Journal of Vibration Testing and System Dynamics
Flow-induced Vibrations of two Staggered Circular Cylinders at Low Reynolds Number
Journal of Vcibration Testing and System Dynamics 3(1) (2019) 39--54 | DOI:10.5890/JVTSD.2019.03.004
Zehua Ye$^{1}$, Xu Sun$^{1}$, Jiazhong Zhang$^{2}$
$^{1}$ National Engineering Laboratory for Pipeline Safety, China University of Petroleum-Beijing, 102249, China
$^{2}$ School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an, 710049, China
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Abstract
The effect of flow interference on the flow-induced vibrations (FIVs) of two staggered circular cylinders at low Reynolds numbers is investigated using fluid-structure interaction (FSI) simulations. The FIV mechanical model of the two staggered circular cylinders in a laminar flow is proposed and the corresponding non-dimensional governing equations are presented. An FSI solution procedure is subsequently developed by combining the modified characteristic-based split (CBS) finite element method, dual-time stepping method, segment spring analogy technique, generalized-α method and loosely-coupled partitioned method. The stability and accuracy of the procedures are validated using a benchmark FSI problem concerning the FIVs of a single circular cylinder in a laminar flow. Finally, using the numerical method proposed, the FIVs of two staggered circular cylinders at Re = 200, T/D (space ratio) = 5∼7 and α (inclined angle of the line connecting the two cylinders centers) = 0°∼ 90° are computed, and the effects of T/D and α on the vortex structure, fluid load and FIVs are discussed in detail.
Acknowledgments
This work is supported by the National Natural Science Foundation of China (No. 51506224) and Science Foundation of China University of Petroleum-Beijing (No. C201602). The authors gratefully acknowledge the support of the two agencies.
References
-
[1]  | Bearman, P.W. (1984), Vortex shedding from oscillating bluff bodies, Annual Review of Fluid Mechanics, 16, 195-222. |
-
[2]  | Sarpkaya, T. (2004), A critical review of the intrinsic nature of vortex-induced vibrations, Journal of Fluids and Structures, 19, 389-447. |
-
[3]  | Williamson, C.H.K. and Govardhan, R. (2004), Vortex induced vibration, Annual Review of Fluid Mechanics, 36, 413-455. |
-
[4]  | Zdravkovich, M.M. (1984), Classification of flow-induced oscillations of two parallel circular cylinders in various arrangements, ASME Winter Annual Meeting, Symposium on Flow-Induced Vibrations, 2, 1-18. |
-
[5]  | Zdravkovich, M.M. (1988), Review of interference-induced oscillations in flow past two parallel circular cylinder in various arrangements, Journal of Wind Engineering, 28, 183-200. |
-
[6]  | Zdravkovich, M.M. (1997), Flow Around Circular Cylinders, vol. 1: Fundamentals, Oxford University Press, Oxford, UK. |
-
[7]  | Sumner, D. (2010), Two circular cylinders in cross flow: a review, Journal of Fluids and Structure, 26,849-899. |
-
[8]  | Zhou, Y. and Alam, M.M. (2016), Wake of two interacting circular cylinders: A review, International Journal of Heat and Fluid Flow, 62,510-537. |
-
[9]  | Mitta, S. and Kumar, V. (2001), Flow-induced oscillations of two cylinders in tandem and staggered arrangements, Journal of Fluids and Structures, 15, 717-736. |
-
[10]  | Deng, J., Ren, A.L., and Chen, W.Q. (2005), Numerical simulation of flow-induced vibration on two circular cylinders in tandem arrangement, Journal of Hydrodynamics, 17(6), 660-666. |
-
[11]  | Assi, G.R.S., et al. (2006), Experimental investigation of flow-induced vibration interference between two circular cylinders, Journal of Fluids and Structures, 22,819-827. |
-
[12]  | Prasanth, T.K. and Mittal, S. (2009), Flow-induced oscillation of two circular cylinders in tandem arrangement at low Re, Journal of Fluids and Structures, 25, 1029-1048. |
