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Marine & Offshore Renewable Energy, 26 – 27 September 2012, London, UK
© 2012: The Royal Institution of Naval Architects
OFFSHORE FLOATING VERTICAL AXIS WIND TURBINES: ADVANTAGES, DISADVANTAGES, AND
DYNAMICS MODELLING STATE OF THE ART
M Borg, M Collu and F P Brennan, Cranfield University, UK
SUMMARY
The desire for more cost-effective wind farms has pushed for offshore projects to move further offshore and into deeper
water depths: i.e. higher wind resources per unit area, ability to exploit new, wider sites (in particular for those countries
with a limited shallow continental shelf), and partial/total elimination of visual impact. As fixed support structures
become not economically viable in deeper waters, a transition to floating support structures is required.
In this paper, the advantages and disadvantages of using vertical axis wind turbines (VAWTs) instead of horizontal axis
wind turbines (HAWTs) on floating support structures are discussed. In recent years, a number of dynamics
mathematical models only for floating HAWTs and their numerical implementation have been developed: research on
floating VAWTs is just starting. In the present work, the dynamics of a floating VAWT system are illustrated and
modelling approaches are discussed. These include aerodynamics, hydrodynamics, mooring line dynamics, structural
dynamics and control system dynamics.
1. INTRODUCTION
To date, the majority of the offshore wind farms have
been located in relatively shallow waters (average of 10-
15 metres) and nearshore (a few km from the coast).
Moving towards deeper sites can offer several
advantages: higher wind resources per unit area, ability
to exploit new, wider sites (in particular for those
countries with a limited shallow continental shelf), and
partial or total elimination of visual impact. Most
importantly, offshore wind farm sites offer the possibility
to further scale up the power (and size) of the wind
turbines used, helping to lower the final cost per kWh of
energy produced. To confirm that this is also the view of
the UK government, the Energy Technologies Institute
(ETI) announced a plan to invest £25m in offshore
floating wind turbine projects1.
The onshore wind industry has reached a relatively
mature level, and a large majority of large scale wind
turbines share the same configuration: horizontal axis of
rotation, three blades, upwind, variable-speed, and
variable blade pitch (with feathering capability). This has
been the result of several decades of research and
development, and originally several configurations had
been considered, including HAWTs with a different
number of blades, but also VAWT configurations. The
conventional design emerged as the optimum techno-
economic trade-off for the onshore large scale wind
market.
The same “evolutionary process” did not take place for
the offshore wind market, substituted by a “marinisation”
of the configurations used for the onshore market. It has
been implicitly assumed that, despite the very different
environmental conditions of an offshore environment, the
optimum configuration for the wind turbine is the same:
the conventional three bladed, upwind, horizontal axis
wind turbine. This has been implicitly assumed not only
1 ETI looks to open new opportunities for offshore wind in the UK
with plans to invest £25m in floating platform projects.
25/10/2011, http://www.energytechnologies.co.uk
for the seabed-fixed offshore wind turbine
configurations, but also for the proposed floating
systems. NREL (USA), with their report “Definition of a
5-MW Reference Wind Turbine for Offshore System
Development” [1], proposed a reference wind turbine to
be used to compare different fixed and floating support
structures for offshore wind turbines. It is widely used
(around 250 citations), and the configuration is basically
the same as a conventional onshore large wind turbine.
It is therefore important to assess the technical and
economic feasibilities of alternative concepts for the
offshore floating wind industry, in order to ensure that
the most suitable configurations are employed. As part of
this task, the present work focuses on VAWTs, and it
aims at presenting a comprehensive literature review, a
fundamental first step toward the development of a
dynamics modelling tool for this alternative
configuration.
2. VAWTS VERSUS HAWTS
State of Technology. Since HAWTs have been the main
focus of the wind energy industry over the past decades,
its state of technology is more mature than that of
VAWTs, with a large number of successfully deployed
projects and the formation of a dedicated supply chain.
VAWTs were investigated in the late 20th century but
interest was lost mainly due to fatigue issues and low
efficiencies [2].
Conversion Efficiency. The maximum theoretical
efficiency of any wind turbine is 59.3% (the Betz limit)
[3]. HAWTs are inherently more efficient than VAWTs
with efficiencies of up to circa 50% compared to circa
40% for VAWTs. This should not be seen as the ultimate
deciding factor between the two configurations as many
other factors affect the final cost of electricity.
Upscaling. A major factor in designing floating wind
turbines is scalability, as the system is more cost-
effective at larger scales. HAWTs have a limiting factor
Marine & Offshore Renewable Energy, 26 – 27 September 2012, London, UK
© 2012: The Royal Institution of Naval Architects
due to gravitational fatigue since the blades undergo
tension-compression cycles as the rotor rotates [3].
VAWTs do not undergo this phenomenon and so far do
not seem to have any major obstacles in upscaling.
