Simulation of the Dynamic Motions of Complex Sub-Sea Structures in the Splash Zone during Deepwater Installations

Simulation of the Dynamic Motions of Complex Sub-Sea structures in the Splash Zone during Deepwater Installations

Tim Bunnik and Bas Buchner

MARIN (Maritime Research Institute Netherlands) Haagsteeg 2 / P.O. Box 28

6700 AA Wageningen, The Netherlands t.bunnik@MARJN.NL; b.buchner@MARIN.NIL Abstract

Existing simulation methods are not able to determine in detail the wave loads on and the motions of a complex subsea structure when it is passing through the splash zone. To determine these loads and motions, model tests are necessary. Otherwise only simplified formulations or empirical relations for added mass and damping can be used. The improved Volume Of Fluid (iVOF) method presented in

this paper is capable of predicting the behaviour of a subsea structure in the splash

zone. The

simulated flow around and through the structure looks very realistic and shows

a strong

resemblance with observations from model tests. The quantitative comparison of the load variations in the hoist wire of the subsea structure shows that the total load levels and dynamics of the subsea structure are well predicted. This good comparison shows the potential of the improved Volume Of Fluid (iVOF) method for the simulation of the behaviour of subsea structures in the splashzone.

However, significant further development is needed before long simulations in irregular waves can be carried out. At the moment, the method is limited to short runs (regular waves) because of the long simulation times required at the moment.

Introduction

For the development of deep and ultra deep fields, the safe and economical installation of subsea

equipment is of vital importance. The practically continuous swells West of Africa result in

significant motions of the installation vessels, in other areas the possible wind seas can induce significant wave loads on the subsea structure when it is lowered through the splash zone.

These subsea structures have a large variety of shapes and their shape is typically very complex, see Figure 1. Consequently, the prediction of the motions and loads during the installation is not an easy task. The state-of-the-art approach for the evaluation of such operations is based on time domain simulations of the combined installation vessel and subsea structure. However, with the existing simulation methods it is impossible to determine in detail the wave loads during the passage through the splash zone, the hydrodynamic reaction forces when the subsea structure is submerged or close to the seabed, and the resulting motions. In order to determine these loads and motions, model testsare

necessary. Otherwise only simplified formulations or empirical relations for added mass and

damping can be used.

Deift University of Technology

Ship Hydromechanics Laboratory

Library

Mekelweg 2, 2628 CD Deift

The Netherlands

The present paper presents a new methodology, which was initially developed for the simulation of sloshing in tanks and green water loading on the deck of ships (Reference [1]). This improved Volume Of Fluid (iVOF) method is able to simulate the non-linear wave loads and hydrodynamic reaction forces on moving structures in the wave zone, including the flow in and out of the structure. The total hydrodynamic loads on the structure are input to a time domain simulation method for the computation of coupled motions of a crane vessel and load. The resulting motions are again used as input to the iVOF method (prescribed motion in iVOF This closed loop enables the computation of

the subsea siriiffons, including the effects of non-linear wave loads and reaction forces. The

present paper focuses on the validation of the coupled tool. The results of model tests will be used for this purpose.

The paper first describes the improved Volume Of Fluid (iVOF) method included in the ComFLOW program and the time domain simulation method for the computation of the coupled motions of crane vessel and subsea structure (LIFSIM). Then results of simulations with a typical subsea structure in the splash zone are presented. A comparison is made with results of dedicated model tests with the same structure. The comparison gives good insight in the special capabilities of the method.

