OTC 25233-MS Fluid-Structure Interaction: Lowering Subsea Structure / Equipment in Splash Zone During Installation
D.Jia, Technip, M.Agrawal, ANSYS

Copyright 2014, Offshore Technology Conference This paper was prepared for presentation at the Offshore Technology Conference held in Houston, Texas, USA, 5–8 May 2014. This paper was selected for presentation by an OTC program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Offshore Technology Conference and are subject to correction by the author(s). The material does not necessarily reflect any position of the Offshore Technology Conference, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Offshore Technology Conference is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract mus t contain conspicuous acknowledgment of OTC copyright.

Abstract Successful installation of subsea structures and equipment is critical for offshore campaigns in development of deep-water fields. This paper presents a novel approach using Fluid-Structure Interaction (FSI) to predict wave induced motions, wave loads, dynamic stresses and deformation of subsea structure and equipments in the splash zone during installation. This approach combines transient multiphase CFD simulation including dynamic mesh motion with transient nonlinear Computational Structural Dynamics including tension forces in non-linear flexible slings. This proposed approach has been successfully implemented for lowering of a subsea manifold in splash zone during installation. This paper has many potential applications, such as, installation of manifold, subsea tree, PLET/PLEM, suction pile, pump station, or other subsea structure and equipments. In this coupled FSI approach, pressure loads on the structure due to wave slamming from CFD model is mapped to FEA model of structure-sling assembly, which provides motion and deformation to CFD model. The results clearly show the advantage of this FSI approach to capture the coupled physics of wave slamming and its interaction with the structure and subsequent motions of structure which is being lowered in the splash zone that other approaches cannot capture. Structural integrity of the subsea structure and equipment as well as the sling forces is well evaluated and predicted with this approach. Traditional approaches for prediction of the motions and loads of subsea structure/equipment during installation rely on simplified formulations or empirical equations or model test to determine the wave loads on structures. It cannot simulate wave-structure interaction, nor the dynamic stress and deformation of structure/equipment due to wave-structure interaction. The approach proposed in this paper provides a state-of-the-art FSI tool which enhances understanding wave-structure interaction in splash zone during installation. The dynamic stress obtained by using this approach can be used for quantifying fatigue damage of every component on the structure/equipment due to wave loads in splash zone during installation. Introduction Lowering subsea structures and equipment into the splash zone is one of the critical phases during offshore installation campaigns. Many installation analyses have to be performed to ensure sufficient crane capacity, sufficient clearance and accessibility, sufficient structural integrity, sufficient stability of the equipment and structures in the installation operations. Accurately simulating lifting large subsea structures and equipment and lowering them through splash zone is a very challenging task. The challenges come from the complex geometry of the subsea structure and equipment, complex flow around the structure and equipment, wave slamming and interacting with the structure and equipment. In reality, the wave and flow interact with the structure and equipment in the splash zone. This is a coupled problem of flow and the structure in transient and dynamic motion. The current practice in the industry is to simplify the problem and use assumed or calculated hydrodynamic properties, such as added mass, drag coefficient in time domain analysis in accordance with the recommendations from DNV-RP-H103 [1]. Steady-state CFD simulations of a stationary equipment or structure are usually used to predict drag coefficient and added masses on submerged structures in installation analyses to account for the complex geometry of the structure. These predicted hydrodynamic parameters are used in time domain analysis. To improve the accuracy of the simulation, one approach is to

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improve the accuracy of added mass and damping of the structures in waves and free surface. Analytic work and experiment have been performed to predict added mass and damping of structures that is submerged below free surface [2] and [3] using this approach. However, this approach still assumes the problem is a de-coupled problem. Therefore, this is a traditional approach. To better predict the forces and the behavior of subsea structures in splash zone, we developed a novel coupled approach in our previous work [4]. In that work, the time domain diffraction simulation is coupled with multiphase CFD simulation of subsea equipment/structure in splash zone. Transient CFD model with rigid body motion for the equipment/structure calculates added masses, forces and moments on the equipment/structure for diffraction analysis, while diffraction analysis calculates linear and angular velocities for CFD simulation. In this paper, we propose a novel FSI approach to solve the problem of lowering subsea structures and equipment into the splash zone. In this state-of-the-art FSI approach, the subsea structure and equipment are modeled as nonlinear deformable structures in transient CSD instead of a rigid body. Therefore, dynamic deformation and dynamic stress are obtained from the FSI simulation along with the dynamic forces and motions of the structure and solution of the waves in fluid domain. Nomenclature CFD CSD FEA FSI PLET PLEM VOF