-
[13]  | Kim, S., et al. Flow-induced vibrations of two circular cylinders in tandem arrangement. Part 1: Characteristics of vibration, Journal of Wind Engineering, 97, 304-311. |
-
[14]  | Kim, S., et al. (2009), Flow-induced vibrations of two circular cylinders in tandem arrangement, Part 2: Suppression of vibrations, Journal of Wind Engineering, 97,312-319. |
-
[15]  | Alam, M.M. and Kim, S. (2009), Free vibration of two identical circular cylinders in staggered arrangement, Fluid dynamics research, 41,035507. |
-
[16]  | Mysa, R.c., Kaboudian, A., and Jaiman, R.K. (2016), On the origin of wake-induced vibration in two tandem circular cylinders at low Reynolds number, Journal of Fluids and Structures, 61, 76-98. |
-
[17]  | Griffith, M.D. et al. (2017), Flow-induced vibration of two cylinders in tandem and staggered arrangements, Journal of Fluid Mechanics, 833, 98-130. |
-
[18]  | Mysa, R.C., Law, Y.Z., and Jaiman, R.K. (2017) , Interaction dynamics of upstream vortex with vibrating tandem circular cylinder at subcritical Reynolds number, Journal of Fluids and Structures, 75, 27-44. |
-
[19]  | Li, X.T., Zhang, W.W., and Gao C.Q. (2018), Proximity-interference wake-induced vibration at subcritical Re: Mechanism analysis using a linear dynamic model, Physics of fluids, 30, 033606. |
-
[20]  | Kim, S., Alam, M.M. (2015), Characteristics and suppression of flow-induced vibrations of two side-by-side circular cylinders, Journal of Fluids and Structures, 54, 629-642. |
-
[21]  | Chen W.L., et al. (2015), Flow-induced vibrations of two side-by-side circular cylinders: Asymmetric vibration, symmetry hysteresis and near-wake patterns, Ocean Engineering, 110, 244-257. |
-
[22]  | Chen W.L., et al. (2015), Response and wake patterns of two side-by-side elastically supported circular cylinders in uniform laminar cross-flow, Journal of Fluids and Structures, 55, 218-236. |
-
[23]  | Huera-Huarte, F.J. and Gharib, M. (2011), Flow-induced vibrations of a side-by-side arrangement of two flexible circular cylinders, Journal of Fluids and Structures, 27, 354-366. |
-
[24]  | Huera-Huarte, F.J. and Bearman, P.W. (2011), Vortex and wake-induced vibrations of a tandem arrangement of two flexible circular cylinders with near wake interference, Journal of Fluids and Structures, 27, 193-211. |
-
[25]  | Liu, B. and Jaiman, R.K. (2018), Dynamics of gap flow interference in a vibrating side-by-side arrangement of two circular cylinders at moderate Reynolds number, Journal of Fluid Mechanics, 16,1-39. |
-
[26]  | Zienkiewicz, O.C., Taylor, R.L. and Nithiarasu, P. (2005), The Finite Element Method for Fluid Dynamics, six edition, Elsevier: Butterworth-Heinemann. |
-
[27]  | Sun, X., Zhang, J.Z. and Ren, X.L. (2012), Characteristic-based split (CBS) finite element method for incompressible viscous flow with moving boundaries, Engineering Applications of Computational Fluid Mechanics, 6(3), 461-474. |
-
[28]  | Sun, X., Zhang, J.Z., and Mei, G.H. (2012), An Improved characteristic-based split (CBS) scheme for compressible and incompressible moving boundary flows., International Journal of Aerospace and Lightweight Structures, 2(2), 281-297. |
-
[29]  | Jameson, J. (1991), Time dependent calculations using multigrid with application to unsteady flows past airfoils and wings, AIAA paper, 91-1596. |
-
[30]  | Blom, F.J. (2000), Considerations on the spring analogy, International Journal for Numerical Methods in Fuids, 32(6), 647-668. |
-
[31]  | Prasanth, T.K. and Mittal, S. (2008), Vortex-induced vibrations of a circular cylinder at low Reynolds numbers, Journal of Fluid Mechanics, 594, 463-491. |
-
[32]  | Tu, J.H., Zhou D., Bao Y., Ma, J., Liu J.B., and Han Z.L. (2015), Flow-induced vibrations of two circular cylinders in tandem with shear flow at low Reynolds number, Journal of Fluids and Structures, 59, 224-251. |