The improved Volume Of Fluid (iVOF) Method

ComFLOW is an improved Volume Of Fluid (iVOF) CDF code based on the Navier-Stokes

equations. The program has been developed by the University of GroningentRuG (Prof.dr. Arthur Veidman), initially to study the sloshing of liquid fuel in satellites. This micro-gravity environment requires an accurate and robust description of the free surface. Coupled dynamics between the sloshing fluid and the satellite were investigated as well (References [2] and [3]). In close co-operation with MARIN, this methodology was later extended to the calculation of green water loading on a fixed bow deck (Reference [4]), see Figure 2 and later to green water loading on a moving bow deck (Reference [10]). Also anti-roll tanks, including the coupling with ship motions (Reference [5]), were investigated and the wave run up on gravity based structures (Reference [9]). The Volume Of Fluid (VOF) algorithm as developed by Flirt and Nichols (see Reference [7]) is used as a basis for the fluid advection. The method solves the incompressible Navier-Stokes equations with a free-surface condition on the free boundary. In the VOF method a VOF function F (with values between 0 and 1) is used, indicating which part of the cell is filled with fluid. The VOF method reconstructs the free surface in each computational cell. This makes it suitable for the prediction of all phases of the local free surface problem.

First the mathematical and numerical model will be summarised. This will be limited to the main aspects, because the detailed numerical aspects are outside the scope of the present paper. Excellent overviews of the numerical details of the method can be found in References [2] through [4]. To distinguish between the original VOF method of Hirt and Nichols (1981) and the present method with its extensive number of modifications, the name improved-VOF (iVOF) method will be used in the rest of this paper.

Mathematical model

The incompressible Navier-Stokes equations describe the motions of a fluid in general terms. They are based on conservation of mass (Expression 1) and momentum (Expressions 2 through 4).

8uôv5w

++--=o

ax 5y az

Ou au au au 1 ap (a2u 52u a2u

+u+v---+w=---+vI +

at ax ôy ax p5x ax2 +_2J+Fx

+u+v+w=---+vI

k-F

at ox ay az pay 5x2 ay2 2)

aw Ow Ow aw 1 Op (a2z a2z a2z '

+u+v+w--=---+vI ++

j+F

at ax ay ax tOx2 ay2 2)

P=(F, F, F) is an external body force, such as gravity. With: p = pressure t time u = velocity in x-direction v = velocity in y-direction w = velocity in z-direction x = x-position y = y-position z = z-position v = kinematic viscosity p = fluid density

The Navier-Stokes equations can also be written in a shorter notation as:

Vü=O (5)

(6)

Here, contains all convective, diffusive and body forces.

Numerical model: geometry andfree surface description

The generation of a computational grid can be done in a number of ways. Basically, the following options are available:

Structured and unstructured grids

Boundary fitted and non-boundary fitted grids

In the iVOF method a structured (Cartesian) non-boundary fitted grid (not necessarily equidistant) is used. This has several advantages, related to the application of the method to the prediction of wave

loading:

Easy generation of the grid around complex structures. Finite differences are well defmed

.

A lot of research on surface tracking on orthogonal grids has been carried out.

Moving objects in the fluid can be dealt with in a similar way as fixed boundaries, without

re-gridding.

The main disadvantage of this discretisation method is the fact that the boundary and free surface are generally not aligned with the gridlines. This requires special attention in the solution method, as will

be shown below. -

-An indicator function is used (volume and edge apertures) to track the amount of flow in a cell and through a cell face:

Volume aperture: the geometry aperture Fb indicates which fraction of a cell is allowed to contain

fluid (0 Fb 1). For bodies moving through the fluid, the geometry aperture may vary in time.

The time-dependent fluid aperture F5 indicates which fraction of a cell is actually occupied by fluid and satisfies the relation 0 Fb.

Edge aperture: the edge apertures A, A, and A define the fraction of a cell surface through which fluid may flow in the x, y and z direction respectively. Obviously, these apertures are between zero and one.

Figure 3 shows a two-dimensional example with Fb=0.8 and F5=0.3.

