The Second Conference of Global Chinese Scholars on Hydrodynamics The effect of top tension on VIV model analysis of a vertical flexible riser Muyu Duan 1,2, Bowen Fu 1, Decheng Wan 1* 1 State Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, Shanghai 200240, China 2 Department of Ship and Port Eng., Jiangsu Maritime Institute, Nanjing 211100, Jiangsu, China * Corresponding author: dcwan@sjtu.edu.cn ABSTRACT: This paper presents the vortex-induced vibration (VIV) of a vertical flexible riser under different top tension. A time-domain approach for predicting the VIV response of riser is proposed based on finite element simulation combined with a hydrodynamic model. The simulation is carried out by a multi-strip method based on OpenFOAM. Three different top tensions, T=1600N, 1900N and 2200N, are studied on its impact to VIV. And one of the top tension for T=1600N, is the same with the bench mark experiment of Huera-Huarte (2006). The simulation results show the consistency with the experimental results. KEY WORDS: Top; flexible riser; OpenFOAM; benchmark VIV. INTRODUCTION Vortex-induced vibration (VIV) is a critical concern for the offshore industry for a variety of structures including pipelines, spar platforms, and risers. As oil exploration and production moves to increasingly deeper waters, there is a growing need to understand the VIV characteristics of long, flexible riser response. Vortexinduced vibration is a major cause of fatigue failure in offshore slender structures. The reliable estimation of fatigue damage of risers requires accurate predictions of the presence and magnitude of VIV displacements and excitation modes. The dynamic features of long slender cylinders are determined by the tension and bending stiffness. The vibration amplitude and mode of riser VIV response is influenced by the complex effect of factors involving the axial tension. Many investigators, under experimental, numerical and empirical models, have addressed this very important topic. Chaplin et al [3] presented an experimental study of a vertical model riser with different top tension exposed to a stepped current. In the experiment of Huera-Huarte and Bearman, three different top tension were adopted. In the smallest tension case, the initial, lower and upper branches were definitely observed in the dynamic response of the model, whereas for the other tension cases, the lower branch of dynamic response vanished. Chen investigated dynamic characteristics and VIV of deepwater riser with axially varying structural properties. This paper presents the vortex-induced vibration (VIV) of a vertical flexible riser under different top tension. Three different top tensions, T=1600N, 1900N and 2200N, are studied on its impact to VIV. And one of the top tension, T=1600N, is the same with the bench mark experiment of Francisco. The numerical results are compared with the benchmark data of Francisco to check our numerical method. Many relevant researches have been published by Duan and Wan, Zhao and Wan, which could validate our approach. NUMERICAL MODELING In this paper, a CFD approach is used to study the riser VIV responses in stepped currents and comparisons are made with experimental results. This approach is essentially a multi-strip numerical method, combing solutions of the incompressible Reynolds Averaged Navier-Stokes (RANS) equations with a finite-element structural dynamics analysis. More precisely, this solution methodology combines a series of 2D simulations of the flow at individual axial strips along the riser with a fully 3D structural analysis to predict overall VIV loads and displacements. - 455 -
Computational Fluid Dynamics The Second Conference of Global Chinese Scholars on Hydrodynamics The incompressible RANS equations is used to simulation the fluid dynamics. ui 0 x i p 2 u u u S u u t x x x i i j ij j i j i j (1) (2) The SST k turbulence model is required to compute the Reynolds stresses for turbulence closure. The solution of the fluid governing equations is achieved by using the PIMPLE (merged PISO-SIMPLE) algorithm in OpenFOAM, which is a large time-step transient solver for incompressible flow. Structural Dynamics The resulting equations of dynamics motion in both in-line and cross-flow directions for structure are a set of second-order ODEs of the following form: [ M ] x [ C] x [ K K ] x F (3) g y g x [ M ] y [ C] y [ K K ] y F (4) A linear Finite Element implementation of the Bernoulli-Euler bending beam equations is used to model the response of the structure to the fluid loading. Each element is 4 DOF, comprised by two transverse displacements and tow angular displacements. Hence, each finite element contributes a 4 4 sub-matrix to the global matrices to obtain the overall structural dynamics formulation. Fluid-structure Interaction The entire flow-structure solution procedure is carried out in the time domain via a loose coupling strategy, such that the hydrodynamic loads from each riser strip are summed to obtain the overall loading along the span of the riser. At