Fatigue. Whilst HAWTs have gravitational fatigue
issues, VAWTs produce a cyclically varying torque that
can have adverse effects on the transmission and control
systems [4]. Whilst this produces high-frequency fatigue
cycles in small-scale VAWTs, multi-megawatt VAWTs
would rotate at a few revolutions per minute, where it
would not be such a significant problem. Also with
advances in materials technology, fatigue can more
easily be remedied today.
Machinery Position. A very important aspect is the
position of the transmission and generation system. In an
HAWT it is at the very top of the tower (considering the
latest offshore wind turbines, the nacelle weight around
400 t, and is around 100 m above the ground), inducing
greater bending moments and motions on the tower,
requiring larger, stronger structures. This would also
require a larger floating platform to deal with the larger
loads. On the other hand VAWTs usually have the
transmission and generation system at the bottom [5],
requiring small support structures and complying more
with fundamental naval architecture principles.
Packing Factor. In wind farms using HAWTs, the
turbines are usually placed a distance of up to ten times
their diameter from one another due to the effect of their
wakes [6], leaving large amounts of unexploited space in
between them. With VAWTs it has been postulated that
their wake dissipates much quicker than those of
HAWTs, allowing them to be packed closer together.
Installation Issues. Floating wind turbines provide the
possibility of the majority of construction being done
dockside rather than on site. Whilst this is beneficial to
both HAWTs and VAWTs, the former still require very
large cranes to mount the machinery and blades,
increasing the capital costs [4]. This aspect is also an
advantage over fixed-support wind turbines, as they are
usually assembled on site.
Operation & Maintenance (O&M) costs. When
comparing HAWTs and VAWTs, the O&M costs are
likely to be higher for HAWTs as the machinery is at the
top of the tower. This would mean technicians need to
ascend the tower to inspect the machinery and major
component changes would require specialist cranes and
longer periods of downtime. A positive impact for both
turbine configurations due to upscaling is that O&M
costs will not increase greatly with increasing size,
making larger units more cost-effective.
3. COUPLED MODELLING APPROACHES
The offshore environment subjects a floating wind
turbine system to loads from differing origins. These
include aerodynamics, hydrodynamics, mooring line
dynamics, structural dynamics and control dynamics. An
in-depth understanding of each of these aspects is needed
to develop an appropriate, efficient coupled model of
dynamics.
3.1 FREQUENCY VS TIME DOMAIN
The first major choice in modelling is to perform the
analysis in the frequency or time domain. The benefits of
using frequency-domain analysis are that it has been used
extensively in the offshore oil & gas industry; it is also
computationally very efficient and is very useful to
determine the natural frequencies of the system.
Frequency-domain methods have also been used for the
preliminary design of a number of offshore floating wind
turbines: Tri-Floater concept (Bulder [7]), tension leg
platforms (TLPs) (Lee [8], Wayman et al. [9]), barges
(Wayman et al. [9]), semisubmersibles (Collu et al. [10],
Lefebvre and Collu [11]).
Whilst frequency-domain analysis may be an important
tool in the preliminary stages of design, it has some
important disadvantages that limit its use in detailed
design. The linearization required for frequency-domain
analysis does not allow for any nonlinear dynamics to be
included. It also cannot capture transient events, which
may be critical in the design of a floating wind turbine.
Matha [12] found that certain couplings between the
tower and horizontal axis blade assembly and platform
modes were not captured in the frequency-domain
analysis. The main cause of this was the use of rigid
blades and tower in the frequency domain, with flexible
components used in the time-domain. This results in
different natural frequencies and system motions. Whilst
it is possible to include a flexible structural model in the
frequency-domain, the approach assumes small
displacements, which is not valid in the case of floating
wind turbines. Therefore a time-domain analysis, where
the inclusion of a complete flexible model is possible, is
preferential to investigate the transient and nonlinear
dynamics of floating wind turbines.
A major contribution to time-domain integrated
dynamics design codes was made by Jonkman [13].
Jonkman developed a comprehensive simulation tool for
the coupled dynamic response of floating HAWTs, and
then performed integrated dynamic analysis on an
HAWT mounted on a barge-type platform according to
the IEC 61400-3 design standard [14]. This tool has
become integrated into FAST, one of the most-widely
used offshore HAWT design codes. Most studies on the
coupled dynamic response of floating HAWTs have used
FAST, or a modified version of it (e.g. [15-19]). Cordle
and Jonkman [20] performed a comprehensive review of
all the current simulation codes available for floating
horizontal axis wind turbines.
Marine & Offshore Renewable Energy, 26 – 27 September 2012, London, UK
© 2012: The Royal Institution of Naval Architects
3.1 CURRENT CHALLENGES WITH COUPLED
DYNAMICS DESIGN CODES
A current issue with performing coupled dynamics
simulations is the interfacing of different software
packages to provide a fully integrated numerical
simulation. Problems with the communication of data
between different programs lead to instabilities and
longer simulation times. This was seen in Cermelli et al.