= = = = = = =

Computational Fluid Dynamics Computational Structural Dynamics Finite Element Analysis Fluid-Structure Interaction Pipe Line End Termination Pipe Line End Manifold Volume of Fluid

Modeling of Fluid-Structure Interaction for Subsea Structures in Splash Zone This section provides the methodology for modelling and fundamental equations of CFD and CSD as well as FSI interface. Multiphase VOF Transient CFD for Fluid Domain Transient multiphase simulation was performed for the motion of manifold structure through the splash zone. Two phase (water and air) Volume of Fluid (VOF) multiphase model was used to capture the trajectory of sea surface for given wave and conditions. VOF approach can model two or more immiscible fluids by solving a single set of momentum equations and tracking the volume fraction of each of the immiscible fluids throughout the domain. The current model only focuses on the ocean hydrodynamics. The ocean waves were modeled in real time simulations. A 3D computational domain was considered, where the detailed manifold geometry was included in the model. The schematic of this computational domain is shown in the Figure 1 along with enlarged view of manifold.

Figure 1: Computaional Domain for CFD simulation

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Mesh was combination of hexahedral and tetrahedral elements. Finer grids were used near to the manifold geometry and near the sea surface (to capture the waves). Boundary layers were created on all surfaces of the manifold geometry. Figure 2 below shows mesh on middle cross sectional plane and zoomed view of mesh on the manifold surface.

Figure 2: Mesh for CFD simulation

The governing equations for CFD are based on conservation of mass, momentum, and energy which are solved using Finite Volume method. Volume of Fluid method (VOF) is used to track the interface between the fluids which are not interpenetrating. If the volume fraction of one fluid in the cell is denoted as α, then the following three conditions are possible: α = 0; the cell is empty α = 1; the cell is full 0< α < 1; the cell is partially filled and contains the interface Summation of volume fraction for all the fluids should be equal to one.

 a 1

(1)

Volume fraction equation is given as,

     u   0 t

(2)

Total continuity equation for incompressible fluid:

 u  0

(3)

A single momentum equation is solved throughout the domain, and the resulting velocity field is shared among the phases.

    u    u  u   p    T  Fb t

(4)

Here

T is the viscous stress tensor.

The properties in the total continuity and momentum equations are volume weighted averaged properties. Transient terms are discredited using Bounded second order time implicit formulation which provides better stability for multiphase flows and allows using significant larger time step size. For convective terms, volume integrals are converted to surface integral using Gauss' divergence theorem. In the volume fraction equation, face values of volume fraction used in the convection term are discretized using the second order reconstruction scheme based on slope limiters.

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Open channel wave boundary conditions were used to simulate the propagation of sea waves. A fifth order stokes wave theory was used to specify the non-linear waves. Various wave theories (Airy, Stokes and Solitary) are applicable depending on different parameters such as, Relative height H r , Ursell Number U r and Wave Steepness S r .

H h H /h Ur  h / L 2 H Sr  L Where, H is the wave height, h is the water depth and L is the wave length. Hr 

(5) (6)

(7)

The waves break when the Relative height exceeds 0.78 and Wave steepness exceeds 0.14. In shallow water regime ( h / L  0.05 ), the most significant parameter is Relative height. In deep water regime ( h / L  0.25 ), the most significant parameter is Wave steepness. Another important parameter in the whole wave regime is Ursell Number, Ur which is used to characterize the waves based on the non-linearity and shallowness. Turbulence was modeled using SST k-omega model with turbulence damping to capture fluid shearing effect at the air-water interface. A Pressure Implicit with Splitting of Operators (PISO) scheme was used for pressure-velocity coupling. Interfacial surface tensions between all the phases were specified. Simulations were conducted for the wavelength of 50m and wave height of 5m with a time period of about 8 seconds. Standard fluid properties of seawater and air were used, interfacial tension between air and water were included in the simulation. Moving Deforming Mesh Motion was used to update solid body position every time step based on linear and angular velocities. Figure 3 below shows initial location of the manifold structure along with initial wave condition.

Figure 3: Initial position of the manifold and wave (isometric and front view)

Transient Structural CSD for Structural Domain Structural domain of the subsea structure is modeled with transient nonlinear structural dynamics. For structural dynamics with the updated Lagrangian formulation in continuum mechanics, the conservation of mass, linear momentum, angular momentum, and energy are as follows:

    v  0



(8)

 v     b  0
 T



(9) (10) (11)

 e  : D    q  s  0



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

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Where

v - velocity, v - material time derivative of v ,  - Cauchy stress tensor, T D  1 [v  (v) ] - strain rate tensor,    x , b – body force per unit mass, e  csT - internal energy per unit 2



- mass density,

mass,

e - material time derivative of e , q  T - heat flux vector, s - heat source per unit mass.