After the apertures have been assigned to the grid cells and the cell edges, every cell is given a label to distinguish between boundary, air and fluid. Two classes of labelling exist: Geometry cell labels and fluid cell labels. The geometry labelling at each time step divides the cells into three classes: F(low)-cells All cells with Fb

B(oundary)-cells All cells adjacent to a F-cell

(e)X(ternal)-cells All remaining cells

The free-surface cell labelling is a subdivision of the F-cells. The subdivision consists of

3

subclasses:

E(mpty) cells All cells with F5=0

S('urface) cells All cells adjacent to an E-cell F'(luid)-cells All remaining F-cells

Figure 4 shows an example of geometry cell labelling and free-surface cell labelling for a wedge entering a fluid.

The discretisation of the Navier-Stokes equations is done on a staggered grid, which means that the pressure is set in the cell centres and the velocity components in the middle of the cell faces between two cells. This is shown in a 2-dimensional case in Figure5.

The Navier-Stokes equations are discretised in time according to the explicit first order Forward Euler method as follows:

v.un+l=0

(7)

ün+l_ün

+v' =i:

(8)

At

t

is the time step and n+l denote the new and old time level. The conservation of mass in

Expression (7) and the pressure in Expression (8) are treated on the new time level n+ 1 to assure that the new is divergence-free (no loss of fluid).

The spatial discretisation will now be explained using the computational cell shown in Figure 6.

pripn X2)i

pp1iJj the

tes of the

lls and acentraLdiscretisationis_used.Jn_the cell with centre w the discretised equation becomes:

n+I n+1 n+1 n+1

UC

h h

The momentum Expression (8) is applied in the centres of the cell faces, thus the discretisation in point C becomes:

ni-I n n+I n+I

U _{_UC+Pe}

h

In the detailed work of Gerrits (Reference [3]) other aspects of the numerical method are described in

detail, such as:

Discretisation of R'

Discretisation near the free-surface In- and outflow discretisation Pressure Poisson equation

Free surface reconstruction and displacement Use of the Courant-Friedrichs-Levy (CFL) number Calculation of forces and moments

Summarising, the following functionalities are presently available in ComFLOW (see References [1] through [10]):

Calculation of the fluid motion by solving the incompressible Navier-Stokes equations. One type of fluid flow is considered, with a void where no fluid is present.

- Possibility to model an arbitrary number of fixed objects in the fluid. The objects are defined piecewise linearly.

Options to use no-slip or free-slip boundary conditions at the solid boundaries. At the free surface continuity of tangential and normal stresses (including capillary effects) is prescribed. Inflow and outflow boundary conditions for fluid velocities and/or pressures can be defmed.

The fluid simulations are carried out on a Cartesian grid with user-defined stretching, fixed in time and space.

-

To distinguish between the different characters of grid cells, the cells are labelled. The

Navier-Stokes equations are discretised and solved in cells that contain fluid. The free-surface

displacement is described by the Volume Of Fluid method with a local height function.

-

The generation of waves by specifying fluid velocities at the inflow boundary of the fluid

domain. Either linear waves or fifth-order Stokes waves can be selected.

- Several types of absorbing boundary conditions at the outflow boundaries. - Arbitrary motions of 1 object.

The possibility to use the velocity field from a (de-coupled) linear diffraction theory. Linear diffraction theory is used to compute body motions and fluid velocities which are then used in

ComFLOW to prescribe the body motions and fluid velocities on the inflow and oufflow

boundaries.

It should however be realised that, although the Navier Stokes equation are discretised, the IVOF method is not able to predict viscous flow effects. These type of predictions require extremeli small grid cells to capture boundary layers and to reduce numerical damping far below the viscous damping level. This cannot be accomplished at the moment due to restrictions on memory and computational time.

An extension of the method with a 2' phase is presently being implemented to study for example fluid-air interaction. This can be an important aspect during wave impact.

