computation and aircraft noise - pennsylvania state · pdf file · 2009-04-27ics...
TRANSCRIPT
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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?
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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
56
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.