-0000mi W41'"64 ---
-
---
14
Hydrodynamic Analysis of the Offshore Floating
Nuclear Power Plant
by
Matthew Brian Strother
@
B.S., University of California, Berkeley (2005)
Submitted to the Department of Mechanical Engineering
ARCHIVES
in partial fulfillment of the requirements for the degrees of
MASsACHsETT
rINSTITUTE
Naval Engineer
C/F
.CA
HNULolGY
and
Master of Science in Engineering and Management
JUL 3 0 2015
at the
LIBRARIES
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2015
Massachusetts Institute of Technology 2015. All rights reserved.
Author ..........................
Signature redacted
Department of Mechanical Engineering
May 18, 2015
Certified by....................
.. Signature redacted
Uit-
Jacopo VBuongiorno
)4hip
C ertified by ...............................
Professor
sr/or
Signature redacted
1Q 1
P.~
L
r
Accepted by................
Signature redacted
Sig nature redactedor
at Hale
ogram Director
A ccepted by .................. : ........................................
David E. Hardt
Chairman, Department Committee on Graduate Theses
2
Hydrodynamic Analysis of the Offshore Floating Nuclear
Power Plant
by
Matthew Brian Strother
Submitted to the Department of Mechanical Engineering
on May 18, 2015, in partial fulfillment of the
requirements for the degrees of
Naval Engineer
and
Master of Science in Engineering and Management
Abstract
Hydrodynamic analysis of two models of the Offshore Floating Nuclear Plant [91 was
conducted. The OFNP-300 and the OFNP-1100 were both exposed to computer simulated sea states in the computer program OrcaFlex: first to sets of monochromatic
waves, each consisting of a single frequency and waveheight, and then to Bretschneider and JONSWAP spectra simulating 100-year storms in, respectively, the Gulf of
Mexico and the North Sea. Hydrodynamic coefficients for these simulations were
obtained using a separate computer program, WAMIT. Both models exhibited satisfactory performance in both heave and pitch. An alternative design of the OFNP-300
was developed and similarly analyzed in attempt to further improve hydrodynamic
performance.
A catenary mooring system was designed and analyzed for both plant models. The
number of chains and the length of each were selected to ensure the mooring systems
would withstand, with sufficient margins of safety, the maximum tension produced in
a 100-year storm. This analysis was conducted both with all the designed mooring
lines intact, and with the worst-case line broken. A lifecycle cost analysis of various
mooring systems was conducted in order to minimize the cost of the mooring system
while maintaining adequate performance.
Thesis Supervisor: Jacopo Buongiorno
Title: Associate Professor
3
Thesis Supervisor: Paul Sclavounos
Title: Professor
Thesis Supervisor: Pat Hale
Title: SDM Program Director
4
Acknowledgments
The entire OFNP Design Team, especially Jake Jurewicz and Professor Jacopo Buongiorno.
Yu Ma (Emily), for her invaluable assistance with WAMIT.
Professor Paul Sclavounos, without whose guidance I could not have finished.
Mr. Pat Hale, my thesis reader for SDM.
The US Navy, and ultimately the American taxpayers, for funding my education,
both undergraduate and graduate.
5
6
Contents
14
1.2
Hydrostatic Theory . . . .
15
1.3
Hydrodynamic Theory . .
17
1.3.1
Added Mass . . . .
17
1.3.2
Damping . . . . . .
20
1.3.3
Sea Spectra . . . .
21
1.3.4
Platform Response to the Ocean Environment
23
.
.
.
.
.
.
Study Objectives . . . . .
Analysis Procedure.....
24
1.5
OFNP Models . . . . . . .
26
1.5.1
OFNP-300 . . . . .
26
1.5.2
OFNP-1100.....
28
1.5.3
OFNP-Coke.....
30
.
.
1.4
35
Analysis of the OFNP
Hydrostatics . . . .
. . . . . . . . . . .
35
2.2
Hydrodynamics . .
. . . . . . . . . . .
38
. .
38
.
.
2.1
2.2.2
Monochromatic Wave Analysis
50
2.2.3
Spectral Analysis . . . . . . . . . . . . . . . . . . . . . . . . .
55
.
Hydrodynamic Parameters .
.
2.2.1
59
Mooring System
3.1
Mooring System Criteria . . . . . . . . . . . . . . . . . . . . . . . .
.
3
1.1
.
2
13
Introduction
.
1
7
59
Environmental Forces . . . . . . . . . . . . . .
. . . . . . . . . .
59
3.3
Mooring System Characteristics . . . . . . . .
. . . . . . . . . .
61
3.4
Mooring Line Tension . . . . . . . . . . . . . .
. . . . . . . . . .
62
3.5
Platform Natural Frequency in Surge . . . . .
. . . . . . . . . .
65
3.6
Orcaflex Simulation . . . . . . . . . . . . . . .
. . . . . . . . . .
66
3.7
Mooring System Cost . . . . . . . . . . . . . .
. . . . . . . . . .
70
3.8
Conclusions
. . . . . . . . . . . . . . . . . . .
. . . . . . . . . .
72
3.9
Future Work . . . . . . . . . . . . . . . . . . .
. . . . . . . . . .
73
3.9.1
Balancing Risk and Cost . . . . . . . .
. . . . . . . . . .
73
3.9.2
Additional Mooring System Scenarios .
. . . . . . . . . .
74
3.9.3
Establishing Plant Limitations . . . . .
. . . . . . . . . .
76
.
.
.
.
.
.
.
.
.
.
.
3.2
79
A Data Validation
.........................
A.1 WAMIT Damping Data ......
79
A.2 WAMIT Added Mass Data ........................
81
A.3 Orcaflex Heave Data ...........................
82
8
List of Figures
Hydrostatic parameters . . . . . . . . . . . . .
18
1-2
Sample Bretschneider and JONSWAP Spectra. H, = 4m TP = 10sec.
22
1-3
OFNP-300 . . . . . . . . . . . . . . . . . . . .
. . . . . . .
27
1-4
OFNP-1100, cross-section view
. . . . . . . .
. . . . . . .
29
1-5
OFNP-1100, cross-section view
. . . . . . . .
. . . . . . .
29
1-6
OFNP-Coke, Normal Operation . . . . . . . .
. . . . . . .
30
1-7
OFNP-Coke, Transport Condition . . . . . . .
. . . . . . .
31
1-8
OFNP-Coke, Maintenance Condition
. . . . .
. . . . . . .
32
2-1
Added Mass in Surge by Wave Frequency . . .
. . . . . . .
40
2-2
Added Mass in Surge by Wave Period . . . . .
. . . . . . .
40
2-3
Added Mass in Heave by Wave Frequency
. . . . . . .
41
2-4
Added Mass in Heave by Wave Period.....
. . . . . . .
41
2-5
Added Mass in Pitch by Wave Frequency . . .
. . . . . . .
42
2-6
Added Mass in Pitch by Wave Period . . . . .
. . . . . . .
42
2-7
Damping in Surge by Wave Frequency.....
. . . . . . .
43
2-8
Damping in Surge by Wave Period
. . . . . . .
43
2-9
Damping in Heave by Wave Frequency.....
. . . . . . .
44
2-10 Damping in Heave by Wave Period . . . . . .
. . . . . . .
44
2-11 Damping in Pitch by Wave Frequency . . . . .
. . . . . . .
45
2-12 Damping in Pitch by Wave Period . . . . . . .
. . . . . . .
45
2-13 Wave Force in Surge by Wave Frequency
. . . . . . .
46
. . . . . . .
46
.
.
.
.
.
.
.
.
.
.
.
.
1-1
.
.
.
.
.
.
. . . . . .
.
2-14 Wave Force in Surge by Wave Period . . . . .
9
47
2-15 Wave Force in Heave by Wave Frequency
. . . . . .
47
. . . . . . .
. . . . . .
48
. . . . . . . . .
. . . . . .
48
. . .
. . . . . .
53
. . . . .
. . . . . .
53
2-21 Plants' Responses in Pitch . . . . . . . . . . . . . . .
. . . . . .
54
2-22 Plants' Responses in Pitch by Wave Period . . . . . .
. . . . . .
54
2-23 Current Velocity vs. Water Depth . . . . . . . . . . .
. . . . . .
56
.
2-19 Plants' Responses in Heave by Wave Frequency
.
.
.
2-20 Plants' Responses in Heave by Wave Period
.
2-18 Wave Force in Pitch by Wave Period
.
2-17 Wave Force in Pitch by Wave Frequency
.
.
2-16 Wave Force in Heave by Wave Period . . . . . . . . .
Worst Case Analysis: Direction of Seas . . . . . . . .
62
3-2
Mooring Line Tension D=140mm, chain length=733m
63
3-3
Chain Link Dimensions . . . . . . . . . . . . . . . . .
64
A-1 Validation of WAMIT Damping Data . . . . . . . . .
80
A-2 Validation of WAMIT Added Mass Data . . . . . . .
81
Validation of Orcaflex Heave Data . . . . . . . . . . .
83
A-3
.
.
.
.
.
.
3-1
10
List of Tables
1.1
Form of Added Mass Matrix for Cylindrical Buoy . . . . . . . . . . .
19
1.2
Form of Damping Matrix for Cylindrical Buoy . . . . . . . . . . . . .
20
1.3
OFNP models' Key Parameters
. . . . . . . . . . . . . . . . . . . . .
33
2.1
OFNP models' Hydrostatic Figures . . . . . . . . . . . . . . . . . . .
36
2.2
OFNP models' Performances in 100-Year Storms . . . . . . . . . . . .
57
3.1
Wave Force Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . .
60
3.2
OFNP model's Performance in 100-Year Storms with mooring systems
D= 150 Chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3
69
OFNP model's Performance in 100-Year Storms with mooring systems
D=120 Grade R5 Chain . . . . . . . . . . . . . . . . . . . . . . . . .
70
3.4
Change in Natural Period in Pitch with Mooring Systems . . . . . . .
70
3.5
Mean and Standard Deviation of Pitch Angle (Degrees) . . . . . . . .
71
3.6
Maximum Tension (kN) with Environment Element Removal . . . . .
71
3.7
Mooring System Costs (Millions of $) . . . . . . . . . . . . . . . . . .
72
11
12
Chapter 1
Introduction
In the world today, the threat of global warming looms large over the power-generation
industry.
While demand for energy continues to increase, so does economic and
political pressure to generate power in ways less detrimental to the environment than
traditional methods such as gas- or coal-fired power plants.
