Generalized Abel transform for the analysis of fluid vibration in a tube

Fluid vibrations in axisymmetric geometry according to the first harmonic in the circumferential direction are analyzed. This problem has a practical application in the analysis of transverse vibrations of fluid in an axisymmetric pipe. The numerical model is developed using finite-element technique...

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Bibliographic Details
Published in:Optical Engineering 2007-06, Vol.46 (6), p.065801-065808
Main Authors: Ragulskis, Minvydas, Palevicius, Arvydas, Ragulskis, Liutauras, Bubulis, Algimantas
Format: Article
Language:English
Subjects:
Abel transform
Axisymmetric
Circumferences
Computational fluid dynamics
Fluid flow
Fluids
Mathematical analysis
Mathematical models
time-average holography
Vibration
volumetric strain
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Summary:Fluid vibrations in axisymmetric geometry according to the first harmonic in the circumferential direction are analyzed. This problem has a practical application in the analysis of transverse vibrations of fluid in an axisymmetric pipe. The numerical model is developed using finite-element techniques in axisymmetric geometry. Irrotational motions of ideal compressible fluid are analyzed. The finite-element model of the system is based on the approximation of nodal displacements via the shape functions. Thus the field of the amplitudes of the circumferential variation of the volumetric strain is calculated, exploiting conjugate approximation techniques. Obtained volumetric strains are used for the numerical construction of the interference pattern of the vibrating fluid. For this purpose the Abel transform, which is usually exploited in axisymmetric problems, is generalized for problems with circumferential variation of displacements. The obtained interference patterns are used in hybrid experimental-numerical procedures and help to interpret experimental results.
ISSN:0091-3286
1560-2303
DOI:10.1117/1.2745820