Numerical Study of New Device for Passive Suppression of Vortex-Induced Vibrations in Deep Water Risers

This paper presents a three dimensional numerical simulation to investigate the effectiveness of a new passive device for vortex-induced vibrations (VIV) suppression of deep water risers based on non-continuous helical strakes in staggered arrangement with two starts. The influence of changing the geometries and design parameters, such as the pitch and shape of strakes, on the VIV was studied. The simulation had been carried out at Reynolds number 104, which satisfies the natural conditions of ocean currents. The presented design has been tested using a numerical solver using OpenFOAM platform, which had been presented and validated using number of published benchmarks. The LES – large-eddy simulation is used for turbulence modeling. The results had been compared with the published numerical and experimental works and other design based on drag coefficient. The comparison shows that the proposed geometry can suppress the VIV, if applied in deep water risers. The drag coefficient of 1.05 is considered a reduced value in the modified strakes shape with two starts and non-continuous helical strakes in staggered arrangement. The addition of strakes to the surface of a flexible cantilever was modeled to give the chance for evaluating the effect of geometry on the VIV.


Introduction
The vortex induced vibration of deep water risers is one of the most critical and important issues in the field of ocean engineering. Although many research works had been carried out along past tens of years, many research points are still open.
In deep water, where the risers are usually working, the so-called deep water current is always going on with different speeds which can generate a water flow, which could be considered as highly turbulent [1]. When these deep water currents meet the risers, the so-called vortex shedding is formed around the riser itself [2]. This phenomenon results lift force unsteady oscillation, because pressure distribution unsteady changes on the riser surface, which directly causes an unsteady oscillating motion for the riser. This unsteady oscillating motion of the riser, or any obstacle in other cases, called VIV. Such motion is very usual resulting long-term harmful effects on the riser in deep water, which can lead to riser failure and eventually an environmental disaster. When the frequency of VIV approaches the natural frequency of the structure, a resonant phenomenon called lock-in is occurring.

Literature Review
Kim et al. [3]  The effect of gap ratio on the force and added mass coefficient is weak for e/D > 2.0, but a significant effect is shown for e/D = 2.0. The study gives the chance for validation of computational work results for the same case. Xu et al. [5]  between symmetric and one-sided PTC-cylinder. They showed that the asymmetrical oscillation and the effect of selective roughness are drawn with respect to the flow speed, damping ratios and the PTC locations angle at the end. 4 The numerical solution of deep water risers using fluid-structure interaction approach had taken a considerable attention in the last years. Because of the high computing capacity needed to carry out such cases of simulation, some research papers went to simplify the regarded cases to be an elastic cantilever for the validation purposes. Di Silvio et al. [11] studied the fluid-elastic vibrations by using both mathematical modeling and experimental work. They had described the VIV as a physical phenomenon by using several mathematical methods. As a first step they had started to get the acting forces on the structure as a function of time. The vortex-origin time concept was regarded to determine the control volume on which the momentum equations will be built. The vortex-origin time is defined as the instant, in which the vortex is entering the stabilized wake. Then the fluid forces had been determined by assuming that the fluid domain is deforming in time as well as an influence of structural vibrations. It is clear that they had modeled an oscillated system. The experimental results had been analyzed and regarded to be a real application of the determined mathematical model. The experimental work had been done for both water and air as working fluids. That presented model was new at this time, because it regards the physical meaning of the wake width in controlling both the frequency and the amplitude of the alternate driving force. Tojo [12] tried to give more efficient fluid-structure interaction solver based on OpenFOAM standard solver ico-Fsi-Foam. The solver of him has actually main weak points, especially with handling the transient turbulent flows, since he had used SIMPLE algorithm to solve the fluid domain. As mentioned in the OpenFOAM user guide [13] the SIMPLE algorithm can handle the steady-state turbulent flows. The work of Habchi et al. [14] was very interesting and close to the present research paper. They presented a very robust solver for fluid-structure interaction based on OpenFOAM, which had been tested at Reynolds number of maximum 1000 which is below the natural conditions of risers environment. Yuan et al. [15] presented an alternative time domain force-decomposition model for flexible risers to predict VIV response under both steady and oscillatory flows. They showed that the VIV response under the oscillatory flows with high maximum decrement velocity needs to be studied with more related experimental facilities. Nguyen et al. [16] introduced numerically an investigation of wake-induced vibrations. Their numerical model depends on an incompressible Navier-Stokes flow solver with a hybrid detached eddy simulation approach for turbulence modelling. They found that Reynolds number has a critical impact in the response variation of amplitude and frequency of cylinders in wake-induced vibrations. Zhuang et al. [17] presented a modification of the shear-stress transport turbulence model to study the fluctuating lift and the 5 drag of the cylinder in VIV. They utilized the embedded program of OpenFoam to perform the numerical modeling of VIV of a cylinder with two degrees of freedom.
In the present study the effect of three strakes shape in addition to the pitch of the helix by further examining in reducing the VIV of a flexible circular cantilever. Based on the literature reviews, the response of continuous helical strakes is still insufficient. Therefore, the novelty of the present work depends on non-continuous helical strakes in staggered arrangement to increase the turbulence intensity in the flow field around the risers. The proposed device was designed and numerically tested to achieve the following objectives; 1. Investigation the main deficiency and advantage of not-continuous helical strakes with three starts in reducing the VIV of a flexible cylinder.
2. Comparing the proposed design with continuous helical strakes and plain risers based on the drag force coefficient.