Nuclear power is ideally suited to meet these demands, but comes with its own set
of drawbacks, including the threats of contamination in cases of severe accidents
with fuel damage, high construction costs, and, in some countries, a negative public
perception created by the high-profile incidents at Chernobyl, Three Mile Island, and
Fukushima.
The Offshore Floating Nuclear Plant (OFNP) concept [9] overcomes these drawbacks,
presenting the possibility of clean affordable energy to meet growing demand worldwide. The OFNP's position several miles offshore renders it invulnerable to damage
resultant from tsunamis and earthquakes and eliminates the threat of land contamination in the event of a nuclear accident. Positioning the containment vessel beneath
sea level eliminates the possibility of meltdown by providing an infinite heat sink.
Lastly, because the OFNP would be constructed modularly in shipyards rather than
on-site in the manner of terrestrial plants, the capital costs of land-procurement and
13
construction would be respectively eliminated and substantially reduced.
1.1
Study Objectives
This thesis examines the hydrostatic and hydrodynamic behavior of the OFNP, and
seeks to answer the following questions:
1. Is the OFNP hydrostatically stable?
This is the starting point for any naval architecture project. The platform must
float and remain stable in an upright position in all operating conditions.
2. Is the hydrodynamic behavior of the OFNP in 100 year storms within acceptable
limits?
In order to prevent damage to the reactor while operating, the platform roll
angle must be kept under 10 degrees. This is based on preliminary analysis
of the plant and further research is needed to refine this limit.
In order to
minimize the probability of operators becoming seasick, vertical accelerations
must be kept below 0.2 times gravitational acceleration.
3. How must the mooring system of the OFNP be designed to ensure the plant
will remain in place during 100 year storms storms?
The mooring system must be able to withstand the environmental forces applied
to the platform in the most extreme circumstances, while keeping tension in each
cable within acceptable limits and ensuring the natural frequency in surge of
the platform is outside of frequency bands excitable by ocean storms. While
strength of the mooring system is the main concern, it must also be designed
to minimize cost.
14
1.2
Hydrostatic Theory
There are two key questions when analyzing the hydrostatics of a floating body. First,
does it float? And second, does it float upright?
For a body to float, its weight must be equal to its buoyancy. Buoyancy is the weight
of water displaced by the floating body. This relationship is expressed mathematically
in equation 1.1.
mg = pgV
(1.1)
Where:
m is mass of the body
g is gravitational acceleration
p is the density of seawater
V is the underwater volume of the body
If a body is sufficiently submerged that equation 1.1 is true, the body is said to be in
hydrostatic equilibrium. At that point, the distance from the surface of the water to
the deepest submerged point on the body is defined as the body's static draft. The
volume of the body above the water line is the body's reserve buoyancy, and, when
multiplied by p, represents the amount of weight that could be added to the body
and have the body remain afloat.
In determining whether a body will float upright, the key figure is metacentric height
(GM). GM is defined as "the vertical distance measured on the ship's vertical centerline between the metacenter and the center of gravity." [6]. The metacenter is defined
as "the intersection of the vertical through the center of buoyancy of an inclined
body or ship with the upright vertical when the angle of inclination approaches zero
as a limit." [6]. In other words, it is the imaginary point about which the center of
buoyancy rotates as the body undergoes small roll angles.
In order for a body to be stable, to remain floating upright when perturbed from
15
equilibrium, the metacenter must be above the center of gravity, making GM a positive
distance.
If GM is positive, the body's buoyant and gravitational forces create a
righting moment when the body experiences a roll angle, causing the body to return
to an upright position.
If, on the other hand, the center of gravity is above the
metacenter, making GM a negative distance, the buoyant and gravitational forces
create an upsetting moment when the body experiences a roll angle. In this situation,
the body would continue to roll and would capsize rather than returning to an upright
position. GM is calculated using equation 1.2.
GM = KB+ BM - KG
(1.2)
Where:
KB is the distance along the vessel axis from the keel to the center of buoyancy,
and is calculated using equation 1.3
BM is the distance along the vessel axis from the center of buoyancy to the
metacenter, and is calculated using equation 1.4
KG is the distance along the vessel axis from the keel to the vessel's center of
gravity.
1 pT
B=V
AzzJo (1.3)
KT
Where:
V is submerged volume.
T the vessel's draft
z is height above the keel
A, is the area of the waterplane at height z
BM
Where:
16
(1.4)
I is the horizontal area moment of inertia at the waterline. In naval architecture
practice, this value is usually approximated using Simpson's Rule. However, in the case of a platform for which the waterplane area is a regular
geometric shape, such as a circle as with the OFNP, it can be calculated
using equation 1.5.
I
JjY2dA
(1.5)
In the case of a circle, this works out to equation 1.6.
(1.6)
I
4
Where:
r is the circle's radius
GM, KB, BM, and KG are all illustrated in Figure 1-1.
The larger GM is, the more stable the body is in water and the more quickly it will
recover from a roll. However, if GM is too large and the recovery is too rapid, personnel comfort can become a concern and seasickness can result. In naval architecture
practice, the ratio of
GM/B,
where B is the ship's beam (or diameter in the case of
circular buoys like the OFNP), is kept between 0.09 and 0.122.
1.3
1.3.1
Hydrodynamic Theory
Added Mass
When an object fully or partially immersed in a fluid accelerates, the fluid is forced to
move around it. The objects acceleration creates a high pressure area ahead of it and
17
L
M
_____
-
_____
G
_________
15
I,
B
B'
K
Figure 1-1: Hydrostatic parameters
a low pressure area behind, which cause the fluid to flow from high to low pressure.
As a result of this fluid motion, the acceleration of an object that would be obtained
using Newton's classic F = ma is greater than the actual acceleration observed,
unless one rigorously accounts for the additional force on the object created by the
aforementioned high and low pressure areas.
To allow for mathematical modeling
of submerged and partially submerged objects without requiring the computational
power required by such accounting, fluid mechanics uses the concept of added mass,
the field of hydrodynamics modifies Newton's Law to equation 1.7
F =(m + ma)a
(1.7)
Where:
F is the net force not the object, not including pressure fields created by the
object's acceleration
m is the object's mass
18
ma is the object's added mass
a is the object's acceleration
Added mass exists for all six degrees of freedom, and also includes coupling terms,
which specify added mass in one direction created by the object's acceleration in
another. In order to analyze the motion of a submerged or floating object, the full
6x6 added mass matrix is required. The expected form of the added mass matrix for
a cylindrical buoy like the OFNP is shown in Table 1.1.
Table 1.1: Form of Added Mass Matrix for Cylindrical Buoy
Surge
a (M)
0
0
0
b (ML)
0
Sway
0
a (M)
0
-b (ML)
0
0
Heave
0
0
c (M)
0
0
0
Roll
0
-b (ML)
0
d (ML 2 )
0
0
Pitch
b (ML)
0
0
0
d (ML2 )
0
Yaw
0
0
0
0
0
e (ML2
)
Surge
Sway
Heave
Roll
Pitch
Yaw
The nautical terms for each motion are indicated outside of the matrix.
Surge is
motion forward and aft, sway to port and starboard, and heave up and down. Roll is
rotation about the fore-aft axis, pitch about the port-starboard axis, and yaw about
the vertical axis. The rows indicate the direction in which added mass is created, and
the columns indicate in direction in which the object accelerated to create said added
mass. For non-zero values, the units are indicated as well. M indicates mass, and L
length. For example, a unit acceleration in surge creates a kg of added mass in surge
and b kg-in of added mass in pitch. Each value in the matrix is referred to as
Aab,
where a indicates the row and b is the column. Several entries in the matrix equal
others (e.g. Al
= A 2 2 ) due to the axi-symmetry of the platform. Entries with the
same value but opposite sign (e.g. A 1 5 = -A
24 )
are due to axi-symmetry combined
with the sign convention of the motion matrix, and do not indicate negative added
mass. While only All, A 2 2 , and A 3 3 have units of mass, each entry is nonetheless
usually referred to as added mass.
An object's added mass depends on several factors, including the object's geometry,
19
proximity to the ocean surface and floor, and the frequency of oscillation (if any).
While added mass for simple objects can be estimated analytically, in modern naval
architecture practice, added mass is usually determined through computer simulations.
1.3.2
Damping
Damping is energy removed from an oscillating object due to the object's velocity,
and takes two main forms. The first is friction damping, in which the object's motion
relative to its environment creates heat, thereby reducing the energy of the object's
oscillation. The second is radiation damping, in which the object creates waves that
carry energy away from the object. These waves can take many forms, including
surface, sound, or electromagnetic.
In the case of buoys oscillating in the ocean,
radiation damping if much more significant than friction, and the waves created are
physical waves on the surface of the ocean.
As with added mass, damping exists in all six degrees of freedom and has coupling
terms. Also similarly to added mass, damping depends on geometry, proximity to the
ocean surface and floor, and oscillation frequency, and is likewise usually determined
through computer simulation. While added mass is proportional to the object's acceleration, however, damping is proportional to the object's velocity, either translational
or rotational as the case may be. The form and units of the damping matrix for an
axi-symmetric floating cylinder is shown is Table 1.2. F represents force, and T time.
Table 1.2: Form of Damping Matrix for Cylindrical Buoy
Surge
Sway
Heave
Roll
Pitch
Yaw
Surge
Sway
Heave
Roll
Pitch
Yaw
f((Lr')
0
0
0
g((/j))
0
0
0
g ((r /T))
0
-F(rT)
0
0
0
-g ((FL))
0
0
k (Lr)
0
0
0
0
0
0
0
0
f
F(T)
0
h (T
-)
0
0
0
0
20
k (
r)
0
m ((rT)
1.3.3
Sea Spectra
The elevation of the sea at any particular point and moment can be expressed as
the sum of the instantaneous waveheights of all the waves present at that point and
time. The waves present at a given time are described by a sea spectrum. The most
commonly used types of sea spectra are the Bretschneider and JONSWAP spectra.
The Bretschneider spectrum is used to simulate a fully developed sea. A sea is said
to be fully developed when the fetch, or distance over which the wind blows and thus
the sea develops, is "unlimited," meaning large enough that the rate at which the
wind imparts energy to the waves is equal to the rate at which the waves dissipate
energy through viscosity and breaking [10}. The JONSWAP spectrum, on the other
hand, is used to simulate seas in areas where fetch is limited, and therefore the seas
are not fully developed (the wind is imparting energy to the water faster than the
waves dissipate it). The JONSWAP spectrum was specifically developed for the North
Sea, where storms develop over relatively short distances. A sample of each of these
spectra is shown in Figure 1-2.
