surface integral methods for jet aeroacoustics anastasios (tasos) lyrintzis aeronautics &...
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Surface Integral Methods for Jet Aeroacoustics
Anastasios (Tasos) LyrintzisAeronautics & Astronautics
Purdue UniversityWest Lafayette, IN 47907-2023
[email protected]://roger.ecn.purdue.edu/~lyrintzi
Motivation
• NASA’s goal: reduce aircraft noise by a factor of 4 within the next twenty years
• Improvements in the current state-of-the-art prediction methodologies are needed
Methods of Acoustic Analysis• Straight CAA – expensive• Perturbation methods (e.g. LES+LEE)• Lighthill’s acoustic analogy (volume integrals)• Kirchhoff method (surface integrals)
near-field: CFD - nonlinearfar-field: Wave equation - linear
• Porous FW-H equation (same as Kirchhoff)
Control Surface
is the source emission angle
Kirchhoff’s Method
S2ret
retS odS
rdS
n̂cosθ
a1
r1
t),x(4
n̂
Wave equation is valid outside a stationary surface
: some acoustic variable, e.g. p’
:free stream sound speedr is the distance from source to observer
implies evaluation at the retarded time t-r/c
(1)
is the Kirchhoff surface normal vector
A dot indicates a source time derivative
ret
oa
θ n̂r̂θ cos
Porous FW-H equation
o
ii ρ
ρuU
nijiji uρun̂PL
Define new variables:
and(2)
(3)
where subscript o implies ambient conditions, superscript implies disturbances'
Porous FW-H equation (continued)
t),x(p't),x(p't),x(p't),x(p' QLT
S ret
noT dS
r
Uρt),xp 4
('π
The integral expression for the porous FW-H equation can be written as
where(4)
(5)
(6)dSr
LdS
rL
a1
t),x(p' 4S ret
2r
retS
r
oL
Jet Noise Predictions• S cannot surround the entire source region• MGB can be used outside S• Refraction corrections
Refraction Corrections
• Pilon and Lyrintzis (1997)
Use geometric acoustics (Amiet, 1977)
Us velocity at the downstream end of S
s sound emission angle wrt the jet axis
o emission angle in the ambient air
s
o
o
ocosθ
acosθ
a U s
Contours of a2’/po (1996)
Mach 0.9, Reynolds Number 400,000 Isothermal Jet LES (Oct. 2003)
• No explicit SGS model• Spatial filter is treated as the implicit SGS model• 15.6 million grid points
• Streamwise physical domain length is 35ro
• Domain width and height are set to 30ro
• 50,000 time steps total• 5.5 days of run time using 200 POWER3
processors on an IBM-SP
Divergence of Velocity Contours
Jet Aeroacoustics
• Far field noise is estimated by coupling near field LES data with the Ffowcs Williams – Hawkings (FWH) and Kirchhoff’s methods
• Overall sound pressure levels and acoustic pressure spectra are computed along an arc located at 60ro from the jet nozzle
• Also investigated the sensitivity of far field noise predictions to the position of the control surface on which aeroacoustic data is collected
Jet Aeroacoustics (continued)• Acoustic data collected every 5 time steps over a
period of 25,000 time steps • Shallow angles ( ) are not accurately captured
since streamwise control surface is relatively short• Maximum Strouhal numbers resolved (based on
grid spacing) : 3.0 for Control Surface #1 2.0 for Control Surface #2 1.5 for Control Surface #3
)/14( ox cLo40
Ffowcs Williams – Hawkings Method Prediction of Acoustic Pressure Spectra
Strouhal number, St = f Dj / Uj
SPL
(dB
/St)
0 0.5 1 1.5 2 2.5 390
95
100
105
110
Control Surface #1Control Surface #2Control Surface #3
Cutoff frequency Cutoff frequencyfor Control Surface #2 for Control Surface #1
Cutoff frequencyfor Control Surface #3
Ffowcs Williams - Hawkingsmethod prediction at = 60o
location on the far field arc
Kirchhoff’s Method Prediction of Acoustic Pressure Spectra
Strouhal number, St = f Dj / Uj
SPL
(dB
/St)
0 0.5 1 1.5 2 2.5 390
95
100
105
110
Control Surface #1Control Surface #2Control Surface #3
Cutoff frequency Cutoff frequencyfor Control Surface #2 for Control Surface #1
Cutoff frequencyfor Control Surface #3
Kirchhoff' s methodprediction at = 60o
location on the far field arc
Ffowcs Williams – Hawkings Method Prediction of OASPL
(deg)
OA
SPL
(dB
)
10 20 30 40 50 60 70 80 90100
102
104
106
108
110
112
114
116
118
120
LES + FWH Control Surface #1LES + FWH Control Surface #2LES + FWH Control Surface #3Previous Re = 105 jet LES + FWHexp. of Mollo-Christensen et al. (cold jet)exp. of Lush (cold jet)exp. of Stromberg et al. (cold jet)
Kirchhoff’s Method Prediction of OASPL
