The impact of extreme wave events on a fixed multicolumn offshore platform
Nagi Abdussamie
1
, Roberto Ojeda
1
, Yuriy Drobyshevski
1
, Giles Thomas
2
, Walid Amin
1
1
Australian Maritime College Search (AMCS), University of Tasmania
Launceston, Tasmania, Australia
2
Department of Mechanical Engineering, University College London (UCL)
London, UK
ABSTRACT
This paper presents an experimental and numerical investigation into
the magnitude and distribution of the hydrodynamic loads affecting a
fixed, multicolumn offshore platform (rigidly mounted TLP) when
subjected to extreme wave events. All wave load components,
including wave-in-deck slamming pressures, were predicted using a
commercial CFD code STAR-CCM+ and compared against
experimental measurements. Slamming pressures were calculated using
both data obtained locally at discrete points and globally averaged over
the whole exposed area of the deck. In all simulated cases, the deck
area exposed to a wave slamming event was found to be in contact with
a water-air mixture with a significant proportion of air phase. It was
concluded that the slamming pressure data for the exposed area
provided better insights into the pressure changes due to air
compressibility and its content.
KEYWORDS: Offshore platforms; Wave-in-deck loads; slamming
pressure.
INTRODUCTION
When a large wave (extreme wave event) impacts the deck of an
offshore structure, significant wave-in-deck and slamming loads occur.
These slamming events could generate major global and local loads
which can cause structural damage to the deck, generating large forces
in the tendons and risers and adversely affect the motions of floating
structure such as Tension Leg Platforms (TLPs) and Semi-
submersibles. The problem of wave-in-deck impact on a floating
platform can be quite complicated because of the contributions of many
parameters such as the platform offset, set-down and tendon dynamics
(API, 2010).
The simplest way to investigate wave-in-deck impact problems is a
simplified rigid model of the deck structure idealised as a flat plate or
as a box-shape (Baarholm, 2009, Bhat, 1994, Scharnke and Hennig,
2015). Current design practices (API, 2007, DNV, 2010, ISO, 2007)
recommend a number of theoretical approaches such as the
global/silhouette approach “simplified loading model” (API, 2007) and
a detailed component approach, e.g., the momentum method (Kaplan et
al., 1995) to evaluate the wave-in-deck loads of fixed platforms. Since
such engineering approaches rely on the potential flow theory to
calculate the change of fluid momentum during the wave impact, using
wave kinematics of a non-disturbed wave field, the effects of
diffraction and entrapped air are neglected. Scharnke et al. (2014)
found that the recommended simplified loading model (API, 2007,
DNV, 2010) underestimates the measured horizontal wave-in-deck
loads on a fixed deck of jacket platform in both regular and irregular
wave tests. Even though the simplified loading model used wave
kinematics obtained by Stokes fifth order wave theory, the
underestimation of the loads was severe, particularly in irregular waves
(Scharnke et al., 2014). The momentum method was also found to
underestimate the magnitude of the wave-in-deck forces on a fixed
horizontal deck subjected to unidirectional regular waves (Abdussamie
et al., 2014b). A more realistic investigation into the wave-in-deck
problems shall include the effect of substructures on the magnitude and
distributions of the deck loads. Scharnke and Hennig (2015) conducted
an experimental study by attaching a fixed box-type deck structure to a
square column. The authors concluded that the column presence
significantly increases the magnitude of global vertical forces and local
pressures.
The current engineering knowledge, required to accurately predict the
resulting global response of a floating structure due to a wave-in-deck
impact event, remains limited. This fact is reflected in the very limited
number of papers reporting on model tests of typical multi-column
floaters currently available in the open literature. Johannessen et al.
(2006) and Hennig et al. (2011) investigated the dynamic air gap, wave
loads and floating platform response under extreme wave conditions.
Both investigations reported that a wave-in-deck event can lead to an
additional extreme response mechanism and a step change in the
extreme loading magnitude in tendons. It must be noted that complete
and detailed results of these types of experiments are usually subjected
to project confidentiality requirements and are therefore not available in
the public domain.
Model tests are arguably the best approach for estimating wave-in-deck
loads (Scharnke et al., 2014). However, model testing is costly, time-
consuming and involves a number of drawbacks such as scaling effects.