Time domain simulation of motions of offshore structures

The iVOF method has the possibility to have 1 moving object in the flow. The motions of this object have to be prescribed and are not computed by the iVOF method itself The iVOF method has however the possibility to return the hydrodynamic forces on an object in the flow. By sending this

information to a time domain simulation tool for the computation of motions, the motions of the object can be computed. The motions can be returned and prescribed to the iVOF method and the position of the object in the flow can be updated. This means that 2 applications (iVOF and the motion analysis tool) have to run simultaneously and share infonnation during run-time. This has been sketched below:

hydrodynamic loads

Integration of equation of motion

F=Ma

The time-domain analysis tool LIFSIM has been used to establish the coupling with the iVOF method. LIFSIM solves the equation of motion of coupled, multi-body systems. Arbitrary external forces can be defmed. This makes it possible to add the hydrodynamic forces from the iVOF method to the equation of motion. LIFSIM has been especially developed to simulate lifting operations. The following items are modelled:

Motions of the crane vessel

Hydrodynamic loads on the crane vessel by means of linear diffraction analysis Motions of the load (subsea structure in this case)

Hydrodynamic loads on the subsea structure by means of the iVOF method

Hoisting arrangement and hoisting forces on the crane vessel and the subsea structure Shielding effects between the crane vessel and the subsea structure are not modelled.

Simulation and model test results

The coupled iVOF method has been applied to compute the behaviour of a subsea structure in the splash zone. Specific model tests were carried out to validate the simulations. Figure 7 shows the model of the subsea structure in the model basin. It was build at scale 1:40 and its main dimensions are given in Figure 8 and Table 1. Two series of tests were carried out:

Tests with the subsea structure captive in a force and moment frame to determine the wave exciting loads in 6 degrees of freedom.

Tests with the subsea structure free-hanging in slings.

The hoist wire was connected to a fixed point in the basin. The crane vessel was therefore not modelled.

The results of test series A were published in reference 6.

For the present paper the results for Series B with the free-hanging model in waves are used. Figure 7 shows the model in the basin during these tests. Three different positions of the subsea structure were tested:

Subsea structure just above water. Subsea structure half submerged. Subsea structure completely submerged.

Figure 9 shows several examples of the complex flow in and around the subsea structure in waves observed during the tests. This flow is characterised by aspects such as:

Added mass and damping effects of the water under, above and in the subsea structure Buoyancy effects in the waves

Impact loads against horizontal plates in the subsea structure Flow through openings in the top and bottom of the subsea structure

Complex flow through the equipment of the subsea structure Water captured temporarely in certain parts of the subsea structure

In the free-hanging situation during the lift, this can result in unwanted oscillations, slack lines and larger vertical loads in the slings than expected.

The numerical model of the subsea structure is shown in Figure 11. This model was built with basic shapes such as beams, boxes and cylinders. Only one half of the structure was modelled because of symmetiy reasoi. The computational domain contained a total number of 181x50x78 ( 705900)

cells.

Figure .10 shows a number of snapshots of the flow around and the motion of the subsea structure in different phases during a simulation in waves. The subsea structure is just above the calm water level. The flow around and through the structure looks very realistic. This also holds for the resulting motions. A strong resemblance with the observation from the model tests is found.

Figure 12 shows the simulated and measured hoisting wire forces in case the structure is just above water. The simulations were limited to 2 wave oscillations because the calculation is extremely time

consuming.

Figure 13 shows a number of snapshots of the flow around and the motion of the subsea structure in different phases during a simulation in waves. The subsea structure is completely submerged in this case. Again, the flow looks very realistic.

The comparison between the simulation and model test is reasonably good. The total load levels are reasonably predicted.

Conclusions

The improved Volume Of Fluid (iVOF) method presented in the present paper is a potential

candidate for the better numerical prediction of the behaviour of a subsea structure in the splash zone. Based on the initial comparison between dedicated model tests and simulations the following conclusions seem justified:

The simulated flow around and through the structure looks very realistic and shows a strong resemblance with observations from model tests.

- The quantitative comparison of the force in the hoist wire shows that the forces on and the dynamic motions of the subsea structure agree reasonably well. The typical hoist wire force variations are captured. The observed differences between the simulation and the measurement are also due to start-up effects in the simulation: Due to the time consuming VOF method, the simulations lasted only 2 wave periods.