[15], where a number of codes were coupled together to
analyse a floating HAWT. Whilst the interfaced codes
provided the required results, the authors noted that there
were issues with the interfaces.
Another issue following on from the above is the need to
have faster and more efficient design codes. With current
design codes achieving a ratio of 1:1 between simulated
and simulation times, there is a great need to have faster
codes to allow for accelerated design cycles and
optimization.
Some initial research to increase the efficiency of a
coupled design code was done by Karimirad and Moan
[21]. The authors simplified the analysis such that it still
gave acceptable results. The authors claim to have
achieved simulation-to-simulated time ratios of 1:4, and
whilst this is an improvement, the reduction in accuracy
of the simulation might not warrant the reduction in
computation time.
As will be mentioned further on, the validity of certain
models will be questionable when applied to the floating
offshore environment. This is evident with the use of
aerodynamic momentum models, as the assumption of
momentum balance may not necessarily apply in the
unsteady conditions found offshore, which has been
discussed in detail by Sebastian [22].
3.2 PREVIOUS FLOATING VAWT RESEARCH
So far, little research has been done on investigating
floating VAWTs. Vita [5] analysed a Darrieus-type rotor
mounted on a spar buoy rotating platform, both at a
technical and economic level. The concept proposed was
envisaged to be simple to construct and transport, thereby
reducing costs. Some shortcomings were that since it has
an extremely large draft, it may be used in water depths
above 150m and had power losses through friction
between the rotating platform and water.
Collu, Brennan and Patel [23] presented the preliminary
conceptual design and optimisation of a floating support
structure for the NOVA rotor. The concept of this novel
vertical axis rotor is to reduce the overturning moment
acting on the support structure whilst maintaining
sufficient power output. Another concept proposed by
Akimoto, Tanaka and Uzawa [24] was the floating axis
wind turbine. This concept differs from that proposed by
Vita because the generator is located outside the floating
platform, with roller bearings transferring torque from
the rotating tower to generators around the tower. The
main idea was to eliminate the need to have large
bearings supporting most of the loads from the rotor and
to allow for much easier access for maintenance. Another
concept was proposed by Cahay et al. [25] for a 3-bladed
H-type Darrieus rotor mounted on a semi-submersible
similar to the Dutch tri-floater design.
So far there has been no dedicated coupled modelling of
floating VAWTs, except for the work done by Vita to a
certain extent. The above studies were not based on fully
coupled analyses, which may lead to certain
characteristics of the system being excluded. There is a
need to develop a general coupled model of dynamics for
floating VAWTs such that their dynamic behaviour may
be investigated in detail. To be able to develop such a
model, one must first identify the most suitable
approaches to model the various aspects of the floating
wind turbine system.
4. AERODYNAMICS
The major aerodynamic modelling approaches used for
VAWTs are the Blade Element Momentum (BEM)
model, Cascade model and Vortex model [26], whilst
panel methods also seem to be a promising approach for
modelling VAWTs [27-30].
4.1 BLADE ELEMENT MOMENTUM MODEL
This model is based on equating the streamwise
momentum change across the turbine to the forces acting
on the turbine blades [31]. The double-multiple
streamtube (DMST) model as described in [32] is the
most elaborate variant, and has the best agreement with
experimental results [26; 33] for momentum models.
Subsequently, further improvements to include
secondary effects were made in [33-35].
Although this model gave good agreement with
experimental results of the overall performance for light-
loaded, low-solidity rotors, it suffers both numerically
and in accuracy when the rotor has a high solidity, is
heavily loaded and/or is operating at high tip-speed ratios
[26; 31; 33]. Furthermore, the assumption of quasi-steady
flow in these models may be violated by the complex
flow field of floating wind turbines [36; 37], thereby
possibly rendering these models invalid. Another issue is
that this model was not inherently developed for floating
turbine applications. To evaluate the loads acting on the
rotor at a particular instance, a whole rotor revolution
must be computed. Therefore for time-domain
simulations this model is not the most suitable.
In spite of these drawbacks, the very efficient and quick
execution times of these models have seen them maintain
popularity. They should not be disposed of, as they can
be an essential tool in the preliminary research and
design of VAWT systems. BEM models can speed up the
initial phases of a project by allowing a vast number of
simulations to be carried out in a relatively short period
of time, narrowing down the number of possible
configurations and therefore allowing a more precise but
more computationally demanding approach.
Marine & Offshore Renewable Energy, 26 – 27 September 2012, London, UK
© 2012: The Royal Institution of Naval Architects
4.2 CASCADE MODEL
This model is based on cascade theory used in
turbomachinery design [38; 39], and was first applied to
VAWTs by Hirsch and Mandal [40]. The blades of the
rotor are assumed to be positioned on a plane surface,
known as a cascade, with the spacing between adjacent
blades equal to the rotor circumference divided by the
number of blades. The development of this model then
follows a similar route as the DMST momentum model.
