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Infrastructure Access Report
Infrastructure: IFREMER Wave-Current Circulation Tank
User-Project: SME - PLAT-O
IFREMER Tank Testing November & December 2012
Marine Renewables Infrastructure Network
Status: Final
Version: 01
Date: 15-Oct-2013
EC FP7 “Capacities” Specific Programme
Research Infrastructure Action
ABOUT MARINET MARINET (Marine Renewables Infrastructure Network for emerging Energy Technologies) is an EC
of research centres and organisations that are working together to accelerate the development of marine renewable
energy - wave, tidal & offshore-wind. The initiative is funded through the EC's Seventh Framework Programme (FP7)
and runs for four years until 2015. The network of
across 11 EU countries and 1 International Cooperation Partner Country (Brazil).
MARINET offers periods of free-of-charge access to test facilities at a range of world
Companies and research groups can avail of this Transnational Access (TA) to test devices at any scale in areas such
as wave energy, tidal energy, offshore-
areas such as power take-off systems, grid integration, materials or moorings. In total, over 700 weeks of access is
available to an estimated 300 projects and 800 external users, with at least four calls for access applications over the
4-year initiative.
MARINET partners are also working to implement common standards for testing in order to streamline the
development process, conducting research to improve testing capabilities across the network, providing training at
various facilities in the network in order to enhance pe
in order to facilitate partnerships and knowledge exchange.
The aim of the initiative is to streamline the capabilities of test infrastructures
accelerate the commercialisation of marine renewable energy.
Partners
University College Cork, HMRC (UCC_HMRC)
Sustainable Energy Authority of Ireland (SEAI_OEDU)
Aalborg Universitet (AAU)
Danmarks Tekniske
Ecole Centrale de Nantes (ECN)
Institut Français de Recherche Pour l'Exploitation de
National Renewable Energy Centre Ltd. (NAREC)
The University of Exeter (UNEXE)
European Marine Energy Centre Ltd. (EMEC)
University of Strathclyde (UNI_STRATH)
The University of Edinburgh (UEDIN)
Queen’s University Belfast (QUB)
Plymouth University(PU)
Ente Vasco de la Energía (EVE)
Tecnalia Research & Innovation Foundation
Infrastructure Access Report:
Rev. 01, 15-Oct-2013
Page 2 of 35
MARINET (Marine Renewables Infrastructure Network for emerging Energy Technologies) is an EC
organisations that are working together to accelerate the development of marine renewable
. The initiative is funded through the EC's Seventh Framework Programme (FP7)
and runs for four years until 2015. The network of 29 partners with 42 specialist marine research facilities is spread
across 11 EU countries and 1 International Cooperation Partner Country (Brazil).
charge access to test facilities at a range of world
Companies and research groups can avail of this Transnational Access (TA) to test devices at any scale in areas such
-wind energy and environmental data or to conduct tests on cross
off systems, grid integration, materials or moorings. In total, over 700 weeks of access is
available to an estimated 300 projects and 800 external users, with at least four calls for access applications over the
re also working to implement common standards for testing in order to streamline the
development process, conducting research to improve testing capabilities across the network, providing training at
various facilities in the network in order to enhance personnel expertise and organising industry networking events
in order to facilitate partnerships and knowledge exchange.
to streamline the capabilities of test infrastructures in order to enhance their impact and
commercialisation of marine renewable energy. See www.fp7-marinet.eu
Ireland
University College Cork, HMRC (UCC_HMRC)
Coordinator
Sustainable Energy Authority of Ireland (SEAI_OEDU)
Denmark
Aalborg Universitet (AAU)
Danmarks Tekniske Universitet (RISOE)
France
Ecole Centrale de Nantes (ECN)
Institut Français de Recherche Pour l'Exploitation de
la Mer (IFREMER)
United Kingdom
National Renewable Energy Centre Ltd. (NAREC)
The University of Exeter (UNEXE)
Marine Energy Centre Ltd. (EMEC)
University of Strathclyde (UNI_STRATH)
The University of Edinburgh (UEDIN)
Queen’s University Belfast (QUB)
Plymouth University(PU)
Spain
Ente Vasco de la Energía (EVE)
Tecnalia Research & Innovation Foundation
(TECNALIA)
Belgium
1-Tech (1_TECH)
Netherlands
Stichting Tidal Testing Centre (TTC)
Stichting Energieonderzoek Centrum Nederland
(ECNeth)
Germany
Fraunhofer-Gesellschaft Zur Foerderung Der
Angewandten Forschung E.V (Fh_IWES)
Gottfried Wilhelm Leibniz Universität Hannover (LUH)
Universitaet Stuttgart (USTUTT)
Portugal
Wave Energy Centre – Centro de Energia das Ondas
(WavEC)
Italy
Università degli Studi di Firenze (UNIFI
Università degli Studi di Firenze (UNIFI
Università degli Studi della Tuscia (UNI_TUS)
Consiglio Nazionale delle Ricerche (CNR
Brazil
Instituto de Pesquisas Tecnológicas do Estado de São
Paulo S.A. (IPT)
Norway
Sintef Energi AS (SINTEF)
Norges Teknisk-Naturvitenskapelige Universitet
(NTNU)
Infrastructure Access Report: SME - PLAT-O
MARINET (Marine Renewables Infrastructure Network for emerging Energy Technologies) is an EC-funded network
organisations that are working together to accelerate the development of marine renewable
. The initiative is funded through the EC's Seventh Framework Programme (FP7)
29 partners with 42 specialist marine research facilities is spread
charge access to test facilities at a range of world-class research centres.
Companies and research groups can avail of this Transnational Access (TA) to test devices at any scale in areas such
wind energy and environmental data or to conduct tests on cross-cutting
off systems, grid integration, materials or moorings. In total, over 700 weeks of access is
available to an estimated 300 projects and 800 external users, with at least four calls for access applications over the
re also working to implement common standards for testing in order to streamline the
development process, conducting research to improve testing capabilities across the network, providing training at
rsonnel expertise and organising industry networking events
in order to enhance their impact and
marinet.eu for more details.