Mathematical Modeling
In this section, the used equation and mathematical interpretation for solving fluid and solid domains as well as coupling will be presented.
The fluid flow is governed by unsteady Navier-Stocks equations for viscous incompressible fluid.
Since these equations are only valid for static meshes [18], the so-called Arbitrary Lagrangian-Eulerian mapping must be used. This kind of mapping is very common to be used in fluidstructure interaction solvers.
The mapped governing equations could be written in the following form [19]: A LES-one-equation model was used for the sub-gride scales (SGS), which solves one turbulent transport equation, usually the turbulent kinetic energy k. That eddy viscosity SGS model uses a modeled balance equation to simulate the behavior of k. 6 The kinematic eddy viscosity could be represented as follows [20]: The used large eddy simulation model is given as follows [20]: The solid domain had been solved by using the incremental strain updated Lagrangian approach.
This mathematical modeling allows strains in a good range, which is needed in the field of deep risers engineering as well as the validation study case of the present paper. This part of solver had been built as explained in the research paper of Tuković et al. [19]. The motion of an iso-thermal continuum in an arbitrary volume V bounded by a surface S is governed by the conservation laws for mass and linear momentum. The final formulation of the momentum equation, which is ready for discretization, is given as follows [21]: where ρ, n, v, vs , σ and fb are the continuum density, the outward pointing unit normal to the surface S, the velocity of the continuum, the velocity of the surface S, the Cauchy stress tensor and the resulting body force respectively.
Adaptive iterative under-relaxation and a strong coupling algorithm Aitken had been used. The coupling formulation could be written as follows [21]: This mathematical modeling had been processed based on OpenFOAM 3.0-ext [15], which namely is an open source C++ toolbox for computational mechanics. The tools of this release of OpenFOAM had been used to approximate the fluid flow and structure displacement by using the 7 finite volume discretization. Moreover, a linear interpolation scheme had been used to interpolate the cell data to face data.
The velocity-based method of Laplacian smoothing had been used for moving the mesh. This part of solver had been built based on the formulation of Laplacian smoothing in both of papers Tuković et al. [21] and Lohner et al. [22].

Solver Algorithms
This section will explain the main parts of the FSI solver, by which the cases in the present study were

Code Validation
This section discusses the numerical results when compared with the published experimental and numerical benchmarks. The validation cases were simulated under the environmental conditions to give a reasonable and fair comparison. The validation had been carried out using an experimental benchmark of a flexible vertical cylindrical cantilever shown in Figure (4). The values and geometry have been determined depending on the experiment of Franzini [7]. Two values of reduced velocity had been considered for validation. The reduced velocities of 3.69 and 6.03 had been selected for the mentioned benchmark case experiments. As mentioned, the results are compared to the experimental work of Franzini [7] for the aim of validation.