An improvement over the model presented by Hirsch and
Mandal was proposed by Mandal and Burton [41] to
include flow curvature and dynamic stall. These
modifications produced results that were comparable
with those from the more complex dynamic vortex
model.
Although this model requires more computational time
than its momentum model counterpart, it provides more
accurate overall values for both low and high solidity
rotors [26], and does not suffer convergence problems at
high solidities and high tip speed ratios [26]. According
to [40], momentum models are not suited for calculating
instantaneous blade forces and wake velocities for high
solidity rotors and for high tip speed ratios.
This type of model can be used in situations where the
momentum models break down. So far there has not been
any research into whether this model can fully
incorporate the unsteady, complex flow associated with
floating wind turbines, although Mandal and Burton [41]
did incorporate dynamic stall.
4.3 VORTEX MODEL
The basis of potential flow is used in this model. The
velocity field in the vicinity of the rotor is obtained by
calculating the influence of vorticity in the wake of the
blades [26; 33]. In this model the airfoil blades are split
up into a number of elements, and each element is
replaced by a bound (or substitution) vortex filament,
also known as a lifting line [31]. Two dimensional vortex
models for VAWTs were first proposed by Larsen [42],
and a further two dimensional models were presented by
others [43], [44] and [45]. These models made several
assumptions such as: high tip-speed ratios, lightly loaded
rotor, small angles of attack to ignore stall, and high
height-to-diameter ratios (for two-dimensional flow).
These assumptions limited the vortex models to specific
situations.
The first three-dimensional model was presented by
Strickland et al. [31]. Further improvements [46]
included dynamic effects, such as dynamic stall, pitching
circulation and added mass. When comparing with
experimental results, it was found that there was good
correlation for instantaneous blade forces and near-wake
velocities. Some discrepancies were attributed to
shortcomings in the experimental set-up [31].
To further enhance this free-vortex model, Cardona [47]
incorporated flow curvature as well as modifying the
dynamic stall model. These modifications were found to
improve the correlation between results for both overall
power coefficient values and instantaneous blade forces.
Vandenberghe and Dick [48] presented a modified
analysis of this model by using a multi-grid approach. It
was found to reduce computational times and was
proposed to be used for the parametric optimisation of
VAWTs and also for pitch-controlled turbines.
Another modification to the free-vortex model was done
by Beyer et al. [37] by using curved vortex filaments
rather than straight ones. Problems with convergence of
the straight line and curved filament models at fine
discretizations were encountered, which still has to be
investigated.
Another approach was taken by Ponta and Jacovkis [49]
to combine the free-vortex model with a finite element
analysis of the flow in the vicinity of the rotor. The
concept behind this approach was to split the analysis
into two separate regions: macro and micro models. This
helped to avoid certain shortcomings of the
abovementioned vortex model, and showed better
agreement with experimental results. One disadvantage
of this approach is that it does not cover all stall
phenomena.
Sebastian [36] recently showed the potential of applying
vortex models to floating horizontal axis wind turbines.
The ability of vortex models to accurately predict the
near wake velocities allowed for more precise
simulations of the wake-rotor interactions. These
interactions may prove to be an important factor, as they
may significantly affect the aerodynamic performance of
the floating turbine. Scheurich and Brown [50] also
recently modelled a VAWT using a vorticity transport
model to investigate the overall turbine efficiency for
different VAWT configurations in both steady and
unsteady wind conditions.
Whilst the vortex model is deemed the most accurate of
the models discussed so far [26], it requires substantially
more computation time than either the momentum or
cascade models. This is an important factor in coupled-
dynamics modelling, as the model has to execute as fast
as possible, and has been the main reason vortex models
have as yet not really been implemented in coupled
dynamics codes (except for Sebastian [36]). Advances in
desktop computational power and parallel computing
have paved the way for much faster computation times of
three-dimensional vortex models [51; 52], with up to a
35.9 fold reduction over single processor times [52]. As
discussed by Muskulus [53], vortex models are a viable
option for use in coupled dynamics modelling of floating
wind turbines. A shortcoming of this large reduction is
that the model is required to be programmed in a
language specific for multi-core processing units, but this
can be overcome in programming environments such as
MATLAB.
4.4 PANEL MODEL
This approach is based upon discretizing the surface of
the rotor into a number of panels subjected to a potential
flow regime. On each panel, an ideal flow element is
placed with a prescribed strength. This method has been
Marine & Offshore Renewable Energy, 26 – 27 September 2012, London, UK
© 2012: The Royal Institution of Naval Architects
applied in ship hydrodynamics as well as aircraft
aerodynamics, as reviewed by Erickson [54].
