DUAN Jinlong, and HUANG Weiping

Department of Ocean Engineering, Shandong Key Laboratory of Ocean Engineering, Engineering College, Ocean University of China, Qingdao 266100, P. R. China

CFD-Based Numerical Analysis of a Variable Cross-Section Cylinder

DUAN Jinlong, and HUANG Weiping*

Department of Ocean Engineering, Shandong Key Laboratory of Ocean Engineering, Engineering College, Ocean University of China, Qingdao 266100, P. R. China

Using ANSYS-CFX, a general purpose fluid dynamics program, the vortex-induced vibration (VIV) of a variable crosssection cylinder is simulated under uniform current with high Reynolds numbers. Large eddy simulation (LES) is conducted for studying the fluid-structure interaction. The vortex shedding in the wake, the motion trajectories of a cylinder, the variation of drag and lift forces on the cylinder are analyzed. The results show that the vortices of variable cross-section cylinder are chaotic and are varying along the cylinder. In places where cross-sections are changing significantly, the vortices are more irregular. The motion trail of the cylinder is almost the same but irregular. The drag and lift coefficients of the cylinder are varying with the changes of diameters.

variable cross-section cylinder; large eddy simulation; fluid-solid interaction; drag coefficient; lift coefficient; vortex shedding

1 Introduction

With the increasing demand for oil and gas around the world, the exploration and production of oil and gas in deep water become more and more important. Risers, playing an important role in connecting platforms and underwater channels, are widely used in the oil and gas industry. Due to vortex-induced vibration (VIV) by environmental loads, risers are easy to fatigue and to be damaged under the influence of VIV, which greatly threatens the safety of platforms. Therefore, the engineering research on VIV has been a hot topic (Sarpkaya, 2004; Gabbai and Benaroya, 2005; Assiet al., 2006; Williamson and Govardhan, 2008). Traditional VIV research mostly focuses on the analysis of a single riser despite the existence of various configurations of risers, such as risers with helical strakes, shrouds, fairings. Vandiveret al.(2006) and Yuan and Huang (2010) showed that affiliated devices, such as buoyancy modules designed to reduce the top tension of risers, have impact on risers. In view of a lack of studies on risers with buoyancy modules, it is necessary and meaningful to discuss VIV of such risers.

A turbulence model mainly consists of Reynolds Averaged Navier-Stoke (RANS), Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS). Under the current with high Reynolds numbers, some models cannot provide detailed information because of the inherent defects of RANS. However, under the similar current conditions, LES can not only provide sufficient information in numerical simulations but the tasks can also be performed on PC computers (Mittal and Moin, 1997; Breuer, 1998; Kravchenko and Moin, 2000; Weiet al., 2004; Xieet al., 2007). In the present work, based on CFD, LES is applied to simulate VIV of a variable crosssection cylinder which is similar to risers with buoyancy modules and some conclusions are drawn accordingly.

2 Numerical Simulations

2.1 Approach

Because LES is a more appropriate practice (ANSYSCFX help) for a flow field with Reynolds numbers larger than 104, LES-WALE is applied here.

2.2 Model

In this simulation, the outer diameters of small diameter sections (SDS) and large diameter sections (LDS) of variable cross-section cylinder are 2 cm and 6 cm, respectively. The uniform flow velocity is 0.6 m s-1. The Reynolds number for SDS is 1.2×104while that for LDS is 3.6×104.

The flow field is 20×40 D (D is the outer diameter of LDS). The depth of the flow field is represented byH(H=100 cm). The upstream area is 10D long while the downstream area is 30D long. The model grid is developed using ANSYS-CFD and is refined around cylinder and the region where vortexes are shed (Figs.1, 2, and 3).

The boundary conditions are listed as follows: the velocityuis 0.6 m s-1and the velocities in the other two directions,vandw, are zero whilep=0. The outlet boundary conditions are the derivative of flow parameters along streamlines, which is 0 while pressure and pressure gradient are 0. The sides of the model domain are treated as slip walls (zero shear stress). Non-slip conditions are applied for the cylinder wall.

