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Development of an open-source simulation tool for mooring systems


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This paper presents the development of an open-source object-oriented program, named OpenMOOR, for static and dynamic analyses of mooring systems in ocean renewable energy applications, including offshore wind turbines and wave energy devices. The program is developed for cross-platform applications. It can be used as a standalone software or a dynamic linking library for developing coupled models of the moored structures/devices. A finite difference model of mooring cables is adopted for solving the motion of a single cable which can deal with the hydrodynamic effect, cable bending/torsional stiffness and nonlinear strain-tension relationship. Parallel computing is implemented for efficient analysis of a mooring system consisting of multiple cables, as common in the practice. OpenMOOR has then applied to analyse a single mooring cable under forced harmonic motions at the top end. The cable responses are found to agree well with the experimental data in the literature, which validates OpenMOOR.
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ABSTRACT: This paper presents the development of an open-source object-oriented program, named OpenMOOR, for static and
dynamic analyses of mooring systems in ocean renewable energy applications, including offshore wind turbines and wave energy
devices. The program is developed for cross-platform applications. It can be used as a standalone software or a dynamic linking
library for developing coupled models of the moored structures/devices. A finite difference model of mooring cables is adopted
for solving the motion of a single cable which can deal with the hydrodynamic effect, cable bending/torsional stiffness and
nonlinear strain-tension relationship. Parallel computing is implemented for efficient analysis of a mooring system consisting of
multiple cables, as common in the practice. OpenMOOR has then applied to analyse a single mooring cable under forced harmonic
motions at the top end. The cable responses are found to agree well with the experimental data in the literature, which validates
KEY WORDS: Mooring systems; Open-source program; Nonlinear cable mechanics; coupled analysis; object-oriented
framework; ocean renewable energy.
Mooring systems are of significant importance for station
keeping of ocean renewable energy applications to harness
offshore wind, wave and tidal current energies. Two main
challenges exist in design and analysis of the mooring systems
(i) the balance of design cost/complexity and the performance
[1], particularly for wave energy devices, and (ii) the numerical
simulation for assessing the safety, survivability, and coupled
analysis of the floating structures [2]. Recent research has
focused on relevant topics. For example, a novel mooring
configuration which combines the tension legs and catenary
chains for floating wind turbines was studied and found to be
able to improve the dynamic performance of the tension leg
platform in operational and extreme conditions [3], via wind-
wave tunnel tests on a scaled model. Cost optimization of
mooring systems for large scale wave energy converters was
performed by [4] to facilitate the commercialization of wave
energy concepts. Based on basin testing, extreme mooring
loads were investigated for an array of wave energy devices [5]
and [6] which analysed the peak mooring load in relation to the
environmental conditions including wave and current and it is
found that increasing pre-tension of cables can reduce the peak
mooring loads which however may reduce the device motion
and hence the energy able to be harvested.
For investigating mooring cables through model tests,
methods have been proposed for developing scaled models, as
in [7]. A method using truncated mooring cables was proposed
by [8]. However, most of the studies resort to mathematical
modelling and numerical simulations considering the large
scale and complexity of the mooring systems. Nonlinear
dynamic analyses have been conducted and compared with
linear and quasi-static analyses for typical offshore wind
turbine concepts with the mooring system, to illustrate the
importance of mooring cable dynamics in coupled analysis of
offshore wind turbines [9-12]. The nonlinear dynamic
behaviour of mooring cables could be more pronounced in the
station keeping of wave energy devices [13], because the
relative-small size devices can experience relatively larger
displacements. While the mooring systems for offshore wind
turbines are more or less similar to those in oil and gas industry,
the mooring systems for wave energy devices are quite
different [14]. Although the quasi-static analytical solution is
still dominantly used in the iterative design procedure for wave
energy devices [15], the design is required to consider the
reliability and survivability at the final step where a fully
nonlinear model is needed. Nonlinear dynamic analysis is also
recommended by DNV-OS-E301 POSMOOR [16]. The
importance of mooring line dynamics has also been illustrated
by experimental measurements [13].
There exist a number of commercial programs providing the
capacity of simulating mooring cable dynamics and many can
also perform coupled analysis of the moored structures. A
recent review on mathematical models and analysis tools can
be found in [17], and available tools have also been examined
in [18]. Apart of commercial software, many in-house codes
have been developed for specific research focus and for the
convenience of coupled analysis to varied extent. For example,
DOOLINES provides a finite element framework for dynamics
of offshore lines, which is currently a proprietary software [19].
