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Published byMaximilian Tyler Oliver Modified over 6 years ago
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Low frequency radiation from a duct exhausting a hot gas
Mico Hirschberg Tango workshop Stockholm May 20-21, 2014
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Mahan et al. (1984)
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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
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Problems Theory Munt simplified but difficult Uniform pipe flow
Infinitely thin shear layers Exponentially growing shear layer oscillation Circular pipe
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Linear perturbations of a uniform stagnant fluid:
Quiescent fluid
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Linearized
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Acoustical energy in quiescent fluid
Represents combustion processes…we assume that it is not associated to an injection of momentum
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Acoustical energy
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Assume local thermodynamical equilibrium:
Constitutive equation Definition speed of sound Linearized
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Frictionless flow
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Acoustical energy and Intensity
Forces (walls) combustion energy Volume source Intensity
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Watch out! For non-uniform fluids and
in presence of flow the definition of acoustical energy is much more complex (Pierce/Myers…).
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Impedance
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Radiation impedance
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Pipe discontinuity
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Pipe discontinuity Energy conservation: Mass conservation:
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Pipe discontinuity
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Pipe discontinuity
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Pipe discontinuity
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Open pipe termination (free field)
Spherical wave Plane waves
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Open pipe termination Spherical wave
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Sound radiation: real part impedance
Spherical wave
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Theory/experiment Mahan et al.
1.0
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Theory/experiments Cummings
1.6 0.8
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Theory/experiments Fricker and Roberts
1.0
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End correction Phase determined by End correction
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Convective losses
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Total enthalpy reflection coefficient
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Energy reflection coefficient
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Which main flow velocity?
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Conclusion What is your opinion? Temperature effects OK.
Which velocity should we use for the convective effect? What is your opinion?
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