Stichting Energieonderzoek Centrum Nederland
Gesellschaft Zur Foerderung Der
Angewandten Forschung E.V (Fh_IWES)
Wilhelm Leibniz Universität Hannover (LUH)
Centro de Energia das Ondas
i Firenze (UNIFI-CRIACIV)
i Firenze (UNIFI-PIN)
Università degli Studi della Tuscia (UNI_TUS)
Consiglio Nazionale delle Ricerche (CNR-INSEAN)
Instituto de Pesquisas Tecnológicas do Estado de São
Naturvitenskapelige Universitet
Infrastructure Access Report: SME - PLAT-O
Rev. 01, 15-Oct-2013
Page 3 of 35
DOCUMENT INFORMATION Title IFREMER Tank Testing November & December 2012
Distribution Public
Document Reference MARINET-TA1-SME - PLAT-O
User-Group Leader, Lead
Author
Jason Hayman Sustainable Marine Energy Ltd
User-Group Members,
Contributing Authors
Fabrizio Fiore Sustainable Marine Energy Ltd
Florent Trarieux Cranfield University
Infrastructure Accessed: IFREMER Wave-Current Circulation Tank
Infrastructure Manager
(or Main Contact)
Gregory Germain
REVISION HISTORY Rev. Date Description Prepared by
(Name)
Approved By
Infrastructure
Manager
Status
(Draft/Final)
01 15/10/2013
Infrastructure Access Report: SME - PLAT-O
Rev. 01, 15-Oct-2013
Page 4 of 35
ABOUT THIS REPORT One of the requirements of the EC in enabling a user group to benefit from free-of-charge access to an infrastructure
is that the user group must be entitled to disseminate the foreground (information and results) that they have
generated under the project in order to progress the state-of-the-art of the sector. Notwithstanding this, the EC also
state that dissemination activities shall be compatible with the protection of intellectual property rights,
confidentiality obligations and the legitimate interests of the owner(s) of the foreground.
The aim of this report is therefore to meet the first requirement of publicly disseminating the knowledge generated
through this MARINET infrastructure access project in an accessible format in order to:
• progress the state-of-the-art
• publicise resulting progress made for the technology/industry
• provide evidence of progress made along the Structured Development Plan
• provide due diligence material for potential future investment and financing
• share lessons learned
• avoid potential future replication by others
• provide opportunities for future collaboration
• etc.
In some cases, the user group may wish to protect some of this information which they deem commercially
sensitive, and so may choose to present results in a normalised (non-dimensional) format or withhold certain design
data – this is acceptable and allowed for in the second requirement outlined above.
ACKNOWLEDGEMENT The work described in this publication has received support from MARINET, a European Community - Research
Infrastructure Action under the FP7 “Capacities” Specific Programme.
LEGAL DISCLAIMER The views expressed, and responsibility for the content of this publication, lie solely with the authors. The European
Commission is not liable for any use that may be made of the information contained herein. This work may rely on
data from sources external to the MARINET project Consortium. Members of the Consortium do not accept liability
for loss or damage suffered by any third party as a result of errors or inaccuracies in such data. The information in
this document is provided “as is” and no guarantee or warranty is given that the information is fit for any particular
purpose. The user thereof uses the information at its sole risk and neither the European Commission nor any
member of the MARINET Consortium is liable for any use that may be made of the information.
Infrastructure Access Report: SME - PLAT-O
Rev. 01, 15-Oct-2013
Page 5 of 35
EXECUTIVE SUMMARY A comprehensive series of tests was undertaken in the water circulation channel at IFREMER on a three-buoyancy-
module/dual-turbine model. The dynamic response of the device was measured in a wide range of flow velocities,
wave conditions (with/against current) and turbulence levels. The main outcome of this experimental campaign has
been the clear influence of the mooring geometry on the motion response, and more precisely a greater
understanding of the levels of pre-tension required in the mooring lines to minimise motion to acceptable levels. By
carefully distributing the hydrostatic loads due to the net buoyancy of the device and the dynamic loads created by
the drag of the device and the thrust generated by the turbines, it is possible to substantially reduce the motion
response of the device under a wide range of combined current and wave scenarios with obvious benefits. The load
cycles on the mooring lines and particularly shock loads or “snatching” can be significantly decreased, reducing the
risk of failure and increasing the lifetime of the mooring components. The turbines operate on a stable platform
without suffering the effects of motion-induced flow particle velocity variations on the blades.
Infrastructure Access Report: SME - PLAT-O
Rev. 01, 15-Oct-2013
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CONTENTS
1 INTRODUCTION & BACKGROUND ...................................................................................................................7
1.1 INTRODUCTION .................................................................................................................................................... 7
1.2 DEVELOPMENT SO FAR .......................................................................................................................................... 8
1.2.1 Stage Gate Progress .................................................................................................................................... 8
1.2.2 Plan For This Access ................................................................................................................................... 10
2 OUTLINE OF WORK CARRIED OUT ................................................................................................................. 10
2.1 SETUP ............................................................................................................................................................... 10
2.1.1 Reference system ...................................................................................................................................... 10
2.1.2 Model calibration ...................................................................................................................................... 11
2.1.3 Mooring lines ............................................................................................................................................. 14
2.1.4 Data recording ........................................................................................................................................... 14
2.2 TESTS ............................................................................................................................................................... 15
2.2.1 Hydrodynamic drag tests .......................................................................................................................... 15
2.2.2 20˚ mooring lines configuration without upper mooring lines tension control (week 1) .......................... 16
2.2.3 20˚ - 30˚ mooring lines configuration with upper mooring lines tension control (week 2) ....................... 16
2.3 RESULTS ............................................................................................................................................................ 17
2.3.1 Introduction ............................................................................................................................................... 17
2.3.2 Drag estimation through mooring lines tension measurements and direct readings .............................. 17
2.3.3 Depth of submergence .............................................................................................................................. 19
2.3.4 Pre-tension of mooring lines ..................................................................................................................... 22
2.3.5 Effect of the turbulence intensity on the mooring lines tension ............................................................... 25
2.3.6 Failure mode tests ..................................................................................................................................... 27
2.3.7 Wave excitation and device motion .......................................................................................................... 29
2.4 ANALYSIS & CONCLUSIONS................................................................................................................................... 31
2.4.1 Drag estimation through mooring lines tension measurements and direct readings .............................. 31
2.4.2 Depth of Submergence .............................................................................................................................. 31
2.4.3 Pre-tensioning ........................................................................................................................................... 31
2.4.4 Effect of Turbulence................................................................................................................................... 31
2.4.5 Failure Mode ............................................................................................................................................. 32
2.4.6 Wave Excitation and Device Motion ......................................................................................................... 32
3 MAIN LEARNING OUTCOMES ....................................................................................................................... 32
3.1 PROGRESS MADE ............................................................................................................................................... 32
3.1.1 Progress Made: For This User-Group or Technology ................................................................................. 32
3.1.2 Progress Made: For Marine Renewable Energy Industry .......................................................................... 32
3.2 KEY LESSONS LEARNED ........................................................................................................................................ 32
4 FURTHER INFORMATION .............................................................................................................................. 33
4.1 SCIENTIFIC PUBLICATIONS .................................................................................................................................... 33
4.2 WEBSITE & SOCIAL MEDIA ................................................................................................................................... 33
5 REFERENCES ................................................................................................................................................ 33
6 APPENDICES ................................................................................................................................................ 33
6.1 SCALING - SIMILARITY LAWS ................................................................................................................................. 33
Infrastructure Access Report: SME - PLAT-O
Rev. 01, 15-Oct-2013
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1 INTRODUCTION & BACKGROUND
1.1 INTRODUCTION The tests were carried out in the IFREMER water circulation channel in Boulogne-sur-mer, Pas-de-Calais, France, and
were split into two sessions: one in November (week 1) and one December 2012 (week 2). A 1:12 scale model of a
250 kW device was tested over a total of 383 tests in current only, regular wave only, and combined current and
regular waves (with and against current). Some direct hydrodynamic drag measurements on the platform (with and
without turbines) were performed using a single tow line, while the “operational” tests were conducted in different
moored configurations (Figure 1.1, Figure 1.2). The mooring system was composed of four lines; the upper mooring
lines connected the buoyancy chambers to the lower mooring lines forming the primary mooring lines, which were
directly attached on the floor using a frame bolted onto the tank.