Fig.1 Grid around cylinder.

Fig.2 Grid side view.

Fig.3 Structure model diagram in WORKBENCH.

3 Results

3.1 Vortex Shedding

Fig.4 Flow streamlines on (a) section A, (b) section B, (c) section C, (d) section D and (e) section E.

Fig.4 shows five vortex street diagrams in sections A, B, C, D, and E. It can be seen that vortices from the variable cross-section cylinder are different. Vortices in sections A and E are irregular near SDS, but become regular a certain distance away from the cylinder. Vortices in section A are more inerratic than those in section E (Figs.4(a) and (e)). The vortex shedding of LDS is more regular and steady in section C (Fig.4(c)). Vortices insection D are more disordered than those in section B (Figs.4(b) and (d)). Comparing vortices among five different sections, a conclusion can be drawn that vortices of a variable cross-section cylinder change due to different diameters. In addition, vortices near the variable crosssections are irregular while away from the variable crosssections they are more regular. Velocity contour surface is shown in Fig.5, which is consistent with the vortice analysis above.

Types of studies: Review articles, peer review articles and some ongoing trials evaluating pancreatic cancer pain management modalities were included in the review. The language of publication of eligible studies was restricted to English.

Fig.5 Cylinder velocity contour surface.

3.2 Drag and Lift Coefficients

The drag and lift force are monitored in this simulation, which are used to calculate the drag and lift coefficients. Fig.6 shows drag and lift coefficient curves of the variable cross-section cylinder, in whichCd1andCl1represent the drag and lift coefficients of SDS whileCd2andCl2are those of LDS, respectively. It can be seen from the figure that the mean drag and lift coefficients of SDS are small and equal to about 0.5 and 0.25, respectively. Pulsating drag coefficient is about 0.1. The mean drag and lift coefficients of LDS are about 0.75 and range between 0.7 and 0.8, respectively. Pulsating drag coefficient is about 0.2. Clearly, drag and lift coefficients are varying for different parts of the variable cross-section cylinder corresponding to changes in Reynolds numbers, and the coefficients of LDS are larger than those of SDS.

Fig.6 Drag coefficient and lift coefficient. Cd1and Cl1are the drag and lift coefficients of SDS while Cd2andCl2are those of LDS.

A Fourier spectral analysis generalizes the characteristics of variables in the frequency domain based on the overall features in the time domain. Fig.7 shows the spectra of the drag and lift coefficients of SDS (Figs.7(a) and (c)) and LDS (Figs.7(b) and (d)). These graphs indicatethat both the drag and lift coefficients have the same dominant frequencies, being 1.896 Hz for drag coefficient and 1.497 Hz for lift coefficient. The drag and lift coefficients also show the generation of multi-frequency vortices caused by variable sections.

Fig.7 Drag and lift coefficients.

3.3 Trajectories of Cylinder Motion

Five particles are monitored for cylinder motion in this simulation (Fig.8). Fig.9 shows the particle trajectories. Due to the model symmetry, particles 1 and 2 have exactly the same motion trajectories, and so do particles 4 and 5. Motion trajectories of particles 1, 3, and 5 in SDS are presented in Figs.9(a) and (c) and particles 2 and 4 in LDS in Fig.9(b). As seen here, the motion trail of the cylinder looks random on account of variable cross- sections, and is different from that of a single riser.

The Fourier spectral analysis results of particle trajectories are shown in Fig.10. Particles 1 and 2 have the same spectra because of symmetry, and so do particles 4 and 5. The dominant frequencies of cross-flow and alongflow are identical with those of the drag and lift coefficients, which are 1.896 Hz and 1.497 Hz, respectively. But multi-frequency vortices are not generated.

Fig.8 Motion of particles.

Fig.9 Trajectories of cylinder motion.

Fig.10 Spectral analysis of cylinder motion.