The governing equations of structure are discretized using Finite Element Method. Newton–Raphson method is used for solving the resulting nonlinear momentum equations discretized in space iteratively. The equations are further discretized with respect to time. An implicit time integration method, Newmark–β time scheme is used for the solution. Figure 4 shows manifold geometry and four slings. Figure 5 shows snapshots of structural mesh on manifold and four slings. 3-D 20-Node Structural Solid element and 3-D 10-Node Tetrahedral Structural Solid element are used for modeling manifold structure. 3-D Finite Strain Link element which is suitable for cables is used for modeling the four slings. Fluid-Structure Interaction Interface Modeling The following mechanical and thermal boundary conditions are satisfied on the fluid–structure interface:

T  n f    ns , q f  qs , T f  Ts

v f  vs

(12) (13)

Here  - stress in solid, T – stress in fluid, q - heat flux, and n - unit normal vector of the interface, subscript s – solid, subscript f – fluid. The equations provide the force balance, no–slip wall conditions for the fluid, heat flux balance, and temperature balance, respectively.

Sling-1 Sling-2

Sling-3 Sling-4

Figure 4 Manifold Geometry with 4 Slings

Figure 5 Structural Domain – Mesh of Manifold and 4 Slings

Numerical Simulation and Results The proposed FSI approach was demonstrated on a manifold with mass of 58 metric ton. Transient simulations were conducted for 10 seconds to capture motion of the manifold in the waves and the flow around it when it is being lowered into the splash zone. Figure 6 to Figure 17 show the results of CFD simulation for two different times, at 7 seconds when the manifold is partially submerged in the water and at 10 seconds when manifold is fully submerged in water. Figure 6, Figure 7 and Figure 12, Figure 13 show the static pressures on manifold surface along with free surface and wave run up. The static pressure increases as the manifold goes down. The results illustrate the wave and manifold interaction in the static pressure field in a realistic way that the traditional approach cannot achieve.

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Figure 8 and Figure 14 show contour plot of water velocity on a vertical plane passing though one of the manifold pipe. They show both water outside manifold in waves and the water that flows into the manifold pipes in complex flows. Water flow rate inside the manifold pipes increases as manifold goes down. Figure 10 and Figure 16 show velocity vector plots for internal & external flows. These plots illustrate complex flow fields outside the pipes around the manifold as well as inside the pipes. While Figure 11 and Figure 17 show the velocity vectors for external flow around the manifold. These vectors plots illustrate that the flow pattern becomes more dramatic as the pressure increases, wave slams, and trapped air tends to escapes from the pipes upwards. Figure 9 and Figure 15 show contours of water volume fraction around the manifold and inside the pipes at 7 seconds and 10 seconds, respectively. These plots clearly show trapped air around the manifold in the waves as it being lowered into splash zone. These also show that air are trapped inside the pipes and mixed with the sea water that flows into the pipes. The trapped air is rising from the pipes while the manifold is being lowered and swinging in the waves. The results illustrate the realistic wave-manifold interaction in complex flows and dynamic motions. These results cannot be achieved by using the traditional approach. Figure 18 to Figure 21 show the results of FEA simulation in the structural domain. The snapshots show the stresses on the manifold in the waves and time history of total wave forces on the manifold, and dynamic sling forces when the manifold is being lowered into the splash zone. Figure 18 and Figure 19 show the von Mises stresses on the manifold at 7 seconds and 10 seconds of flow time, respectively. Dynamic stresses are obtained for all the components on the manifold. These dynamics stresses are caused by lifting and wave slamming. Lifting points and manifold piping have higher stresses as shown in the results. Figure 20 shows the dynamic forces on the four slings. Four slings have about the same tension force until before 4 seconds when the wave hits the manifold. After that the four slings move as two pairs, sling 1 and sling 2 have about the same tension while sling 3 and sling 4 have about the same tension due to the wave slamming on the manifold. This means that the manifold swings in the plane of the wave direction while it is being lowered into the splash zone until about 9 seconds. From 9 seconds to 10 seconds, sling 1 and sling 2 starts to become slack as their tension approach to almost zero at 10 seconds, while sling 3 and sling 4 tension increases and takes most of the load. Near 10 seconds, the manifold appears to have a slight twist at the sling 4 due to the wave, and tension of sling is reduced while the tension of sling 3 is increased. Figure 21 shows total forces from the wave acted on the manifold in wave direction and in vertical direction. It shows there are two peak slamming forces at near 5 seconds and near 9 seconds when the wave passes through the manifold. The second peak is heigher then the first peak because more area of manifold gets submerged into water. The negative force from the wave in wave direction from about 6 seconds to 8.5 seconds is observed. The slamming force in wave direction changes direction due to the wave-manifold interaction. In other cases, wave force could change its direction in vertical direction, such as water inundation on a platform structure after the wave impact, which is responsible for the downward vertical loading as reported by Lubeena et.al [5].