Figure 1.1 20 degrees mooring configuration
Figure 1.2 30 degrees mooring configuration
Several tests were conducted for a range of flow velocity, turbulence intensity, wave amplitude/period (with/against
current) and turbine speed. Tests where the turbines were operating at different speeds were also performed, as
well as accidental failure tests, in which either an upper or lower mooring line, or both, parted. During the
operational tests, several quantities were recorded, such as mooring line tensions, turbine speed/torque, wave
elevation and, using a motion capture system, the translations and rotations of the model (Figure 1.3Error!
Reference source not found.). To utilise existing, fully instrumented, nacelles, the turbines speed was controlled via
a motor and braking module. Although turbines to be connected to a generator would ideally be used, the use of
driven turbines was deemed to be appropriate for a first experimental assessment of the concept, as long as the
freewheeling speed was not exceeded. This was achieved through the monitoring of the turbines torque signals.
Infrastructure Access Report: SME - PLAT-O
Rev. 01, 15-Oct-2013
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Figure 1.3 Motion capture system
In Figure 1.4 are shown all the different structural elements characterising the 1:12 scale model of the PLAT-O 250
kW prototype.
Figure 1.4 - 3D CAD view of the PLAT-O 250 kW prototype (1:12 scale model)
1.2 DEVELOPMENT SO FAR
1.2.1 Stage Gate Progress Previously completed: �
Planned for this project: �
STAGE GATE CRITERIA Status
Stage 1 – Concept Validation
• Linear monochromatic waves to validate or calibrate numerical models of the system (25 – 100 waves) �
• Finite monochromatic waves to include higher order effects (25 –100 waves)
• Hull(s) sea worthiness in real seas (scaled duration at 3 hours)
Infrastructure Access Report: SME - PLAT-O
Rev. 01, 15-Oct-2013
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STAGE GATE CRITERIA Status
• Restricted degrees of freedom (DofF) if required by the early mathematical models
• Provide the empirical hydrodynamic co-efficient associated with the device (for mathematical modelling
tuning)
�
• Investigate physical process governing device response. May not be well defined theoretically or
numerically solvable
�
• Real seaway productivity (scaled duration at 20-30 minutes)
• Initially 2-D (flume) test programme �
• Short crested seas need only be run at this early stage if the devices anticipated performance would be
significantly affected by them
• Evidence of the device seaworthiness
• Initial indication of the full system load regimes �
Stage 2 – Design Validation
• Accurately simulated PTO characteristics
• Performance in real seaways (long and short crested)
• Survival loading and extreme motion behaviour. �
• Active damping control (may be deferred to Stage 3)
• Device design changes and modifications
• Mooring arrangements and effects on motion �
• Data for proposed PTO design and bench testing (Stage 3)
• Engineering Design (Prototype), feasibility and costing
• Site Review for Stage 3 and Stage 4 deployments
• Over topping rates
Stage 3 – Sub-Systems Validation
• To investigate physical properties not well scaled & validate performance figures
• To employ a realistic/actual PTO and generating system & develop control strategies
• To qualify environmental factors (i.e. the device on the environment and vice versa) e.g. marine growth,
corrosion, windage and current drag
• To validate electrical supply quality and power electronic requirements.
• To quantify survival conditions, mooring behaviour and hull seaworthiness
• Manufacturing, deployment, recovery and O&M (component reliability)
• Project planning and management, including licensing, certification, insurance etc.
Stage 4 – Solo Device Validation
• Hull seaworthiness and survival strategies
• Mooring and cable connection issues, including failure modes
• PTO performance and reliability
• Component and assembly longevity
• Electricity supply quality (absorbed/pneumatic power-converted/electrical power)
• Application in local wave climate conditions
• Project management, manufacturing, deployment, recovery, etc
• Service, maintenance and operational experience [O&M]
• Accepted EIA
Stage 5 – Multi-Device Demonstration
• Economic Feasibility/Profitability
Infrastructure Access Report: SME - PLAT-O
Rev. 01, 15-Oct-2013
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STAGE GATE CRITERIA Status
• Multiple units performance
• Device array interactions
• Power supply interaction & quality
• Environmental impact issues
• Full technical and economic due diligence
• Compliance of all operations with existing legal requirements
1.2.2 Plan For This Access Provide the empirical hydrodynamic co-efficient associated with the device (for mathematical modelling tuning)
The outcomes of the drag tests on the device will allow to determine the drag coefficient relative to a longitudinal
steady flow at different current speeds. That will be used to better define the loads on the device during the design
phase of the full scale prototype.
Investigate physical process governing device response
Using the tensions in the lines recorded during the tests with current and waves, the forces on the device will be
estimated. The mathematical model which is meant to manage the loads on the platform will be calibrated using
those outcomes. That will allow to use the model to determine the device physical process (in terms of global loads)
even for different environmental conditions than those tested.
