Numerical simulation of fluid-structure interaction and vortex induced vibration of the circular and truncated cylinders

Document Type : Research Article

Authors

1 Faculty of Engineering, Kharazmi University, Tehran, Iran.

2 School of Mechanical Engineering, Arak University of Technology, Arak, Iran.

Abstract

Introduction
Vortex induced vibration is a well-known phenomenon in the engineering applications involving the fluid/structure interaction. Especially, it has been observed in various ocean engineering applications such as offshore risers, deep water bridge piers and oil pipelines. In the flow around bluff bodies such as marine risers, in a specific range of Reynolds numbers, the asymmetric vortex shedding at the bluff body wake results in periodic hydrodynamic forces on the riser and consequently the vortex-induced- vibration. When the vortex shedding frequency is close to the natural frequency of the structure, the cylinder tends to dramatically vibrates in transverse direction which is commonly termed as the "lock-in" phenomenon. Since vortex induced vibration is one of the most important causes of fatigue damage and structural instability in marine risers, exploring efficient ways to reduce or suppress vortex induced vibrations, has attracted the attention of many ocean engineering researchers. In the present study, two-way fluid/structure interaction simulation of vortex induced vibration of the circular and truncated cylinders are conducted. For this purpose, laminar flow around an elastically supported two degree of freedom cylinder (circular or truncated), which can freely vibrate in stream-wise and transverse directions, is considered.

Methodology
To solve the governing equations of two-dimensional, unsteady and incompressible flow over circular and truncated cylinders, a finite volume technique is employed. Moreover, the rigid body motion equations in stream-wise and transverse directions are incorporated into the computational fluid dynamics solver to treat the coupling which exists between the fluid flow and cylinder movement. To calculate the rigid body motion of cylinder and treat the fluid-cylinder interaction, a User-Defined Function is used. In every time step, the temporal variation of hydrodynamic forces (lift and drag) determined by solving the mass and momentum equations are employed as the source terms in rigid body motion equations to compute the velocity and displacement of cylinders. Fluid-structure interaction is handled using the Fluent's moving deforming mesh feature which deforms and remeshes cells during transverse and streamwise motions of the cylinders. The pressure-based solver with first-order implicit unsteady formulation is employed to solve the discretized continuity and momentum equations. The coupling between pressure and velocity fields are handled by using computationally efficient fractional step method along with the non-iterative time-advancement algorithm for time matching strategy in computational fluid dynamics solver. To solve the governing equation for the velocity fields, one needs suitable boundary conditions at the inlet, outlet, lower and upper boundaries, and on the surface of cylinders. A uniform profile of free-stream velocity is used at the inlet. At the outlet, the downstream boundary is located far from the cylinders such that the streamwise gradients for the velocity vectors could safely be set equal to zero. Along the upper and lower boundaries, the y-component velocity is considered to be zero while for the x-component velocity, the gradient in the y-direction is set equal to zero. At the cylinder’ walls, the no-slip condition is imposed on both velocity components.

Results and discussion
In order to validate the numerical method used in the study of fluid-structure interaction, the results for the transverse oscillations of the circular cylinder and truncated one (with truncation angle of 45 degrees) at different Reynolds numbers are compared with the results of Kumar et al. (2018). It is noteworthy that the obtained results in the present study are in good agreement with those of Kumar et al. (2018) and the numerical model accurately predicts the maximum amplitude of transverse vibration and the width of the lock-in region. Moreover, the influence of the truncation angle (behind the cylinder) on the vibration suppression of truncated cylinders is evaluated. The results show that as the Reynolds number increases from 80 to 85, the vibration of the truncated cylinders enters the lock-in region and experiences a sharp jump in their transverse displacement. Also, in this region, the truncation angle does not have a significant effect on the transverse vibrations of the cylinders and merely reduces their in-line vibration. However, changing the structural design of the cylinder (making a truncation at the back of the cylinder) has a substantial effect on the vibration reduction in the right half of the synchronization region. At Re = 100 (Reynolds number corresponding to the lock-out region), when the truncation angle increases from zero to 60 degrees, the transverse vibration of the cylinder is reduced by about 66%.

Conclusion
In summary, it is concluded that the significant difference in the oscillation amplitude of the circular and truncated cylinders is in the right half of the lock-in region. When the truncation angle increases, the width of the lock-in region decreases.