Analytical catenary solution has been extended to deal with
multi-segment cables, especially for crowfoot mooring, and to
account for the cable-seabed friction [20], leading to a
comprehensive quasi-static mooring analysis program named
MAP++ [21]. A finite element code called FEAMooring has
been developed particularly for coupled offshore wind turbine
analysis by [22,23]. A lumped mass model, named MoorDyn,
has been developed and validated against experimental tests on
a floating wind turbine model [24]. Another lumped mass
Development of an open-source simulation tool for mooring systems
Lin Chen, Biswajit Basu
1School of Engineering, Trinity College Dublin, Dublin 2, Ireland
model, OPASS code, is based on finite element formulation
while with linear interpolation of the element mass [25] and it
has been validated using experimental data on a single cable. A
hp-adaptive discontinuous Galerkin method was developed for
modelling snap loads in mooring cables in particular for wave
energy devices which are probably subjected to large
displacements due to the extreme wave loadings [26,27] and
the program is named MooDy. In addition, a nonlinear finite
element model based on bar elements with three translational
degrees of freedom per node is used for coupled analysis in
Among all the in-house codes, to the best knowledge of the
authors, three are made open-source, namely MAP++,
FEMooring, and MoorDyn. MAP++ is a well-documented
program while due to its quasi-static nature, it is receiving less
attention for further development. FEMooring was developed
in Fortran especially used as a module of FAST, a widely used
open-source wind turbine analysis tool [29]. MoorDyn has also
been coupled with FAST and is still under intensive
development. Recently, it has been improved to consider the
seabed friction and applied to connect multiple floaters [30].
Another option is building mooring models based on available
open-source general-purpose finite element libraries. For
example, one effort has been made by [31] using software
package Code_Aster. Other popular libraries such as DEAL.II
[32] and FEniCS [33] can also be explored. Nevertheless,
considerable effort is still needed to tailor those general-
purpose library to simulate mooring cables.
This study is aimed at the development of a cross-platform
open-source program for mooring cable simulation with
improved capacity, named OpenMOOR. The mathematical
model developed by [34,35] is used as the basis, which was also
used by WHOI Cable [34,35]. WHOI cable was developed for
towed cables and risers in ship and oil industry and it is a
proprietary software of Woods Hole Oceanographic Institution.
The mathematical model has some advantages as compared to
those implemented in available open-source programs,
including the capacity to include the current effect, cable
bending stiffness and torsional stiffness, and also the nonlinear
strain-stress relationship. Particularly, the nonlinear strain-
stress relationship could be important for optimize the design
of mooring cables for wave energy devices. For example, a
novel fibre rope mooring tether with lower axial stiffness was
studied by [36] to reduce the peak and fatigue loads in the rope.
The so-called "Exeter Tether" also provides capacity of
selectable axial stiffness and the experimental results clearly
showed a nonlinear strain-stress relationship.
The rest of the paper is organized as follows. Section 2
introduces the OpenMOOR implementation. Section 3 presents
validation and verification results. OpenMOOR is further
applied to study the wave and current effects on a floating
offshore wind turbine in Section 4. A brief summary is
provided in Section 5.
A typical mooring system is composed of multiple cables, each
of which exhibits strongly nonlinear behaviour and requires
careful treatment in numerical simulation. Fig. 1 shows one
cable of a floating structure. The mooring cables provide
restoring stiffness for the structure preventing it from drifting
far away from the desired spot. In operational/extreme
conditions, the cables are subjected to loads due to surface
waves and underlying current. OpenMOOR is aimed to
simulate such multi-cable mooring systems in ocean renewable
energy applications and also to be a framework to conveniently
implement other mooring models.
Figure 1. Station keeping using mooring cables in renewable
energy applications.
Several mathematical models for mooring cable mechanics
along with the numerical solving methods are available in the
literature. The most widely used model formulates the
governing equations of a cable without bending stiffness in
Cartesian coordinate, leading to second-order partial
differential equations, which have been often solved using
finite element methods [37,38]. A more comprehensive model
based on rod theory was derived by[39], able to take into
account both bending and torsional effects and it is also solved
using finite element method.
Another popular model establishes the balance equations in
the local Lagrangian coordinate along the cable, leading to
first-order partial differential equations [40-43]. It can consider
the bending stiffness, torsional stiffness and the nonlinear
strain-stress relationship easily. The box method is normally
used for solving the equations, which is able to achieve a
second-order accuracy. By using this model, the governing
equations are expressed in matrix form as
! " #"
#$ % &'"( #"
#) % * " + , (1)
where ! " and & " are stiffness and mass matrices
depending on cable state and " is the state vector. For three-
dimensional problems as described in [41] when the Euler
Angle formulation is applied the state vector is defined as " +
- ./.01 2 3 4 5 67689:with -= strain, ./
and .0 are shear forces, 1,92 and 3 are cable velocity
components in the local coordinate, 4 and 5 are Euler angles
and 67and 68 are material curvatures. The interested readers
are advised to [40] for details and the quaternion formulation.