Initially 2-D (flume) test programme
An extensive series of tests was carried out during the two weeks at the IFREMER research centre. They included
drag tests, operational tests adopting a four mooring lines configuration and failure mode tests. The tests were
performed in current only, with a range of flow speeds from 0.25 to 1.3m/sec at model scale, and also with waves,
with a range of wave amplitudes from 50 to 150mm at model scale.
Initial indication of the full system load regimes
Monitoring the tensions in the four primary mooring lines, it will be possible to resolve the former into forces acting
on the device. Later on, the results will be used to calibrate a mathematical model, which will allow to divide those
loads into drag, thrust and inertial components.
Survival loading and extreme motion behaviour
Tests were performed in high waves and current, to monitor how device motions and tensions in the lines would be
affected by those extreme conditions. Also, always in severe environmental conditions, several tests simulating a
failure of a mooring line were performed.
Mooring arrangements and effects on motion
During this tank testing campaign different mooring arrangements were tested. The aim was to better understand
how the angle of the mooring lines with the seabed and the pre-tension of the upper lines would affect the motions
of the device.
2 OUTLINE OF WORK CARRIED OUT
2.1 SETUP
2.1.1 Reference system The reference system used for all the data presented in this report is shown in Figure 2.1. The axes are centred
halfway along the lower horizontal beam, and follow a right-handed orientation.
Infrastructure Access Report: SME - PLAT-O
Rev. 01, 15-Oct-2013
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Figure 2.1 - PLAT-O model reference system - side view
2.1.2 Model calibration Before running the tests in the tank the position of the centre of gravity was measured. In order to have reliable
results out of the tests in the tank, one should always ensure that the physical properties responsible of the
dynamical behaviour of the device are scaled correctly. Those are basically the total mass, the position of the centre
of gravity and the 3 main moments of the inertia of the body. Once those quantities are measured, one should add
mass if missing until it reaches the proper value, and in doing so, adding it in such a way that affects positively the
position of the centroid and the inertias. The case studied was a bit different though, being the position of the centre
of gravity and the moments of inertia not defined yet at full scale, and the mass higher than it should have been (due
to heavier nacelles), and so presenting the impossibility of adding weights to correct those geometrical quantities,
without further boosting the mass of the model. The position of the centroid was just measured at model scale,
while the inertia tests were postponed due to the presence of the umbilicals connecting the nacelles to the power
i/o, uneasy to remove at the time, and they would have affected badly the reliability of those calibration tests. It was
not a great issue though, because as it has been said previously those quantities were not known at full scale, so
postponing the measurements seemed to make sense. About the longitudinal position of the centroid, before
measuring it the model was put in the water, and the pontoons were slid back/forth until the longitudinal trim was
even.
2.1.2.1 Centre of gravity - week 1
Here below the procedures to calculate the total mass and the position of the centre of gravity of the model.
Between November and December some modifications on the model were made, so the calibration presents two
different sets of results.
Weight of the model
The device full scale presents a structure of approximately 17.7 tonnes in the air, housing two turbines of 9 tonnes
each in the water, which scaled down to model scale gives a target mass for the model of 23.2 kg in the air. Due to
the heavier nacelles housed on it, the model weighed instead 30.7 kg in the air, fact that reduced the net buoyancy
from a target of 18.1 kg to 9.7 kg at model scale.
Longitudinal position
The model was hung from 2 lifting lines, one tied by the origin of the axes, i.e. by the centre of the lower beam,
while the other one by the rear end of the central pontoon. For the test to work the centroid has to be in between
those 2 lines, but it was already known that it would have been in the aft part of the model. The tension in the rear
Infrastructure Access Report: SME - PLAT-O
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line was then measured using a load cell and, knowing the total mass of the model, it was so possible to calculate the
longitudinal position of the centroid, using [2.1].
[2.1]. �� = �1 �1�
where � is the tension recorded in the rear line [N] � is the distance between the lines [m] � is the total mass [kg]
Transversal position
Although the centroid should have been centered transversally, due to the symmetry of the model, it was worth
running this test anyway, to spot if the pontoons or the nacelles were misaligned, or to detect some asymmetry due
to manufacturing. The formula used, expressed by [2.2], is identical to the one used for the longitudinal position.
[2.2]. �� = �2 �2�
Vertical position
As done for the longitudinal and the transversal position of the centroid, [2.3] shows how to determine its vertical
position.
[2.3]. � = �3 �3�
Results
Table 2.1, Table 2.2 and Table 2.3 show the results of the calibration.
Unit
Absolute
value
Absolute
error
Relative
error
Total mass g 30722 10 0.0%
Mass measured by the load cell in the "2lifting lines" configuration g 4947 10 0.2%
X coordinate of the line with the load cell mm 580 3 0.5%
X coordinate of the centre of gravity mm 93 -1 0.8%
Table 2.1 - Longitudinal position of the centre of gravity of the PLAT-O model (week 1 measurements)
Unit
Absolute
value
Absolute
error
Relative
error
Total mass g 30722 10 0.0%
Mass measured by the load cell in the "2lifting lines" configuration g 15769 10 0.1%
Distance between the lifting points mm 782 3 0.4%
Y coordinate of the centre of gravity mm 10 0 0.5%
Table 2.2 - Transversal position of the centre of gravity of the PLAT-O model (week 1 measurements)
Unit Absolute Absolute Relative
Infrastructure Access Report: SME - PLAT-O
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value error error
Total mass g 30722 10 0.0%
Mass measured by the load cell in the "2lifting lines" configuration g 2857 10 0.3%
Distance between the lifting points mm 373 3 0.8%
Z coordinate of the centre of gravity mm -338 4 1.2%
Table 2.3 - Vertical position of the centre of gravity of the PLAT-O model (week 1 measurements)
2.1.2.2 Centre of gravity - week 2
The procedure was the same as for the tests in November. Table 2.4, Table 2.5 and Table 2.6 show the results.
Unit
Absolute
value
Absolute
error
Relative
error
Total mass g 32439 10 0.0%
Mass measured by the load cell in the "2lifting lines" configuration g 25647 10 0.0%
X coordinate of the line with the load cell mm 580 3 0.5%
X coordinate of the centre of gravity mm 121 -1 0.6%
Table 2.4 - Longitudinal position of the centre of gravity of the PLAT-O model (week 2 measurements)
Unit
Absolute
value
Absolute
error
Relative
error
Total mass g 32439 10 0.0%
Mass measured by the load cell in the "2lifting lines" configuration g 15984 10 0.1%
Distance between the lifting points mm 790 3 0.4%
Y coordinate of the centre of gravity mm 6 0 0.5%
Table 2.5 - Transversal position of the centre of gravity of the PLAT-O model (week 2 measurements)
Unit
Absolute
value
Absolute
error
Relative
error
Total mass g 32439 10 0.0%
Mass measured by the load cell in the "2lifting lines" configuration g 2977 10 0.3%
Distance between the lifting points mm 393 3 0.8%
Z coordinate of the centre of gravity mm -357 4 1.1%
Table 2.6 - Vertical position of the centre of gravity of the PLAT-O model (week 2 measurements)
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2.1.3 Mooring lines In Table 2.7 the characteristics of the ropes used for the tests at the IFREMER centre are presented.