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Figure 6 Contour of Static Pressure (psi) at manifold surface at t = 7 seconds (isometric view)

Figure 7 Contour of Static Pressure (psi) at manifold surface at t = 7 seconds (Front View)

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Figure 8 Contours of Water Velocity Magnitude (m/s) on a middle vertical plane at t = 7 seconds (Front View)

Figure 9 Contours of Water Volume Fraction on middle Vertical Plane at t = 7 seconds (Front View)

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Figure 10 Water Velocity Vector – External and Internal Flows

Figure 11 Water Velocity Vector – External Flow t = 7 seconds

Figure 12 Contour of Static Pressure (psi) at manifold surface at t = 10 seconds (isometric view)

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Figure 13 Contour of Static Pressure (psi) at manifold surface at t = 10 seconds (Front View)

Figure 14 Contours of Water Velocity Magnitude (m/s) on a middle vertical plane at t = 10 seconds (Front View)

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Figure 15 Contours of Water Volume Fraction on middle Vertical Plane at t = 10 seconds (Front View)

Figure 16 Water Velocity Vectors – External and Internal Flows

Figure 17 Water Velocity Vectors – External Flow t = 10 seconds

Figure 18 Stress on Manifold t = 7 seconds

Figure 19 Stress on Manifold t = 10 seconds

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Figure 20 Time History of Maximum Forces on Slings

Figure 21 – Time History of Total Forces from Wave on Manifold Surface in Wave Direction as well in Vertical Direction

Summary and Conclusion This paper proposes a novel FSI approach for high fidelity simulation of lowering subsea structures and equipment into splash zone, and demonstrates this approach for lowering a subsea manifold into the splash zone. Wave-structure interaction is captured by this coupled FSI approach. Transient CFD in fluid domain is coupled with transient CSD in structural domain. Pressure and velocity fields of fluid are solved for the complex flows around the manifold using CFD when it is being lowered into splash zone. The pressures are mapped to the manifold in transient structural simulation by the FSI approach. The wave induced motions, wave forces on the manifold, stresses on the manifold and dynamic sling forces are solved in a more realistic way instead of relying on assumed or calculated added mass and hydrodynamic properties in the current practice in the industry. The dynamic stress on the manifold that is obtained in the simulation can be used for evaluating fatigue damage of the manifold component caused by wave and lowering process. The potential applications of this novel approach are simulations of subsea structures and equipment, such as, manifold, subsea tree, PLET/PLEM, suction pile, pump station, etc., lowering into splash zone.

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Acknowledgments The authors would like to thank Deepwater Engineering Division (Genesis, Houston) and Subsea Structures and Foundation Department of Genesis, Technip for encouraging this study and allowing this paper to be published. References
1. 2. 3. 4. DNV-RP-H103 (April 2011), Modelling and Analysis of Marine Operations. Molin B. (2001), On the added mass and damping of periodic arrays of fully or partially porous disks, J. Fluids & Structures, 15, 275290. Molin, B. and Nielsen, F.G. (2004), Heave Added Mass And Damping of a Perforated Disk below the Free Surface, 19th Int. Workshop on Water Waves and Floating Bodies, Cortona, Italy, 28-31 March 2004. D.Jia and M. Agrawal (2013), Coupled Transient CFD and Diffraction Modeling for Installation of Subsea Equipment/Structures in Splash Zone, Proceedings of the ASME 2013 32nd International Conference on Ocean, Offshore and Arctic Engineering, OMAE2013, June 9-14, 2013, Nantes, France. R. Lubeena and V. Gupta (2013), Hydrodynamic Wave Loading on Offshore Structures, Offshore Technology Conference, May 6-9, 2013, Houston TX, USA

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