Noteworthy is that in all the formulations Morison's equation
is used to account for hydrodynamic effect on cables [44],
including the drag force, inertia force and the Froude-Krylov
force, which is valid considering the slenderness of the mooring
cables. The model described by Eq. (1) is implemented in
OpenMOOR. The equations are first discretized in space and
then the generalized-; method is implemented for time
stepping to add numerical dissipation for improving the
computation stability [45-47].
OpenMOOR is developed in C++ using object-oriented
programming. The Eigen Library is used for matrix and vector
manipulation [48], which is a C++ template library including
only header files and hence simple to use. The Eigen Library
provides a Matlab-like development environment, which
enables efficient implementation of novel models by structural
engineers. The odeint library [49] is used for integration in
solving the platform motion, which contains also only header
files. The source code of OpenMOOR is hosted by GitHub
along with documentation and examples
( The key classes of
OpenMOOR and their relationship are demonstrated in Fig. 2.
Figure 2. OpenMOOR main classes and their relationships.
The main classes of OpenMOOR are described as follows.
Class Node. A Node is defined by its arc-length coordinate
originated from one end of the cable which it belongs to,
corresponding structural and hydrodynamic properties and
associated seabed parameters if it is in contact with the
seabed. Those properties are defined using StructProperty,
HydroProperty and SeabedProperty classes respectively.
This arrangement allows the consideration of nonuniform
properties along the cable length. Methods are defined to
formulate the nodal mass matrix and stiffness matrix and
the nodal force vector based on the present nodal state. For
boundary nodes, methods are provided to define the
constraint equations.
Class Catenary: An extensible Catenary in two-
dimensional space is defined by its chord vector and its
unstretched length, weight per unit length and axial
stiffness. It is used to initialize the nonlinear solving
procedure. Analytical catenary solution is important for
reducing the time taken for dissipating out the transient
responses and also important for developing linearized
model for the mooring system. The linear stiffness matrix
is required to approximate the restoring stiffness of a
mooring system on the platform [50], which can further be
used to carry out a shooting procedure for solving the
coupled static problems. The two-dimensional elastic
catenary theory considering the seabed contact is
implemented [50,51]. In case of cables with non-uniform
structural property, the averaged cable weight per unit
length and axial stiffness are used for obtaining the
analytical catenary solutions.
Class Cable: A Cable in OpenMOOR is defined by its
unstretched length and the initial positions of its two
connections in global coordinate system. A Cartesian
coordinate system is defined for each cable with the origin
placed at one end. Methods are defined for discretizing a
cable into uniformly distributed or non-uniformly
distributed nodes and initializing the nodal states using
catenary solutions. Initial cable nodal states can also be
read from input files. Other main methods include the
formulation of the discretized equations from relevant
nodes and solving the equations using a specified Solver
for updating cable state.
Class Platform: A Platform is a rigid body of six-degree-
of-freedom for simulating the moored floating
structure/device. Its motion is defined by one reference
point. Each platform can have multiple fairleads each of
which is connected to a cable. At each time instant, the
platform displacement and velocity are given at the
reference point. The fairlead motions are calculated
accordingly and then used as instantaneous boundary
conditions in cable analysis. After the cable analysis, the
total mooring load is assembled from the cable fairlead
tension based on the instantaneous relative fairlead
position with respect to the reference point. In addition,
functions are provided to set up mass matrix and the
restoring stiffness due to hydrostatic effect for the purpose
of dynamic relaxation analysis and static analysis using
shooting method. Time integration is implemented to solve
the six-degree-of-freedom motion of the platform.
Noteworthy is that in the simulation once the fairlead states
are updated, the static/dynamic analysis of the cable is
independent of each other. Parallel computing is well-
suited and important since the cable analysis requires the
most computational effort, which is implemented using
OpenMP ( in C++.
Class Solver: A Solver is solves Eq. (1) after finite
difference discretization which is then expressed as
augmented matrix. A Newton-type iteration with
relaxation is used and the method for adjusting the
relaxation factor according to the error evolution is also
provided. In addition, parameters for using generalized-;
method to formulate the algebraic equations for each cable
from the nodes are also stored as members of the cable
solver. The development of the solver class is referred to
the numerical recipes [52] for two-boundary-point
problems. In OpenMOOR, each cable is assigned with one
solver and different solver can be used for the cables.
Class Setting: the Setting class specifies the path to read
input files and output results. It also defines the analysis
type and prepares corresponding parameters.
Class Simulation: A Simulation performs a particular
analysis according to the Setting. Currently, OpenMOOR
supports three types of analysis if used as a standalone
program, i.e. static analysis using shooting method,
dynamic relaxation [52] and dynamic analysis if the
motion of the platform is specified. In case of using
OpenMOOR as a dynamic linking library, only dynamic
analysis is supported, while the dynamic relaxation can be
easily implemented in coupled analysis.
