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TUE CASA Day 22 November 2006 Wiener-Hopf Solutions of Aircraft Engine Noise Models

TUE CASA Day 22 November 2006 Wiener-Hopf Solutions of Aircraft Engine Noise Models. Ahmet Demir Generalisation and Implementation of Munt’s Model. Munt’s Model.

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TUE CASA Day 22 November 2006 Wiener-Hopf Solutions of Aircraft Engine Noise Models

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  1. TUE CASA Day 22 November 2006Wiener-Hopf Solutions of Aircraft Engine Noise Models Ahmet Demir Generalisation and Implementation of Munt’s Model

  2. Munt’s Model • For over 25 years (1977-2003) there was “asleep” the very advanced but technically complicated solution by Munt for sound radiation from a straight hard-walled hollow duct with piecewise uniform mean flow. • It was proposed for TURNEX to take this as a starting point for similar, but extended and more advanced models.

  3. New Models based on Munt Model Case 1 : Hollow duct Case 1a : Annular duct Case 1b : Lined Centerbody Case 1c : Lined Afterbody lining lining

  4. R0 R1 R0 R1 Coplanar Exhaust and Burried Nozzle • More advanced generalisations:

  5. Analytical Solution • Solution is in the form of a complex Fourier integral (where P is also defined by a complex integral) constructed by subtle complex-functional methods, variations of the Wiener-Hopf method. • Important issues, which can now be studied more exactly : - Vortex shedding from trailing edge - Kutta condition at trailing edge - Instability of the jet (vortex sheet unstable for all frequencies; finite shear layer not)

  6. Formulation of Lined afterbody scattered field: convected wave equations

  7. Dimensionless parameters: • Incident wave (hard-walled mode): where: is axial wave number, is the root of equation

  8. hard wall boundary conditions at hub and r = 1 soft wall continuity of displacement continuity ofpressure at vortex sheet

  9. Kutta condition and instability: trailing edge behaviour, vortex shedding, excitation of instability • singular, stable • smooth, unstable • singular, unstable

  10. Fourier Integral Representation of Velocity Potentials

  11. Simultaneous Wiener-Hopf Equations (results from B.C.r=1) note : B.C. at hub yields relation between B(u) and C(u).

  12. Splitting first Equation: weak factorization in lined duct wave number note : no left running contribution in z>0

  13. Splitting second Equation: essentially with the same way:weak factorization in lined duct wave number note : no right running soft wall modes from z<0.

  14. Solution to second Equation: for far field we need only F+ Coefficients amp and bmpare determined by the following infinite linear system

  15. Complex Contour Integral • Careful management & bookkeeping of poles and other singularities is necessary for correct answer

  16. Total field (double integral: takes more time) Lined Centerbody w = 15, Mode(4,1) w = 25, Mode(4,1)

  17. Far Field • Far field pressure for ωr → ∞. directivity

  18. Numerical Examples • Case 1 with mean flow without mean flow Approach Mode(0,1)

  19. with mean flow without mean flow Approach Mode(17,1) with mean flow without mean flow Cutback Mode(23,1)

  20. Case 1a : Effect of hub (Kutta on) Approach Mode(0,1) Approach Mode(17,1)

  21. Cutback Mode(0,1) Cutback Mode(23,1)

  22. Case 1b,1c : Effect of lining and semi-lining (Kutta on) Approach Mode(0,1) Approach Mode(9,1) Approach and Cutback mean : different flows inside and outside the duct (specific parameters for the project)

  23. Cutback Mode(0,1) Cutback Mode(23,1)

  24. Comparison with numerical models • Case 1: Flesturn (METU) and Actran (FFT) results Approach parameters Modes (0,1),(10,1),(19,1)

  25. Zero flow Mode(0,1) Zero flow Mode(19,1)

  26. Case 1a : METU, NLR and FFT results Approach Mode(17,1)

  27. Cutback Mode(0,1) Cutback Mode(23,1)

  28. Case 1c : METU and FFT results (liner impedance Z = 2 - i)

  29. FFT-Actran vs TUE results

  30. R0 R1 Coplanar Exhaust : TUE and METU results Zero flow Mode(2,1) Zero flow Mode(10,1)

  31. R0 R1 Approach Mode(10,1)

  32. Conclusions • A series of non-trivial extensions of the classical Munt problem have been successfully solved and implemented. • Comparison with fully numerical solutions have been very favourable and encourages their trustful use in industrial applications. • Case 1b+1c (lined centerbody+lined afterbody) has been published: Sound Radiation from an Annular Duct with Jet Flow and a Lined Center Body, A. Demir and S.W. Rienstra, AIAA 2006-2718, 12th AIAA/CEAS Aeroacoustics Conference, 8-10 May 2006, Cambridge, MA, USA • First results show that lining of centerbody reduces sound field only in crosswise direction. • Effect of instability is for these high frequencies acoustically small in all cases considered

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