It is therefore not surprising that the use of computational fluid
dynamics (CFD) based methods for calculating wave induced loads on
offshore structures has received increasing amount of attention in later
years. Commonly used commercial codes such as STAR-CCM+ and
ANSYS FLUENT are available for modelling and solving wave-in-
deck impact problems using the volume of fluid (VOF) method to
capture free-surface hydrodynamic flows (CD-Adapco, 2012, Fluent,
2009). There is a large body of work on CFD investigations of wave
impact loads on fixed deck structures (Birknes-Berg and Johannessen,
2015, Iwanowski et al., 2014, Ren and Wang, 2004). However, very
little work on fixed with columns and floating structures has been
reported to date (Iwanowski et al., 2009, Lee et al., 2014).
The scope of the present investigation is to predict the global and local
wave loads of a fixed multicolumn offshore platform (rigidly mounted
TLP) at a model scale of 1:125 due to extreme wave events
corresponding to a 10,000-year cyclonic condition (H
s
= 22.125 m, T
p
=
17.0 s at full scale). Regular wave tests with H = 1.13 – 1.36 H
s
were
conducted in the Australian Maritime College (AMC) towing tank.
Using data from repeated runs, uncertainty tests of wave elevations,
global wave impact forces and slamming pressures at the deck
underside were performed. In addition, the commercial CFD code
STAR-CCM+ was used to investigate the characteristics of
unidirectional regular wave impact on the model. The numerical results
were then validated against the measurements acquired in model tests.
EXPERIMENTAL SETUP
The TLP model used in this investigation was tested as a rigid body
(Fixed multicolumn TLP). The model had two main modules namely a
hull module (columns and pontoons) and a topside deck module. The
hull module was represented by four circular columns and four square
pontoons with their scaled dimensions derived from the SNORRE-A
TLP. The model was fixed by attaching it to a rigid beam mounted
across the AMC towing tank. All details of model’s dimensions and
instrumentation, as well as the experimental setup, can be found in the
open literature (Abdussamie et al., 2016a, Abdussamie et al., 2016b).
The model had a static deck clearance (freeboard), a
0
, of 120 mm at the
operating draft. The effect of deck clearance reduction on the
magnitude of global and local wave impact loads was investigated by
reducing the original a
0
by 10 mm. A total of seven conditions were
examined experimentally and numerically with the TLP model being
fixed-in-place (Table 1).
Table 1: Test conditions at wave period T = 1.52 s (17.0 s full scale).
Test
condition
Full scale
Model scale (1:125)
a
0
(m)
H (m)
a
0
(mm)
H (mm)
1
15.00
25.00
120
200
2
15.00
27.50
120
220
3
15.00
28.88
120
231
4
15.00
30.00
120
240
5
13.75
25.00
110
200
6
13.75
27.50
110
220
7
13.75
30.00
110
240
The natural frequency of the testing assembly in the x- and z-directions
was obtained from free decay tests in water as 7.33 Hz and 15.00 Hz,
respectively.
EXPERIMENTAL DATA ANALYSIS
Condition 2 (H = 220 mm, T = 1.52 s and a
0
= 120 mm) is presented to
illustrate the good repeatability of the towing tank test. Fig. 1 shows the
surface wave elevations measured at approximately 700 mm in front of
the deck leading edge, in four repeated runs. Good qualitative
repeatability can be seen among the four runs for both wave probes. A
coefficient of variation (CV = σ/mean) in crest height of approximately
3.6%. Lower values of CV (≈ 2.0 %) were obtained during wave
calibration process; without the model being in the tank.
Fig. 1: Time history of wave surface elevation at the front of the model
measured in four repeated runs for condition 2.
The global forces in the x- and z-direction, denoted by F
x
and F
z
, are
shown in Figs. 2 and 3, respectively. Force peaks of the horizontal
force, F
x
, were obtained for both directions as defined by F
x
(+) and F
x
(-
), whilst the upward and downward components of F
z
are denoted as
F
z
(+) and F
z
(-). By analysing the time history of F
x
and F
z
using Fast
Fourier Transform (FFT), the dynamic response of the model was
found to contaminate the load cell signal response in the z-direction,
whereas a minimal effect of such was observed in the x-direction. Table
2 summarises the peaks of force components where a large CV was
obtained for F
z
, particularly in the downward direction which can be
attributed to the contribution of the structural dynamic response.
Fig. 2: Simultaneous measurements in four repeated runs for condition
2: wave elevation at 100 from the deck LE; wave impact horizontal
force, F
x
(bottom).