The y-axis in Figure 1-2 represents energy per square meter. Because the waves at
various frequencies combine linearly, the total wave energy per unit area of the ocean
surface is equal to the sum of the energies per unit area of the waves in each discrete
frequency band. The energy per unit area of these frequency bands can be expressed
using equation 1.8 [10], and the total energy per unit area can be expressed using
equation 1.9.
0 o(1.8)
E, =
Ell
Eot =
n=O
Where:
Ett is the total wave energy per unit area
21
(1.9)
Sample Bretschneider and JONSWAP Spectra
6
Bretschneider
__JONSWAP
U
CD
C3
C
9)
0)
N
0
0
0.2
1.4
1.2
1
0.8
0.6
Frequency (radians/second)
0.4
1.6
1.8
2
Figure 1-2: Sample Bretschneider and JONSWAP Spectra. Hs = 4m Tp = 10sec
E, is average energy per unit area of waves in the nih frequency range.
p is the density of seawater
g is gravitational acceleration
(no is the height above or below mean sea level of the ocean as a result of a
wave at in the nth frequency range.
It is this energy, divided by pg, that is represented by a wave spectrum. More precisely,
the area under the curve in Figure 1-2 between any two points on the x-axis represents
the energy of waves between those two frequencies per unit area of ocean surface.
The Bretschneider and JONSWAP spectra can be respectively by equations 1.10
and 1.11. These equations are mathematical approximations to Laplace transforms
of autocorrelations of the statistically expected values of ocean surface height data
obtained through observation.
SBs(w) =
5
-5
W4
22
-5w4
H3
(1.10)
Where:
2
SBS(w) is the Bretschneider spectrum, and has units of
w is angular frequency
wn is peak angular frequency, defined as the modal angular frequency in the
spectrum
H1 t is the significant waveheight, defined as the average waveheight of the highest A of all waves in the spectrum.
ag 2
-5w4
(1.11)
= W5 e 4w47"
SJsMw
Where:
Sjs(w) is the JONSWAP spectrum, and has units of
2
a, -y, and b are nondimensional values that can be approximated by equations 1.12, 1.13, and 1.14 respectively. [8]
g is gravitational acceleration
4ir3 H2
a
(1.12)
=1/3
9 2T1
Where:
T, is the zero crossing period, which is related to the peak frequency by equation 1.15
0.0027
)
7(1 -
e
b
0
1.3.4
(1.14)
5
2wr
Wm = -
(1.13)
+ y
O. 8 +
T P r R 8 9+
(1.15)
Platform Response to the Ocean Environment
When the slope of incident waves is sufficiently shallow(i.e. the waves are not breaking
or nearly breaking) and the responses of the vessel are sufficiently small, linear wave
23
theory can be used to model the vessel's response. [4J.
For waves at a given frequency, the platform's response to the waves is proportional
to the waveheight.
The magnitude of this response varies with frequency and is
dependent on several factors, including the proximity of the wave frequency to the
platform's natural frequency, the vessel's added mass and damping coefficient at that
frequency, and the Response Amplitude Operator (RAO) of the platform's interaction
with the wave, which defines how much force or moment the wave imparts on the
vessel per unit of waveheight.
1.4
Analysis Procedure
The hydrostatic and hydrodynamic analysis of a platform consists of five basic steps.
1. Geometry and Mass
The geometry of the platform ultimately determines how it will respond to the
ocean environment.
Therefore, the geometry of the platform must be estab-
lished before any analysis can begin. In the case of the OFNP, the geometric
parameters which must be specified are the radius and length of the various
cylinders comprising the platform and the water depth in which it is expected
to operate.
The mass and the distribution thereof within the platform is also of critical importance. The overall mass of the platform determines its static draft, while the
distribution of the mass determines the platform's KG. The weight distribution
also determines the platform's mass moments of inertia, which figure into the
equations of motion as described below.
2. Hydrostatic Analysis
Once the geometry and weight distribution are known, the next step is to de-
24
termine whether the platform is stable in all conditions and evaluate its ability
to right itself when exposed to high winds.
3. Hydrodynamic Parameters
After the platform's hydrostatic stability is assured, the next step is to determine
the added mass, damping, and RAOs of the platform. These values depend on
the platform's geometry and draft, as well as the water depth and vary with
wave frequency.
4. Monochromatic Wave Analysis
While monochromatic waves do not exist is the ocean, it is a necessary step
to analyze the platform's response to them, as doing so allows for validation
of later analytic results and provides incite into the nature of the platform's
behavior in the ocean environment.
The platform's response to monochromatic waves, in both heave and pitch, can
be estimated using the equations of motion, equations 1.16 and 1.17 respectively.
(m + A 33 )
(15 + A 5 )Q 5
=
3
= Mg - pgV - C333 - B 33
(GM +
BMtan 2 g
2
2
3
+ X 3A
) sin (O)A - B5 5Q 5 + X5 A
(1.16)
(1.17)
Where:
3 is heave acceleration
C33 is the heave restoring coefficient, and is calculated using equation 1.18
3 is heave velocity
X 3 is the heave RAO
A is wave amplitude
I is the platform's mass moment of inertia in pitch
Q 5 is pitch angular acceleration
# is pitch angle
A is displacement
Q 5 is pitch angular velocity
25
X 5 is the pitch RAO
C 33 =
pgS
(1.18)
Where:
S is waterplane area
In equation 1.17, the term GM sin (q)V accounts for the horizontal shift in
the position of the center of buoyancy resultant from the body's roll, and is
significant at any roll angle. The term BMRtn
sin (q)V accounts for the vertical
shift in the center of buoyancy, and is significant at roll angles above 10 degrees.
5. Ocean Spectral Analysis The last step is to analyze the platforms response
to the ocean wave spectrum. In linear theory, the platform's response to the
ocean spectrum would be a linear combination of its responses to monochromatic waves multiplied by their energy levels specified in the ocean spectrum.
However, in reality, non-linearities complicate this analysis and thus spectral
analysis is usually performed through scale models or through computer simulation. After this step is complete, the final results can be compared to the
evaluation criteria and the quality of the design can be determined.
1.5
OFNP Models
Analysis was conducted on three models of the OFNP, each of which is introduced
below.
1.5.1
OFNP-300
The OFNP-300 is built around a small modular reactor (SMR) with an electric power
rating of around 300MW, such as the Westinghouse Small Modular Reactor. With
26
detail below.
1.5.2
OFNP-1100
The OFNP-1100 was designed after and is a scaled-up version of the OFNP-300, and
thus is expected to achieve greater economies of scale. It is designed to house the
Westinghouse AP1000, a much larger-capacity reactor with electric power rating of
about 1100 MW, and already certified by the U.S. Nuclear Regulatory Commission
(NRC). The containment vessel on the OFNP-1100 is much larger than that on the
OFNP-300, thus the OFNP-1100 has a deeper draft in addition to a wider diameter.
The skirt volume of the OFNP-1100 is not sufficient to decrease the draft as much
as necessary when flooded, and therefore of floodable volumes are designed into the
central portion of the platform as well. Cross-section views of the OFNP-1100 are
shown in Figure 1-4 and Figure 1-5. The OFNP-1100's key parameters are presented
in Table 1.3.
28
Figure 1-4: OFNP-1100, cross-section view
Figure 1-5: OFNP-1100, cross-section view
29
this design, the OFNP leverages the SMR's advantages of low capital investment and
easy manufacturability. A diagram of the OFNP-300 is shown in Figure 1-3, and its
key parameters are presented in Table 1.3.
Helipad
Figure 1-3: OFNP-300
The skirt on the OFNP-300 serves two functions. The first is to allow the platform
to be transported aboard a heavy-lift ship, while still allowing for the containment
vessel to be well beneath the waterline, which is necessary to protect the containment
in the unlikely event of a deep-draft ship accidentally or deliberately colliding with
the platform. With the skirt empty, the draft of the OFNP-300 is approximately 15
meters, shallow enough to be lifted and transported by a large heavy-lift ship. Such
transportation would be necessary after the platform is initially constructed in order
to get it to the area for which it is to generate electricity, as well as for moving the
platform back to the shipyard for major overhauls and ultimately for decommissioning. When the skirt is flooded with seawater, the platform's draft increases to that
listed in Table 1.3, which is its normal operating condition. The second function of
the skirt is to improve hydrodynamic performance, which will be discussed in greater
27
1.5.3
OFNP-Coke
The OFNP-Coke is so named due to its resemblance to a soda bottle floating upright
in the water. This concept was created as a modification to the OFNP-300 design
to explore the limits of hydrodynamic performance by decreasing the waterplane
area and increasing
GM/B.
At the present time, the design of OFNP-Coke is much
less developed than those of OFNP-300 and OFNP-1100. A simple diagram of the
OFNP-Coke in its normal operating condition is presented in Figure 1-6.
20m
Figure 1-6: OFNP-Coke, Normal Operation
In the design of OFNP-Coke, the size and shape of the containment vessel and surrounding freshwater flooded volume, shown in gray on Figure 1-6, remain unchanged
from the OFNP-300. Further, the amount of usable volume, shown in red, outside of
the containment remains unchanged; it merely changes shape. Specifically, the diameter increases and the height decreases while keeping volume constant. The "chimney"
above the main part of the platform, shown in yellow, would be used primarily as an
access trunk to the upper deck.
30
While the volume of the OFNP-Coke is similar to that of the OFNP-300, more of the
OFNP-Coke is submerged. In order to achieve this, a layer of iron-ore ballast, shown
in black, is included beneath the containment vessel. This would be pumped on after
the plant initially reaches its destination, and then jettisoned in order to deballast
once the plant is ready to return to the shipyard. With neither the iron-ore ballast
nor the seawater ballast, shown in light blue, aboard, the OFNP-Coke can, like the
OFNP-300, achieve a sufficiently low draft for transport by a large heavy-lift vessel.
The transport condition of the OFNP-Coke is illustrated in Figure 1-7.
20M
44.4m
47.3m
Figure 1-7: OFNP-Coke, Transport Condition
While the OFNP-300 and OFNP-1100 had two conditions, those of normal operation
and of transport, the OFNP-Coke added a third: maintenance. In the OFNP-300, the
turbine is located directly below the upper deck and is accessible by the crane on the
deck. This is necessary in order to perform major maintenance on the turbine while
deployed. The turbine sector of the OFNP-Coke would also be located directly below
the main deck, however in this case that area is submerged in normal operation. In
order to access the turbine, therefore, the plant would be deballasted by pumping out
31
flooded seawater until the main deck is sufficiently above the waterline to conduct the
desired maintenance. The maintenance condition of the OFNP-Coke is illustrated in
Figure 1-8.