Cable Platform
The input files include the setting file and the main input file
providing cable and platform geometry and structural and
hydrodynamic properties and so on. They are supposed to be
provided as XML files and handled using the rapidXML
( for extracting the parameters.
Other possible inputs including the initial cable state and the
current profile data can be supplied as simple text files. The
cable nodal state and platform state can be output upon
requirement as text files. They can be easily read into Matlab
or Python for post-processing. The Reader and Writer classes
are available to deal with file reading and writing in
After creating the platform and cables and finishing the
initialization, for a new platform state (updated displacements
and velocities), OpenMOOR solves the mooring load following
the steps described below:
Update the fairlead displacements and velocities;
Perform cable analysis in parallel and update the cable
tension at the fairlead;
Transform cable tension into global coordinate system and
assemble the mooring load.
In this section, OpenMOOR is validated using experimental
data from a scaled mooring cable model. The experiment was
carried out by [54] while the digitalized measurement data
provided by [7] is used. The experiment is briefly described
here for the sake of completeness. The experiment setup is
illustrated in Fig. 3. The tests were conducted in a manoeuvring
basin on a chain cable with an unstretched length of 33 m. The
cable was anchored to the basin bottom at one end and the other
cable end was attached, via a ball bearing, to a sheave on the
axis of the motor at a distance from its centre.
Figure 3. The experiment setup (adapted from [7]).
Table 1. Two of the test cases [7].
Case No.
Radius (m)
Several test cases have been carried out with the upper cable
end attached at different distances from the motor axis and at
varying motor rotating speeds. The water depth was 3.0 m. The
force at the upper cable end was measured by a force probe, and
the force data for two of the test cases is made publicly
accessible by [7]. The corresponding forced motions of the
cable upper end in those two cases are listed in Table 1.
In using OpenMOOR to simulate the cable motions, the input
model data derived in [7] is used, as listed in Table 2. The
present version of OpenMOOR ignores the friction effect of the
bottom and hence the related parameters are not listed. The
damping effect of seabed is marginal and is also ignored here.
Noting that the tangential drag coefficient in [7] was applied to
the cable diameter while in OpenMOOR it is applied to the
circumference and hence a value of < =>?@ is used instead.
Besides, a small bending stiffness, i.e. 1 NAm2 is considered to
avoid the ill-posed problem of a perfectly flexible cable in the
absence of positive tension [55]. This small magnitude of the
bending stiffness, however, has limited effect on the solution.
In addition, the seabed stiffness in the calculation is assumed to
be 3E5 Pa which is much smaller than the value presented in
the table. However, parametric studies have been conducted,
showing that this affect the upper end cable tension marginally
while a large stiffness may cause numerical instability and also
increase the computation time.
Table 2. Input data of the model for numerical simulation [7].
Water density
Water depth
Bottom stiffness
Unstretched length
Horizontal span
Vertical span
Axial stiffness
Mass per unit length
Wet weight per unit length
Steel diameter
Normal drag coefficient
Tangential drag coefficient
Added mass coefficient
In the simulation, to deal with these challenging cases when
the cable tension could become zeros, a total of 200 nodes are
used for discretion. A time step of 0.002 second is used and the
generalized-; method is applied. In each case, the simulation
is conducted for 25 seconds. It is also assured that when the
cable nodes are above the still water level the hydrodynamic
effects are automatically excluded. The simulation begins with
the cable upper end at the lowest point of its motion trajectory,
as shown in Fig. 3. For the comparison with experimental
measurements, the transient responses are truncated. The
simulated results are plotted in Fig. 4 and Fig. 5 for the two
cases, respectively, along with the corresponding experimental
measurements of the tension at the upper cable end. Animations
of the full cable motion during numerical simulation can be
found in the GitHub repository.
Overall, the simulated cable tension is consistent with the
experimental measurement in each case. This validates the
capacity of OpenMOOR for modelling the mooring cables in
these challenging situations. In general, it also achieves a
comparable accuracy as MooDy which was used in [7]. The
inclusion of bending stiffness in OpenMOOR makes the
simulated responses smoother, while Moody seems to be able
to capture the high frequency oscillations quite well. The same
experimental data have also been used by [28] for validating
0.0 m
-3.0 m
32.554 m
3.3 m
rotating sheave
chain cable of 33 m
the finite element model developed thereof. By comparing to
the results presented in [28], it seems that OpenMOOR
achieves a better accuracy as compared to the cable model in
that study.
Figure 4. Comparison of the tension at the cable upper end in
case 1.
Figure 5. Comparison of the tension at the cable upper end in
case 2.