each time step, the hydrodynamic force is mapped to the nodes of the structural model. The structural model uses this loading to explicitly compute the pipe s motion. STRUCTURE PARAMETERS The numerical simulation model of this paper follows Huera-Huarte experiments, the experimental device as shown in Fig.1. Note that the layout of this experiments is the same as the experiments of Chaplin et al. Table 1 Summary of main parameter of the model riser Fig. 1 Layout of the experiments of F. J. Huera-Huarte (2006) The riser is 28mm in diameter and 13.12m long, with an aspect ratio of about L/D=469. The lower 45% of its length was subject to a uniform current, the rest was in still water. The riser is pinned at both the top and bottom ends and free to move in the in-line (x) and cross-flow (y) directions. Detailed information about the riser is summarized in 错误! 未找到引用源. A top tension T is applied on the top end of the riser. To investigate the - 456 -
The Second Conference of Global Chinese Scholars on Hydrodynamics impact of pre-tension on the VIV response of riser, three different top tension, T=1600N, 1900N, 2200N, are imposed on the top of riser. And one of pre-tension, which is T=1600N, is the same with the experimental parameter of F.J. Huera-Huarte (2006). RESULTS Cross-Flow (CF) Motion Analysis The cross-flow instantaneous deflected shapes appear the 4th mode shape when top tension equals to 1600N and 1900N, as shown in Fig.2, Fig.4. Comparing the numerical results of Fig.2 with Huera-Huarte experimental results of Fig.3, the numerical results show that the numerically predicted cross-flow displacement and the experiment have great consistency. For T=1600N, the vibration mode is unmixed 4th mode. While for T=1900N, the most deflected shapes is composed by the 4th mode shape. But there is also a little of the 3th mode shape. When top tension equals to 2200N, the cross-flow vibration is dominated by the 3th mode, as shown in Fig.5. Fig.2 Deflected shapes,t=1600n Fig.3 Deflected shapes by Exp. Fig.4 Deflected shapes,t=1900n Fig.5 Deflected shapes,t=2200n Fig.6 The 3th and 4th CF modal amplitude when T=1600N Fig.7 The 3th and 4th CF modal amplitude when T=1900N Fig.6 and Fig.7 give the 3th and 4th cross-flow displacement modal amplitude for the cases of T=1600N and T=1900N respectively. The amplitude of Mode 4 is greater than the amplitude of Mode3 all the time for the case of top tension T=1600N. So the mode shape is a very stable 4th order. The 3th mode when T=1900N carries a - 457 -
The Second Conference of Global Chinese Scholars on Hydrodynamics bigger weight than the 3 th mode when T=1600N. So at some times, the mode shape present 3 th order. The mode shape is unsteady 4 th order. Fig.8 is the spactio-temporal plot of cross-flow response, which gives the procedure of transformation of Mode 4 and Mode 3 when T=1900N. The vibration of riser is in the process of mode transition at the top tension equals to 1900N In-line (IL) Motion Analysis Fig.8 Spatio-temporal plot of CF response, T=1900N Fig.9 depicts the mean in-line displacement for the case of T=1600N, plotted against the relative elevation z/ L. The red line represents the experimental results and the blue line is the present numerical results. The maximum displacement is not in the middle of the length because the displacement of the upper part of the riser (in still water) is smaller than the displacement of the lower part exposed to the current. The numerically obtained both the value and location of the maximum in-line displacement agrees well with the experimental one. The instantaneous in-line deflected riser shapes by present numerical model is shown in Fig.10, and the experiment one is shown in Fig.11. Both of the deflected shapes present the 7 th mode shape. But the saddle points of numerical deflected shapes is not as clear as the experiment one. It seems that the numerical in-line deflected shapes is mixed with other mode shape except the 7th mode shape. Fig.12 shows the numerical results of the instantaneous spatio-temporal plot of the non-dimensional in-line displacement from the mean position during five seconds. Fig.12 shows a very unstable 7th mode. It suggests that there are more than one type of mode shape during this period, such as the 7th and 8th mode. The mode transition between modes makes Fig.12 appears complicated and it shows a travelling wave response. Fig.9 Mean IL displacement Fig.10 Instantaneous IL Fig.11 IL deflected shapes of deflected riser shapes, T=1600N riser obtained by experiment - 458 -