(deg)
OA
SPL
(dB
)
10 20 30 40 50 60 70 80 90100
102
104
106
108
110
112
114
116
118
120
LES + Kirchhoff Control Surface #1LES + Kirchhoff Control Surface #2LES + Kirchhoff Control Surface #3Previous Re = 105 jet LES + FWHexp. of Mollo-Christensen et al. (cold jet)exp. of Lush (cold jet)exp. of Stromberg et al. (cold jet)
Acoustic Pressure Spectra Comparison with Bogey and Bailly’s Reynolds number 400,000 LES
St = f Dj / Uj
SPL
(dB
/St)
0 0.5 1 1.5 2 2.5 390
100
110
120
130 Our spectrum at x = 29ro and r = 12ro
Bogey and Bailly' s spectrum at x = 29ro and r = 12ro
Our cutoff frequencyBogey and Bailly' scutoff frequency
Acoustic Pressure Spectra Comparison with Bogey and Bailly’s Reynolds number 400,000 LES
St = f Dj / Uj
SPL
(dB
/St)
0 0.5 1 1.5 2 2.5 390
100
110
120
130 Our spectrum at x = 11ro and r = 15ro
Bogey and Bailly' s spectrum at x = 11ro and r = 15ro
Our cutoff frequency
Bogey and Bailly' scutoff frequency
Closed Control Surface Calculations
• The control surface is closed on the outflow
• FWH method is used only with the closed control surface
• No refraction corrections employed
OASPL Comparison
(deg)
OA
SPL
(dB
)
10 20 30 40 50 60 70 80 90 100 110 120100
102
104
106
108
110
112
114
116
118
120
Open control surfaceClosed control surfaceMollo-Christensen et al. data (cold jet)Lush data (cold jet)Stromberg et al. data (cold jet)
Spectra Comparison at R = 60ro, = 30o
Strouhal number, St = f Dj / Uo
SPL
(dB
/St)
0 0.5 1 1.5 2 2.5 388
90
92
94
96
98
100
102
104
106
108
110
112
114
116
118
120
Open control surfaceClosed control surface
Noise Calculations Using Lighthill’s Acoustic Analogy
• Recently developed a parallel code which integrates Lighthill’s source term over a turbulent volume to compute far-field noise
• The code has the capability to compute the noise from the individual components of the Lighthill stress tensor
Lighthill Code
• Code employs the time derivative formulation of Lighthill’s volume integral
• Uses the time history of the jet flow data provided by the 3-D LES code
• 8th-order accurate explicit scheme to compute the time derivatives
• Cubic spline interpolation to evaluate the source term at retarded times
Far-field Noise
• Time accurate data was saved inside the jet at every 10 time steps over a period of 40,000 time steps
• 1.2 Terabytes (TB) of total data to process
• Used 1160 processors in parallel for the volume integrals
• Cut-off frequency corresponds to Strouhal number 4.0 due to the fine grid spacing inside the jet
)/23( ox cL
OASPL Predictions Using Lighthill Analogy
(deg)
OA
SPL
(dB
)
0 10 20 30 40 50 60 70 80 90 100 110 120100
102
104
106
108
110
112
114
116
118
120
122
Lighthill' s integral until x = 24ro
Lighthill' s integral until x = 28ro
Lighthill' s integral until x = 32ro
LES + FWH open control surface #1exp. of Mollo-Christensen et al. (cold jet)exp. of Lush (cold jet)exp. of Stromberg et al. (cold jet)
Spectra comparison with FWH Predictionsat R = 60ro, = 60o
Strouhal number, St = f Dj / Uo
SPL
(dB
/St)
0 0.5 1 1.5 2 2.5 394
96
98
100
102
104
106
108
110
112
Open control surfaceClosed control surfaceLighthill' s volume integral until x = 32ro
Jet Noise Conclusions• Both Ffowcs Williams – Hawkings and
Kirchhoff’s methods give almost identical results for all open control surfaces
• Closed control surface + FWH give predictions comparable to Lighthill’s acoustic analogy prediction
Jet Noise Conclusions (continued)
• There are acoustic sources (that cause cancellations) located in the region 32ro < x which were not captured in the LES due to short domain size
• Due to the inflow forcing, OASPL levels are overpredicted relative to experiments
General Conclusion
• A simple set of portable subroutines based on porous FWH/Kirchhoff methods can be developed to evaluate the far-field noise from any aerodynamic near-field code
AARC Project
• Review paper presented in CEAS Workshop in Athens Greece (from CFD to CAA);
also, Int. Journal of Aeroacoustics (in press)
• Visited and delivered Kirchhoff/FW-H codes to NASA and all AARC industry affiliates
Future Directions• Noise from unresolved LES scales:
- Resolved Scales: LES + FW-H
- Unresolved Scales: MGB/Tam’s approach
(as currently used for RANS)• Supersonic jets• Include nozzle lips• Complicated geometries (DES for chevrons,
mixers -- multi-block code)