The relatively fast computational times in comparison to
using the full Navier-Stokes equations is one of the main
benefits of this method. Another major benefit of panel
methods is that the geometry is arbitrary, and does not
rely on airfoil data.
Eliassen and Muskulus [30] implemented and validated a
fast hybrid vortex-panel model on a general purpose
GPU, showcasing the potential of this model and
computational strategy.
A three-dimensional panel method for VAWTs was first
presented by Dixon et al. [29] and was then validated by
[55] and [56]. In [55], Stereo-PIV experimental results
and smoke-trail studies for a straight-bladed VAWT were
used to demonstrate the validity of the model. This
model was developed to analyse and understand the
development of the near wake and tip vortices of a
VAWT.
Since this type of model is based on potential flow,
viscous effects such as dynamic stall are not implicitly
included. Therefore there is a need to incorporate a
boundary layer model such as the lag-entrainment
method [57], which is not a trivial task. It has yet to be
seen whether panel models can compete with the
previously described methods with regard to computation
time, but they do offer a detailed analysis of the near
wake of a VAWT, allowing for the analysis of novel
rotors and the interaction between the rotor and its wake.
5. HYDRODYNAMICS
As mentioned before, modelling may be done in two
main approaches: frequency-domain and time-domain.
Whilst they both have their advantages and
disadvantages, the frequency-domain has been more
widely used in the offshore oil and gas industry.
The frequency-domain has been an attractive approach
due to its relative ease of implementation and fast
computational speed. These are important factors during
the design of an offshore structure, as a large number of
simulations are usually required. The downfall of this
approach is that it requires linearization of the system of
dynamics, which results in the inability to capture
nonlinearities and transient events, as illustrated by
Wayman [9] and Matha [12] with regard to floating wind
turbines. Philippe et al. [58] also performed a
comparative study between frequency and time domain
simulations of a floating wind turbine and highlighted the
importance of including nonlinear effects.
Whilst frequency-domain analysis is all but absent from
floating wind turbine design codes, it may still play an
essential role in the preliminary design of the floating
structure, as it is very useful to establish the natural
frequencies of the system. With this knowledge and that
of the wave energy spectrum, the preliminary design’s
natural frequencies can be shifted away from the high-
energy wave frequencies.
5.1 TIME-DOMAIN MODELLING
The Morison equation [59] is one of the most widely-
used modelling tools in wind turbine simulation tools. It
is an empirical relation describing the viscous and
inertial loads on a vertical slender cylinder subjected to
small amplitude, high frequency oscillations. Whilst it
has been used successfully for fixed offshore wind
turbine structures, its assumptions do not hold for most
floating wind turbine support structure concepts. As
many designs involve the use of large-volume structures
that change the characteristics of the incident waves and
are subjected to large-amplitude motion, the Morison
equation is inadequate for a generalised hydrodynamic
model. One possible use of the Morison equation is to
integrate the viscous term into the time-domain model to
account for loads on slender structural members, such as
braces and secondary struts.
The first ab initio approach to the time-domain
hydrodynamics modelling of floating bodies was done by
Cummins [60], with later expansion of its
implementation by Ogilvie [61]. In this approach the
loads acting on the floating body are separated into three
problems that are solved separately, relying on the linear
superposition of the effects. They consist of radiation,
diffraction and hydrostatic loads. The use of this
approach allows the inclusion of nonlinear effects in the
equations of motion. This method has been implemented
by Jonkman [62] in the HydroDyn module of the open
source code FAST.
The downfall of this method is that the convolution
integrals are computationally expensive. This can be
remedied by truncating the integral to a set length of time
beyond which there is no noticeable contribution, as done
by Jonkman [62]. A recent approach has been to
approximate the convolution integrals with state space
models as done by [63-66]. One of the major
characteristics of state space modelling is that it is
inherently computationally very efficient, with
Taghipour et al. [66] finding that the state space
approach runs about 80 times faster than by calculating
the actual convolution integrals. It was noted that this
difference increased with smaller time steps and longer
simulated times. Hence this method is very beneficial for
the detailed analysis of floating structures, and matches
very well with the requirement of having very fast
computational models.
As the state space approach involves approximations, it
is important to identify the errors involved and if they are
small enough to be acceptable. During the construction
of the state space representation, frequency-dependent
hydrodynamic coefficients are required. These are
usually obtained from potential-flow software packages
such as SESAM [67] and WAMIT [68]. With these in
hand, there are two approaches to applying them in the
state space model: direct time-domain identification and
frequency-domain identification. Taghipour et al. [66;
69] describe in detail the advantages and disadvantages
of the different state space model identification methods,
with the frequency-domain variant being more accurate.
