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Research Papers

Characterization of Variable Hydrodynamic Coefficients and Maximum Responses in Two-Dimensional Vortex-Induced Vibrations With Dual Resonances

[+] Author and Article Information
Hossein Zanganeh

Department of Naval Architecture,
Ocean and Marine Engineering,
University of Strathclyde,
Glasgow G4 0LZ, Scotland, UK

Narakorn Srinil

Mem. ASME
Department of Naval Architecture,
Ocean and Marine Engineering,
University of Strathclyde,
Glasgow G4 0LZ, Scotland, UK
e-mail: narakorn.srinil@strath.ac.uk

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received January 18, 2014; final manuscript received June 2, 2014; published online July 25, 2014. Assoc. Editor: Walter Lacarbonara.

J. Vib. Acoust 136(5), 051010 (Jul 25, 2014) (15 pages) Paper No: VIB-14-1017; doi: 10.1115/1.4027805 History: Received January 18, 2014; Revised June 02, 2014

A phenomenological model and analytical–numerical approach to systematically characterize variable hydrodynamic coefficients and maximum achievable responses in two-dimensional vortex-induced vibrations with dual two-to-one resonances are presented. The model is based on double Duffing and van der Pol oscillators which simulate a flexibly mounted circular cylinder subjected to uniform flow and oscillating in simultaneous cross-flow/in-line directions. Depending on system quadratic and cubic nonlinearities, amplitudes, oscillation frequencies and phase relationships, analytical closed-form expressions are derived to parametrically evaluate key hydrodynamic coefficients governing the fluid excitation, inertia and added mass force components, as well as maximum dual-resonant responses. The amplification of the mean drag is ascertained. Qualitative validations of numerical predictions with experimental comparisons are discussed. Parametric investigations are performed to highlight the important effects of system nonlinearities, mass, damping, and natural frequency ratios.

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Figures

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Fig. 1

(a) A schematic model of a spring-mounted circular cylinder undergoing two-dimensional VIV and (b) associated hydrodynamic force components

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Fig. 2

Comparison of numerical and experimental x–y phase differences θxy with f* = 1 and 2 and associated figures of eight: CCW (CW) denotes counter-clockwise (clockwise) orbit

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Fig. 3

Contour plots of (a) Ay/D and (b) Ax/D as functions of m* and Vr compared with experimental lock-in ranges (circles); plots of ω and Ω as function of m* is also depicted in (a)

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Fig. 4

Plots of system phase differences (circulars) governing hydrodynamic coefficients as functions of Ax/D or Ay/D (dashed lines) and Vr: (a) and (c) ((b) and (d)) correspond to linear (nonlinear) fluid forces; darker shading (lighter shading) (pink (green) in online version) denotes positive (negative) output through Eqs. (14) and (15)

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Fig. 5

Comparison of numerical and experimental mean drag coefficients as function of (a) Vr and (b) Ay/D

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Fig. 6

Contour plots of CDT as functions of (a) m* and (b) Ay/D with varying Vr: plots of Cdv,max as function of m* is also depicted in (a)

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Fig. 7

Plots of (a) Cvy and (b) Cvx as function of Vr with experimental comparisons

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Fig. 8

Maps of ((a) and (c)) Cvy and ((b) and (d)) Cvx as functions of m* and Vr: ((a) and (b)) f* = 1 and ((c) and (d)) f = 2

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Fig. 9

Plots of (a) Cay, (b) CMy, (c) Cax, and (d) CMx as function of Vr with experimental comparisons

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Fig. 10

Maps of ((a) and (c)) Cay and ((b) and (d)) Cax as functions of m* and Vr: ((a) and (b)) f* = 1 and ((c) and (d)) f* = 2

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Fig. 11

Contour plots of maximum dual-resonant responses as functions of m* and ξ: (a) Aym/D and (b) Axm/D

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Fig. 12

Contour plots of (a) CL, (b) CD, and (c) Cdv as functions of m* and ξ, associated with Fig. 11

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Fig. 13

Contour plots of ((a) and (b)) Aym/D and ((c) and (d)) Axm/D as functions of m*  and ξ: ((a) and (c)) models with neglected nonlinearities and variable εy depending on m* (Eq. (7)); ((b) and (d)) model with neglected nonlinearities and fixed εy

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