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Refraction Corrections for Surface Integral Methods in Jet Aeroacoustics

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. Outline. Surface Integral Methods Porous FW-H method

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Refraction Corrections for Surface Integral Methods in Jet Aeroacoustics

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  1. 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

  2. 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

  3. Far-field observer Surface integral methods (linear) source (nonlinear) Surface Integral Methods CFD (near-field) Acoustics far-field

  4. Porous FW-H Method (Time Domain) where

  5. are Fourier transform of Lr and Un and Porous FW-H Method (Frequency Domain)

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

  7. 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

  8. 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 Simple Geometric Acoustics(GA) Ray Theory Asymmetric parallel shear flow

  9. where P:acoustic pressure fluctuation normalized by G :acoustic source distribution :mean flow velocity Lilley’s Equation (1974)

  10. Lilley’s Equation : Green’s function associated to Fourier transformed solution of Lilley’s wave equation xs : source position

  11. 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 = w/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)

  12. : reduced Green’s function : free-space Green’s function Lilley’s Approximation Solutions

  13. Asymmetric, Far-field Approximation where

  14. Quasi-symmetric, Far-field Approximation where

  15. Comparisons of asymmetric and symmetric approximations

  16. Simple Point Source -Validation Lk = 40rj ; rk = 5rj ; R = 60rj

  17. Refraction Corrections for Simple Point Source

  18. 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

  19. Boundary Conditions Tam & Dong’s radiation boundary conditions Tam & Dong’s Radiation bcs Tam & Dong’s outflow boundary conditions Tam & Dong’s radiation boundary conditions

  20. FW-H Control Surface 7.8rj 30rj

  21. Jet Mean-Flow Profile MJ = 0.46 A = -0.14 B = 0.0044

  22. OASPL Results

  23. 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

  24. 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

  25. 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

  26. 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, q = 30o on the far-field arc

  27. OASPL Predictions Using Lighthill Analogy

  28. 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

  29. The End

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