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Research Papers: Fluid-Structure Interaction

Transient Fluid Forces on a Rigid Circular Cylinder Subjected to Small Amplitude Motions

[+] Author and Article Information
Cédric Leblond, Vincent Melot, Christian Lainé

DCNS Propulsion, Service Technique et Scientifique, 44620 La Montagne, France

Jean-François Sigrist1

DCNS Propulsion, Service Technique et Scientifique, 44620 La Montagne, Francejean-francois.sigrist@dcnsgroup.com

Bruno Auvity, Hassan Peerhossaini

 Laboratoire de Thermocinétique, CNRS UMR 6607, Rue Christian Pauc, BP 50609, 44306 Nantes, France

1

Corresponding author.

J. Pressure Vessel Technol 130(3), 031302 (Jun 18, 2008) (8 pages) doi:10.1115/1.2937766 History: Received October 27, 2006; Revised April 06, 2007; Published June 18, 2008

The present paper treats the transient fluid forces experienced by a rigid circular cylinder moving along a radial line in a fluid initially at rest. The body is subjected to a rapid displacement of relatively small amplitude in relation to its radius. Both infinite and cylindrically confined fluid domains are considered. Furthermore, non-negligible amplitude motions of the inner cylinder, and viscous and compressible fluid effects are addressed, successively. Different analytical methods and models are used to tackle each of these issues. For motions of non-negligible amplitude of the inner cylinder, a potential flow is assumed and the model, formulated as a two-dimensional boundary perturbation problem, is solved using a regular expansion up to second order. Subsequently, viscous and compressible effects are handled by assuming infinitesimal amplitude motions. The viscous fluid forces are formulated by solving a singular perturbation problem of the first order. Compressible fluid forces are then determined from the wave equation. A nonlinear formulation is obtained for the non-negligible amplitude motion. The viscous and compressible fluid forces, formulated in terms of convolution products, are linked to fluid history effects induced by wave propagation phenomena in the fluid domain. These models are expressed with dimensionless parameters and illustrated for a specific motion imposed on the inner cylinder. The different analytical models permit coverage of a broad range of motions. Hence, for a given geometry and imposed displacement, the appropriate fluid model can be identified and the resulting fluid forces rapidly estimated. The limits of these formulations are also discussed.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Geometrical configuration

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Figure 2

Evolution of the compressible fluid forces kernel with Ω=1, for different confinement numbers α: (⋯) 1.5, (– – –) 2, and (—) 10

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Figure 3

Evolution of the nondimensional fluid forces normalized with the maximum of the Fritz fluid force model (19) for α=2. Comparison between the Fritz model (⋯) and the non-negligible displacement model for different Keulegan–Carpenter numbers λ: (– – –) 0.19 and (—) 0.28

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Figure 4

Maximum nondimensional fluid forces, obtained with the non-negligible displacement model and normalized with the maximum of the Fritz fluid force model (19), in function of the Keulegan–Carpenter number and for different confinement numbers α: (⋯) 4, (–⋅–) 2, (– – –) 1.5 and (—) 1.1

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Figure 5

Evolution of the nondimensional fluid forces normalized with the maximum of the Fritz fluid force model (19) for α=2. Comparison between the Fritz model (⋯) and the viscous model for different β: (– – –) 500 and (––) 50.

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Figure 6

Maximum nondimensional fluid forces, obtained with the viscous model and normalized with the maximum of the Fritz fluid force model (19), in function of the Stokes number and for different confinement numbers α: (⋯) ∞, (–⋅–) 2, (– – –) 1.5 and (—) 1.1

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Figure 7

Evolution of the nondimensional fluid forces normalized with the maximum of the Fritz fluid force model (19) for α=2. Comparison between the Fritz model (⋯) and the compressible model for different Ω: (– – –) 0.08 and (—) 0.2.

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Figure 8

Maximum nondimensional fluid forces, obtained with the compressible model and normalized with the maximum of the Fritz fluid force model (19), in function of the compressibility number and for different confinement numbers α: (⋯) 4, (–⋅–) 2, (– – –) 1.5 and (—) 1.1

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Figure 9

Maximum fluid forces obtained with the different models and normalized with the maximum of the Fritz fluid force model (19), in function of the dimensional imposed motion pulsation, for different confinement numbers α: (⋯) 4, (– – –) 2, and (—) 1.1

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