Suppression of vortex-induced vibrations of a flexible riser by adding helical strakes *

Dong-yang Chen , Laith K. Abbas, Guo-ping Wang, Xiao-ting Rui, Wei-jie Lu

1. School of Hydraulic, Energy and Power Engineering, Yangzhou University, Yangzhou 225127, China

2. Institute of Launch Dynamics, Nanjing University of Science and Technology, Nanjing 210094, China

3. Nanjing Aerosun Corporation, Nanjing 210000, China

Abstract: 3-D computational fluid dynamics/ computational structure dynamics (CFD/CSD) numerical two-way coupling simulations are conducted for a flexible rise in order to study the dynamic response performance of the riser with and without helical strakes exposed to the vortex-induced vibration (VIV). The VIV responses of a PVC riser without helical strakes are computed and compared with experimental data, to verify the accuracy of the present two-way coupling method. Subsequently, the dynamic behaviors of a short PVC riser with different kinds of helical strakes are studied. The vibration amplitudes along the riser, the trajectories of the riser's monitor point and the vortex shedding contours are obtained in a series of simulations. The helical strakes' VIV suppression mechanisms are found involving the breaking of the vortex structures and the reduction of the vortex shedding frequency of the bare riser. Moreover, a good suppression effect can be achieved by attaching the helical strake structure with a reasonable geometrical configuration (such as the appropriate strake height, strake pitch, the number of starts and strake coverages) to the flexible riser. The effect is also diverse at different reduced velocity . The remarkable effect is found at for the short riser, with about 97%reduction in the transverse vibration response.

Key words: Vortex-induced vibration (VIV), fluid structure interaction (FSI) , Two-way coupling, Helical strakes, SST-SAS

Introduction

The marine riser is an important facility and the key part in the offshore oil/gas transportation. It is the main connection between the offshore platform and the subsea wellheads and the most fragile components in the oil/gas exploiting system. The riser is affected by the transmission medium and subjected to large forces, due to the waves and the underwater currents[1].When vortices are shed from a riser, the riser is subjected to the time-dependent drag and lift forces in flows of certain Reynolds number. The lift may induce cross-flow (CF) vibrations, and the drag may induce in-line (IL) vibrations. These forces deform the riser, and over time, and at the same time, the flow field around the riser changes accordingly. This interaction between the fluid and the structure is called vortex-induced vibration (VIV)[2-6]. The prediction of the VIV is quite important for the design of the slender marine riser. When the shedding frequency of the vortices behind the structure synchronizes with the natural frequency of the structure, we will have“l(fā)ock-in”, usually accompanied with a significant vibration[7]. If the riser vibrates under the synchronization for a long period, the riser might has a considerable fatigue damage, with detrimental effects.There are mainly two types of ways to suppress the VIV of the riser: the active control and the passive control. The latter has gained much more attention in practice due to its simple treatment. If the “l(fā)ock-in”occurs, generally, some passive VIV suppression devices such as helical strakes are added somewhere along the riser to eliminate/ or reduce the vibration.The underlying mechanism of the vibration reduction with the helical strakes is to disrupt the spatial correlation of vortices by gradually changing the flow separation angle in the longitudinal direction. Thus,the vortices are weakened in intensity and the fluid force is reduced. This will prevent the riser's fatigue damage[8].

The fluid-structure interaction (FSI) is a challenging field in engineering. With the complexity of the fluid solution and the structural solution,different coupling methods have to be considered for different problems. In Fig. 1, the FSI problems are listed according to the complexity in the physical and numerical coupling. The stronger the physical coupling is, the tougher the numerical coupling will be.A number of FSI studies of the VIV of flexible risers might be mentioned. Willden and Graham used a quasi-three-dimensional (Q-3-D) method to numerically simulate the transverse vibration of a riser with(length to diameter) is 100 and subject to a sheared current at low Reynolds numbers[9]. It was shown that the most shedding frequencies along the riser were modified towards the natural frequency.Meneghini et al.[10], Yamamoto et al.[11]investigated the long risers with L/ D up to 4 600 based on the Q-3-D method. It was concluded that the vortex shedding patterns along the riser with a 2S mode occurred in the regions of small amplitudes, and a 2P mode in the regions of larger amplitudes. For the VIV simulation, where the riser is flexible, the 3-D computational fluid dynamics/computational structure dynamics (CFD/CSD) two-way coupling simulation as illustrated in Fig. 2[12-14]becomes very important. It is a weak coupling method. This numerical method overcomes the shortcomings of combining the Q-3-D method with a series of strip or 2-D simulations to calculate the fluid forces on the riser. The 3-D CFD simulations can directly capture the vortex structures.In addition, the risers with complex geometrical suppression device, under complex flow conditions and with the interactions between risers, can be studied directly[15-17].