Unit Week 1 Week 2
Mooring line type Marlow Excel Vectran Marlow Excel Pro
Diameter mm 1.5 4
Breaking load kg 112 377
Weight kg/m 0.19 0.90
Table 2.7 - PLAT-O tank testing campaign - model scale mooring lines characteristics
2.1.4 Data recording The data was recorded during the operational tests as follows:
• The tensions in the mooring lines were recorded with a system of four load cells. During week 1 they were
mounted on each intersection between the upper and lower lines and the primary lines (see Figure 2.5),
while during week 2 they were mounted only on the upstream upper and lower lines (see Figure 2.2-a).
• The TECs speed and torque were recorded via an umbilical connection (see Figure 2.2-b and Figure 2.3-b).
• The wave elevation was recorded via a wave measurement probe installed in the immediate vicinity of the
model (see Figure 2.3-c)
• The translations and rotations of the model were recorded by the Qualisys motion tracking system, which
monitored the motions of the targets on the model (see Figure 2.2-d).
Figure 2.2 - PLAT-O model data acquisition - tension in the lines and motions
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Figure 2.3 - PLAT-O data acquisition - TECs speed and torque and wave elevation
2.2 TESTS
2.2.1 Hydrodynamic drag tests To simplify the measurement of the drag on the model, the model was placed at a set depth using a vertical tether
and connected to a load cell on a single horizontal tow line. The tests were undertaken with and without the
turbines, and run at a range of flow velocities from 0.25 to 1.3 m/sec. Figure 2.4 shows the increase in drag with the
flow velocity and the respective contributions of the frame and turbines. It can be seen that even with the turbines
at rest, the contribution of the turbines is very significant compared to the support structure.
Figure 2.4 - PLAT-O drag tests
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2.2.2 20˚ mooring lines configuration without upper mooring lines tension control (week 1)
2.2.2.1 Test set-up
The second series of tests were conducted using an operational setup, with four mooring lines attached at the
bottom of the tank, at an angle of approximately 20° to the horizontal. The upper lines were not pre-tensioned and
were attached to the lower mooring lines. The line tension induced by the net buoyancy was distributed amongst
the lower lines only in the static case, with neither current nor waves. The tests included a series of runs with current
only at a range of flow rates, from 0.25 m/sec up to 1 m/sec, and with waves, both with and in the opposite direction
to the current, over a range of amplitudes and frequencies. The quantities recorded were the tension in the four
mooring lines (at the intersection of upper and lower lines, Figure 2.5), turbine speed/torque, nacelle temperature,
and the motions of the device, i.e. surge, sway, heave, roll, pitch and yaw.
Figure 2.5 - Tension load cell (x4) mounted at intersection of upper and lower mooring lines (week 1)
2.2.3 20˚ - 30˚ mooring lines configuration with upper mooring lines tension control (week 2)
2.2.3.1 Test set-up
Based on the findings of week 1, a more advanced configuration was adopted, which enabled pre-tension due to
buoyancy to be distributed between the upper and lower mooring lines, and to vary the angle of the lower moorings
lines from 20 to 30 degrees. The four load cells were no longer mounted at the intersection of the upper and lower
mooring lines but directly on the model (Figure 2.6) on the upstream end. All line controls were retrieved to the
surface via a system of blocks and cam cleats (Figure 2.7). Only four load cells with the appropriate range (200 N)
were available. The load cells were selected for their very low aspect ratio and very light weight characteristics (Essor
Français de l’Electronique EFE- F5070B). During week 2, the tests performed with waves, were only against the
current, and the tests were run at two different levels of turbulence, i.e. 5% as in week 1 and 25%.
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Figure 2.6 - Tension load cell (x4) mounted directly on the upstream end of the model (week 2)
Figure 2.7 - Mooring arrangement at floor level showing individual controls of upper, lower and height of intersection of
upper/lower mooring lines
2.3 RESULTS
2.3.1 Introduction During the test campaign a number of mooring parameters were varied, such as the depth of submergence, the line
angles and the distribution of pre-tension amongst the mooring lines. During week 2, a 30° configuration was tested
alongside the baseline 20° configuration, where the lines experienced lower tensions in the static case (no current
and no waves).
2.3.2 Drag estimation through mooring lines tension measurements and direct readings
The following analysis shows how reliable is to determine the global loads acting on the platform using the
recordings of the load cells, mounted on the four primary lines. From the drag tests we had a supposedly accurate
measurement of the drag acting on the model, with the turbines parked. With the mathematical model explained in
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2.3.2.1 and in 2.3.2.2, the drag was also calculated, for the same environmental conditions (different current speeds,
no waves and 5% of turbulence intensity in the channel), using the tensions in the four primary lines.
2.3.2.1 Rear lines in tension
The procedure described below is about a configuration where, under the effect of the drag, the rear lines have not
yet become loose, so the platform is still in the same position as in the static case, and also the angles of the lines
have not changed. [2.4] and [2.5] show how to calculate the horizontal component of the fore and rear line tensions,
using the absolute recorded tensions T and T� and the tangents t� and t�. These refer to the horizontal and vertical
angles the lines form with the bottom of the tank. [2.6] calculates, using tensions and angles, the total drag acting on
the platform.
[2.4]. T � = ��� �������� [2.5]. T�� = ��� �������� [2.6]. D = 2�T � − T��� = ��������� ��������
where T is the line tension [N] D is the drag o the model [N]
2.3.2.2 Rear lines loose
In this case instead the rear lines have become loose and so the platform squats, varying its depth and the angles of
the lines. Assuming that the transversal component of the tensions does not vary with the change of position, [2.7]
and [2.8] show how to determine respectively transversal and vertical components of the tensions, using the angles
in the static configuration and the tension recorded. [2.9] and [2.10] show how to determine respectively the
horizontal component of the tension and the drag.