Figure 1-8: OFNP-Coke, Maintenance Condition
32
Table 1.3: OFNP models' Key Parameters
Parameter
Lightship Displacement (tonnes)
Full Load Displacement (tonnes)
Diameter at waterline (meters)
Draft (meters)
Skirt Diameter (meters)
OFNP-Coke
65,500
222,130
OFNP-300
34,873
115,520
OFNP-1100
145,591
376,410
45
75
48.6
68.1
71.65
75
106
75
47.3
20
Skirt Height (meters)
12.5
15
Height above waterline (meters)
22.5
31.9
Production Capacity (MW)
300
1100
300
Natural period in heave (seconds)
Natural period in pitch (seconds)
24.5
32.7
25.9
51.3
74.5
46.2
33
20
34
Chapter 2
Analysis of the OFNP
2.1
Hydrostatics
Key hydrostatic figures each design condition of each OFNP design are presented in
Table 2.1.
In addition, figures are presented for the "transient condition." This is
the moment immediately after the top of the skirt submerges during ballasting or
immediately before it surfaces during deballasting. The platform will be least stable
at the transient condition because KB(equation 1.3) will be low due to the platform
being only partially submerged , KG will be high because the low-lying ballast has
not been fully added, and most importantly BM(equation 1.4) will be low due to the
decrease in moment of inertia as the waterplane area suddenly decreases . These three
factors combine to produce lowest GM(equation 1.2) the platform will experience in
any condition.
GM/B
is not a concern at the transient condition because ballasting
and deballasting evolutions are not long enough to induce seasickness.
They are,
however, long enough to capsize the platform if an instability exists.
Each OFNP model is stable in all operating conditions. However,
GM/B
is outside of
common practice in all cases except for the OFNP-300 in normal operation. This is
not a large concern for the transport conditions, as the platforms will only be free-
35
Table 2.1: OFNP models' Hydrostatic Figures
OFNP-Coke
OFNP-300
OFNP-1100
16.0
4.4
0.098
30.2
3.1
0.041
20.5
.4
0.22
28.2
21.3
0.47
35.8
15.9
0.21
19.75
11.8
0.57
KG (meters)
GM (meters)
GM/B (dimensionless)
NA
NA
NA
NA
NA
NA
19.8
10.6
0.14U
Transient
KG (meters)
GM (meters)
18.8
-8.9
38.5
-19.2
20.1
10.3
Parameter
Normal Operation
KG (meters)
GM(meters)
GM/B (dimensionless)
Transport
KG (meters)
GM (meters)
GM/B(dimensionless)
Maintenance
1
floating in this condition for a brief time. It is also not a concern for OFNP-Coke in
the maintenance condition because this condition is intended only for craning major
components of the platform, which would only be done in calm conditions.
GM/B
is,
however, of concern in the normal operating conditions. In the case of OFNP-1100,
GM/B in the normal operating condition is lower than standard practice, indicating
that the platform will tend to recover from rolls very slowly. This is acceptable in the
OFNP-1100 because in all except the most extreme weather conditions, the magnitude
of rolls experienced by the platform will be very small and thus the time to recover to
equilibrium from rolls is not a large concern.
GM/B
in the normal operating condition
of OFNP-Coke is very high, indicating recovery from rolls will be very rapid, greatly
increasing the risk of personnel becoming seasick. This is a significant concern and a
major drawback to that design.
Also of concern are the negative values for GM in the transient condition for OFNP300 and OFNP-1100.
This indicates the platforms are unstable in this state and
would likely capsize during ballasting and deballasting. One method for solving this
problem is to artificially increase the waterplane area during ballasting and deballasting. This could be done at a minimal cost by manufacturing a set of plastic docks to
36
fit around the platform, extending from the outside of the main platform to the skirt
radius. These docks would be transported with the platform aboard the heavy-lift
vessel and would be positioned on top of the skirt prior to beginning the ballasting
evolution. The docks would remain floating as the platform submerged, thus artificially increasing the waterplane area and adding stability throughout the evolution.
The docks would then return to port with the heavy-lift vessel. This would allow
the platform to safely complete the ballasting and deballasting evolutions without
modifying the current design.
The problem of instability during ballasting and deballasting could also potentially
be solved by temporarily shifting weight to low in the platform prior to the evolution,
lowering the platforms center of gravity, and increasing GM. Shifting sufficient weight
to maintain GM positive throughout ballasting would be difficult and time-consuming
under the best of circumstances, and may require modification of the current design.
The stability of the platforms during ballasting and deballasting is further reduced
by the free-surface correction, which accounts for the movement of water in partially
filled tanks as the platform rolls. During a roll, the water in the tank will shift toward
the side of the tank toward which the platform is rolling. This shifts the center of
gravity of the platform from centerline, adding to the upsetting moment. In practice,
it is assumed that the roll angle is not great enough for the liquid to either touch the
top of the tank nor expose the bottom, and the free surface correction is calculated
using equation 2.2, which treats it as a vertical change in the platforms center of
gravity, effectively lowering GM per equation 2.1.
GMeff = GM - FSC
FSC =(2.2)
Where:
GMeff is the effective metacentric height after the free surface correction
37
(2.1)
FSC is free surface correction
-yt and -y, are the specific gravities of, respectively, the fluid in the tank and
the fluid in which the platform is floating. In the case of the OFNP, both
fluids are seawater and thus the term 2 is unity and can be disregarded.
i is the area moment of inertia, with respect to the platform's centerline, of the
surface of the fluid in the tank when the platform is at an even keel.
V, is the platform's displacement.
The free surface correction becomes largest when tanks are half full, and, while expressed as a change in GM, effectively limits the maximum angle to which the platform
can roll while remaining stable. This maximum roll angle determines the maximum
sea state in which a ballasting or deballasting evolution can be safely conducted. The
magnitude of the free surface correction can be reduced by subdividing the ballast
tanks. This reduces the total area moment of inertia of the tanks, and increases the
stability of the platform during the ballasting and deballasting evolutions.
2.2
2.2.1
Hydrodynamics
Hydrodynamic Parameters
To complete step three of section 1.4, the computer program WAMIT was used.
WAMIT is an industry standard program which uses the three dimensional panel
method to analyze marine structures with a given displacement, shape, wave frequency, and water depth.
"The objective of WAMIT is to evaluate the unsteady
hydrodynamic pressure, loads and motions of [a floating] body, as well as the induced
pressure and velocity in the fluid domain. The free-surface and body-boundary conditions are linearized, the flow is assumed to be potential, free of separation or lifting
effects."
[16].
WAMIT was used to obtain added mass and damping matrices and wave force RAOs
and phases for wave frequencies ranging from 0.01 to 1.5 mdz"n for all three versions
38
of the OFNP. Added mass in surge is plotted against wave frequency in Figure 2-1
and against wave period in Figure 2-2. Added mass in heave is likewise plotted in
Figures 2-3 and 2-4, added mass in pitch in Figures 2-5 and 2-6, damping in surge in
Figures 2-7 and 2-8, damping in heave in Figures 2-9 and 2-10, and damping in pitch
in Figures 2-11 and 2-12. The RAOs for surge are presented in Figures 2-13 and 2-14,
for heave in Figures 2-15 and 2-16, and for pitch in Figures 2-17 and 2-18.
39
x 105
3J.b
I
Added Mass in Surge
I
OFNP, 1 100
OFNP 300
OFNP Coke
3
a)
2.5
C
C
2
a)
2
-..
-....................
C
1.5
U)
cc
1
0.5
I
0
0
i
1.5
1
0.5
Wave Frequency (rad/sec)
Figure 2-1: Added Mass in Surge by Wave Frequency
3.5-
x 105
Added Mass inSurge
OFNP 1100
OFNP 300
OFNP Coke
30,
a,
C
C
0
U)
0)
2.512
C,)
C
U,
ci)
1.5
-o
a,
-o
-o
0.5
n
100
I
10 1
102
Wave Period (sec)
Figure 2-2: Added Mass in Surge by Wave Period
40
10
Added Mass in Heave
x 105
5
I
OFNP 1100
OFNP 300
OFNP Coke
4.5
(A,
U)
C
0
U)
4
3.6F
Cu
0)
C
3
0,
0,
Cu
2.5 [
~0
U)
2
I
1'
0
1.5
1
Wave Frequency (rad/sec)
Figure 2-3: Added Mass in Heave by Wave Frequency
5
x 105
Added Mass inHeave
-OFNP
4.5 I-
1100
OFNP 300.
OFNP Coke
4
3.6 1
C
2
-0
a)
C0
0
3
2.5 [
2
1.5
1
100
101
102
Wave Period (sec)
Figure 2-4: Added Mass in Heave by Wave Period
41
10
7
Added Mass in Pitch
x 108
OFNP 1100
OFNP 300
OFNP Coke
6
4C
JC 34
03
2)
1
0.
1
1
0.5
Wave Frequency (rad/sec)
01
0
1.5
Figure 2-5: Added Mass in Pitch by Wave Frequency
x
6
Added Mass in Pitch
108
OFNP 1100
OFNP 300
OFNP Coke~
-
a)
C
C
2
-
4
ca 3
2
-0
a)
2
0
100
101
102
Wave Period (sec)
Figure 2-6: Added Mass in Pitch by Wave Period
42
103
X
Damping in Surge
Damping in Surge
104
4
1 2 x10
OFNP 1100
OFNP 300
OFNP Coke
101a)
a
6
0)
4
2-
I
0
1.5
0.5
1
Wave Frequency (rad/sec)
Figure 2-7: Damping in Surge by Wave Frequency
12
10
Damping in Surge
X 104
OFNP 1100
OFNP 300
OFNP Coke
I-
C-)
a)
0)
E
8
z
6
0)
4
2-
0.
10
I
--
101
102
Wave Period (sec)
Figure 2-8: Damping in Surge by Wave Period
43
103
Damping in Heave
Damping in Heave
x 10 4
x
OFNP 1100
OFNP 300
OFNP Coke
4.5
4
a)
3
a)
cc
2.51
-IN
2
ECU
1
0.5
0
0
1.