Problem statement
The considered case of a straked flexible cantilever subjected to a water cross flow has the same design and operational parameters as the validation case of a bar cantilever. The only difference between both designs is adding the strakes as a suppression device to the cantilever.
The straked cantilever has a free and a fixed end as well. The concept of the mentioned device  (5) and (6) (all dimensions in mm), which will be called "shape two", while "shape one" is a straked cylinder 9 with three starts and continuous helical restricting. The shape two is a cylinder with noncontinuous helical strakes in staggered arrangement with two starts. The strake shape designs are presented in Table (3). Figure (7) shows the geometry of the considered computational domain with boundary conditions. The upper and lower boundaries in z-direction, namely perpendicular to the Figure (7), are considered to be symmetry planes, while the zero-velocity boundary condition is considered for "walls" surfaces. The fluid is pure water with a density of 1000 kg/m3  Table (4). Where S, D, l, m * , f1 and EI are the distance between cantilever moving end and the bed of the water tank, the cantilever diameter, the cantilever length, the mass ratio m * = the mass of the oscillating body divided by the mass of displaced fluid, the first natural frequency and the bending stiffness respectively.

Mesh and discretization
A fluid domain has been divided into 641598 tetrahedral cells. The mesh near to the cylinder wall is refined for better wall treatment, at which the interaction between both domains are taking place. The mesh refinement at the interaction region aims to insure high accuracy at forces transfer, which is playing the main role in the vibrations of the elastic cylinder. The concept of meshing was to focus on the accuracy of vibration rather than downstream flow, since the save of computational resources was important. Figure (8) shows the mesh used in the staked cylinder with pitch = 15D simulation in different cross sectional views. A mesh independence test has been carried out to ensure the accuracy of results in terms of discretization error for each case.
Figures (9)(10)(11) show the mesh independence tests for the shape two, shape one and plain cylinder respectively. These mesh sizes give a small change in results after more refinement.

Straked shape one
In Figure (14

Straked shape two
In the present section, a straked shape one is modified as shown in Figure ( The drag and lift coefficients have been calculated as: where FL is the lift force, FD is the drag force, A is the reference area of the obstetrical, and S is the relevant plan area of the obstetrical. The suppression efficiency SE can be obtained by using the Eq. (11): According to the values of y/D in Lissajous curve as shown in Figure (19), the suppression efficiency of the modified strakes shape two was 88.72%. The value of y/D for bar obstacle has been taken from the experimental work of Franzini [7].

Effect of helical strakes pitch
In the present section, a straked shape one of a rigid continuous helical obstacle (shape one) is considered. The selected design parameter is the pitch of the helical shape of strakes. The pitch of strakes varied between 1D to 17D with an increment of 2D. Figures (20) and (21)  show that increasing the pitch value has reduced lift and increased drag force coefficients.

Conclusions
This paper presents a numerical simulation investigation to study the effect of new suppression device attached to a deep water risers subjected to a cross water flow at Re = 104.
The VIV effect with regard to different geometries and design parameters such as the effect of the pitch and shape of strakes are studied. The presented design has been tested using an OpenFOAM fluid-structure interaction solver, which had been presented and validated. From the present results the following points were concluded: 1. Numerical solution for suppression device of vortex-induced vibrations in deep water risers have been introduced and numerically investigated.

A numerical solver based on OpenFoam C++ platform concerned with fluid-structure
interaction problems is presented.
3. The solver validation had been done by comparing its results with published experimental and numerical results and had shown a good agreement.
4. The drag coefficient of 1.05 is considered a reduced value in the modified strakes shape two.
5. The formation of vortex shedding has been weakened as a result of adding the side vortex generators according to the modified strakes shape to design and achieved a suppression efficiency about 88.72% compared to the plain cantilever.

Latin Symbols
A area, m2 y vibration amplitude in X direction, m.
x vibration amplitude in Y direction, m.
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