Marine & Offshore Renewable Energy, 26 – 27 September 2012, London, UK
© 2012: The Royal Institution of Naval Architects
6. MOORING LINE DYNAMICS
The mooring line effects on the dynamic response of a
floating structure, in particular floating wind turbines,
can be significant when situated in deep to very deep
water. The most rudimentary model for mooring lines is
the linear force-displacement relationship. In this model
resistances to surge and sway are introduced to represent
the station-keeping characteristics. There is also the
possibility to include resistances in roll and pitch. This
model is not very accurate, but may be used in the very
initial analysis of a moored floating structure.
An improvement on this model is the quasi-static
approach. This approach has been adopted by some, but
may yield unsatisfactory results and a move towards
nonlinear dynamic models is required [53; 70; 71]. One
issue that has not arisen with floating HAWTs due to
their inherent design is the effect of the rotating rotor-
generator assembly. With no fixed structure to
compensate for the torque generated, the mooring lines
will have to accommodate this extra load in a VAWT
configuration.
One promising approach able to model this nonlinearity
is the multibody formulation as described by Cordle [53;
70; 71]. Its ability to accommodate large-amplitude,
three-dimensional motion and hydrodynamic drag forces,
whilst not being too computationally expensive, makes
this approach very attractive. Another advantage is that
the multibody formulation uses the same underlying
mathematics that describe the structural dynamics (see
below), thereby using common modules for simulation
execution. This will lead to less development time and a
more streamlined and robust model.
7. STRUCTURAL DYNAMICS
To model the dynamics of the system, some sort of
discretization is usually required. The most basic level is
to model each major component as a rigid body with the
appropriate number of degrees of freedom (DOFs). More
detailed analysis requires the discretization of each body
into a number of elements, each with its own set of
DOFs. The level of discretization and the types of
elements used vary significantly depending on the
application and method used.
Two main methods that use discretization of components
are the multibody formulation and the finite element
method (FEM). FEM is very computationally intensive
since it usually results in thousands of equations to be
solved simultaneously. To reduce this large
computational requirement, reduced order models may
be implemented that still represent system components
sufficiently [72]. The multibody formulation fits into this
niche.
To model the motion and flexible behaviour, the
multibody formulation introduces a moving frame of
reference to each substructure [72]. This allows for
elastic deformations of each component to be solved
linearly since the relative displacements (to the moving
reference frame) are small. A more in-depth review is
given by [72] and subsequent references.
The choice of method is heavily dependent on the
application; the amount of detail required (preliminary
versus detailed design), the type of system being
analysed and the computational resources available.
Table 1 summarizes the three main approaches and their
characteristics.
Table 1: Comparison of structural modelling
approaches
7.2 GYROSCOPIC EFFECTS
Gyroscopic effects due to the rotating wind turbine rotor
are an important aspect to consider. As yet there has been
very little research into gyroscopic effects on floating
VAWTs. Blusseau and Patel [74] conducted a frequency-
domain analysis of the gyroscopic effect on a VAWT
mounted on a semi-submersible floating platform. It was
found that the roll and pitch motions were adversely
affected, with significant increases in peak amplitudes. In
this analysis the gyroscopic effect was represented by a
damping matrix in the equations of motion.
There are different ways to integrate gyroscopic effects
into the coupled dynamics model, depending on the
kinematical formulation employed. With the time-
domain formulation with radiation state space
representation that is very computationally efficient,
gyroscopic effects have to be explicitly included as
external forces in the equations of motion. On the other
hand with some multibody formulations such as that
found in [75], the rotor gyroscopic effect may be
implicitly included in the equations of motion.
7.3 AEROELASTICITY
Aeroelasticity may play a major role in the structural
loads of the rotor blades, and there appear to be two
levels of aeroelastic modelling that may be implemented.
The first is to only include deformations of the structure
as a whole, i.e., modelling the blades as flexible beams
with rigid airfoil cross sections. Examples of how this is
implemented may be found in [76-78]. The second is to
also include deformations to the cross-section of the
blade which is mentioned in [79; 80]. It has yet to be
seen whether the latter would affect the global motions of
the floating wind turbine. Hansen et al. [81] provide an
excellent overview of how aeroelasticity is integrated
into different aerodynamic models.
Rigid
Body
Multibody
Formulation
Finite
Element
Complexity
Low
Medium
High
Elastic Analysis
No
Yes
Yes
Computational
Effort
Low
Low-Medium
High
Ease of
Implementation
Easy
Easy-Medium
Medium
to Hard
Detailed Stress
Analysis
No
Only with
coupled FE model
[73]
Yes
Marine & Offshore Renewable Energy, 26 – 27 September 2012, London, UK
© 2012: The Royal Institution of Naval Architects
7.4 HYDROELASTICITY
Hydroelasticity is defined as the study of motion and
distortion of deformable bodies responding to
environmental excitations in the sea [82; 83], in
particular the interaction between hydrodynamic, inertial
and elastic forces. A number of theories have been
developed to implement hydroelasticity for marine
structures, ranging from linear two-dimensional models
to nonlinear three-dimensional models. An excellent
review of these theories may be found in [82].