This paper introduces the development, validation and
applications of OpenMOOR, an object-oriented framework for
nonlinear mechanical analysis of mooring systems in offshore
renewable energy applications. The program attempts to be
useful for carrying out nonlinear static and dynamic analysis of
mooring systems for offshore wind turbines and wave energy
devices in the concept design and also for cross verification in
developing novel models of mooring cables. The program can
also be a framework for the implementation of other
mathematical models and numerical schemes for mooring cable
Currently, OpenMOOR is able to handle cables with
nonuniform property along the cable but ignores the seabed
friction and wave loading on the cable. It will be further
developed to include these effects and implement novel solving
schemes like harmonic balance method for periodic responses
analysis [56-59]. It will also be used for studying coupled
dynamics of typical floating wind turbine and wave energy
device concepts for the purpose of design optimization and
control [60-66].
This work has received funding from the European Union’s
Horizon 2020 research and innovation programme under the
Marie Skłodowska-Curie EID project ICONN Grant
Agreement No. 675659 and the Irish Research Council (IRC)
via the Government of Ireland Postdoctoral Fellowship (Project
ID: GOIPD/2017/1260).
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... The research of mooring systems admits several classifications, being one of them the methodology employed. The most common methodologies are the experimental ones [2,7] that use scaled models, and the numerical one [8,9] where full-scale models are able to be employed. Additionally, there is a vast number of published articles where both approaches are used [10,11]. ...
... For each of these methodologies, two types of experiments/simulations have been found in the context of mooring systems, either moored floating objects/structures are placed in a towing tank and are excited by currents or waves [12][13][14][15][16][17][18][19][20], or isolated mooring lines are forced to move the fairlead with prescribed motion. These last ones can include clumped weights [6,21] or otherwise only the mooring line [2,[7][8][9]11,[22][23][24][25]. In this experimental and computational study, we follow the second approach and we focus on the isolated mooring dynamics with prescribed motion for the fairlead. ...
... For the numerical computation of the mooring line, the OPASS [10] code based on the finite element method is used. Other numerical alternatives such as the Open-Moor software, similar to OPASS, is explained in [8] and validated against the forced isolated mooring line described in [25]. An interesting advantage of this latter one is that the time integration is performed using the generalized α-method that permits larger time steps. ...
Full-text available
Recently, several experimental and numerical studies have underlined the advantages of adding clumped weights at discrete positions of mooring lines. To confirm the influence of these weights, an experimental study was performed for a 1:30 scale model of a mooring line. In this study, the clumped weight is modeled as a scaled disc placed at different positions along the mooring line. The series of experiments has been carried out at the CEHIPAR towing tank using a submerged studless chain both with and without clumped weights. The experiments consist of the excitation of the suspension point with horizontal periodic motions using different amplitudes and periods, where the mooring line’s tension at the fairlead is measured using a load cell and a dynamometer, and the motion of a part of the line is recorded using low-cost submerged cameras. Similarly to previous experiments, the fairlead tensions increase with higher amplitudes and lower periods, and a clear pattern in the motions of the line at different depths is found. The dissipated energy and the fairlead tension is also increased by the addition of the clumped weight, and the variation of this energy with its position along the line is monitored. The presence of clumped weights is also implemented into a finite element numerical code, previously validated without clumped weights, where all the previous experiments with clumped weights are replicated with remarkable accuracy. This double experimental and computational approach to the problem provides an important dataset for numerical code validations and opens future discussions about the impact of clumped weights on floating platforms.
... These formulations also include more variable as the spin of the element in addition to the spatial three DOF. Most of the models use variations of the Newmark's time scheme integration, like the HHT alpha-method presented by Hilber et al. [19], or the generalized-α method presented by Chung and Hulbert [20] which applies numerical damping dissipation to overcome numerical instabilities [21,22]. ...
... The damping term (c) of the dynamic equation of a vibrating system, Eq. (21), is usually characterized by critical damping coefficient (c cr ) through the damping ratio by = c c • cr . The critical damping coefficient and the natural frequency is defined by Eq. (22) and Eq. (23) respectively [36]. ...
... This value has been set to avoid the use of an artificial numerical damping. The ballast seabed coefficient does not match the value provided by Palm et al. [34], and is set to 3E+05 Pa as set Chen and Basu [22]. ...
Efficient and accurate modelling of mooring and cable systems for Floating Offshore Wind Turbines are a key factor in the coupled dynamic analysis for the realistic assessment of such floating structures. In order to improve the modelling of the mooring and cable systems, a new extension of the slender rod finite element model proposed by Garret with the inclusion of rheological damping is presented. The model takes into account the damping produced for the rod material in both the axial and the bending forces. Derivation of the axial and bending damping forces is presented and assessed in terms of the critical damping. The implementation of the model is presented and tested through three verification simulations and two validation examples, which show a good agreement when comparing with experimental results and prove the capacity and robustness of the model.
