Finite-Wavelength Scattering of Incident Vorticity and Acoustic Waves at a Shrouded -Jet Exit
Samanta, Arnab
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https://hdl.handle.net/2142/87755
Description
Title
Finite-Wavelength Scattering of Incident Vorticity and Acoustic Waves at a Shrouded -Jet Exit
Author(s)
Samanta, Arnab
Issue Date
2009
Doctoral Committee Chair(s)
Freund, Jonathan B.
Department of Study
Theoretical and Applied Mechanics
Discipline
Theoretical and Applied Mechanics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Mechanical
Language
eng
Abstract
"We consider a round jet shrouded for a finite downstream distance by a sharply-terminated concentric cylinder. As the vortical disturbances supported by a vortex-sheet model of the jet pass the sharp edge of the shroud exit some of the energy is scattered into acoustic waves. We quantify scattering into radiating acoustic modes by obtaining the far-field directivities. Of greater interest in the present study, however, is the scattering into upstream propagating acoustic modes, which is a potential mechanism for closing the resonance loop in the high-amplitude ""howling"" resonances that have been observed in various shrouded jet configurations over the years. We develop a model for this interaction at the shroud exit. The jet is represented as a uniform flow separated by a cylindrical vortex sheet from a concentric co-flow within the cylindrical shroud. A second vortex sheet separates the co-flow from an ambient flow outside the shroud, downstream of its exit. The Wiener-Hopf technique is used to solve the scattering problem and compute reflectivities at the shroud exit. Finite-wavelength (finite-frequency) analysis is essential for investigating this mechanism: the long-wavelength limit degenerates to a fully reflective fixed-pressure condition at the shroud exit, while the short-wavelength limit produces no reflection since the vortex sheet in this case does not interact with the shroud. The focus here is on wavelengths comparable to the shroud exit diameter for which resonances are observed. For some conditions it appears that the reflection of finite-wavelength hydrodynamic vorticity modes on the vortex sheet defining the jet could be sufficient to reinforce the shroud acoustic modes in a way that facilitate resonance. The analysis also gives the reflectivities for the shroud acoustic modes, which would also be important in establishing resonance conditions. Interestingly, it is also predicted that the shroud exit can be ""transparent"" for ranges of Mach numbers, with no reflection into any upstream propagating acoustic mode. This is phenomenologically consistent with observations in certain experiments that indicate a peculiar sensitivity of resonances of this kind to, say, jet Mach number."
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