Fig. 1 FSI modeling approaches

Menter et al.[18]proposed the scale-adaptive simulation (SAS) concept based on the shear stresstransport(SST)modelsandlarge-eddysimulation(LES)-like behaviors were captured in detached flow regions, without an explicit use of the grid spacing.This allows for a safer passage from the RANS to the LES and avoids some problems related to the grid sensitivities of the detached-eddy simulation (DES)approach, especially for complex applications[19-20].Thus, the SST-SAS turbulent model is used in the CFD solver module to simulate this high nonlinear vortex shedding phenomenon. Moreover, a direct CSD method is used in this two-way coupling simulation to overcome the shortcoming of the modal superposition method (the wet modal frequencies and modal shapes are affected by the flow environment[21-22]).

Fig. 2 (Color online) General sketch of FSI process

In the present work, the VIV response of the PVC riser is numerically calculated based on the CFD(SST-SAS) / CSD two-way coupling approach. The simulation results are compared with experimental data to verify the accuracy of this two-way coupling method. Subsequently, the hydroelastic responses of the short PVC riser with and without helical strakes are simulated based on the same approach. In order to reduce the computational cost and increase the reliability of the computations, a short riser (to guarantee that the short riser have the synchronization phenomenon in the low Re region, with a reduction in the stiffness and an increase of the mass ratio to certain values) is considered instead of the full-scale PVC riser. This work is carried out on the ANSYS Workbench multi-physics coupling platform. The fluid solver is the CFX while the structure solver is the ANSYS.

1. Fluid structure interaction dynamics model

1.1 Fluid model

The Navier-Stokes (N-S) equations are expressed in a Reynolds averaged Navier-Stokes (RANS) form.It is possible to simulate viscous fluid dynamics phenomena. The RANS equations can be expressed as

where the subscripts i, j take values of (1, 2, 3).u, ρ , p, μ andiS are the fluid velocity, the density, the pressure, the dynamic viscosity and the generalized source term of the momentum conservation equation, respectively. Equation (1) introduces a set of unknowns called the Reynolds stresses, which are functions of the velocity fluctuations. The present simulations use the Scale-Adaptive Simulation, based on the SST turbulence model (SST-SAS) developed by Menter to compute the Reynolds stresses to closure Eq. (1)[23-24].

1.2 Structural model

The VIV response due to the vortex structures is analyzed using the direct finite-element method. The hydroelastic equations of motion of the riser are

where x, ˙x and ˙˙x are the displacement, velocity and acceleration vectors. M , C and K are the mass, damping and stiffness matrices, respectively.F is the force vector due to the hydrodynamics which is calculated by the CFD based on the SST-SAS. According to the physical meaning of F,. Ffis the hydrodynamic load and FFSIincludes the radiation and restoring forces.Thus,K are the added mass, the added damping and the added stiffness matrices induced by the vibration acceleration, velocity and displacement of the riser,respectively. To this end, the hydroelastic equation of the riser can be written in the following form

1.3 FSI coupling procedure

In some simulations, there may be a strong and potentially nonlinear relationship between the fields that are coupled in the FSI. Under these conditions,the ability to have a converged solution will likely require the use of the two-way coupling FSI. The fluid and structure solvers advance through a sequence of iterations. During every one stagger iteration, each field solver collects the required loads from the other field solver and then solves its physical fields. The flow field grid motion is achieved by the displacement diffusion method, based on the cell volume in the CFX software. By decreasing the mesh stiffness in larger cells, those cells will absorb more grid deformation. On the other hand, it is better to preserve the quality of smaller cells, near the motion boundary,to preserve the computational accuracy. In the present work, the residual convergence criteria require the displacements between the fluid domain and the mesh less than 1×10-4. The fluid and structure domains have the same time step of about (reference length /velocity)×(0.1-0.5). Figure 3 shows the hydroelastic two-way coupling procedures, and the simulation will not be stopped until the time reaches the total time prescribed by the user.