... The mooring system load vector f r,m (t) is calculated with OpenMOOR program [64]. The hydrostatic buoyancy load vector f r,b (t) is expressed as: ...
This paper investigated the dynamic responses and the incurred structural damage of a 5 MW spar-type floating offshore wind turbine (FOWT) and a ship when they collide. Ansys/LS-DYNA was used to establish the finite element models (FEMs) of the FOWT and the ship and to subsequently conduct the collision analysis. The global dynamics of the FOWT are captured well by the FEM comparing with FAST code and a simplified 8-degree of freedom (8-DOF) model established in MATLAB. The validity of the ship FEM was guaranteed by the fact that the model outputs agree well with empirical formulas. A series of simulations were then carried out using the FEMs to analyze the impact forces, displacements, accelerations, damages and energy dissipation during the ship collision for various impact velocities. The results show that the peak collision force, peak spar platform displacement and peak tower top displacement increase almost linearly with the initial velocity of the ship. The maximum tower top acceleration during the collision consistently exceeds 0.2 g, severely affecting the normal operation of the FOWT. The collision causes dents on the spar platform rather than the collapse of the whole wind turbine. After the collision, the initial kinetic energy of the ship is mainly transformed into the plastic deformation energy of the FOWT and the energy dissipated in the water. In addition, assuming a rigid ship bow results in accurate FOWT dynamic responses but fails to provide a good evaluation of the spar platform deformation.
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The concept of monitoring mooring stress response in real-time is not new, but its direct implementation in offshore wind energy activities is still a challenge. The study aims to present a simulation technique for controlling the hydrodynamic forces acting on the finite element mooring lines depending on a user-subroutine of an explicit finite element software. By controlling the mooring forces based on mooring nodal displacement in real-time, the mooring stress response is possible to be calculated using the finite element method. We introduced the theoretical background to develop the present method. In order to validate the present method, the five typical mooring configurations proposed by international standards were prepared: Catenary, Semi-taut, Taut, Lazy-S configuration type, and Catenary mooring with the inclined seabed type, respectively. The present method predicted the stress distributions along the mooring line where the upper end was excited by a typical wave frequency motion and the other end was anchored to the seabed. And the experimental and numerical results of five typical mooring configurations were compared to the results calculated from the present method. A good agreement was drawn from the comparative study of both quasi-static and dynamic mooring responses. The validation of the present method is helpful for further investigating the effects of the fluid loads, the mooring geometrical, and material nonlinearity on the real-time structural responses of mooring lines in service life.
The utilization of renewable energy has great significance to reduce CO2 emissions. Floating offshore wind turbines (FOWTs) is regarded as most cost-effective solution to harness the offshore renewable energy in deep-water. Fully coupled analysis is regarded as the state-of-art simulation method for FOWT's design and analysis. Until now, various methods (lumped mass model, quasi-static model, finite element model et al.) are used in mooring line modelling in the fully coupled simulation for FOWTs. In this paper, a new dynamic model for catenary mooring line is proposed based on the vector form intrinsic finite element (VFIFE) method. This method is designed to calculate motions of a system, which the motion may include large rigid body motions and large geometrical changes, or very large deformations. The inertia and hydrodynamic and the seabed interaction are contained in this model. Newton's law of particle is assumed to derive the governing equations of motion. An explicit algorithm is used to calculate the numerical results. The feasible and accurate of the dynamic model are verified by comparing with the experimental data and other validated codes. In the comparisons the results of VFIFE method has a good agreement with the references. Thus, the dynamic model proposed in this paper is capable for the dynamic analysis of mooring lines. Furthermore, the influence of the forced motion frequency (and amplitude) of mooring system on the hysteresis loop area is studied, which reveals the mechanism of the energy dissipation from the viscous damping of fluid and the gravitational potential energy of the line.
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This study develops a coupled nonlinear hydrodynamic model of a mooring system consisting of multiple cables for analyses of floating offshore wind turbines (FOWTs). The model is based on a finite difference model of submerged cables which considers cable-seabed interaction, current effect, cable bending and torsional stiffness. The implementation of the model proposes a parallelization scheme for solving the cable responses to improve the computational efficiency. The developed program is then coupled with a spar type FOWT and verified using an experimentally validated open source mooring simulation program. Furthermore, the model is used to study the impact of nonlinear dynamics of the mooring system on FOWT responses in the presence of current. Both static responses of a spar FOWT under current load and dynamic responses of the spar FOWT under wind, wave and current loads are investigated. Responses are compared where varied mooring models are used including the linear model, quasi-static model and nonlinear mooring models without and with current effect on cables considered. The results show that the current effect on cables can have a considerable impact on the restoring effect of the mooring system and hence the spar and cable responses. The current effect on mooring cables needs to be properly considered in the FOWT analysis.