The Second Conference of Global Chinese Scholars on Hydrodynamics Fig.12 Spatio-temporal plot of IL response, T=1600N Fig.13 Spatio-temporal plot of IL response, T=1900N When the top tension increase to 1900N, the IL vibration will become more stable 7 th mode. Fig.13 shows the spatio-temporal plot of non-dimensional IL response, obtained by numerical simulation. It shows that the dominant mode shape is controlled by the only 7 th mode. There is no transition of mode and it shows a standing wave response. When the top tension continue to increase to 2200N, the IL vibration mode is decreased to the 6 th order, as shown in the Fig.15. Fig.14 Instantaneous deflected IL shapes of riser, T=1900N Fig.15 Instantaneous deflected IL shapes of riser, T=2200N The numerical results of VIV of long flexible riser at different top tension are summarized in table 2. It includes the maximum IL mean displacement ( x / max D ), the location of maximum IL mean displacement (Z/L), the maximum IL RMS displacement, the maximum CF RMS displacement, dominate IL mode and dominate CF mode. As the top tension increases, the VIV response of riser has the following rule: the maximum IL mean displacement decreases. While the location of maximum IL mean displacement is almost unchangeable in any case. The dominant IL mode decreases from the 7 th order to the 6 th order, and the dominant CF mode decreases form the 4 th order to the 3 th order. According to the above analysis, the IL VIV responses for the case of T=1600N present a multi-mode vibration. There is mode transition between the 7 th and 8 th mode. And the CF VIV responses for the case of T=1900N also presents a multi-mode vibration of the 3 th and 4 th mode. Table 2 VIV response with different top tension Top tension x / D Location of Max of Max of max x (Z/L) / D / D max xrms yrms In-line Mode Cross-flow Mode T=1600N 3.072 0.367 0.177 0.561 7 (unstable) 4 T=1900N 2.440 0.352 0.111 0.243 7 4 (unstable) - 459 -
CONCLUSIONS The Second Conference of Global Chinese Scholars on Hydrodynamics T=2200N 2.282 0.367 0.150 0.484 6 3 In this study, we carried out numerical simulations of vortex-induced vibrations of a vertical tension riser subjected to a stepped current. A multi-strip method numerical method has been developed based on OpenFOAM. The method is combined a number of two dimensional RANS solutions with a three-dimensional finite element method based on Euler-Bernoulli beam theory. Parameter analysis of top tension is investigated in detail to figure out its effect on the VIV response of long flexible riser. Three different top tensions, T=1600N, 1900N and 2200N, are chosen to study its impact to VIV. And one of the top tension, T=1600N, is the same with the bench mark experiment of Francisco (2006). The good agreement between the numerical and experimental results show that the multi-strip method is reliable. The vibration response is analyzed in detail in in-line and cross-flow direction respectively. From the study of this paper, many conclusion is obtained. The maximum IL mean displacement decreases with the increasing of top tension. But the location is almost unchangeable in any case. The trend of mode order reduction is obtained as the top tension increases. And the standing wave and travelling wave response are captured for different top tension case. ACKNOWLEDGEMENTS This work is supported by the National Natural Science Foundation of China (51379125, 51490675, 11432009, 51579145, 11272120), Chang Jiang Scholars Program (T2014099), Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning (2013022), Innovative Special Project of Numerical Tank of Ministry of Industry and Information Technology of China (2016-23/09), to which the authors are most grateful. REFERENCES [1] F.J. Huera-Huarte, P.W. Bearman. Wake structures and vortex-induced vibrations of along flexible cylinder-part 1: Dynamic response [J], Journal of Fluids and Structures, 2009, 25, pp.969-990. [2] Weimin Chen, Min Li, Zhongqin Zheng, Tiancai Tan. Dynamic characteris and VIV of deepwater riser with axially varying structural properties [J], Journal of Ocean Engineering, 2012, 42, pp.7-12. [3] J.R. Chaplin, P.W. Bearman, F.J. Huera Huarte, R.J. Pattenden. Laboratory measurements of vortex-induced vibrations of a vertical tension riser in a stepped current [J]. Journal of Fluids and Structures, 2005, 21, pp.3-24. [4] F.J. Huera-Huarte. Multi-mode Vortex-Induced Vibrations of a Flexible Circular Cylinder [D], Ph. D. Thesis, London, the University of London, 2006. [5] Muyu Duan, Decheng Wan, Large eddy simulation of flow around the cylinders with different aspects [J]. Chinese Journal of Hydrodynamics, 2016, Vol. 31, No. 3, pp. 295-302 [6] Muyu Duan, Decheng Wan, Hongxiang Xue, Prediction of response for vortex-induced vibrations of a flexible riser pipe by using multi-strip method [C]. Proceedings of the Twenty-sixth (2016) International Ocean and Polar Engineering Conference Rhodes, Greece, June 26-July 1, 2016, pp. 1065-1073 [7] Weiwen Zhao, Decheng Wan, Ren Sun. Detached-Eddy simulation of flows over a circular cylinder at high Reynolds number [C]. Proceedings of the Twenty-sixth (2016) International Ocean and Polar Engineering Conference Rhodes, Greece, June 26-July 1, 2016, pp. 1074-1079. [8] Weiwen Zhao, Decheng Wan. Numerical computations of spar vortex-induced motions at different current headings. [C]. Proceedings of the Twenty-sixth (2016) International Ocean and Polar Engineering Conference Rhodes, Greece, June 26- July 1, 2016, pp. 1122-1127. - 460 -