Fig. 3 Flow chart of two-way coupling

2. Validation of a PVC riser

2.1 Computational conditions

The geometry parameters, the boundary conditions and the experimental device of the PVC riser are given in Ref. [2] and shown with the coordinate directions in Fig. 4.

Fig. 4 3-D model of the PVC riser under tension T

The parameters for modeling the PVC riser in the ANSYS workbench is tabulated in Table 1. The flow field and the RANS equations are spatially discretized,and the solution is based on the implicit finite-volume method. These unsteady numerical simulations for the entire 3-D region of the flow domain (Fig. 5(a)) are performed using 1885863 hexahedral structured grids and Fig. 5(b) illustrates the CFD mesh generation. The mesh is refined near the wall region to ensure Y+＜1.The distances between the PVC riser and the upstream and downstream boundaries are 10D, 35D, respectively, where D is the diameter of the riser. The no-slip boundary condition is imposed on the surface of the riser, and the symmetry conditions are imposed on the top and the bottom and both sides boundaries of the fluid domain. The model in-flow and out-flow boundaries are the velocity inlet and the pressure outlet, respectively.

Table 1 PVC riser parameters

Fig. 5 (Color online) Fluid domain and computational mesh

18734 SOLID186 elements (twenty nodes for each hexahedron element) are used for the CSD mesh structural domain as illustrated in Fig. 5(c). The remote displacement constraints of the ANSYS Workbench are implemented to decide the boundary conditions of the riser. The bottom end of the riser is assumed to be fixed to the base, x=0, y=0, z=0 and subject to the rotational constraint =free xθ ,. At the top, the riser is assumed to be connected by a hinge to a floating structure, expressed as x=0, y=free, z=0,,, with a top tension (T ) .

Fig. 6 1f vs. tension T

Fig. 7 (Color online) RMS vs. Ur

The force coefficients and the displacements of the ANSYS are displayed, as coded based on the CFX Expression Language (CEL), in the CFX Command Language (CCL) files, to be read in the CFX software.The reduced velocity is, where U is the free-stream velocity. f0is the wet modal frequency of the riser ( f0is tested in Ref. [2]), and its analytical result is easy to be obtained from the equation

Fig. 8 (Color online) Simulation results ( T=60 N, U =0.15 m/s )

where n=1,2,3…, EI is the bending stiffness, M is the mass of the PVC riser (including the internal water mass) and m is the added mass.

2.2 VIV simulation and validation of a PVC riser

The analytical and simulation (ANSYS Workbench) results of the first order frequency are in an acceptable agreement with the experiment data as shown in Fig. 6. A/ D is the non-dimensional response in the CF and IL directions. In this paper,based on the CFD (SST-SAS) /CSD two-way coupling method, the dynamic responses of the hinge-hinge constraint PVC riser with T (60 N, 260 N)are calculated. The FSI investigations for the lowmass ratio PVC riser ( m*=1) are performed and the“l(fā)ock in” range is=4.39-12.67 as depicted in Fig. 7 with a significant increase in the amplitude[2].Moreover, it is shown in Fig. 7 that eight sets of simulation results are in good agreement with the experimental data[2]. This illustrates that the precision of the two-way coupling method based on the SST-SAS turbulent model is high.

The RMS vibration amplitudes in the CF and IL directions along the riser are plotted in Figs. 8(a), 9(a).The results show that the CF vibration ampli- tudes are larger than those of the IL ones, and, however, the latter ones are as important as the CF amplitudes. The CF amplitudes at the riser's mid-point are 0.4413( T=60 N,and 0.497,respectively (see Figs. 7, 8(a) and 9(a)).

