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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

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

Ahmet Demir

Generalisation and Implementation of Munt’s Model

munt s model
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.
new models based on munt model
New Models based on Munt Model

Case 1 : Hollow duct

Case 1a : Annular duct

Case 1b : Lined Centerbody

Case 1c : Lined Afterbody

lining

lining

coplanar exhaust and burried nozzle

R0

R1

R0

R1

Coplanar Exhaust and Burried Nozzle
  • More advanced generalisations:
analytical solution
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)

formulation of lined afterbody
Formulation of Lined afterbody

scattered field:

convected

wave equations

slide7

Dimensionless parameters:

  • Incident wave (hard-walled mode):

where:

is axial wave number, is the root of equation

slide8

hard wall

boundary

conditions

at hub and

r = 1

soft wall

continuity of displacement

continuity ofpressure at vortex sheet

kutta condition and instability trailing edge behaviour vortex shedding excitation of instability
Kutta condition and instability: trailing edge behaviour, vortex shedding, excitation of instability
  • singular, stable
  • smooth, unstable
  • singular, unstable
simultaneous wiener hopf equations results from b c r 1
Simultaneous Wiener-Hopf Equations (results from B.C.r=1)

note : B.C. at hub yields relation between B(u) and C(u).

splitting first equation weak factorization in lined duct wave number
Splitting first Equation: weak factorization in lined duct wave number

note : no left running contribution in z>0

slide13
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.

solution to second equation for far field we need only f
Solution to second Equation: for far field we need only F+

Coefficients amp and bmpare determined by the following infinite linear system

complex contour integral
Complex Contour Integral
  • Careful management & bookkeeping of poles and other singularities is necessary for correct answer
slide16

Total field (double integral: takes more time)

Lined Centerbody

w = 15, Mode(4,1)

w = 25, Mode(4,1)

far field
Far Field
  • Far field pressure for ωr → ∞.

directivity

numerical examples
Numerical Examples
  • Case 1

with mean flow

without mean flow

Approach Mode(0,1)

slide19

with mean flow

without mean flow

Approach Mode(17,1)

with mean flow

without mean flow

Cutback Mode(23,1)

case 1a effect of hub kutta on
Case 1a : Effect of hub (Kutta on)

Approach Mode(0,1)

Approach Mode(17,1)

slide21

Cutback Mode(0,1)

Cutback Mode(23,1)

case 1b 1c effect of lining and semi lining kutta on
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)

slide23

Cutback Mode(0,1)

Cutback Mode(23,1)

comparison with numerical models
Comparison with numerical models
  • Case 1: Flesturn (METU)

and Actran (FFT) results

Approach parameters

Modes (0,1),(10,1),(19,1)

slide25

Zero flow Mode(0,1)

Zero flow Mode(19,1)

slide27

Cutback Mode(0,1)

Cutback Mode(23,1)

coplanar exhaust tue and metu results

R0

R1

Coplanar Exhaust : TUE and METU results

Zero flow Mode(2,1)

Zero flow Mode(10,1)

slide31

R0

R1

Approach Mode(10,1)

conclusions
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