no further artificial excitation is needed.

Self-Excitation at Nozzle Lip

Grid in present computations

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Background

Fan exhaust noise important at take-off Previous approaches

Irrotational flowAd hoc correction for exhaust shear layer

Modified LEEAxisymmetric

Useful for parametric studies

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Present Approach

Frequency domainInitially axisymmetric

Three-dimensional potentialUnstructured grid

General geometries

Based on the Linearized Euler Equations (LEE)Finite Element MethodStreamline Upwind Petrov Galerkin Method (SUPG)FW – H acoustic analogy for far field (or near field)Parallel Implementation

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Advanced Noise Control Fan

From AIAA-2003-3193

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ANCF Grid

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Predictions With Realistic Mean Flow

Experiment

FW-H, 30”

FW-H, 48”

No mean flow

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Conclusions

Computational aeroacoustics presents many unique challengesA combination of computational resources, specialized algorithms and strategic decisions on accuracy requirements, can make computation of practical problems computationally viable.