The middle part of the riser is not only affected by its own self-excited vibration but also the forced vibration. Moreover, this superposition effect contributes to the relatively large vibration amplitude in the IL, CF directions as compared to other areas along the riser. More importantly, the riser's wake exhibits a strong three-dimensional flow structure effect at a high flow velocity . Therefore, with all these factors,the mid-point trajectories of the riser may be significantly in chaos (see Figs. 8(b), 9(b)). Furthermore, the IL direction vibration should not be ignored during the simulation to evaluate the realistic motion behavior of this low-mass ratio riser.

The form of the wake at the riser middle region is mainly the vortex of the 2P, while the vortices have the form of 2S at the tip and end areas of the riser (see Figs. 8(c), 9(c)). This is primarily due to the differences in the vibration amplitude with variableformsofvortexshedding.The2Pmodevorticityintensity is comparatively large, with a relatively strong energy input, maintaining a sizeable amplitude vibration. And, in turn, the greater amplitude of the vibration will strengthen the 2P mode vorticity.Nevertheless, the 2S vorticity intensity is weak,accompanied by a lower energy, to maintain a low amplitude vibration.

Fig. 9 (Color online) Simulation results ( T =260 N, U =0.40 m/s )

Figures 8(d), 9(d) are the frequency spectrum results along the riser in the CF and IL directions,respectively. It is illustrated clearly that a large amplitude is observed in the IL direction due to the bending of the riser, and the frequency is near zero Hz.It might have no effect on the riser's fatigue damage.Along the riser, there is a region with a large vibration amplitude together with a high frequency and as a by-product it may contribute to the fatigue damage of the riser. In Figs. 8(d), 9(d), the vibration response in the CF direction of the riser's central region is particularly large, and the strain in the mid-part is also relatively large. That is, the middle region of the riser is subjected to a sizable strain with multi-frequency vibrations, therefore, the riser's middle region has fatigue problems. Figures 8(e), 9(e) show the time history of the riser's vibration amplitude in the CF direction. The red and blue contours indicate the deformation value in positive (+ Z) and negative( -Z) directions. Theriserdynamicvibrationinthe

CF direction is mainly decided by the first-order mode shape as shown in Fig. 8(e). However, Fig. 9(e) shows the CF vibration response by mixing and switching of the first and second-order mode shapes.

3. VIV simulation of 3-D riser with helical strakes

3.1 Computational conditions

A short riser instead of the full-scale PVC riser is considered in order to reduce the computational cost and to study the VIV with and without helical strakes.

For the assumed short riser, we adopt the following parameters;5, =200and the boundary condition of the short riser is set as fixedfixed. Therefore,0= / ==f U UD ReD 0.1238 Hz . Normally,/ =0.196-0.200D U when =200, where fsis the shedding frequency and/ ==0.1213 Hz-St U D St Re 0.1238 Hz . Consequently, one of the structural frequencies is close to the vortex shedding frequency.The length of the short riser is 10D. With the same D of the full-scale PVC riser for the short riser, the elastic modulus is reduced and the density of the short riser is increased to make the first wet mode frequency equal to 0.1238 Hz and the mass ratio is 10. In this? ? case, the “l(fā)ock in” occurs on the short riser at a small lock-in region.

As shown in Fig. 10, the geometric parameters of the helical strakes are the strake height h, the strake pitch p, the number of starts, and the helical strakes'surface coverages. The number of starts in the simulation is set as 1, 2 and 3, the pitch and the height are expressed as the ratios of their values to the riser diameter. In the FSI simulation, the pitch sizes are 5D, 10D and 15D, while the heights are 0.05D,0.10D and 0.20D. Moreover, the coverages of the helical strakes are 100% and 1/3 (top, middle and bottom). The helical strakes are of the same material as the short riser. As shown in Table 2, 11 numerical simulation cases are studied.