Once again there are different levels of analysis
available. Simple finite element or multibody
representations of the floating body as interconnected
beams allows for a rudimentary inclusion of
hydroelasticity. On the other hand a detailed finite
element model may be used to accurately predict the
body deformations. The amount of detail required does
not only depend on the stage of design, but also on the
hydrodynamic and structural models being used. Without
detailed distributed hydrodynamic pressure data, one
may not use a detailed structural finite element model
appropriately. Therefore careful consideration should be
used when selecting the modelling requirements for the
design of a floating structure.
Over recent years the importance of hydroelasticity in
very large floating structures, such as floating airports,
has generated a number of investigations to efficiently
model this phenomenon [83]. Such research has the
potential to be exploited for the development of an
efficient code for modelling floating VAWTs. One
particular study by Taghipour et al. [84] presented the
results of including hydroelasticity in a hydrodynamic
state space model for a flexible barge with good
agreement between predicted and experimental results.
As this type of hydrodynamic model is already
established as being computationally very efficient (see
e.g.: [66]), this method of incorporating hydroelasticity is
very promising.
In a comparative study by Karimirad et al. [85], it was
found that there are differences in motions of a floating
wind turbine between a rigid model and elastic model.
The rigid body model produced larger motions in certain
degrees of freedom than the elastic model due to the lack
of structural damping. This is indicative of the
importance of including hydroelasticity in a coupled
dynamics model as such differences in motion will affect
the fatigue and reliability analysis of the system.
7.5 COMPUTATIONAL ISSUES
With the need for more computationally efficient design
codes, a review of implementing the different structural
models efficiently is required. The multibody
formulation is one of the most promising approaches and
there are a number of publications outlining
computational methods to accelerate the execution of
such models.
In [86] one may find an extensive review of modelling
flexible multibody systems. Here the authors discuss the
characteristics of different multibody modelling
approaches and their computational advantages.
Particular attention is directed to Section 6.2 in [86],
where the authors review strategies for including fluid-
structure interactions in flexible multibody systems.
Other publications such as [87-89] describe various
methodologies to increase the computational efficiency
based on system identification and order reduction.
As desktop computing resources available to researchers
are ever increasing, a shift to parallel computing is more
viable. It has been implemented successfully in
computational fluid dynamics as well as finite element
analysis and has the potential to significantly reduce
computational times in flexible multibody models [90;
91].
8. CONTROL DYNAMICS
As yet the control of the generator and electrical output
of a floating VAWT have not been researched to the best
of the author’s knowledge. Control dynamics also
incorporate structural control of the system, where in this
case it would imply changing the platform’s inertial,
damping and stiffness characteristics, to adapt it to
different weather conditions, as well as active blade
control.
Extensive research has been done on active blade control
for floating HAWTs, but since floating VAWTs are a
more recent concept and tend to have fixed blades
(mainly due to reliability issues), there has not been any
research into this topic. With regard to the structural
control of floating wind turbines, a number of studies
have been published [92-96] and may prove to be a
popular area of research in the coming years.
9. CURRENT IMPLEMENTATIONS
9.1 AERODYNAMICS
Through comparative studies by Jonkman and Musial
[20; 97; 98], and Cordle [20], it was found that all major
offshore wind design codes employ the BEM model as
well as the generalised dynamic wake model in some
cases. Sebastian [36] applied a free-vortex model
coupled with NREL’s FAST code for a floating HAWT.
Whilst the authors were investigating the evolution of the
wake of the rotor, it was not a fully coupled simulation
and might have led to certain effects being ignored.
As yet these are restricted to HAWTs and no dedicated
coupled dynamics code exists for floating VAWTs that
the author is aware of, although Vita [5] applied the
DMST momentum model coupled with the HAWC2
code to model a Darrieus turbine mounted on a rotating
platform.
9.2 HYDRODYNAMICS
So far offshore wind turbine codes have almost
exclusively been based on the Morison equation [53],
although there now is a trend to implement the Cummins
Marine & Offshore Renewable Energy, 26 – 27 September 2012, London, UK
© 2012: The Royal Institution of Naval Architects
approach [97]. Integrating these two approaches has also
been proposed and implemented recently by Phillipe et
al. [99]. These studies were all investigating floating
HAWTs. In his study of a floating VAWT, Vita [5]
implemented the Morison equation since the floating
structure was a slender spar.
9.3 MOORING LINE AND STRUCTURAL
DYNAMICS
The trend in current design codes has been to implement
the multibody formulation [20; 53; 97], and in some
cases coupling this with a finite element model.
In the FAST code, a modal finite element approach is
used to establish the natural modes of vibration for the
wind turbine blades and tower which are in turn used to
represent the deflections of these components. Whilst
this is computationally very efficient, it assumes small
deflections, which may not be the case with floating
wind turbines.