4 Conclusions

Using ANSYS-CFX, a general purpose fluid dynamics program, VIV of a variable cross-section cylinder, is simulated and the fluid-structure interaction is investigated under uniform current with high Reynolds numbers over 104. The results show that the variable cross-section cylinder can generate VIV with irregular and multi- frequency vortices in different parts of the cylinder, especially in SDS. Due to changes in cross-section areas, vortices in the wake near SDS are irregular but become regular a certain distance away from SDS. Vortices generated near the areas with highly varying cross-sections are especially chaotic. Drag and lift coefficients of LDS are larger than those of SDS. Besides the dominant frequencies, drag and lift coefficients show the multi- frequency features. The cylinder motion trajectories appear random. Comparing with a single riser, the varying crosssections of a variable cross-section riser are the primary reason causing the differences in vortices, drag and lift coefficients, and motion trajectories.

A preliminary study on fluid-solid interaction has been conducted for a variable cross-section cylinder. Further research is needed to understand how variable cross- sections influence VIV and how VIV of variable cross- section risers behaves under flows with low Reynolds numbers.

Acknowledgements

This study is supported by the National Natural Science Foundation of China (Nos. 51179179 and 51079136). We would like to express our thanks to all who have helped us.

Assi, G. R. S., Meneghini, J. R., Aranha, J. A. P., Bearman, P. W., and Casaprima, E., 2006. Experimental investigation of flowinduced vibration interference between two circular cylinders. Journal of Fluids and Structures, 22: 819-827.

Breuer, M., 1998. Large eddy simulation of the subcritical flow past a circular cylinder: Numerical and modeling aspects. International Journal for Numerical Methods in Fluids, 28: 1281-1302.

Gabbai, R. D., and Benaroya, H., 2005. An overview of modeling and experiments of vortex-induced vibration of cylinders．Journal of Sound and Vibrations, 282 (3-5): 575-616．

Kravchenko, A. G., and Moin, P., 2000. Numerical studies of flow over a circular cylinder at ReD=3900. Physics of Fluids, 12 (2): 403-417.

Mittal, R., and Moin, P., 1997. Suitability of up wind-biased finite-difference schemes for large eddy simulation of turbulent flow. American Institute of Aeronautics and Astronautics Journal, 35 (8): 1415-1417.

Sarpkaya, T., 2004. A critical review of the intrinsic nature of vortex-induced vibrations. Journal of Fluids and Structures, 19: 389-447.

Su, M. D., and Huang, S. Y., 1997, Foundation of Computational Fluid Dynamics. Tsinghua University Press, Beijing, 597pp (in Chinese).

Vandiver, J. K., Swithenbank, S., Jaiswal, V., and Marcollo, H., 2006. The effectiveness of helical strakes in the suppression of high-mode-number VIV. Offshore Technology Conference, Houston, Texas, 1–4 May 2006, OTC 18276.

Wei, Y. J., Zhu, M. S., and He, Z. Y., 2004, Large eddy simulation and spectrum analysis of flow around two square cylinders arranged side by side. Applied Mathematics and Mechanics, 25 (8): 824-830 (in Chinese with English abstract).

Williamson, C. H. K., and Govardhan, R., 2008. A brief review of recent results in vortex-induced vibrations. Journal of Wind Engineering and Industrial Aerodymuics, 96 (6-7): 714-735.

Xie, Z. G., Xu, C. X., Cui, G. X., and Zhang, Z. S., 2007. Large eddy simulation of flows around a square cylinder. Journal of Computational Physics, 24 (2): 171-180 (in Chinese with English abstract).

Yuan, J. K., and Huang, W. P., 2010. Ansys-CFD analysis on the flow field of helical strakes around riser. Ship & Ocean Engineering, 39 (4): 151-155 (in Chinese with English abstract).

Zhang, Z. S., Cui, G. X., and Xu, C. X., 2005. Theory and Modeling of Turbulence. Tsinghua University Press, Beijing, 277pp (in Chinese).

(Edited by Xie Jun)

(Received May 17, 2012; revised September 13, 2012; accepted January 20, 2014)

? Ocean University of China, Science Press and Springer-Verlag Berlin Heidelberg 2014

* Corresponding author. Tel: 0086-532-66781850

E-mail: wphuang@ouc.edu.cn