Fig. 10 (Color online) Riser fitted with helical strakes

Table 2 Study cases

3.2 Simulation results and discussions

As the flow passes over a bare riser, vortices are formed in the wake and shed away with a specific frequency. The simulation results show that the helical strakes can suppress significantly the VIV in the CF and IL directions of the risers. Figure 11(a) shows the trajectories of the vibration of the bare riser (the middle point of the riser is taken as a monitor point) at different Ur. The combined vibration of the cylinder in the IL and CF directions typically assumes a motion in the shape of “8” when =6, 7, 8 and 9. The lock-in region is in the range of =6-9to 9, where the amplitudes are higher than in other areas. Figure 11 (b) shows the trajectories of the monitor point at the middle of the riser with helical strakes (100%coverages, 3starts, p=10D , h=0.10D ). It is obvious that the vibration amplitude in the CF direction sees a distinct decrease in comparison with the results of the bare riser.

Fig. 11 (Color online) Simulation results of trajectories of the short riser's monitor point and power spectral density

Fig. 12 (Color online) Trajectories of the short riser's monitor point under different conditions

Moreover, most trajectories are straight lines because the vibration in the IL direction is significantly smaller when. To further see the dynamic behaviors of the short riser with and without helical strakes, the frequency spectrum curves are depicted in Figs. 11(c), 11(d) by power spectral density (PSD) analysis. It is clear that the main frequency of the riser with helical strakes (100%coverages, 3starts, p=10D, h=0.10D) is 0 and the sub-frequency is less than the main frequency of the riser without helical strakes. One may draw a conclusion that the mechanism of the helical strakes'VIV suppression involves changing the vortex shedding frequency of the bare riser.

Fig. 13 (Color online) Vortex core and contour

Figure 12 shows the effects of the strake height,the strake pitch, the number of starts and 1/3 coverages position on the vibrations in the IL and CF directions. The results for the bare cylinder are also included for comparison. With the same h=0.10D and the increase of the number of starts, the simulation results are depicted in Fig. 12(a). It is shown that the increase of the number of starts reduces the CF and IL vibrations and increases the bending deformation in the IL direction. It should be noted that the CF vibrations of 2 starts and 3 starts are very similar. One may observe when the strake pitch is 5D, the CF vibration is less than in the other two cases of p=10D, p=15D (see Fig. 12(b)). In addition, the vibration in the IL direction has a slight decrease with the decrease of the length of the strake pitch. However, the riser bending deformation increases with the decrease of the length of the strake pitch. Figure 12(c) illustrates the simulations in 4 cases (the bare riser, h= 0.05D, 0.10D, 0.20D and 3 starts). It is shown that the vibration suppression(in the CF direction) is more effective with h increasing.

The strakes can suppress the vibration in the IL direction. However, the drag is dominant with h increasing, which may lead to large riser bending deformation. The simulation results show thatcan suppress the vibrations in the CF and IL directions and increase the drag slightly. 1/3 coverages of helical strakes of the riser in different positions (top, middle, and bottom) are also considered as shown in Fig. 12(d). It can be found that with regard to the coverages, the top position is slightly better than the other two positions.

Figures 13(a), 13(c) shows the vortex core of the short riser with and without helical strakes. It is clear that the helical strakes can break the vortex structures into small ones. This is why the shedding frequency sees a significant reduction. The contours of the vortices and the role of the strakes for the suppression/delay of the generation of vortices are presented in Figs. 13(b), 13(d).

4. Conclusion

Hydroelastic research of the VIV characteristics of a flexible PVC riser based on the SST-SAS turbulent model and the CSD is presented. A short riser instead of the full-scale PVC riser is considered to reduce the computational cost. Then, the displacement responses of the short riser with and without helical strakes are computed, and the VIV suppression mechanism is investigated. The results show that the displacement response in the CF direction of the riser is greater than that in the IL direction, and the vibration response in the IL direction is as important as that in the CF direction.The motion of the middle section of the riser is in chaos due to the 3-D effect of the flow and the vibration in the IL direction. The vibration suppression is more effective with increasing the number of starts and the height of the helical strakes and decreasing the pitch of the strakes. From the analyses of the simulation results, it is shown that with regard to the coverages, the top position is slightly better than the other two positions. However, the drag is dominant, which may lead to a larger bending deformation of the riser in the IL direction. The mechanisms of the VIV suppression devices involve the breaking of the vortex structures and the decrease of the vortex shedding frequency.