[2.7]. T � = ��∙��� �������� [2.8]. T = !�
[2.9]. T � = �T � − T �� − T � = "T � − #!�$� −% ��∙��� ��������&�
[2.10]. D = 2T � = 2"T � − #!�$� −% ��∙��� ��������&�
where B is the model buoyancy
2.3.2.3 Results
2.3.2.4
Figure 2.8 shows the comparison for a certain range of current speeds. It can be noticed that for higher speeds the
discrepancy becomes less significant. That is a positive outcome, since we want the mathematical model to be
reliable for harsh environmental conditions, because the methodology is supposed to be used mainly to calculate,
during the design phase, the tension in the mooring lines associated to extreme loads on the platform, in order to
size them. Table 2.8 shows the error between the two methods at 1 m/sec current speed, which is of 1.1%.
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Figure 2.8 - Comparison between two different methods to calculate the drag on the model (turbines parked)
Unit Drag tests Operational tests
Measured/derived drag (turbines parked, 1 m/sec current) N 87.2 88.2
Error % reference 1.1
Table 2.8 - Validation of the mathematical model to relate drag and tension in the lines
2.3.3 Depth of submergence Figure 2.9 and Figure 2.10 show the mooring line tensions and the heave motions respectively for two different
depths for the 20 degrees configuration which are presented in Table 2.9. As the model gets closer to the surface,
the variation of tension and heave increases due to the additional wave induced motion. The heave signals show
remarkably high frequency components; and the results are shown in Figure 2.11 with the frequencies higher than
1.6 Hz filtered out, i.e. 2 times 0.8 Hz, which is the frequency of the wave pattern.
Unit Run 298 Run 303
Current speed m/sec 0.50 0.50
Wave amplitude mm 100 100
Wave frequency Hz 0.8 0.8
Turbines speed rpm 75 75
Angle of the mooring lines deg 22 25
Distance of the lower beam from the bottom of the tank mm 624 1160
Table 2.9 - Tests characteristics: depth of submergence comparison 1
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Figure 2.9 - Depth of submergence comparison 1 - starboard lower line tension variation
Figure 2.10 - Depth of submergence comparison 1 – heave motion
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Figure 2.11 - Depth of submergence comparison 1 – heave motion (high frequency components filtered out)
Table 2.10 presents another set of tests for comparison with waves present and no current. Figure 2.12 and Figure
2.13 show very clearly the increase in variation of tension and heave as the device moves closer to the surface
regardless of the vertical angle of the mooring lines.
Unit Run 294 Run 293 Run 299
Current speed m/sec 0 0 0
Wave amplitude mm 100 100 100
Wave frequency Hz 0.55 0.55 0.55
Turbines speed rpm 0 0 0
Angle of the mooring lines deg 22 30 25
Distance of the lower beam from the bottom of the tank mm 624 924 1160
Table 2.10 - Tests characteristics: depth of submergence comparison 2
Figure 2.12 - Depth of submergence comparison 2 - starboard lower line tension variation
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Figure 2.13 - Depth of submergence comparison 2 – heave motion
2.3.4 Pre-tension of mooring lines As mentioned previously, the layout of the lines was modified during week 2, i.e. the loads were distributed between
the upper and lower lines, not only under the effect of drag and thrust, but also in the static case. This arrangement
provided more dynamic stability and reduced the amplitudes of the oscillations of both the line tensions and the
motions of the device. During some of the tests, the tension was adjusted to split the tension equally between upper
and lower lines. In the following analysis, a series of tests (Table 2.11) is considered to show how the mooring
configurations affect the amplitude of the loads and the overall stability of the device. For this purpose, wave only
tests were considered.
2.3.4.1 Waves only tests
Unit Run 101 Run 306 Run 345
Current speed m/sec 0 0 0
Wave amplitude mm 100 100 100
Wave frequency Hz 0.55 0.55 0.55
Turbines speed rpm 0 0 0
Lower lines angle deg 20 20 20
Upper lines pre-tension no yes yes (equally split)
Table 2.11 - Tests characteristics: waves only tests
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Figure 2.14 - Wave only tests – starboard lower line tension variation
Figure 2.15 - Wave only tests – heave motion
The time series (Figure 2.14 and Figure 2.15), from test 101 show an average tension in the mooring lines higher
than in the other tests, and a wider amplitude of oscillation for both the tensions and the motions. The heave
motion is particularly significant, due to the configuration adopted. The test 306 still presents the 20° configuration,
having the upper and lower lines pre-tensioned, which leads to lower tensions and motions than in the test 101. The
test 345 appears to provide the best solution comparatively, where the pre-tension is set so that the load is equally
split between upper and lower lines in the static condition.
2.3.4.2 Waves against current
Two tests, one made in November (test 117) and the other one in December (test 351) are of particular interest
(Table 2.12). They both present the same current speed, wave against current, same wave amplitude but slightly
different frequency. In test 351, the turbines were both operating at 75 rpm, while in test 117, the starboard turbine
is operating at 75 rpm and the port one at 125 rpm. The aim of this analysis is to compare the relative behaviour in
the two different mooring setups despite the fact that one turbine was rotating at a higher speed. Figure 2.16 and
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Figure 2.17 show again the higher tension and motion (pitch shown here) in the absence of upper mooring line pre-
tension.
Unit Run 117 Run 351
Current speed m/sec 0.75 0.75
Wave amplitude mm 100 100
Wave frequency Hz 0.55 0.45
Stbd turbine speed rpm 75 75
Port turbine speed rpm 125 75
Lower lines angle deg 20 20
Upper lines pre-tension mm no yes (equally split
Table 2.12 - Tests characteristics: waves against current tests
Figure 2.16 - Wave against current tests – starboard lower line tension variation
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Figure 2.17 - Wave against current tests – pitch motion variation
2.3.5 Effect of the turbulence intensity on the mooring lines tension First of all, the turbulence intensity is defined as the root-mean-square of the turbulent velocity fluctuations with
respect to the mean velocity (Myers, 2013).
[2.11]. ( = ��)�*+′��*,′��*-′���.+��.,��.-�
where ( is the turbulence intensity [%] /′ is the fluctuating velocity component [m/sec] 0′ is the mean velocity [m/sec]
In the water circulation channel at the IFREMER research centre the turbulence intensity was controlled using a
honeycomb placed upstream the model. When present, it straightens the flow, setting the turbulence level in the
channel at 5%, that is otherwise left at 25%. Table 2.13 below shows two tests at 1 m/sec with no waves, with
turbines parked, at both 5 and 25% of turbulence. Figure 2.18 shows the tension in the starboard lower line for the
two tests while Figure 2.19 and Figure 2.20 show how the tension is distributed in the frequency domain. It can be
seen that the higher level of turbulence leads to higher tension peaks occurring at higher frequencies. Figure 2.21
shows the probability density functions of the tension for the two levels of turbulence and illustrates the higher
tension levels reached in 25% turbulence.