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The increasing desire for using renewable energy sources throughout the world has resulted in a considerable amount of research into and development of concepts for wave energy converters. By now, many different concepts exist, but still, the wave energy sector is not at a stage that is considered commercial yet, primarily due to the relatively high cost of energy. A considerable amount of the wave energy converters are floating structures, which consequently need mooring systems in order to ensure station keeping. Despite being a well-known concept, mooring in wave energy application has proven to be expensive and has a high rate of failure. Therefore, there is a need for further improvement, investigation into new concepts and sophistication of design procedures. This study uses four Danish wave energy converters, all considered as large floating structures, to investigate a methodology in order to find an inexpensive and reliable mooring solution for each device. The study uses a surrogate-based optimization routine in order to find a feasible solution in only a limited number of evaluations and a constructed cost database for determination of the mooring cost. Based on the outcome, the mooring parameters influencing the cost are identified and the optimum solution determined.
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The design of reliable station-keeping systems for permanent floating structures such as offshore renewable energy devices is vital to their lifelong integrity. In highly dynamic and/or deep-water applications, including hydrodynamics and structural dynamics in the mooring analysis is paramount for the accurate prediction of the loading on the lines and hence their dimensioning. This article presents a new workflow based on EDF R&D's open-source, finite-element analysis tool Code_Aster, enabling the dynamic analysis of catenary mooring systems, with application to a floating wind turbine concept. The University of Maine DeepCwind-OC4 basin test campaign is used for validation, showing that Code_Aster can satisfactorily predict the fairlead tensions in both regular and irregular waves. In the latter case, all of the three main spectral components of tension observed in the experiments are found numerically. Also, the dynamic line tension is systematically compared with that provided by the classic quasi-static approach, thereby confirming its limitations. Robust dynamic simulation of catenary moorings is shown to be possible using this generalist finite-element software, provided that the inputs be organised consistently with the physics of offshore hydromechanics.
Conference Paper
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Mooring cables are of significant importance to floating offshore structures in renewable energy applications such as floating offshore wind turbines and wave energy converters. They typically exhibit strong nonlinear behaviour. Recently, modelling mooring cable dynamics has received considerable attention driven by the increasing need for cleaner energy. Several models, including lumped-mass model, finite element model and finite difference model, are already available for considering the nonlinear geometric, hydro-dynamics, and cable-seabed interaction. Some of them have been experimentally validated and incorporated into coupled dynamic analysis of floating structures. Therefore, it still lacks in general understanding of the mooring cable dynamic characteristics. On the other hand, the dynamic characterisation is substantial for mooring cable design and model reduction. In this regard, this study focuses on mooring force responses of cables when subjected to top end harmonic excitations from the floating platform. A finite difference model able to account for the cable geometrical nonlinearity, fluid current and cable-seabed interaction is adopted for numerical studies. In practical three-dimensional case, the mooring cables of a floating platform are subjected to in-plane as well as out-of-plane excitations. The cable responses when the cable top end is under excitations in all the three directions are thus considered. In all the cases super-harmonic responses have been observed. In particular, this phenomenon appears more significant when the excitation is in the out-of-plane direction. In addition, it is observed that the fluid current velocity in the out-of-plane is influential on such kind of cable responses.
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This paper focuses on modelling snap loads in mooring cables. Snap loads are a known problem for the established oil and gas industry, and they pose a major challenge to robust mooring design for the growing industry of wave energy conversion. We present a discontinuous Galerkin formulation using a local Lax-Friedrich Riemann solver to capture snap loads in mooring cables with high accuracy. An hpÀadaptive scheme is used to dynamically change the mesh size h and the polynomial order p, based on the local solution quality. We implement an error indicator and a shock identifier to capture shocks with slope-limited linear elements, while using high-order Legendre polynomials for smooth solution regions. The results show exponential error convergence of order p þ 1∕2 for smooth solutions. Efficient and accurate computations of idealised shock waves in both linear and nonlinear materials were achieved using hpÀadaptivity. Comparison with experimental data gives excellent results , including snap load propagation in a mooring chain. Application on a wave energy device using coupled simulations highlights the importance of the touchdown region in catenary moorings. We conclude that the formulation is able to handle snap loads with good accuracy, with implications for both maximum peak load and fatigue load estimates of mooring cables.