1
0.5
Wave Frequency (rad/sec)
Figure 2-9: Damping in Heave by Wave Frequency
Damping in Heave
x 104
4.6
-OFNP 1100
OFNP 300
OFNP Coke
[
4
C-)
CD)
3.5 F
3
2.6 F
CL
2
ECU 1.5
in
1
n'
100
. I
101
102
Wave Period (sec)
Figure 2-10: Damping in Heave by Wave Period
44
13
12
Damping in Pitch
x 10 7
[
101-
OFNP 1100
OFNP 300
OFNP Coke
8
z
6
0
4
2
I
0'
0
1
0.5
Wave Frequency (rad/sec)
Figure 2-11: Damping in Pitch by Wave Frequency
12
Damping in Pitch
x 107
OFNP 1100
OFNP 300
OFNP Coke
10CO
C5
8
r
CL
6
z
CU)
0
4
2
n
100
-I
--
10 1
102
Wave Period (sec)
Figure 2-12: Damping in Pitch by Wave Period
45
10
X 10
7
4
Wave Force in Surge
---
6 -OFNP
OFNP 1100
OFNP 300
Coke
z
-
4
C
3 --
U-
2
-
1
0
1.5
1
0.5
Wave Frequency (rad/sec)
0
Figure 2-13: Wave Force in Surge by Wave Frequency
7
Wave Force in Surge
x 104
-OFNP 1100
---- OFNP 300
-OFNP
Coke
6
z
a)
-
4
232-
1-
10
102
10
Wave Period (sec)
Figure 2-14: Wave Force in Surge by Wave Period
46
10
4
3.51
z
a)
Wave Force in Heave
Wave Force in Heave
-
x
L
OFNP 1100
OFNP 300
OFNP Coke
-
X 104
3
2.5
2
C
1.5
1
0.5
0
I
W
I
1
0.5
Wave Frequency (rad/sec)
)
1
Figure 2-15: Wave Force in Heave by Wave Frequency
Wave Force in Heave
x 104
4.5
4
-OFNP
1100
OFNP 300
OFNP Coke
-
3.5
z
3
2.5
2
1.5
1
0.5
0
10
101
102
Wave Period (sec)
Figure 2-16: Wave Force in Heave by Wave Period
47
103
Wave Force in Pitch
x 100
2.5
-
OFNP 1100
OFNP 300
OFNP Coke
2
E
z
1.5
-
0.5
0O
C
1
0.5
Wave Frequency (rad/sec)
Figure 2-17: Wave Force in Pitch by Wave Frequency
2.5
Wave Force in Pitch
x 100
-OFNP
2
1100
-OFNP 30 k
OFNP Co ke
E
I--
1.5
a)
1
0
100
-
L
a)
101
102
Wave Period (sec)
Figure 2-18: Wave Force in Pitch by Wave Period
48
10 3
As can be seen from Figure 2-3, added mass in heave of the OFNP-300 and OFNP1100 vary similarly with frequency, differing only in magnitude. This is due to the two
platforms being roughly proportional to each other; the added mass of the OFNP1100 is larger simply because the platform is larger. The added mass in heave for
the OFNP-Coke, however, is heavily influenced by the proximity of the free surface
to the top of the lower cylinder of the platform. The sharp drop in added mass in
heave for the OFNP-Coke from 0.4 to 0.7
ra"ians
is due to waves at those frequencies
approaching those that would produce standing waves on the upper surface of the
lower cylinder. Mciver and Evans showed that this situation can even produce negative added mass in heave when the depth of submergence is sufficiently small [111. In
water where the wavelength is greater than half of the water depth, wavelength can
be approximated based on frequency using equation 2.3. A wave frequency of 0.64
radians
produces a wavelength of approximately 150 meters, which would produce a
standing wave of one half wavelength over the diameter of OFNP-Coke's lower cylinder.
OFNP-300 and OFNP-1100 do not experience this phenomena because their
skirts are submerged much more deeply than the lower cylinder of OFNP-Coke.
A = 2gr
(2.3)
Where:
A is wave length
g is gravitational acceleration
w is wave angular frequency
From Figure 2-3, one can see the hydrodynamic benefit of the skirts on OFNP-300
and OFNP-1100.
The added mass in heave of a simple floating cylinder can be
approximated uses equation 2.4 [5].
A 33 = 4pr 3
3
49
(2.4)
Where:
A 33 is added mass in heave
p is seawater density
r is the radius of the cylinder
A cylinder the diameter of the skirt of the OFNP-300 (75 meters) would have an
added mass in heave of approximately 7.2 x 10' tonnes, whereas the added mass in
5
heave of the OFNP-300 is approximately 1.3 x 10 tonnes. Thus the OFNP-300 has
80% more added mass in heave and only 54% of the displacement the simple cylinder
would have. Similarly, the OFNP-1100 has a minimum of 77% more added mass in
heave with 63% of the displacement. In both cases, the additional added mass due to
the skirt improves hydrodynamic performance by decreasing the heave accelerations
and amplitudes the platform would otherwise experience.
In Figure 2-15, the shape of the graphs of all three platforms are characteristic of
floating platforms comprised of two co-centric cylinders. The force applied in heave
to such structures by low frequency waves is high, the force decreases with increasing
wave frequency until reaching a minimum, and then rises and falls again as frequency
continues to increase.
The frequency at which the minimum occurs is related to
the ratio of the diameters of the two cylinders. By ensuring this minimum in wave
force applied to the platform occurs near the peak frequency of the ocean spectra
in which the platform will operate, the designers can further improve hydrodynamic
performance.
Validation of the data from WAMIT was conducted and is discussed in Appendix A.
2.2.2
Monochromatic Wave Analysis
Step four was completed using another computer program, Orcaflex.
"Orcaflex is
a fully 3D non-linear time domain finite element program capable of dealing with
arbitrarily large deflections of the flexible from the initial configuration." [13].
It
calculates the forces and moments in all six degrees of freedom on a floating object
50
due to environmental forces and the object's motion in response to those forces at each
time step, and accounts for both linear and non-linear effects. Orcaflex requires the
user the specify added mass, damping, and RAO coefficients for the floating object
being analyzed. The coefficients used were those calculated by WAMIT.
The plants were exposed to sea states comprised of monochromatic waves, 2 meters
in amplitude, at the frequencies from 0.01 to 0.8
whole range of 0.01 to 1.5
frequencies (0.8 to 1.5
adian;
so.
While frequencies over the
were analyzed in WAMIT, simulations of the higher
radians) were
not conducted in Orcaflex due to the low amount
of variation in the responses of the plants at the higher frequencies. The length of
each simulation was the greater of 3 hours or 100 wave periods. For each frequency
analyzed in Orcaflex,the magnitudes of pitch and heave with a 2.3% risk of being
exceeded by the plant were recorded in each case.
The data for heave is plotted
against wave frequency in Figure 2-19 and against wave period in Figure 2-20. The
data for pitch is plotted against wave frequency in Figure 2-21 and against wave
period in Figure 2-22. The graphs are truncated to focus on the more interesting
portions of the responses.
OFNP-Coke's responses to heave and pitch both show a very large peak at a wave
period 43 seconds due to the platform's natural period in pitch, estimated by calculation at 46.2 seconds. In waves near this period, the platform experienced very
large pitch angles, and the large values in heave are a second-order affect of these
large pitch angles. While OFNP-Coke experiences another peak response in heave
near its natural period in heave of 74.5 seconds, this peak is much smaller than that
at because, as can be seen from Figure 2-16, the waves of that period put very little
force in heave on the platform, whereas, as can be seen from Figure 2-18, the pitch
moment applied to OFNP-Coke by waves with periods between 40 and 50 seconds is
much more substantial. The pitch response of OFNP-Coke also shows a second peak,
much smaller than the first, at a period of 90 seconds due to the 2nd harmonic of the
natural period in pitch.
51
OFNP-300's responses can also be explained in terms of natural frequencies.
This
platform's peak response in pitch is near its estimated natural period in pitch of 32.7
seconds. As with OFNP-Coke, this peak in pitch produces a peak in heave at the
same period as a second order effect. The lower peak on OFNP-300's heave response
is near its natural period in heave, estimated at 24.5 seconds.
OFNP-1100 shows a small peak in heave response near its natural period in heave of
25.9 seconds, and another near the 2nd harmonic thereof. The response in pitch of
the OFNP-1100 tends to be either very large or very small, and transitions between
the two very quickly. This can be seen by the near vertical portions of its response
curve in Figures 2-21 and 2-22, and is likely a result of OFNP-1100's low value of
GAM/B.
As this platform is very slow to recover from rolls, the maximum roll angle
of the platform will tend to be large if it begins to roll past a certain angle. This
explains the relative lack of moderate roll angles of OFNP-1100.
52
Plants Heave vs. Wave Frequency
25
OFNP 300
OFNP 1100
OFNP Coke
LM
a)
1
20
a)
E 151
La)
CL
10a)
m
(D
a)
5
n
0
0.05
0.1
0.25
0.15
0.2
Wave Frequency (rad/sec)
0.3
0.35
Figure 2-19: Plants' Responses in Heave by Wave Frequency
Plants Heave vs. Wave Period
25
OFNP 300
OFNP 1100
OFNP Coke
a)
20
-
a)
CD,
0-
15
E
a)
101a)
CL
a)
xi
m,
M,
0'0L
30
40
60
70
50
Wave Period (sec)
80
90
Figure 2-20: Plants' Responses in Heave by Wave Period
53
100
Plants Pitch vs. Wave Frequency
60
-OFNP
OD
50-
a)
E
OFNP 300
1100
OFNP Coke
40-
La)
CL
0)
30-
CL
20-
a)
10-
0'
0
0.05
0.1
0.25
0.15
0.2
Wave Frequency (rad/sec)
0.3
0.35
Figure 2-21: Plants' Responses in Pitch
Plants Pitch vs. Wave Period
I
-
60
I
C
_-
0)
E
50
-
OD
I
OFN P 300
OFN P 1100
OFN P Coke
40r
0)
CD
CA)
CD
30
0
0)
0)
CL
20
CD)
10
)
01
2
II
30
40
50
60
70
Wave Period (sec)
80
90
Figure 2-22: Plants' Responses in Pitch by Wave Period
54
100
2.2.3
Spectral Analysis
To complete step five, ORCAflex was used to expose the models to simulated Bretschneider and Jon-Swap spectra.
The Bretschneider spectrum used for the analysis simulates the recording conditions
of Hurricane Camille, as reported by Earle [3]. Hurricane Camille was the second
most severe hurricane, in terms of barometric pressure, to hit the mainland United
States in recorded history, making it a reasonable approximation of a hundred year
storm in the Gulf of Mexico. The JONSWAP spectrum used for the analysis simulates
a hundred year storm in the North Sea, as estimated by Haver [151.
In each sea-state, the platforms were also subjected to winds of 67
ocean current of 4 m/s at the surface.
rm/s,
and to an
This is based on the work of Wang [141,
which concluded the maximum current experienced during Hurricane Katrina was
3.8
rn/s.