13 13.2 13.4 13.6 13.8 14 14.2 14.4 14.6 14.8 15
-200
-100
0
100
200
Elevation [mm]
13 13.2 13.4 13.6 13.8 14 14.2 14.4 14.6 14.8 15
-200
-100
0
100
200
Time [s]
Horizontal force, F
x
[N]
Run 1
Run 2
Run 3
Run 4
a
0
= 120 mm
F
x
(+)
F
x
(-)
Fig. 3: Simultaneous measurements in four repeated runs for condition
2: wave elevation at the deck mid-span (top); wave impact vertical
force, F
z
(bottom).
Table 2: Force maxima (+) and minima (-) of F
x
and F
z
extracted from
four repeated runs for condition 2.
Run id
Force [N]
F
x
(+)
F
x
(-)
F
z
(+)
F
z
(-)
1
113.1
-117.1
85.4
-24.8
2
111.8
-117.3
77.9
-17.92
3
110.8
-111.8
80.8
-11.4
4
113.0
-115.4
109.8
-22.6
Mean
112.2
-115.4
88.5
-19.2
σ
1.1
2.5
14.5
5.9
CV
1%
2%
16%
31%
The time history of the corresponding wave-in-deck impact pressures
measured around the aft columns at pressure transducers PT#15 and
PT#16 are presented in Fig. 4. Overall, a large variation in pressure
measurements amongst repeated runs having almost identical wave
condition can be appreciated. The values of slamming pressure, P
i
,
extracted from the associated runs are summarised in Table 3 which
demonstrated high variability.
Fig. 4: Wave-in-deck pressures around the aft column measured in four
repeated runs for condition 2: PT#15 (top); PT#16 (bottom).
Table 3: Slamming pressures, P
i
, (kPa) measured in four repeated runs
around the aft column for condition 2.
PT#
Run 1
Run 2
Run 3
Run 4
Mean
σ
CV
15
3.1
4.3
3.1
5.2
3.9
1.0
26%
16
1.7
3.2
1.9
1.8
2.2
0.7
33%
CFD MODELLING
A commercial CFD code STAR-CCM+ (Release 10) developed by
CD-adapco was used for simulating the physics of the wave-in-deck
problem. In this work, since the CFD results were validated against
model test results at a small scale, laminar flow was assumed for all
numerical simulations. Based on isothermal and laminar flow
assumptions, a system of partial differential equations governing the
conservation of mass and momentum of a fluid was solved numerically
using the finite volume method (Versteeg and Malalasekera, 2007). The
VOF model implemented in the code was used for capturing the
interface between two immiscible fluids, hereafter water and air phases.
This implies that the trapped air involved in the wave-in-deck problem
was accounted for. Both phases were modelled as an incompressible
fluid unless otherwise mentioned. The physical properties (e.g.,
density) of water and air were expressed as a volume fraction of each
fluid during solving the process. Further theoretical details of the
numerical method can be found in the STAR-CCM+ user guide (CD-
Adapco, 2012). For the present numerical study, two different
computational domains were created namely: a wave generation
domain and a wave-structure interaction domain for the fixed TLP
model. In the later, an overset mesh was used to allow for modelling
the rigid body motions. The CFD analyses were conducted as per the
following procedure:
1- Wave generation (similar to the wave calibration conducted
in model tests) – a numerical wave tank (NWT) or wave
generation domain was created without the TLP model being
present in order to investigate wave quality generated against
the theoretical wave elevations.
2- Wave-structure interaction (similar to the wave impact tests
conducted in towing tank) – the TLP model was setup in the
domain and subjected to unidirectional regular waves tested
in step 1.
A 3D trimmed mesh with 1 cell layer into the y-direction was generated
to investigate the numerical quality of the generated waves. A
numerical domain was bounded by x ∈ [0, 22], y ∈ [0, 0.1] and z ∈ [0,
2] m. The length of the domain (22 m) was approximately 6λ where λ
is the wavelength (λ = 3.61 m). The mesh domain was divided into
several parts in the vertical z-direction including “water”, “free surface”
and “air” zones. The authors have previously identified that
approximately 20 – 30 cells per wave height and 80 cells per
wavelength are essential for the accurate prediction of wave
propagation in the free surface part (Abdussamie et al., 2014a).