This good initial comparison shows the potential of the improved Volumes Of Fluid (iVOF) method for the simulation of the behaviour of subsea structures in the splash zone.

References

Buchner, B.; "Green Water on Ship-type Offshore Structures", PhD thesis Delfi University of Technology, 2002.

Gerrits, J., Loots, G.E., Fekken, G. and Veldman, A.E.P.; "Liquid Sloshing on Earth and in Space", In: Moving Boundaries V (Sarler, B., Brebbia, C.A. and Power, H. Eds.) WIT Press, Southampton, pp 111-120, 1999.

Gerrits, J.; "Dynamics of Liquid-Filled Spacecraft", Numerical Simulation of Coupled Solid-Liquid Dynamics, PhD thesis, RuG, 2001.

Fekken, G., Veidman, A.E.P. and Bucimer, B.; "Simulation of Green Water Flow Using the Navier-Stokes Equations", Seventh International Conference on Numerical Ship

Hydromechanics, Nantes, 1999.

Daalen, E.F.G. van, Kleefsman, K.M.T., Gerrits, J., Luth, H.R. and Veldman, A.E.P.; "Anti Roll Tank Simulations with a Volume Of Fluid (VOF) based Navier-Stokes Solver", 23rd Symposium on Naval Hydrodynamics, Val de Reuil, September 2000.

chnerR,Bup, T;

"A

Ne SJ _!

Mcfr cJ

llaf

Sb&ructures",

DOT conference, 2003.

Hirt, C.W. and Nichols, B.D.; "Volume Of Fluid (VOF) Method for the Dynamics of Free Boundaries", Journal of Computational Physics, 39, pp 201-225, 1981.

Kleefsman, K.M.T., Fekken, G., Veidman, A.E.P., Bunnik, T., Buchner, B. and Iwanowski, B.; "Prediction of green water and wave impact loading using a Navier-Stokes Based Simulation Tool", OMAE conference, Oslo, 2002.

Loots,E. and Buchner, B.; "Wave run up as important hydrodynamic issue for gravity based structures", OMAE conference, Vancouver, 2004.

Kjeefsman, T., Loots, E., Veldman, A., Buchner, B., Bunnik, T. and Falkenberg, E.; "The numerical simulation of green water loading including the vessel motions and the incoming wave field", OMAE conference, Halkidiki, 2005.

Table 1: Main dimensions and weight distribution of the subsea structure (1:40 scale)

Figure 1: Examples of different complex subsea structures in the splash zone

Figure 2: Example of earlier application of the method: green water on the deck of an FPSO

M 266 t

KG 4.96m

Kc,c 2.68m

K), 4.96 m

y

Figure 3: Two-dimensional example of a grid cell using apertures

Figure 4: Geometry cell labelling (left) and free-surface cell labelling (right) for a wedge entering a fluid

'p

V

:u

.P

V

uP

Figure 5: Location of the pressure and velocity components in the staggered grid

B F F F F F B F F F F K B F4 F F F K

V F

_F F B

4

F F F B F F F E E E B E E £ S S S

VF'

F F' F F F F F F F F' F' F F' F F' O.2

Fb-FS= 0.5

F5 = 0.3

A=0.5

Figure 6: Spatial discretisation cell, using compass indication for cell phases

-Figure 7: Subsea structure in hoisting wires during tests in waves in the model basin

a EU

Y

x

Figure 8: Main dimensions of the subsea structure model (dimensions in m full-scale, scale model 1:40)

-5

.io

Figure 11: Numerical model of subsea structure. only 1 halve is modelled. 4000 3500 F 3000 2500 2000 1500 0 ₁₀₀₀ 500 0 measured

- -

computed 0 2 4 6 time (s]

Figure 12: Simulated (pink) and measured (blue) force in the hoist-wire with -the subsea structure just above the calm water level

trnte s 80 seooncfs