While data on how precisely to model the change in the velocity of ocean
current with depth is sparse and largely inconclusive[71, a reasonable approximation
can be obtained using equation 2.5[12], the results of which are shown graphically in
Figure 2-23. This current profile was used for these simulations.
U(Z) = U
7 nax(
)i
(2.5)
Where:
U(z) is the velocity of the ocean current at a water depth z
Urnaxis
the current velocity at the ocean surface
H is the total water depth
In each case, the simulations were 3 hours of simulated time in length. The plants' performances in these conditions are presented in Table 2.2.
Both the OFNP-300 and the OFNP-1100 are able to withstand very severe weather
events. The vertical accelerations are all under the limit 0.2 times gravitational accel-
55
I
I
I
I
I
'
3
'
Current vs. Water Depth, Total depth 100m
100
-
90
8070
-
E
C
CU
0
40 -50-
a)
0
-0
40
30
30
-
20
100
0
0.5
1
'
2.5
2
1.5
Current Speed (m/sec)
3.5
4
Figure 2-23: Current Velocity vs. Water Depth
eration, indicating that seasickness is unlikely to become a concern even in the most
extreme weather events. The pitch angles experienced by the platforms, however, are
all higher than the operational limit of 10 degrees, and in some cases higher even than
20 degrees. These angles do not represent a physical danger to personnel or equipment as long as appropriate precautions are taken prior to the storms arrival. Such
measures including ensuring all equipment is properly stowed and perhaps locking
shut all doors and lockers to prevent them from coming open unexpectedly.
Further research is required to determine the maximum angle to which the platform
can roll and continue to operate. Once these values are known, further simulations
can be conducted to determine the what significant waveheights in which the plant
can safely operate, and at what minimum significant waveheight the plant should be
shut down.
The values in Table 2.2 are without considering the mooring systems of the platforms, which are discussed in the next chapter and have significant impact on the
56
Table 2.2: OFNP models' Performances in 100-Year Storms
OFNP-300
OFNP-1100
OFNP-Coke
Significant Waveheight (M)
Peak Period (seconds)
Max Expected Vertical Acceleration (gs)
Max Expected Pitch (degrees)
Max Expected Vertical Acceleration (gs)
Max Expected Pitch (degrees)
Max Expected Vertical Acceleration (gs)
Max Expected Pitch (degrees)
hydrodynamic performance of the platforms.
57
Bretschneider
13.45
14.07
0.04
17.5
JONSWAP
14.5
16
0.06
24.3
0.02
11.6
0.05
15.5
0.08
17.2
0.09
25.3
58
Chapter 3
Mooring System
3.1
Mooring System Criteria
The design of the OFNP's mooring system must satisfy three criteria, while at the
same time weighing and therefore costing as little as possible.
1. The mooring system as a whole must be capable of holding the platform in
place during a 100-year storm.
2. The maximum tension in each mooring line during a 100-year storm must be
below its breaking load divided by a factor of safety.
3. The platform's natural frequency in surge must be outside of the peak energy
area of the sea spectra in which in the platform will be located.
3.2
Environmental Forces
To approximate conditions during a 100-year storm, the same wind and current conditions from Section 2.2.3 were reused here. The seastate used was the Bretschneider
59
spectrum approximating Hurricane Camille.
The surge forces on the platform from wind and current are assumed to be the average
surge force on the platform, and can be calculated using equation 3.1. The force on
the platform from the waves is assumed to be in addition to the forces from wind
and current, and is assumed oscillate randomly about zero. The force applied by the
waves at any given moment is a linear combination of the forces from each wave in
the ocean spectrum, each of which is the product of the waveheight and the force
per unit waveheight associated with the wave's frequency. The force applied by each
wave varies sinusoidally, and has a phase angle, which also varies with the frequency
of the wave, between the peak of the wave and the peak of the force. The minimum,
maximum, mean, and standard deviations of the wave force are presented in Table 3.1.
F1 = 0.5CdpU 2 A
(3.1)
Where:
F1 is the horizontal force due to wind or current
Cd
is the drag coefficient, and is assumed to be 0.92 for cylinders like the
OFNP[4]
p is the density of the air or sea water, as appropriate
U is the velocity of the wind or current
A is the projected area of the platform subject to the wind or current
Table 3.1: Wave Force Statistics
OFNP-300
OFNP-1100
Minimum
(kN)
Maximum
(kN)
Mean
(kN)
-287,198
-625,719
290,798
543,658
66
-67
60
Standard
Deviation
(kN)
78,214
163,705
3.3
Mooring System Characteristics
Due to the large underwater areas of both the OFNP-300 and the OFNP-1100, and
therefore the large forces in surge to which the platforms would be subjected, it
was necessary to consider only catenary mooring systems. An advantage catenary
mooring systems have over taut mooring systems is the ability of the platform to
move horizontally on the ocean surface.
With the platform held rigidly in place,
as with a taut mooring system, the mooring chains would have to be designed to
withstand the peak force applied to the vessel during a storm. This is not the case
with catenary mooring, as the ability of the platform to translate on the ocean surface
and thus dissipate some of the force applied to it by the ocean environment reduces the
amount of tension the cables must be able to withstand. This reduces the number and
size of mooring chains required, which in turn reduce the overall cost of the mooring
system.
With the assumed water depth of 100 meters, the mooring lines were assumed to be
made of chain only, rather than the chain-cable-chain system that would be used in
water deeper than about 150 meters.
The fairleads are placed on the main deck of the OFNP, uniformly spaced around the
perimeter of the deck. Most existing platforms lines are arranged four sets of lines
spaced 90 degrees apart. Model testing for the OFNP's mooring system began with
similar arrangements, however the uniform spacing turned out to be more efficient in
the case of the OFNP, largely due to the number of lines required.
In order to determine the worst case angle of seas, the cross-sectional area of lines
required for the platform to withstand a set environmental force from any angle was
computed. This was done assuming a 16 line mooring system arranged in four groups,
with 10 degrees separating the lines within a group. The results of this analysis can
be seen in Figure 3-1. The heaviest lines were required with the seas coming directly
between two adjacent sets of mooring lines, in this case at an angle of 30 degrees.
61
Therefore, all analyses on mooring systems with lines arranged in groups assumed
the wind, current, and seas all came at an angle halfway between the first intact line
of two adjacent mooring line sets. For uniformly spaced mooring systems, the wind,
current and seas were assumed to come from directly between two adjacent lines.
Chain size based on angle of Seas
0.37
0.36
0.35
E
0.34
,41
0.33
0
C.)
0.32
03,
0n
0.31
0.3
0.29
0
10
20
30
40
50
60
Angle of Incoming Wav.es (degrees)
70
80
90
Figure 3-1: Worst Case Analysis: Direction of Seas
3.4
Mooring Line Tension
The horizontal tension in a mooring line can be determined from equation 3.2 [4],
and is shown graphically in Figure 3-2.
X = I - h( + 2TH
0.5
+ TH
wh
w
Where:
62
-1hw
TH
(3.2)
X is the horizontal distance from the anchoring point of the mooring line to
the point on the platform to which the mooring line is attached.
h is the water depth
1 is the total length of the mooring line
TH is the horizontal tension in the mooring line
w is the weight of the mooring chain in water, which can be calculated using
equation 3.3[2]
2.5
Tension in a Cable with Platform Movement parallel to Cable
xlo1
I
I
I
Platform Position
I
Equilibrium Position
2
Zi
1.51-
0
C
1
-
0.5
n'L
630
640
710
680 690 700
660 670
650
Distance from Anchor to Nearest Platform Edge (m)
720
730
Figure 3-2: Mooring Line Tension D=140mm, chain length=733m
w = 0.1875
D2
1000
(3.3)
Where:
D is diameter of the chain link in mm, as shown in Figure 3-3
If a given horizontal displacement of the platform is assumed, the value of X for
each mooring line can be computed geometrically. From these lengths, the horizontal
tension in the cables can be determined using equation 3.2. The force necessary to
63
cr)
6D
Figure 3-3: Chain Link Dimensions
achieve the assumed displacement can then be calculated using equation 3.4[2]
n
(TH, COS(/i))
F1 =
(3.4)
i==1
Where:
F1 is the total horizontal force applied to the platform by the n mooring lines
pi is the angle
between the ith mooring line and the direction of seas.
By iterating with equations 3.2 and 3.4 until F from equation 3.4 equals that from
equation 3.1, the mean position of the platform and the mean tension in the of the
mooring lines can be determined.
The breaking load of a mooring line is calculated using equation 3.5[2].
TB = cD 2 (44 - 0.08D)
64
(3.5)
Where:
TB is the theoretical tension at which the chain would break
c is a constant depending on the grade of chain. For grade R5 chain, which is
used in this analysis, c = 0.32.
The International Association of Classification Societies (IACS) standard is to use a
factor of safety of 1.8 with all mooring lines intact, and 1.25 with one mooring line
broken, when analyzing performance in a severe storm. The IACS defines "severe
storm" as "the most severe design environmental condition for severe storm as defined
by the owner or designer. [11, and provides that the aforementioned safety factors
should be applied for the tension in each mooring line when the platform is at its
most extreme excursion.
3.5
Platform Natural Frequency in Surge
The natural frequency in surge of the platform depends on the mass and added mass
in surge of the platform, and on the number, weight, and pretension of the mooring
lines.
As with pitch and heave, it is necessary to ensure the natural frequency in
surge lies outside of the peak frequencies of the ocean spectra. Natural frequency in
surge can be calculated using equation 3.6[4].
Wn=
(M C
+ 1All
)0.5
(3.6)
Where:
w), is natural frequency in surge
Cu is the restoring coefficient of the mooring lines, and can be calculated using
equation 3.7
M is the mass of the platform
Al
is the platform's added mass in surge at its natural frequency.
65
C11
ci
(3.7)
cos2V)
i=1
Where:
n is the total number of mooring lines
cu1 is the restoring coefficient of the ith mooring line, and can be calculated
using equation 3.8
C
-2
= w(
-2
wh
))_1
+ cosh 1 (1 +
(1+2Th71 )O.5
3.6
(3.8)
ThM
Orcaflex Simulation
The OFNP platforms with their moorings systems were simulated in Orcaflex. The platforms
were exposed to Hurricane Camille conditions for three hours of simulated time, both with all
lines intact and with the worst-case line removed to simulate operation with one line broken.
The worst-case line was considered to be that which experienced the greatest tension during
the simulation with all lines intact.
As expected, in each case the worst-case line that
nearest the angle from which the sea was applied. For the broken line simulations, which
was conducted only on uniformly spaced arrangements, the angle of sea was adjusted to be
coming directly at the angle of the broken line, and thus halfway between the two intact
lines which were furthest apart.
