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Sub-harmonic wake-induced vibration of five tandem circular cylinders at low Reynolds number of 100

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Abstract

Dynamic response characteristics of five tandem circular cylinders in laminar uniform flow are studied numerically by fluid–structure interaction (FSI) computation. The Reynolds number of the incoming flow is fixed at Re \(=100\). The five cylinders are elastically mounted in both transverse and streamwise directions with an even center-to-center distance of 4, 6 and 8 times of the cylinder diameter. The non-dimensional mass of each cylinder is \(m^{*}=5\), 10 and 15, while the reduced velocity varies in the range of \(U_{\mathrm{r}}=\) 2–18. An FSI solver based on a modified characteristic-based split finite element method is developed for computation, and its accuracy is validated by evaluating the flow around five stationary circular cylinder and flow-induced vibrations (FIVs) of the one-cylinder and two-tandem-cylinder models against benchmark solutions. By numerical experiments, dynamic behaviors of five tandem cylinders as well as the underlying mechanisms are investigated by analyzing the generated vibration amplitude, frequency, fluid load and vortex pattern in the flow field. Sub-harmonic wake-induced vibration that has not been revealed by the existing two-cylinder and three-cylinder models is observed, and the underlying physics is discussed in detail. The results obtained are insightful into the understanding and control of FIVs of an array of cylindrical structures encountered frequently in various engineering applications.

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Abbreviations

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

Drag coefficient

\(C_{\mathrm{D},\mathrm{mean}}\) :

Time-averaged drag coefficient

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

Lift coefficient

\(C_{\mathrm{L},\mathrm{max}}\) :

Maximum lift coefficient

D :

Diameter of the cylinder

\(f_{\mathrm{CL}}\) :

Frequency component of the oscillating lift coefficient normalized by U/D

\(f_{Y}\) :

Dominant transverse vibration frequency normalized by U/D

\(F_{\mathrm{N}}\) :

Natural frequency of the cylinder normalized by U/D

L :

Center-to-center distance between neighbor cylinders normalized by D

\(m^{*}\) :

Mass of the cylinder per unit length normalized by \(\pi \rho _{\mathrm{F}} D^{2}/4\)

NE:

Total number of grid elements in the flow domain

NP:

Total number of grid nodes in the flow domain

p :

Pressure normalized by \(\rho _{\mathrm{F}} U^{2}\)

Re:

Reynolds number, Re \(=UD/\upsilon \)

\(\rho _{\mathrm{F}}\) :

Fluid density

St:

Dominant vortex shedding frequency normalized by U/D

t :

Time normalized by D/U

T :

Vortex shedding period normalized by D/U

\(u_{1}\), \(u_{2}\) :

Streamwise and transverse component of fluid velocity normalized by U

U :

Velocity component of the free stream in x direction

\(U_{\mathrm{r}}\) :

Reduced velocity, \(U_{\mathrm{r}} =1/F_{\mathrm{N}}\)

\(\upsilon \) :

Kinematic viscosity of the fluid

\(_{x,y}\) :

Coordinate components of the flow domain normalized by D

X, Y :

Streamwise and transverse displacements of the cylinder normalized by D

\(X_{\mathrm{mean}}\), \(X_{\mathrm{rms}}\) :

Time-averaged and root-mean-square streamwise displacements of the cylinder normalized by D

\(Y_{\mathrm{max}}\), \(Y_{\mathrm{rms}}\) :

Maximum and root-mean-square transverse displacement of the cylinder normalized by D

\(\dot{X}\), \(\dot{Y}\) :

Streamwise and transverse velocities of the cylinder normalized by U

\(\ddot{X}\), \(\ddot{Y}\) :

Streamwise and transverse accelerations normalized by \(U^{2}/D\)

\(\zeta \) :

Damping ratio of the structure

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (No. 51506224). The authors gratefully acknowledge the support of this funding.

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Authors and Affiliations

  1. National Engineering Laboratory for Pipeline Safety/MOE Key Laboratory of Petroleum Engineering, China University of Petroleum-Beijing, Beijing, 102249, China

    Xu Sun & Yi-Xin Zhang

  2. Nonlinear Engineering and Control Lab, Mechanical Engineering Department, Texas A &M University, College Station, TX, 77843, USA

    Xu Sun & Steve Suh

  3. Sinopec Oilfield Equipment Corporation, Wuhan, 430075, China

    Ze-Hua Ye

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  1. Xu Sun
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Correspondence to Xu Sun.

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The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Communicated by Vassilios Theofilis.

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Sun, X., Suh, S., Ye, ZH. et al. Sub-harmonic wake-induced vibration of five tandem circular cylinders at low Reynolds number of 100. Theor. Comput. Fluid Dyn. 36, 671–687 (2022). https://doi.org/10.1007/s00162-022-00615-0

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  • DOI: https://doi.org/10.1007/s00162-022-00615-0

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