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Towards an understanding of the marine fouling effects on VIV of circular cylinders: a probe into the chaotic features

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Abstract

The current paper addresses the possibility of chaotic dynamics in the VIV response of cylinders covered by marine biofouling. The fouling was simulated by machining uniformly distributed pyramidal protrusions on the surface of the test cylinder. The Reynolds number varied from \(5.8\times 10^{3}\) to \(6.6\times 10^{4}\). The zero-one tests, Hilbert Transforms and Poincaré maps were used to analyse the VIV test results. The chaos analysis showed that in the early initial branch and in the ending part of the synchronisation, the VIV signals for both the smooth and the artificially biofouled cylinders happened to be chaotic. The signals in between showed non-chaotic dynamics. The chaotic extent grew wider with the artificially biofouled cylinder than those with the smooth cylinder and in the lift force signals as compared to the displacement signals. Our estimates for the chaotic regions in the low mass-damping smooth cylinder interestingly agreed well with (i) zones for the “quasi-periodic” regime and (ii) the region marked as “no observed shedding pattern” in the literature. They singled out these regions because of their irregular dynamics but failed to appreciate these as chaotic. Here, we argue that these regions are in fact quite susceptible to chaos.

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Abbreviations

\(A^{*}\) :

Non-dimensional amplitude \((A/D_\mathrm{O})\)

A :

Cross-flow oscillation amplitude

\(C_\mathrm{L}\) :

Lift force coefficient

\(C_{\mathrm{LRMS}}\) :

Root-mean-square of the lift force coefficient

\(D_\mathrm{o}\) :

The outer diameter of the cylinder

f :

Cross-flow oscillation frequency

\(f^{*}\) :

Reduced frequency

\(F_\mathrm{l}\) :

Lift force

\(f_\mathrm{N}\) :

Natural frequency (in-water)

\(f_\mathrm{s}\) :

Vortices’ frequency (Strouhal frequency)

\(\mathbf{H}_\mathrm{d}(t)\) :

Hilbert Transform of the cross-flow displacement

\(\mathbf{H}_\mathrm{F}(t)\) :

Hilbert Transform of the lift force

K :

System stiffness

\(K_\mathrm{c}\) :

The asymptotic growth rate in the zero-one test

\(K_\mathrm{D}\) :

Surface roughness coefficient

\(L_\mathrm{i}\) :

Immersed length of the cylinder

\(m^{*}\) :

Mass ratio

\(M_{c}(n)\) :

Smoothed mean square displacement

\(\hbox {Max}_{n}, \hbox {Max}_{n+1}\) :

Normalised successive maxima

Re:

Reynolds number

St:

Strouhal number

t :

Time

\(U^{*}\) :

Reduced velocity

\(U_{\infty }\) :

Free stream velocity

\(\xi \) :

Damping ratio (in-air)

\(\Phi (t)\) :

The phase shift between the lift force and the cross-flow displacement

\(\Phi _\mathrm{d} (t)\) :

The analytical phase angle of the cross-flow displacement

\(\Phi _\mathrm{F} (t)\) :

The analytical phase angle of the lift force

\(\rho \) :

Water density

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Authors and Affiliations

  1. Faculty of Civil Engineering, K. N. Toosi University of Technology, Tehran, Iran

    M. Zeinoddini, A. Bakhtiari & S. Asil Gharebaghi

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  1. M. Zeinoddini
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  2. A. Bakhtiari
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  3. S. Asil Gharebaghi
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Correspondence to A. Bakhtiari.

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Zeinoddini, M., Bakhtiari, A. & Gharebaghi, S.A. Towards an understanding of the marine fouling effects on VIV of circular cylinders: a probe into the chaotic features. Nonlinear Dyn 94, 575–595 (2018). https://doi.org/10.1007/s11071-018-4378-8

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  • DOI: https://doi.org/10.1007/s11071-018-4378-8

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