Since Orcaflex does not allow mooring lines to "break" during simulations, unless specifically
requested by the user, it was not necessary to verify the mooring system was able to hold
the platform in place. Instead, it was only necessary to ensure that the maximum tension
achieved by any line was less than the breaking strength divided by the appropriate factor
of safety.
The minimum required length of the mooring chains in each scenario is calculated using
equation 3.9.
66
27r+
A
1min = h(2 T
hw
-
1).5
(3.9)
Where:
imin is the minimum chain length
Tmax is the maximum tension expected to be experienced by the chain. For
this, I use the maximum expected tension from the simulation with one
line broken.
The results of the simulations are shown in Tables 3.2 and 3.3, and values without mooring
of pitch, heave, and heave acceleration are repeated there for comparison purposes. The
presence of the mooring systems significantly increased the maximum pitch the platforms can
be expected to experience. This is due to two factors. First, the mean pitch angle increased
due to the upsetting moment created by the waves and current pushing the submerged
portion of the platform in one direction, while the mooring lines pull the upper portion
of the platform in the opposite direction. There is also an upsetting moment created by
the current without the mooring system, which is why we see non-zero mean pitch angles
without mooring as well, but the total upsetting moment is greater with the mooring lines,
which explains the increase in mean pitch angle.
Secondly, the presence of the mooring system decreases the natural period in pitch of the
platform, bringing it closer to the peak period of the storm waves, resulting in more motion.
This is due to the restoring moment provided by the mooring lines. If the platform pitches
while in its equilibrium surge position, the lines on the side toward which the platform pitches
will slacken, while those on the side away from which the platform pitches will tighten. This
produces a net force pulling the top of the platform in the direction away from which it is
pitching. The moment arm associated with this force is the height above the waterline of
the fairleads, and the moment produced becomes a restoring coefficient in equation 1.17.
Thus, the natural period in pitch with a mooring system attached can be calculated using
equation 3.10.
(3.10)
TN5
+ A 55
Vmri5
pgVGM + FAlr
67
Where:
TN5 is the platform's natural period in pitch
M is the platform's mass
r 55 is the platform's radius of gyration
Fr, is the net force created by the mooring lines when the platform pitches by
1 radian
Am is the vertical distance from the fairleads to the static waterline
The magnitude of Fm varies with the platform's position in surge. As surge increases,
the tension in the lines away from which the platform is surging increases, moving
closer to the steep portion of Figure 3-2. This causes the response in pitch to become
increasingly stiff, increasing F. and lowering T,5.
The changes in T,.5 due to the
various mooring systems are shown in Table 3.4.
In these cases, the platform is
assumed to be in its equilibrium surge position.
Mean and standard deviations of pitch data are presented in Table3.5.
While the
maximum pitch angle experienced with mooring is greater than that experienced
without, the variation in angles experienced by the platform is similar with the mooring system and without. This indicates that the change in natural period due to the
mooring systems is a small effect compared to the upsetting moment created by the
combination of the ocean current and the mooring lines. While the change in natural
period is large, especially in the case of ONFP-1100, the importance of the change
is what is small. Even with the significant decrease, all natural periods remain well
above 20 seconds, indicating there is little energy in the ocean at the natural periods
of the platforms.
While all three aspects of the environment (wind, current, and waves) contribute to
the overall load on the mooring system, the relative importance of each is unclear
from the above analyses.
In order to determine the relative significance of each
environmental element, additional simulations were run on the OFNP models with
the mooring system comprised of 150mm chain, in which each environmental element
in turn was removed, and the tension resultant from the other two was recorded. The
68
Table 3.2: OFNP model's Performance in 100-Year Storms with mooring systems
D=150 Chain
Number of mooring lines
Chain Grade
Chain Length (m)
Mooring Chain Mass (total,
OFNP300
28
R4S
822
11,387
OFNP1100
40
R5
878
17,375
34.5
57.5
tonnes)
Natural Period in Surge (seconds)
Max
Max
Max
Max
Max
Acceptable Tension (kN)
Expected Tension (kN)
Expected Surge (m)
Expected Pitch (degrees)
Expected Pitch, without
All Lines Intact
12160
11270
28.3
20.7
17.9
Line
One
Broken
17510
12829
29.1
20.7
NA
All Lines Intact
12800
12455
41.1
19.9
11.6
Line
One
Broken
18432
13509
42.0
20.0
NA
0.04
0.04
0.02
0.02
0.04
NA
0.02
NA
2.6
2.6
2.6
NA
3.6
3.4
3.6
NA
mooring (degrees)
Max Expected Vertical Acceleration (gs)
Max Expected Vertical Acceleration, without mooring (gs)
Max Expected Heave (m)
Max Expected Heave, without
mooring (m)
results of these simulations are presented in Table 3.6, and indicate that the ocean
current is the single most important environmental factor in terms of influencing the
maximum tension in the mooring lines. The waves are of second-greatest importance,
with the wind playing a minor but certainly appreciable role.
The relative importance of the current to that of the waves can also be seen in
Table 3.5.
The moment created by the current determines the mean pitch angle,
while that created by the waves determines the standard deviation. That the mean is
greater than the standard deviation suggests that the current is of greater importance
to the response of the platform, in this particular environment, than the waves.
69
Table 3.3: OFNP model's Performance in 100-Year Storms with mooring systems
D=120 Grade R5 Chain
Number of mooring lines
Chain Length (m)
Mooring Chain Mass (total,
OFNP300
36
879
10,021
OFNP1100
62
903
17,726
33.1
98.9
tonnes)
Natural Period in Surge (seconds)
Max Acceptable Tension (kN)
Max Expected Tension (kN)
Max Expected Surge (m)
Max Expected Pitch (degrees)
Max Expected Vertical Acceleration (gs)
Max Expected Heave (m)
All Lines Intact
8806
8432
42.0
22.2
0.04
Line
One
Broken
12,680
9370
43.3
22.4
0.04
All Lines Intact
8806
8702
41.0
19.4
0.02
Line
One
Broken
12,680
9135
41.6
19.4
0.02
2.7
2.7
3.6
3.5
Table 3.4: Change in Natural Period in Pitch with Mooring Systems
Fm (kN)
Am (m)
Natural Period in Pitch (Sec-
onds,
3.7
OFNP300,
D=150
33,451
12.5
31.5
OFNP1100,
D=120
304,720
31.9
38.0
OFNP1100,
D=150
126,108
31.9
44.3
32.7
32.7
51.3
51.3
with mooring)
Natural Period in Pitch (Sec-
onds,
OFNP300,
D=120
61,931
12.5
30.5
without mooring)
Mooring System Cost
The capital cost of the mooring system consists of the lines themselves, the fairleads
and winches, and installation. All the equipment can, with minimal maintenance and
barring a very major storm that breaks one of more lines, be expected to last as long
as the platform itself, so it is not necessary to consider the replacement interval.
The cost of chain depends on the total mass thereof, which in turn depends of the
length and diameter, and on the grade of the chain.
70
According to representative
Table 3.5: Mean and Standard Deviation of Pitch Angle (Degrees)
OFNP300
OFNP1100
Mean Pitch Angle
Standard Deviation
D=-150, all lines intact
4.9
2.8
5.5
1.3
Mean Pitch Angle
Standard Deviation
D=150, one line broken
Mean Pitch Angle
10.0
2.3
12.8
.5
9.8
12.7
Standard Deviation
2.3
1.5
D=120, all lines intact
Mean Pitch Angle
10.5
12.7
Standard Deviation
2.5
1.4
D=120, one line broken
Mean Pitch Angle
10.4
12.7
Standard Deviation
2.6
Without Mooring
_
_
_1.4
Table 3.6: Maximum Tension (kN) with Environment Element Removal
All elements included
Current Removed
Waves Removed
Wind Removed
OFNP-300
11,270
4496
5071
9963
OFNP-1100
12,455
5449
7465
11870
of Vicinay International, a mooring chain manufacturer, grade R5 and R4S chain,
which are used in the mooring systems proposed the preceding section, costs approximately 3.25 Euro ($3.64) per kilogram. According to a representative from Vryhof,
another multinational mooring system manufacturer, grade R4 chains are 10-20% less
expensive than grade R5.
Each mooring line requires a fairlead and winch. The cost of the fairlead and winch
do not vary significantly with chain grade, size, or maximum expected tension. The
cost of this equipment, therefore, depends only on the number of lines installed, and
costs, according to the Vryhof representative, roughly $750,000 per mooring line.
Installation cost is perhaps the single largest factor in determining the cost of a
71
mooring system. Installing the mooring lines requires the use of a heavy lift vessel,
which are quite expensive to rent. Furthermore, there are very few vessels in the
world capable of installing chain with a diameter greater than 120mm. Therefore,
the installation cost of the mooring systems with D=150 chain would cost about
$120 million, while that of the systems with D=120mm chain would cost much less,
perhaps $60 million.
The costs of each mooring system are shown in Table 3.7. It can be easily seen that
despite having more lines, the D=120 mooring systems are less expensive overall due
to installation cost. The tradeoff with this decrease in cost, however, is that more
deck space will be taken up by the fairleads and winches.
This will have various
operational and design impacts, such as the ability to land a helicopter on deck and
the location and size of other facilities.
Table 3.7: Mooring System Costs (Millions of $)
OFNP-300, D=120
OFNP-300, D=150
FNP-1100, D=120
OFNP-1100, D=150
3.8
Chain
Fairleads/Winches
Installation
Total
36.3
41.3
64.3
63.0
27.0
21.0
46.5
30.0
60
120
60
120
123.3
182.3
170.8
213
Conclusions
Safely putting a nuclear power plant in a floating platform, permanently moored to
the ocean floor is possible with today's technology. The current designs of both OFNP
platforms float in a stable manner in an upright position. Their natural periods in
heave, pitch, and surge are outside of the wave periods they will encounter in the
ocean environment. While the nuclear plant aboard the platforms will likely have to
be shut down in extreme storms, such storms do not represent a danger neither to
the personnel aboard the platform nor to the platform itself.
Designing a mooring system for such a platform to withstand extreme weather events
72
would require the most robust mooring system ever built, and such a mooring system
would be extremely expensive. However, the materials of which the mooring system
must be constructed are currently available, and their feasibility and robustness has
been proven on other platforms.
In addition, the number and size of lines, and
required to moor the OFNP presents practical difficulties. For example, the presence
of so many lines will make it difficult if not impossible for a ship to approach the
OFNP. While is may be beneficial for security, it is also a detriment to day-to-day
operation of the plant, which includes resupply ships pulling alongside. This difficulty
may be able to be overcome by slackening one or several lines to allow for the approach
of the resupply vessel.