Moreover, a time step of 0.001 s was found to be adequate to capture
the dynamics of a sharp wave free surface and to maintain optimal
solution using the High-Resolution Interface Capturing (HRIC) scheme
(Abdussamie et al., 2014a). It should be noted that the used CFD solver
automatically changes the scheme used for transport volume fraction
based upon the upper and lower limits of the Courant number. Pure
HRIC scheme is used when the local Courant number is below the
lower limit (0.5), whereas a pure first-order upwind scheme is
automatically activated for Courant number higher than the upper limit
(1.0). Both schemes are blended for intermediate values (CD-Adapco,
13 13.2 13.4 13.6 13.8 14 14.2 14.4 14.6 14.8 15
-200
-100
0
100
200
Elevation [mm]
13 13.2 13.4 13.6 13.8 14 14.2 14.4 14.6 14.8 15
-100
-50
0
50
100
150
Time [s]
Vertical force, F
z
[N]
Run 1
Run 2
Run 3
Run 4
a
0
= 120 mm
F
z
(+)
F
z
(-)
14 14.05 14.1 14.15 14.2 14.25 14.3 14.35 14.4 14.45 14.5
-2
0
2
4
6
Pressure [kPa]
14 14.05 14.1 14.15 14.2 14.25 14.3 14.35 14.4 14.45 14.5
-1
0
1
2
3
4
Time [s]
Pressure [kPa]
Run 1
Run 2
Run 3
Run 4
slam pressure, P
i
2012).
At the initial condition (time = 0.0), the wave profile was fully
developed in the zone x = 0 to x = 2λ. This minimised the time required
for incoming waves to reach x = 10.8 m which was selected to be the
location of the model’s centroid during the simulations of wave-
structure interaction. Wave damping was applied over the last 2λ
“damping zone” before the downstream boundary (x = 22.0 m). The
method proposed by Choi and Yoon (2009) is implemented into the
code for damping the vertical motion of the free surface.
In order to minimise reflected waves from the far-field boundaries,
which can corrupt the numerical solution, the model’s centroid was set
at x = 10.8 m (≈ 3λ upstream and 3λ downstream). Same mesh and time
settings used during wave generation was employed during wave
impact tests except (i) domain size in y-direction increased from 0.1 m
to 1.775 m (half of the width of AMC towing tank). (ii) mesh
refinement was created around the model in order to capture fine flow
details such that a surface mesh of 3.125 mm was applied on the entire
body surfaces.
In order to accurately predict wave impact forces and pressures acting
on the deck underside of the model, a uniform surface mesh with
different levels of refinement was examined throughout the deck
underside area (608 mm × 304 mm). Table 4 summarises three levels
of mesh refinement conducted in this study.
Table 4: Mesh size levels at the deck underside tested.
Level
Mesh size at the
model’s surfaces
(mm)
Mesh size at the
deck underside
(mm)
Total no. of
cells
1
3.125
3.125
2.33 × 10
6
2
3.125
1.5625
2.69 × 10
6
3
3.125
0.78125
4.10 × 10
6
Air density and its pressure derivative were defined by means of user-
defined field functions derived from the following equations:
𝜌
𝑎𝑖𝑟
= 𝜌
𝑎𝑖𝑟
′
+
𝑝
𝐶
𝑎𝑖𝑟
2
(1)
𝑑𝜌
𝑎𝑖𝑟
𝑑𝑝
=
1
𝐶
𝑎𝑖𝑟
2
(2)
where 𝜌
𝑎𝑖𝑟
′
= 1.18415 kg/m
3
is the incompressible air density, C = 331
m/s is the sound speed in air, and p is pressure.
In order to model the desired wave characteristics, an incoming wave
with appropriate height and wave period was specified at the inflow
domain boundary (x = 0.0). At this boundary of the domain, a velocity
inlet condition was specified, where the velocity field and volume
fraction of water and air were defined using the Stokes fifth order wave
theory (Fenton, 1985). Hydrostatic pressure boundary condition was
assigned at the top of the tank (z = 2.0 m) and its end at x = 22.0 m. No-
slip boundary condition was used on the tank bottom (z = 0), tank side
(y = 1.775 m) and the TLP model boundary surfaces. Whilst the other
side of the domain (y = 0) was set with a symmetry boundary condition.
In the simulations of floating conditions, the model was released 50
time steps after starting the solution (CD-Adapco, 2012).
The second-order discretisation of unsteady terms in momentum
equations and HRIC scheme for the solution of the volume fraction
equations was adopted in all simulations. The pressure-velocity
coupling was performed by the SIMPLE (Semi-Implicit Method for
Pressure-Linked Equations) algorithm. Second order discretisation for
convective terms of VOF model. These settings were selected as a
reasonable compromise between accuracy and computational time.
