10th AIAA/CEAS Aeroacoustics Conference, Manchester, UK, 10 -12 May, 2004 1 Refraction Corrections for Surface Integral Methods in Jet Aeroacoustics FongLoon

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110th AIAA/CEAS Aeroacoustics Conference, Manchester, UK, 10 -12 May, 2004

Refraction Corrections for Surface Integral Methods in Jet Aeroacoustics

FongLoon PanPurdue University, West Lafayette, IN

Ali UzunFlorida State University, Tallahassee, FL

Anastasios LyrintzisPurdue University, West Lafayette, IN


Outline

Surface Integral Methods– Porous FW-H method

Refraction Corrections– Simple geometric acoustics theory (GA)– Lilley’s equation

Validation (Simple point source)

Application (Jet noise prediction using LES)

Conclusions


Surface Integral Methods

CFD (near-field) Acoustics far-field

source

Far-fieldobserver

(nonlinear)

(linear)

Surface integral methods


Porous FW-H Method (Time Domain)

nijiji

o

ii

Sret

r

Sret

r

oL

Sret

noT

noisequadrupole

QLT

uunPL

uU

dSr

LdS

r

L

atxp

dSr

Utxp

txptxptxptxp

ˆ

1),(4

),(4

),(),(),(),(

2'

'

''''

where


Porous FW-H Method (Frequency Domain)

nUr

S

r

S

rari

oL

S

noariT

LT

L

dSr

LdS

r

Le

a

ixp

dSr

Ueixp

xpxpxp

o

o

ˆ

ˆˆ),(ˆ4

ˆ),(ˆ4

),(ˆ),(ˆ),(ˆ

2/'

/'

'''

and are Fourier transform of Lr and Un


Jet Noise Predictions• S cannot surround the entire source region• MGB can be used outside S• Refraction corrections (predict zone of silence)


Simple Geometric Acoustics(GA) Ray Theory (1977)

• Refraction of sound through thick cylindrical shear layer

• Acoustic wavelength < shear layer thickness

• Ray angle & amplitude correction

From Papamochou


Simple Geometric Acoustics(GA) Ray Theory

coscoso

o

o aU

a

U : the velocity at the downstream end of the control surface : the sound emission angle with respect to the jet axis : the emission angle in the ambient air

o

Asymmetric parallel shear flow


Lilley’s Equation (1974)

:acoustic pressure fluctuation normalized by :acoustic source distribution :mean flow velocity

where

u


Lilley’s Equation

: Green’s function associated to Fourier transformed solution of Lilley’s wave equationxs : source position


High-Frequency Asymptotic Approximations

Assumptions:•Distance between source and jet centerline axis is sufficiently large (i.e. several factors of 1/ko), R (ko is streamwise wavenumber, ko = /ao)

Critical azimuthal wavenumber, n can be scaled to the order of ko

i.e. (Asymmetric, high-frequency)

As source moves closer to the jet centerline axis

i.e. (Quasi-symmetric, high-frequency)


Lilley’s Approximation Solutions

: reduced Green’s function: free-space Green’s function


Asymmetric, Far-field Approximation

where


Quasi-symmetric, Far-field Approximation

where


Comparisons of asymmetric and symmetric approximations


Simple Point Source -ValidationLk = 40rj ; rk = 5rj ; R = 60rj


Refraction Corrections for Simple Point Source


Mach 0.9, Reynolds Number 400,000 Isothermal Jet LES

• 6-th order compact spatial differencing• 6-th order compact spacial filter• No explicit SGS model• 15.6 million grid points

• Streamwise length 35ro ;width and height 30ro

• 50,000 time steps• 5.5 days of run time using 200 POWER3

processors on an IBM-SP


Boundary ConditionsTam & Dong’s radiation boundary conditions

Tam & Dong’s radiation boundary conditions

Tam & Dong’s Radiationbcs

Tam & Dong’s outflow boundary conditions


FW-H Control Surface

30rj

7.8rj


Jet Mean-Flow Profile

MJ = 0.46A = -0.14B = 0.0044


OASPL Results


Jet Aeroacoustics• Acoustic data collected every 5 time steps over a

period of 25,000 time steps • Maximum Strouhal numbers resolved (based on

grid spacing) St=3.0• Open surface: shallow angles ( ) not accurate,

since streamwise control surface is relatively short• Closed surface: spurious effects at ( ) due to a

line of dipoles on the outflow surface, as quadrupoles exit the domain

)/14( ox cL

o40

o80


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


Lighthill Code (continued)

• 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


Animation

• Animation on the next slide shows the time variation of the Lighthill sources that radiate noise in the direction of the observer located at R = 60ro, = 30o on the far-field arc



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



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)


Conclusions• Simple GA method and Lilley’s equation are

added to the surface integral methods to predict zone of silence

• Jet noise LES results were improved

• GA method is simpler, but does not take azimuthal variation into account

• Lilley’s equation is up to 60 times more expensive


The End

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10th AIAA/CEAS Aeroacoustics Conference, Manchester, UK, 10 -12 May, 2004 1 Refraction Corrections for Surface Integral Methods in Jet Aeroacoustics FongLoon