Unit Run 225 Run 335
Current speed m/sec 0.75 0.75
Wave amplitude mm - -
Wave frequency Hz - -
Turbine speed rpm 0 0
Turbulence level % 5 25
Table 2.13 - Tests characteristics: effect of turbulence comparison
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Figure 2.18 - Effect of turbulence – starboard lower line tension variation
Figure 2.19 - Effect of turbulence – starboard lower line tension in the frequency domain at 5% turbulence
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Figure 2.20 - Effect of turbulence – starboard lower line tension in the frequency domain at 25% turbulence
Figure 2.21 - Effect of turbulence – probability density function of the starboard lower line tension (raw signal)
2.3.6 Failure mode tests During week 2 several failure mode tests were performed, where the parameters were recorded during a line failure
incident. Table 2.14 presents the characteristics of three cases where an upstream primary line was suddenly
released in the case of current only and with waves. The aim of this analysis is to evaluate the effect of the failure on
the tensions in the remaining lines; Failure of an upstream primary line was considered the most extreme case. Table
2.15 presents the ratio of the tension before and after failure for both upper and lower lines.
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Unit Run 358 Run 360 Run 363
Current speed m/sec 0.50 0.75 0.75
Wave amplitude mm - - 150
Wave frequency Hz - - 0.45
Turbines speed rpm 0 0 0
Lower lines angle deg 20 20 20
Failure case upstream port primary line upstream port primary line upstream port primary line
Table 2.14 - Tests characteristics: failure mode tests
Run 358 Run 360 Run 363
Stbd lower line 0.6 1.1 1.2
Stbd upper line 2.5 3.0 2.2
Table 2.15 - Tension coefficients between before and after the failure
The probability distribution of the tensions was calculated, both before and after failure (Figure 2.22 and Figure
2.23), to determine their peak values in both conditions in order to determine the relative ratios. This information is
useful for ensuring that appropriate safety factors are used during the design phase. [2.12] shows how the peaks are
calculated. The value considered is the tension in the line at the 95th percentile, using a Gaussian function for the
probability distribution.
[2.12]. �1234 = 5 + 27
where 5 is the mean value of the tension [N] 7 the standard deviation of the tension [N]
Once the peak values in both operational and failure condition have been calculated, and the ratios between them
indicate how the incident would affect the remaining lines. From Table 2.15, it can be seen that the highest tension
is reached in the starboard upper line with current and waves. The case for which a line would experience greater
resulting tensions is in current only (test 360) where the tension in the starboard upper line reaches three times the
value in the operational case.
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Figure 2.22 - Test 360 – probability density function of line tension before failure
Figure 2.23 - Test 360 – probability density function of line tension after failure
2.3.7 Wave excitation and device motion The aim of this section is to evaluate the horizontal wave particle velocity and to investigate how it affects the
tensions in the lines. The wave particle horizontal velocity is calculated according to the DNV recommended practice
(DNV-RP-C205 Environmental Conditions and Environmental Loads), and the tensions in the lines are resolved along
the x axis. The wave period is calculated using [2.13], then [2.14], [2.15] and [2.16] allow to determine the wave
length.
[2.13]. � = 8
[2.14]. 9: = ;<�=>?�
[2.15]. @�9:� = 1 + ∑ BC;CD 9:C
where � is the wave period [sec] @ is the wave frequency [Hz]
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E is the channel depth [m] B , … , BCare 4 dimensionless coefficients. In particular: B = 0.666 B = 0.445 B = −0.105 B = 0.272
[2.16]. N = ��OE��� P 8�Q:� �Q:8�Q:�R��
where N is the wave length [m] O is the acceleration of gravity [m/sec2]
[2.17] calculates the wave number, while [2.18] the angular frequency. Finally [2.19] determines the horizontal wave
particle velocity.
[2.17]. S = �<T
[2.18]. 9 = UOS ∙ VWXℎ�SE�Z��
[2.19]. / = �<[? \]^_U4�`�=�Z^aC_U4=Z
where S is the wave number [rad/m] 9 is the wave angular frequency [rad/sec] / is the horizontal wave particle velocity [m/sec] b is the wave elevation [m]
The horizontal component of the tension in the lines is resolved along the x axis, using [2.20]. Then [2.21] determines
the sum of those components.
For c = 1,… ,4
[2.20]. �da = ?e� �f3C�ghije k�f3C�ghile k
where � is the line tension [N]
Then the sum of these components is considered:
[2.21]. �df]f = ∑ �da;aD
Figure 2.24 shows clearly the correlation between this last quantity (horizontal component of the tension) and the
horizontal wave particle velocity.
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Figure 2.24 - Test 310 – horizontal line tension component vs horizontal wave particle velocity
As expected, the horizontal particle velocity induced by the waves is in phase with the horizontal component of the
tensions in the upstream lines. It can be seen that the additional flow velocity due to the waves results in an increase
in the drag created by the support structure.
2.4 ANALYSIS & CONCLUSIONS
2.4.1 Drag estimation through mooring lines tension measurements and direct readings
The outcome of the analysis demonstrates that the mathematical model developed to establish a relationship
between the drag on the platform and the tension in the mooring lines is sufficiently accurate. The method did not
include any vertical loads though, so there is still some uncertainty about whether the model would be as good if
applied to a case with significant vertical wave-induced forces.
2.4.2 Depth of Submergence Although the current is usually stronger closer to the surface, this an ideal spot to locate the platform for maximising
power extraction, the effect of wave induced motion and load variation in the mooring lines is also greater.
However, with careful pre-tensioning of the mooring lines, the device can remain relatively motion free close to the
surface. Because of this, a great deal of freedom exists when determining the appropriate position for the support
structure in the water column at a given site. Besides the environmental conditions (current speed and metocean),
other factors, such as providing safe overhead clearance for small vessels that are working at the site, or that may
stray into the site, must be considered.
2.4.3 Pre-tensioning Pre-tensioning the lines in order to divide the loads between upper and lower lines seems to be the most efficient
method of ensuring the dynamic stability of the platform; a more stable device dramatically decreases the load
cycling in the mooring lines and greatly increases fatigue life.
