1. Low frequency radiation from a duct exhausting a hot gas
Mico Hirschberg
Tango workshop Stockholm May 20-21, 2014

2. Mahan et al. (1984)

3. Literature Munt (1977-1990) theory
Fricker and Roberts/ Cummings (1977) experiments M=>0
Howe (1979), Bechert (1980) theory St=>0
Cargill (1982), Rienstra (1983) theory St=>0
Mahan et al. (1984) experiments M=>0
Kim and Koss (1990) M=>0
Tiikoja (2014) experiments

4. Problems Theory Munt simplified but difficult Uniform pipe flow
Infinitely thin shear layers
Exponentially growing shear layer oscillation
Circular pipe

5. Linear perturbations of a uniform stagnant fluid:
Quiescent fluid

6. Linearized

7. Acoustical energy in quiescent fluid
Represents combustion
processes…we assume
that it is not associated
to an injection of momentum

8. Acoustical energy

9. Assume local thermodynamical equilibrium:
Constitutive equation
Definition speed of sound
Linearized

10. Frictionless flow

11. Acoustical energy and Intensity
Forces (walls)
combustion
energy
Volume source
Intensity

12. Watch out! For non-uniform fluids and
in presence of flow the definition
of acoustical energy is much
more complex (Pierce/Myers…).

13. Impedance

14. Radiation impedance

15. Pipe discontinuity

16. Pipe discontinuity
Energy conservation:
Mass conservation:

17. Pipe discontinuity

18. Pipe discontinuity

19. Pipe discontinuity

20. Open pipe termination (free field)
Spherical wave
Plane waves

21. Open pipe termination
Spherical wave

22. Sound radiation: real part impedance
Spherical wave

23. Theory/experiment Mahan et al.
1.0

24. Theory/experiments Cummings
1.6
0.8

25. Theory/experiments Fricker and Roberts
1.0

26. End correction
Phase determined by
End correction

27. Convective losses

28. Total enthalpy reflection coefficient

29. Energy reflection coefficient

30. Which main flow velocity?

31. Conclusion What is your opinion? Temperature effects OK.
Which velocity should we use for the convective effect?
What is your opinion?