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
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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
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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
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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.
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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.
1.2 DEVELOPMENT SO FAR .......................................................................................................................................... 8
1.2.2 Plan For This Access ................................................................................................................................... 10
2 OUTLINE OF WORK CARRIED OUT ................................................................................................................. 10
2.1.1 Reference system ...................................................................................................................................... 10
2.1.2 Model calibration ...................................................................................................................................... 11
2.1.4 Data recording ........................................................................................................................................... 14
2.4.4 Effect of Turbulence................................................................................................................................... 31
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
4 FURTHER INFORMATION .............................................................................................................................. 33
4.2 WEBSITE & SOCIAL MEDIA ................................................................................................................................... 33
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 2.15 - 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
Infrastructure Access Report: SME - PLAT-O
Rev. 01, 15-Oct-2013
Page 35 of 35
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)