10th AIAA/CEAS Aeroacoustics Conference, Manchester, UK, May, Refraction Corrections for Surface Integral Methods in Jet Aeroacoustics FongLoon Pan Purdue University, West Lafayette, IN Ali Uzun Florida State University, Tallahassee, FL Anastasios Lyrintzis Purdue University, West Lafayette, IN

10th AIAA/CEAS Aeroacoustics Conference, Manchester, UK, May, 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

10th AIAA/CEAS Aeroacoustics Conference, Manchester, UK, May, Surface Integral Methods CFD (near-field)Acoustics far-field source Far-field observer (nonlinear) (linear) Surface integral methods

10th AIAA/CEAS Aeroacoustics Conference, Manchester, UK, May, Porous FW-H Method (Time Domain) where

10th AIAA/CEAS Aeroacoustics Conference, Manchester, UK, May, Porous FW-H Method (Frequency Domain) and are Fourier transform of L r and U n

10th AIAA/CEAS Aeroacoustics Conference, Manchester, UK, May, Jet Noise Predictions S cannot surround the entire source region MGB can be used outside S Refraction corrections (predict zone of silence)

10th AIAA/CEAS Aeroacoustics Conference, Manchester, UK, May, 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

10th AIAA/CEAS Aeroacoustics Conference, Manchester, UK, May, Simple Geometric Acoustics (GA) Ray Theory 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 Asymmetric parallel shear flow

10th AIAA/CEAS Aeroacoustics Conference, Manchester, UK, May, Lilley’s Equation (1974)  :acoustic pressure fluctuation normalized by  :acoustic source distribution :mean flow velocity where

10th AIAA/CEAS Aeroacoustics Conference, Manchester, UK, May, Lilley’s Equation : Green’s function associated to Fourier transformed solution of Lilley’s wave equation x s : source position

10th AIAA/CEAS Aeroacoustics Conference, Manchester, UK, May, High-Frequency Asymptotic Approximations Assumptions: Distance between source and jet centerline axis is sufficiently large (i.e. several factors of 1/k o ), R (k o is streamwise wavenumber, k o =  /a o ) Critical azimuthal wavenumber, n can be scaled to the order of k o i.e. (Asymmetric, high-frequency) As source moves closer to the jet centerline axis i.e. (Quasi-symmetric, high-frequency)

10th AIAA/CEAS Aeroacoustics Conference, Manchester, UK, May, Lilley’s Approximation Solutions : reduced Green’s function : free-space Green’s function

10th AIAA/CEAS Aeroacoustics Conference, Manchester, UK, May, Asymmetric, Far-field Approximation where

10th AIAA/CEAS Aeroacoustics Conference, Manchester, UK, May, Quasi-symmetric, Far-field Approximation where

10th AIAA/CEAS Aeroacoustics Conference, Manchester, UK, May, Comparisons of asymmetric and symmetric approximations

10th AIAA/CEAS Aeroacoustics Conference, Manchester, UK, May, Simple Point Source -Validation L k = 40r j ; r k = 5r j ; R = 60r j

10th AIAA/CEAS Aeroacoustics Conference, Manchester, UK, May, Refraction Corrections for Simple Point Source

10th AIAA/CEAS Aeroacoustics Conference, Manchester, UK, May, 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 35r o ;width and height 30r o 50,000 time steps 5.5 days of run time using 200 POWER3 processors on an IBM-SP

10th AIAA/CEAS Aeroacoustics Conference, Manchester, UK, May, Boundary Conditions Tam & Dong’s radiation boundary conditions Tam & Dong’s Radiation bcs Tam & Dong’s outflow boundary conditions

10th AIAA/CEAS Aeroacoustics Conference, Manchester, UK, May, FW-H Control Surface 30r j 7.8r j

10th AIAA/CEAS Aeroacoustics Conference, Manchester, UK, May, Jet Mean-Flow Profile M J = 0.46 A = B =

10th AIAA/CEAS Aeroacoustics Conference, Manchester, UK, May, OASPL Results

10th AIAA/CEAS Aeroacoustics Conference, Manchester, UK, May, 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

10th AIAA/CEAS Aeroacoustics Conference, Manchester, UK, May, 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 8 th -order accurate explicit scheme to compute the time derivatives Cubic spline interpolation to evaluate the source term at retarded times

10th AIAA/CEAS Aeroacoustics Conference, Manchester, UK, May, 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

10th AIAA/CEAS Aeroacoustics Conference, Manchester, UK, May, 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 = 60r o,  = 30 o on the far-field arc

10th AIAA/CEAS Aeroacoustics Conference, Manchester, UK, May,

10th AIAA/CEAS Aeroacoustics Conference, Manchester, UK, May, OASPL Predictions Using Lighthill Analogy

10th AIAA/CEAS Aeroacoustics Conference, Manchester, UK, May, 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

10th AIAA/CEAS Aeroacoustics Conference, Manchester, UK, May, The End