Wave surface elevations were obtained at a volume fraction of the
water of 0.5 along the computational domain with and without the
model in place. As an example, Fig. 5 shows the wave elevation for
condition 1 compared with the theoretical one. The theoretical wave
was approximated by Stokes fifth order without the TLP model being
in place. The effect of the model’s presence on the approaching waves
can be seen at times 3T and 6T where a slight phase shift started to
form between the predicted and theoretical wave elevations far away
from the inlet boundary condition. The damping zone, starting from x =
14.8 m, was also affected by the simulation time. It should be noted
that it is difficult to simulate waves with zero transport losses
numerically due to relaxed spatial and temporal discretisation (Saripilli
et al., 2014).
Fig. 5: Comparisons between the CFD (dashed line) and theoretical
(solid line) surface elevation of propagating waves along the
computational domain for condition 1 at: t = T (top); t = 3T (middle); t
= 6T (bottom).
The effect of mesh refinement on the magnitude of wave impact loads
was also tested. Fig. 6 shows the time history of F
x
and F
z
acting on the
fixed model for condition 2 (H = 220 mm, T = 1.52 s, a
0
= 120 mm).
CFD does not show oscillations in the force time histories, confirming
the oscillations in the model test are due to the structural response.
Fig. 6: Time history of the global wave impact forces predicted by CFD
using different levels for mesh size for condition 2: horizontal force, F
x
(top); vertical force, F
z
.
0 2 4 6 8 10 12 14 16 18 20 22
-0.5
0
0.5
1
/H [mm]
CFD
Theory
0 2 4 6 8 10 12 14 16 18 20 22
-0.5
0
0.5
1
/H [-]
0 2 4 6 8 10 12 14 16 18 20 22
-0.5
0
0.5
1
x [m]
/H [-]
AFT column CL
Damping zone starts
FWD column CL
RESULTS AND DISCUSSION
Raw experimental data and CFD results are discussed and compared
below. In all CFD simulations, the reference mesh (level 1) was used
when evaluating the global wave impact loads. Local wave impact
loads at the deck underside were captured using the mesh refinement at
level 2.
Fig. 7 shows the CFD wave elevation and the measured one (H = 231
m, T = 1.52 s). The theoretical wave elevation based on Stokes 5th
order is also given. It is shown that CFD predicts well both the
amplitude and the frequency of the incoming waves.
Fig. 7: Wave calibration of incident wave elevation (H = 231 m, T =
1.52 s).
The time history of global wave impact forces acting on the fixed TLP
model associated with test condition 1 obtained by CFD and
experiments is presented in Fig. 8. Good agreement between the CFD
predictions and measured F
x
in all conditions with a mean relative error
of 4% for the F
x
(+) and 4% for the F
x
(-).
Fig. 8: Time history of global wave impact forces obtained by CFD
(dashed line) and experiments (solid line) for condition 1.
The effect of air gap reduction on the global forces was examined
numerically and experimentally by reducing the original deck
clearance; a
0
by 10 mm (1.25 m full-scale). It was found that the
reduction of deck clearance has no a large effect on the force
magnitudes in both x- and z-directions. Fig. 9 shows an example of this
finding for conditions 2 and 6 (H = 220 mm, T = 1.52 s).
CFD models enabled the wave impact force component acting on the
topside deck (wave-in-deck force) to be isolated from the total
hydrodynamic wave force acting on the TLP model. In most cases, the
magnitude of the horizontal wave-in-deck forces (F
xd
) was found to be
much smaller than the vertical wave-in-deck forces (F
zd
). However, the
effect of deck clearance reduction on the force magnitudes was found
to be more pronounced in F
xd
than in F
zd
. For instance, at time = 11.0 s
(Figs. 10 and 11) an additional water reflection and the column
overtopping at lower deck clearance (a
0
= 110 mm), which might
decrease the amount of wave energy reaching into the underdeck
region, can be seen.
Fig. 9: The effect of deck clearance a
0
on the horizontal force acting on
the TLP model: condition 2 (left) and condition 6 (right).
Fig. 10: The effect of deck clearance on wave forces acting on topside
deck: condition 2 (top) and condition 6 (bottom).
a
0
= 120 mm
a
0
= 110 mm
Fig. 11: Snapshots showing the interaction between a large wave and
the TLP model at t = 11.0 s: condition 2 (left) and condition 6 (right).
4 6 8 10 12 14 16 18 20
-200
-100
0
100
200
Horizontal force, F
x
[N]
4 6 8 10 12 14 16 18 20
-50
0
50
100
Time [s]
Vertical force,F
z
[N]
Measured
CFD