The OFNP concept represents a necessary step forward in the people of the world's
effort toward achieving a sustainable existence. It should continue to be designed,
and should be built and launched as soon as possible.
3.9
3.9.1
Future Work
Balancing Risk and Cost
The mooring systems presented in this thesis are designed based on very conservative
assumptions.
An extreme sea state is combined with a strong, constant wind and
an ocean current that will very seldom, if ever, exist. This combination of factors is
imposed in shallow water, where the dynamic forces on the mooring system will be
at there most extreme. The result of analyzing these conditions is the design of a
mooring system that will withstand any conditions mother nature will ever produce
in the Gulf of Mexico.
However, the mooring system may be over-designed. There is always some risk associated with any design, but the risk associated with this design in its environment is
extremely low. There may be room to assume greater risk, and thereby design a less
73
robust and less expensive mooring system. For example, any of the current speed,
wind speed, and significant wave height could be reduced. It could be assumed that
the combination of all three at their historic extremes occurring simultaneously is a
scenario so unlikely that it needn't be designed for. The question of balancing risk
with cost becomes a business decision, and has not yet been addressed.
3.9.2
Additional Mooring System Scenarios
Thus far, analysis has only been conducted for a water depth of 100 meters and a flat
ocean bottom. Initial analysis of the characteristics of tsunami waves indicated this
to be the minimum depth at which the tsunami wavelengths were sufficiently long to
allow the platform to ride them out with ease. However, it is by no means necessary
to only position the OFNP in 100 meters of water. It will be necessary to custom design a mooring system for each location, taking into account expected environmental
conditions, water depth, ocean bottom type and slope, and other factors.
Initial analysis of a water depth of 200 meters, again with a flat ocean bottom,
indicates the OFNP-300 could be successfully moored with 36 mooring lines, each
comprises of 125 meters of D=120 grade R5 studlink chain connected to the platform,
followed by 810 meters of D=130 steel cable, followed again by 475 meters of the same
chain. While this is the same number of lines as were used to moor the OFNP-300
in 100 meters of water, there is less chain, which is expensive, and more cable, which
is less so, in each line. The overall mooring system may, then, actually become less
expensive in deeper water. This mooring system is in very early stages of design at
the present time, and significantly more work is required to optimize the design of it
with respect to cost.
However, siting the platform in deeper water in general means siting it further from
land. While the mooring system may be less expensive, other aspects of the platform,
such as the transmission cables connecting the platform to land, will become more
costly as distance from land increases.
The optimal balance of these potentially
74
competing factors will be different at each potential site.
This question requires
study in general to determine the nature of any correlation between water depth
and mooring system cost, and the optimization of each site will need to be studied
specifically.
In addition, the mooring systems were only analyzed in the sea conditions simulating
Hurricane Camille. While this certainly represents an extreme weather event, other
parts of the world will have different storm characteristics.
Even if the significant
waveheight of the storms in other parts of the world prove to be less than that
used here, the peak frequency of the storms will almost certainly be different, and
it has been shown that the platforms will behave differently in waves of different
frequencies.
Therefore, the 100 year storm in each potential siting location of the
OFNP will have to be analyzed and have a mooring system designed to withstand it.
It cannot be assumed that a mooring system designed for one environment will be
adequate for another. Even if the mooring system designed for the Gulf of Mexico,
for example, does prove entirely adequate for the Mediterranean, it is highly likely
that cost reductions could be achieved by designing a less robust mooring system for
the new environment.
As indicated above, the cost of mooring chains depends heavily on the grade of the
chain. The systems designed so far include only grades R5 and R4S chain. Additional
systems with lower chain grades should be designed and analyzed for cost. With a
lower grade of chain, the maximum tension acceptable in the line decreases, which will
ultimately result in the platform requiring more mooring lines, obviously increasing
the cost. Whether the lower cost of chain manufacturer outweighs the increase in
cost due to number must be evaluated on a case-by-case basis.
Moreover, at this
point, mooring systems for the OFNP have only been designed from chain (except for
the preliminary analysis of the chain-cable-chain setup for deeper water). Mooring
systems can also be made from synthetic materials, such as polyester rope. A different
material for the mooring lines may reduce cost and plant motions, and this warrants
further investigation.
75
Lastly, simulations were only conducted with the fairleads in one position for each
vessel: on the main deck. There is no reason the mooring lines must be positioned
there. While positioning the fairleads further up on the platform reduces the tension
experienced by the lines and therefore the number of lines required, positioning them
lower, closer to the centroid of the force applied by ocean current, would reduce the
maximum expected pitch angle experienced during a storm. This has the potential to
increase the operational time of the platforms and to reduce any damage that might
occur during a storm. This is a tradeoff that requires further investigation.
3.9.3
Establishing Plant Limitations
At this point in time, the limitations on the motion of the plant are not well established. The limit of 0.2 times gravitational acceleration for heave is based on an old
standard to prevent seasickness, and the pitch limit of 10 degrees for the plant to
remain operational is based on a limit for terrestrial plants that would never expect
to experience motions anywhere near that large. The limits of the power transmission cable, connecting the OFNP to the terrestrial grid, are unknown. It is possible
that the projected motions of surge and heave are too much for the cable, and it is
likewise possible that the projected pitch angles will exceed the limits of any of the
many components of the nuclear plant.
A detailed analysis of the nuclear plant itself, as well as of the associated support
systems contained on the platforms, needs to be conducted to establish meaningful
limits and the bases behind them. Once these limits are established, it will be possible to analyze the hydrodynamic performance of the platform in storms of increasing
severity to determine the minimum significant waveheight and peak frequency combinations which will cause the platform to exceed one or more of these limits. Based
on this analysis, operational guidelines can be established, telling the plant operators
in which storms they may continue to operate the nuclear plant, and in which storms
they must temporarily shut down. Until such guidelines are established, any OFNP
76
built and installed will have to be shut down for any significant storm, resulting in
interruptions of service that, while prudent given the lack of information, may have
been unnecessary were the limits known.
77
78
Appendix A
Data Validation
In order to ensure the validity of the outputs from WAMIT and Orcaflex, several of
said outputs were compared to hand calculations and previously published results.
A.1
WAMIT Damping Data
First, the heave damping forces predicted by WAMIT were compared to those calcuated by hand using equation A.1, which is valid for all axi-symmetric structures
(reference needed).
B 33
-
k
pgVg
(A.1)
B 33 is damping in heave
k is the wavenumber as calculated by inverting equation A.2 for a given frequency
X3 is the force in heave applied by the waves as supplied by WAMIT
p is the density of seawater
g is gravity
79
and Vg is the wave group velocity, as calculated in equation A.3.
(A.2)
W2 = gktanh(kh)
L 1
2kh
V =Sk 2 (1+
sinh(2kh)
)
(A.3)
wave
w isSis
second
wae hfrequency
in
,adian
h is water depth
The damping forces predicted by WAMIT and those calculated by equation A.1, for
OFNP-300 plant in both cases, are shown in Figure A-1. The two lines on the graph
are coincident for all frequencies, suggesting WAMIT is performing this calculation
correctly and likewise that the program is being used correctly.
2500
Ideal 833
WAMIT B33
2000-
1500
C
0
w
U,
0)
C
C
0
1000
500
0
-500
0
0.2I
0.2
0.4I
0.4
1.2
1
0.8
0.6
1
1.2
0.6
0.8
Wave Frequency (radians/second)
-
I
I
I
1.4
1.4
I
Figure A-1: Validation of WAMIT Damping Data
80
1.6
1.6
A.2
WAMIT Added Mass Data
To ensure the validity of the added mass data supplied by WAMIT, the predicted
added mass in heave of OFNP-Coke in the maintenance and the transport conditions were compared to the analytical results published by Yeung [171. These conditions were selected for use in the comparison because they represent the same simple
cylinder submerged to different fractions of water depth (specifically 45% and 14%
respectively), making for an apt comparison to the analysis done by Yeung.
Figure A-2 shows the added mass in heave for the first coke iteration in the maintenance and transport conditions, after applying the same non-dimensionalization used
by Professor Yeung, plotted against dimensional wave frequency. One can see that
Added Mass in Heave
9
1
8
.2
1
1
1
Yeung d=0.10
Yeung d=0.25
Maintenance Condition (d=0.55)
Yeung d=0.75
Transport Condition (d=0.86)
Yeung d=0.90
7
E6
Yeung d=-1.0
-
2
0
0
0.5
1
3
2.5
2
1.5
Wave Frequency (non-dimensional)
3.5
4
Figure A-2: Validation of WAMIT Added Mass Data
the curves all follow similar patterns, and that at higher frequencies, transport condition line falls between the d = 0.90 and the d = 0.75 lines, and that the maintenance
condition line falls between the d = 0.75 and the d = 0.25 lines, as expected in both
81
cases, confirming the accuracy of the added mass data predicted by WAMIT.
A.3
Orcaflex Heave Data
To ensure the validity of the simulation results produced by Orcaflex, OFNP-Coke in
the maintenance condition was simulated with small waves (1 meter wave height) to
minimize non-linear effects. The results were compared to those of a hand calculation
modeling the buoy as a linear harmonic oscillator, including the effects of added mass
and damping.
The expected heave amplitude of floating circular cylinder modeled as a simple harmonic oscillator can be predicted using equation A.4.
I3 =AX
(M + A 33)
(A.4)
3
W- W 2 ) 2 + (B33
)2w2
13 is heave amplitude
A is waveheight
X3 is heave force applied to the buoy per meter of waveheight as supplied by
WAMIT
M is the mass of the buoy
A 33 is added mass in heave for a given frequency as supplied by WAMIT
wo is natural frequency as calculated by equation A.5
w is wave frequency
B 3 3 is damping force in heave as supplied by WAMIT.
7r2=A
'I+ A33
r is the radius of the buoy
p is the density of sea water
82
(A.5)
g is gravity.
The comparison of the analytic results from equation A.4 and those of the simulations
in orcaflex are presented in Figure A-3. The results are in reasonable agreement at all
frequencies, giving assurance that Orcaflex produces valid results and is being used
properly.
Heave Amplitude versus frequency
5
-B- Analytic Heavi
- Orcaflex Heavi
4
3
E)
E
2
1
0
-1-
0
0.1
0.2
0.3
0.4
0.5
0.6
Wave Frequency (rad/sec)
0.7
0.8
Figure A-3: Validation of Orcaflex Heave Data
83
0.9
84
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