Keywords


Artana, G., Sosa, R., Moreau, E. and Touchard G. (2003). Control of the near-wake flow around a circular cylinder with electrohydrodynamic actuators. Experiments in Fluids, 35(6), 580-588.
Assi, G.R. and Bearman, P.W. (2018). Vortex-induced vibration of a wavy elliptic cylinder. Journal of Fluids and Structures 80, 1-21.
Baek, S.-J. and Sung, H.J. (1998). Numerical simulation of the flow behind a rotary oscillating circular cylinder. Physics of Fluids 10(4), 869-876.
Blevins, R.D. (1990). Flow-Induced Vibration, Nostrand Reinhold. New York, 104-110.
Chen, Z.-S. and Kim, W.-J. (2010). Numerical investigation of vortex shedding and vortex-induced vibration for flexible riser models. International Journal of Naval Architecture and Ocean Engineering, 2(2), 112-118.
Chen, Z.-S. and Kim, W.-J. (2012). Effect of bidirectional internal flow on fluid–structure interaction dynamics of conveying marine riser model subject to shear current. International Journal of Naval Architecture and Ocean Engineering 4(1), 58-71.
Gao, Y., Zong, Z., Zou, L., Takagi, S. and Jiang, Z. (2018). Numerical simulation of vortex-induced vibration of a circular cylinder with different surface roughnesses. Marine Structures, 57, 165-179.
Hasheminejad, S. M., Rabiee, A.H., Jarrahi, M. and Markazi, A. (2014). Active vortex-induced vibration control of a circular cylinder at low Reynolds numbers using an adaptive fuzzy sliding mode controller. Journal of Fluids and Structures, 50, 49-65.
Kumar, D., Singh, A.K. and Sen, S. (2018). Identification of response branches for oscillators with curved and straight contours executing VIV. Ocean Engineering, 164, 616-627.
Li, P., Liu, L., Dong, Z., Wang, F. and Guo, H. (2020). Investigation on the spoiler vibration suppression mechanism of discrete helical strakes of deep-sea riser undergoing vortex-induced vibration. International Journal of Mechanical Sciences, 172, 105410.
Li, Z., Navon, I., Hussaini, M. and Le Dimet, F.-X. (2003). Optimal control of cylinder wakes via suction and blowing. Computers & Fluids, 32(2), 149-171.
Liu, Q., Hao, W., Li, C., Miao, W. and Ding, Q. (2019). Numerical simulation on the forced oscillation of rigid riser with helical strakes in different section shapes. Ocean Engineering, 190, 106439.
Lou, M., Wu, W.-g. and Chen, P. (2017). Experimental study on vortex induced vibration of risers with fairing considering wake interference. International Journal of Naval Architecture and Ocean Engineering, 9(2), 127-134.
Park, H., Kumar, R. A. and Bernitsas, M. M. (2016). Suppression of vortex-induced vibrations of rigid circular cylinder on springs by localized surface roughness at 3× 104≤ Re≤ 1.2× 105. Ocean Engineering, 111, 218-233.
Placzek, A., Sigrist, J.F. and Hamdouni, A. (2009). Numerical simulation of an oscillating cylinder in a cross-flow at low Reynolds number: Forced and free oscillations. Computers & Fluids, 38(1), 80-100.
Quen, L.K., Abu, A., Kato, N., Muhamad, P., Sahekhaini, A. and Abdullah, H. (2014). Investigation on the effectiveness of helical strakes in suppressing VIV of flexible riser. Applied Ocean Research, 44, 82-91.
Rabiee, A. H. and Esmaeili, M. (2019). Simultaneous vortex-and wake-induced vibration suppression of tandem-arranged circular cylinders using active feedback control system. Journal of Sound and Vibration, 115131.
Sui, J., Wang, J., Liang, S. and Tian, Q. (2016). VIV suppression for a large mass-damping cylinder attached with helical strakes. Journal of Fluids and Structures, 62, 125-146.
Wang, W., Song, B., Mao, Z., Tian, W. and Zhang, T. (2019). Numerical investigation on VIV suppression of marine riser with triangle groove strips attached on its surface. International Journal of Naval Architecture and Ocean Engineering, 11(2), 875-882.
Xue, H., Wang, K. and Tang, W. (2015). A practical approach to predicting cross-flow and in-line VIV response for deepwater risers. Applied ocean research, 52, 92-101.
Zdravkovich, M. (1981). Review and classification of various aerodynamic and hydrodynamic means for suppressing vortex shedding. Journal of Wind Engineering and Industrial Aerodynamics, 7(2), 145-189.
Zhu, H., Gao, Y. and Zhou, T. (2018). Flow-induced vibration of a locally rough cylinder with two symmetrical strips attached on its surface: Effect of the location and shape of strips. Applied Ocean Research, 72, 122-140.
Zhu, H. and Yao, J. (2015). Numerical evaluation of passive control of VIV by small control rods. Applied Ocean Research, 51, 93-116.