2.4.4 Effect of Turbulence A greater level of turbulence induces greater amplitudes of tension fluctuations in the mooring lines at higher
frequencies.
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2.4.5 Failure Mode The most severe case is the failure of an upstream primary line. The tension in the opposite upstream upper line
increases up to three times more than in the intact case. In the failure tests performed, the turbines were always
parked, and it is recommended that further work is undertaken in this area to understand the consequences when
the turbines are operating.
2.4.6 Wave Excitation and Device Motion After calculating the horizontal wave particle velocity and comparing its behaviour with time with the horizontal
component of the tension in the lines, it can be seen that the two parameters are in phase, at least in regular waves.
This demonstrates that the structure is dominated by viscous drag forces, as would be expected on a fully
submerged object.
3 MAIN LEARNING OUTCOMES
3.1 PROGRESS MADE Provide the empirical hydrodynamic co-efficient associated with the device (for mathematical modelling tuning)
The experience has proven to be successful. That investigation though provided only the horizontal drag coefficient
for the whole device. It would be very useful to obtain as well the vertical coefficient, and even better would be to
gain knowledge of the hydrodynamic properties of each component.
Investigate physical process governing device response & Initial indication of the full system load regimes
The discrepancy between the forces on the device, evaluated using the recorded mooring line tensions, and those
calculated with the mathematical model resulted to be sufficiently small. That gives confidence in using the latter to
determine the loads on the device, dividing them into drag and inertial forces, even for different environmental
conditions.
Mooring arrangements and effects on motion
It was possible to notice that a lower angle of the mooring lines with the seabed, while increasing the average
tension in the lines, reduced the amplitude of the motions of the device, with a consequent reduction also in terms
of oscillations of the mooring line tensions. The same benefits were obtained as well by pre-tensioning the upper
mooring lines.
3.1.1 Progress Made: For This User-Group or Technology
3.1.1.1 Next Steps for Research or Staged Development Plan – Exit/Change & Retest/Proceed?
3.1.2 Progress Made: For Marine Renewable Energy Industry The experience proved that, for an underwater platform housing tidal turbines, the buoyancy can be used to
counteract the effect of drag and thrust, providing the device with a sufficient level of stability to operate even in
severe environmental conditions.
3.2 KEY LESSONS LEARNED 5-10 bullet points which will be useful and helpful to the User-Group and particularly to others
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4 FURTHER INFORMATION
4.1 SCIENTIFIC PUBLICATIONS List of any scientific publications made (already or planned) as a result of this work:
• F. Fiore, F. Trarieux, J. Hayman, Experimental investigation of the dynamic response of an underwater taut
moored supporting platform for tidal energy converters in unidirectional current and waves. "European
Wave and Tidal Energy Conference 2013".
4.2 WEBSITE & SOCIAL MEDIA Website: www.sustainablemarine.com
LinkedIn/Twitter/Facebook Links: Follow @Sustain_Marine on Twitter
5 REFERENCES
[1]. L. Myers, K. Shah, P. Galloway, Design, commissioning and performance of a device to vary the turbulence in
a recirculating flume. "European Wave and Tidal Energy Conference 2013".
[2]. S. K. Chakrabarti, "Handbook of Offshore Engineering". Elsevier, 2005.
[3]. Det Norske Veritas, "Recommended Practice DNV-RP-C205 2005-04 Environmental Conditions And
Environmental Loads". Updated April 2007.
6 APPENDICES
6.1 SCALING - SIMILARITY LAWS The dimensions of the model are scaled linearly, while for the environmental conditions the Froude scaling laws
have been used. For the turbines the tip speed ratio (TSR) has been maintained constant between model and full
scale. Then, if m denotes the “model” and p the “full scale prototype”, [6.1], [6.2] and [6.3] determine the flow
velocity at model scale, in order to maintain the Froude number constant.
[6.1]. mno = pqr>sq = mn1 = ptr>st
[6.2]. → √Tpqr>st = ptr>st
[6.3]. → wo = pt√T
where mn is the Froude number [-] w is the flow speed [m/sec] O is the gravity acceleration [m/sec2] x is the representative wetted length [m] N is the scaling factor for lengths [-]
[6.4], [6.5] and [6.6] determine the turbine speed at model scale, in order to maintain constant the TSR.
[6.4]. �yzo = �yz1
[6.5]. → .qpq = .tpt
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[6.6]. → {qQqpq = {tQtpt
where �yz is the Tip Speed Ratio [-] 0 is the tangential speed of the blade tip [m/sec2] z is the rotor radius [m] 9 is the rotor rotational speed [rad/sec]
The dimensions of the rotor were scaled linearly, as shown in [6.7].
[6.7]. zo = {tT
[6.8] and [6.9] determine the angular velocity at model scale.
[6.8]. 9o = N pqpt 91
[6.9]. 9o = √N91
Therefore, the turbine rotates ~3.5 times faster at model scale. In [6.10] and [6.11] the turbine speed is expressed in
rotations per minute (rpm).
[6.10]. |}�< ∗ 9o = |}�< ∗ √N91
[6.11]. → Xo = √NX1
where X is the rotor rotational speed [rpm]
[6.12] and [6.13] express the hydrodynamic pressure both at model and at full scale, while [6.14] shows the ratio
between the densities for sea and fresh water. Since [6.15] and [6.16] are valid, [6.17] finally expresses the
relationship between the pressure at model and at full scale, while [6.18] shows the relation between the
hydrodynamic forces.
[6.12]. �o = ��owo�
[6.13]. �1 = ��1w1�
[6.14]. B = �t�q
where � is the hydrodynamic pressure [Pa] � is the water density [kg/m3] B = 1.025 is the ratio between the fluid density at full scale (sea water) and at model scale (fresh water) [-]
[6.15]. �o = �tT�
[6.16]. m = ��
[6.17]. �o = 1thT
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where � is the area subject to the hydrodynamic pressure [m2] m is the total force acting on the wetted area, due to the hydrodynamic pressure [N]
[6.18]. mo = �thT)
[6.19] shows how the moments scale, while [6.20] and [6.21] express the relationship between the mechanical
power at model and at full scale.
[6.19]. �o = mo × �o = �thT) × �tT = �thT�
[6.20]. � = � ∙ 9
[6.21]. �o = �o ∙ 9o = �thT� ∙ √N91 = �thT).�
where � is the moment of force [N*m] � is the moment arm [m] � is the mechanical power [W]
Table 6.1 Scaling of variables using Froude laws (Chakrabarti, 2005)
Recommended