Besides dedicated floating wind turbine codes, there are a
number of general-use codes that have the potential to be
integrated into a coupled dynamics code. Two examples
are SIMPACK and MBDyn, with applications to wind
turbines presented in [100] and [101], respectively.
One of the main reasons that the multibody formulation
is so popular is that it accommodates large-amplitude
motions. Previously this inherent characteristic of
floating wind turbines contributed to errors in model
predictions. It has also been postulated that since the
system is undergoing large-amplitude motions, some of
the assumptions taken in the hydrodynamic model are
invalidated [97].
A number of publications have presented variations of
the multibody formulation for floating wind turbines [75;
102]. Wang et al. [75] in particular produced a method
which requires only six equations of motion to compute
the general motion, no matter how many DOFs are
present in the system.
The adaptability of the multibody formulation allows it
to be used to model not only the main structural
components of the floating wind turbine, but also the
mechanical subsystems within, in particular the drive
train and generator [103-105]. This would also improve
code execution as the same subroutines may be applied
to more than one section of the model.
A review on current state of the art floating wind turbine
design codes by Cordle and Jonkman [20] found that
almost all major codes implement the multibody
formulation or a modification thereof. Although the
multibody formulation might seem to be the ideal
solution, the finite element method still has applications
in certain design stages. For example in [87], the need to
establish localised hydrodynamic loads on the floating
structure resulted in a coupled boundary-element-method
and FEM model, such that the distribution of
hydrodynamic pressures calculated by the boundary-
element-method routine is directly translated to the FEM
procedure. In this case FEM was the optimal approach to
use.
10. CONCLUSIONS
The onshore wind industry has reached a relatively
mature level, and in parallel the horizontal axis of
rotation, three blades, upwind, variable-speed, variable
blade pitch (with feathering capability) configuration
emerged as the optimum techno-economic trade-off for
the onshore large scale wind market. It results from
several decades of research and development, originally
considering several configurations, including VAWTs.
The same “evolutionary process” did not take place for
the offshore wind market, substituted by a “marinisation”
of the configurations used for the onshore market. This
happened despite the very different environmental
conditions, especially if a floating wind turbine is
considered.
As part of the task of assessing the technical and
economic feasibilities of alternative concepts that could
be potentially be more suitable for the offshore
environment, a comprehensive literature review on the
model of dynamics used for HAWTs and VAWTs is
presented, with considerations of their capabilities if used
for VAWT systems, and addressing each major aspect of
the dynamics of a floating wind turbine system:
aerodynamics, hydrodynamics, structural dynamics,
mooring system dynamics, and control system dynamics.
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12. AUTHORS’ BIOGRAPHIES
Mr Michael Borg AMRINA is currently a Researcher at
Cranfield University. He is investigating the coupled
dynamics of floating vertical axis wind turbines and is
developing a generalised efficient coupled model of
dynamics for such systems.
Dr Maurizio Collu, CEng MRINA MEI is a University
Lecturer in Fluid Mechanics and Loading in the Offshore
Renewable Energy group, and Course Director of the
MSc in Advanced Mechanical Engineering, within the
School of Engineering, Cranfield University. He has
been working in the field of dynamics of marine systems
for seven years, investigating the dynamics of high speed
marine vehicles, offshore floating support structures, and
offshore floating microalgae cultivation platforms for
biofuel production. He was in charge of the preliminary
design of the floating support structure in the NOVA
project, the first ETI consortium to be funded (£30m),
and he is now part of the FP7 project H2OCEAN, in
charge of the hydrodynamics of a coupled wave-wind
platform. He has published over fifteen papers in peer
reviewed technical journals and conferences in this field,
and received the RINA "Calder Prize", for the best paper
on the subject of high speed craft by an author under the
age of 30.
Professor Feargal P. Brennan is Professor of Offshore
Engineering, head of the Offshore, Process and Energy
Engineering department and its Offshore Renewable
Energy Group. He is a leading authority on the
development and assessment of offshore renewables
including wind, wave, tidal stream and the production of
sustainable biofuel feedstocks in the ocean environment.
Professor Brennan has for twenty years been at the
forefront of internationally leading research in structural
integrity and its application to ships, offshore renewables
and the oil & gas sector. He has published over one
hundred papers in peer reviewed technical journals and
conferences. He is the chairman of the ISSC
(International Ship and Offshore Structures Congress)
Offshore Renewable Energy committee, sits on the BSI
committee for fatigue testing of metals, the Engineering
Integrity Society (EIS) durability & fatigue committee,
the IMechE Offshore Engineering Committee, the
EPSRC peer review college, is an Editorial Board
Member of the Journal of Process Mechanical
Engineering and co-editor of the international journal
Fatigue & Fracture of Engineering Materials and
Structures.