Surface Integral Methods for Jet Aeroacoustics

Anastasios (Tasos) LyrintzisAeronautics & Astronautics

Purdue UniversityWest Lafayette, IN 47907-2023

lyrintzi@ecn.purdue.eduhttp://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)• Include nozzle lips• Complicated geometries (DES for chevrons,

mixers -- multi-block code)• Supersonic jets