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The focus on alternative energy sources has increased significantly throughout the last few decades, leading to a considerable development in the wave energy sector. In spite of this, the sector cannot yet be considered commercialized, and many challenges still exist, in which mooring of floating wave energy converters is included. Different methods for assessment and design of mooring systems have been described by now, covering simple quasi-static analysis and more advanced and sophisticated dynamic analysis. Design standards for mooring systems already exist, and new ones are being developed specifically for wave energy converter moorings, which results in other requirements to the chosen tools, since these often have been aimed at other offshore sectors. The present analysis assesses a number of relevant commercial software packages for full dynamic mooring analysis in order to highlight the advantages and drawbacks. The focus of the assessment is to ensure that the software packages are capable of fulfilling the requirements of modeling, as defined in design standards and thereby ensuring that the analysis can be used to get a certified mooring system. Based on the initial assessment, the two software packages DeepC and OrcaFlex are found to best suit the requirements. They are therefore used in a case study in order to evaluate motion and mooring load response, and the results are compared in order to provide guidelines for which software package to choose. In the present study, the OrcaFlex code was found to satisfy all requirements.
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Mathematical analysis is an essential tool for the successful development and operation of wave energy converters (WECs). Mathematical models of moorings systems are therefore a requisite in the overall techno-economic design and operation of floating WECs. Mooring models (MMs) can be applied to a range of areas, such as WEC simulation, performance evaluation and optimisation, control design and implementation, extreme load calculation, mooring line fatigue life evaluation, mooring design, and array layout optimisation. The mathematical modelling of mooring systems is a venture from physics to numerics, and as such, there are a broad range of details to consider when applying MMs to WEC analysis. A large body of work exists on MMs, developed within other related ocean engineering fields, due to the common requirement of mooring floating bodies, such as vessels and offshore oil and gas platforms. This paper reviews the mathematical modelling of the mooring systems for WECs, detailing the relevant material developed in other offshore industries and presenting the published usage of MMs for WEC analysis.
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The goal of the chapter is that the reader shall be able to self-dependently make a first, preliminary analysis of wave-induced horizontal forces, motions and mooring tensions for a moored floating wave energy device. Necessary prerequisites to attain that goal are the understanding of the physical phenomena, awareness of simplifying assumptions and some insight into the available mathematical and numerical tools. It is demanding to establish the hydrodynamic forces and reactions for wave-energy devices, because they may undergo very large resonant motions, have very complex shapes being composed of articulated connected bodies or involve a net flow of water through the device. This makes it difficult to use conventional potential methods. Most devices need undergo extensive tank and field testing. However, here we will sketch simplified methods for first estimates of environmental forces, response forces, and response motions useful in the concept stage and for planning tank tests.
Mooring cables are critical components of ocean renewable energy systems including offshore floating wind turbines and wave energy converters. Mooring cable dynamics is strongly nonlinear resulting from the geometric effect, hydrodynamic loads and probably seabed interactions. Time-domain methods are commonly used for numerical simulation. This study formulates a nonlinear frequency domain multi-harmonic balance method for efficient analysis of a mooring cable subjected to periodic fairlead motions. The periodic responses are of particular interest to investigate the mooring effect on the platform. In the formulation, the governing equations of the three-dimensional cable motions are spatially discretized using the finite difference method; the nonlinear ordinary differential equations are subsequently transformed into the frequency domain by expanding both the structural responses and the nonlinear nodal forces using truncated Fourier series, leading to a set of nonlinear algebraic equations of the Fourier coefficients. The equations are eventually solved using Newton's method where the alternating frequency/time domain method is used to handle the nonlinearity effect. The presented method is then compared to a time-domain method by numerical studies of a mooring cable. The results show that the method is of comparable accuracy as the time-domain method while it is generally more efficient. The proposed method shows promising results even when the cable tension becomes non-positive for a period of time during the cable motion, which is a known ill-posed problem for time-domain methods.
This paper considers the effects of current and wave-current interactions in fatigue analysis of floating offshore wind turbines (FOWTs). Surface water waves experience frequency shifts and wave shape modification when traveling on underlying currents. The wave-current interactions are known to be important for the responses of offshore structures, however, they have not been considered in FOWT fatigue analysis. To include such interactions, a nonlinear mooring hydrodynamics model is presented which is able to consider the cable geometric nonlinearity, seabed contact, and the current effect. The mooring model is then coupled with a spar-type FOWT model which simulates the structural dynamics of turbine blades and tower; aerodynamics of the wind-blade interaction and wave-current actions on the spar. Analytical wave-current interaction models based on Airy's theory considering the current effect are applied for generating the flow field. Based on a spar-type FOWT and the wave-current interaction model, numerical simulations have been performed for three cases with only waves, wave and current without and with interactions. The comparison of the structural responses shows that the current and the wave-current interaction can have significant influences on FOWT tower and cable responses. Furthermore, cable fatigue life is estimated for two particular cases when the cable tension is decreased and increased respectively due to the presence of current. It is found that if the current tends to increase the cable tension, neglecting the current and wave-current interactions leads to overestimate of the cable fatigue life.