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An Introduction to Tidal Power
Professor Ian G Bryden
University of Edinburgh
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The Tides
Definition
The rise and fall of the ocean surface under
the influence of the gravitational and
dynamic influence of the Earth/Moon/Sun
system
The first effective theory was produced by
Newton
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Newtons Theory
Earth
CoMm
CoMs
CoMe
R
r
A B
C
D
Rotation of the Earth aboutthe centre of mass of theEarth-Moonsystem
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The Earth Moon system rotates around a common centre of mass
(CoMs) and the radius of this circulation is given by r.
The separation of the centre of mass of the Earth (CoMe) from the
centre of mass of the Moon (CoMm) is given by R. If the Earth were not itself rotating, each point on, or in, the Earth
would rotate about its own centre of rotation, the radius of the
rotation would also be given by rand the period of rotation would
be equal to the rotational period of the Earth-Moon system. This results in acceleration towards the local centre of rotation.
Earth
CoMm
CoMs
CoMe
R
r
A B
C
D
Rotation of the Earth aboutthe centre of mass of theEarth-Moonsystem
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At the centre of the Earth, the centrifugal acceleration, resulting from
the rotation, exactly matches the gravitational acceleration.
At all other points, there is an imbalance between gravitational and
centrifugal effects.
At the point B the centrifugal effects exceed the lunar gravitational
attraction.
At the surface of the Earth, there will be a net flow of water from
C&D to A&B.
The equilibrium theory suggests, therefore, the establishment of tidal
bulges in the fluid surrounding the Earth.
Earth
tidal bulge
Moon
Earth
CoMm
CoMs
CoMe
R
r
A B
C
D
Rotation of the Earth aboutthe centre of mass of theEarth-Moonsystem
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The Earth of course rotates and the two tidal bulges, inorder to maintain their position with respect to the Moon,
have to travel round the Earth at the same rate as the
Earths rotation.
The Moon rotates around the CoMs every 27.3 days in the
same direction that the Earth rotates every 24 hours.
Because the rotations are the same direction, the net effect
is that the period of the Earths rotation, with respect to the
Earth Moon system, is 24 hours and 50 minutes.
This explains why the tides are approximately an hour later
each day.
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Further Lunar Influences on the
Tidal Period The Lunar orbit is not circular but is elliptical in form and
the tide producing forces vary by approximately 40% over
the month.
Similarly, the Moon does not orbit around the Earths
equator!
Instead there is 280 between the equator and the plane of
the lunar orbit. This also results in monthly variations.
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Influence of the Sun on the Tides
The Earth Sun system is also elliptical but with only a 4%
difference between the maximum and minimum distance
from the Earth to the Sun.
The relative positions of the Earth, Moon and Sun produce
the most noticeable variations in the size of the tides. In
particular the Spring-Neap cycle
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New Moon:- Spring Tide
Moon
Earth
Lunar tide
solar tide
Sun
In this configuration, the
influence of the Moon and
Sun reinforce each other toproduce the large tides
known as Spring Tides, or
Long Tides.
A similar superposition also
exists at the time of Full
Moon.
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Half Moon:- Neap Tides
When the Sun and Moon are at 90o to each other, the effect is of
cancellation as shown.
Moon
Earth
Lunar tide
solar tide
Sun
This configuration
results in Neap Tides,
which are also know as
Short Tides.
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The Presence of Land and the
Resulting Tidal Dynamics
The oceans are not all of a constant depth and the presence
of continents and islands severely influences the behaviour
of the oceans under tidal influences.
Coriolis Force which, in the Northern hemisphere, diverts
moving objects to the right and, in the Southern
Hemisphere, diverts moving objects to the left, has a
substantial influence on the tides.
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Semi-enclosed Basin in the
Northern Hemisphere On the way into the channel the water is diverted to the
right towards the lower boundary. When the tidal forcing is
reversed, the water is diverted towards the upper boundary.
This results in a substantially higher tidal range at the basinboundaries than at the centre.
diversion of
inflowingwater
diversion of
outflowing water
Open
boundary
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The net result of this effect is to generate a tidal wave
which processes anti-clockwise around a point in the
centre of the basin.
progression of
tidal wave
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Tidal
Structure in
the North
Sea
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Energy Available in the Tides
It has been estimated that the total energy from the tides,which is currently dissipated through friction and drag, is
equivalent to 3000GW of thermal energy worldwide.
Much of this power is in inaccessible places but up to 1000
GW is available in relatively shallow coastal regions. Estimates of the achievable worldwide electrical power
capability range from about 120 GW of rated capacity to
approaching 400 GW.
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Extracting Tidal Energy
1:Tide Mills
The extraction of energy from the tides is not a new idea.
Mills, which used tidal flows in bays and estuaries to drive
machinery to grind cereal, were used in medieval times.
Despite the global nature of tidal energy, there is little
evidence of tide mill development outside southern
England and, even there, the distribution is mainly
localised to Hampshire, West Sussex and the Fal andTamar estuaries in Devon and Cornwall.
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Tide mills were generally used in areas with only small
streams where good sites for conventional watermills are
uncommon.
Tide mills frequently suffered from damage resulting from
tidal surges.
This, and changing labour markets following the First
World War, resulted in traditional tide mills becoming rare
and of historical interest only.
More recently, however, the tides have been seriously re-examined as a potential source of energy for industry and
commerce.
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Eling Tide Mill
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Tidal Barrage Systems
Essentially modern electrical generation developments of
the traditional tidemill
In the nineteenth and twentieth centuries, there were
numerous proposals to exploit the tidal energy potential of
the Severn Estuary. None have yet been developed.
The world's first serious scheme to exploit tidal energy was
constructed in France, at La Rance in Brittany, between
1961 and 1967 and consists of a barrage across a tidalestuary to utilise the rise and fall in sea level induced by
the tides.
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Tidal Barrage Systems
Designed to harness the rise and fall of the
sea by enclosing tidal estuaries eg
LaRance, Severn, Solway
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LaRance
The worlds first serious scheme to exploit tidal energy
was constructed in France, at La Rance in Brittany,
between 1961 and 1967.
It consists of a barrage across a tidal estuary to utilise the
rise and fall in sea level induced by the tides.
This scheme has proven itself to be highly successful
despite some early teething problems.
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La Rance Tidal Barrage
Now 36 years old!
Currently undergoing a
10 year maintenance
programme
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Site mean tidal range
(m)
Barrage
length (m)
estimated annual energy
production (GWh)
Severn Estuary(UK) 7.0 17,000 12,900
Solway Firth (UK) 5.5 30,000 10,050
Bay of Fundy
(Canada)
11.7 8,000 11,700
Gulf of Cambay(India)
6.1 25,000 16,400
Possible Sites World Wide
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Ebb Generation
This is the most likely approach to be used commercially
Sluices are opened during the flood tide allowing the basin
to fill up.
Sluices are closed at high tide and during the ebb tide a
head is initially allowed to develop
Once a sufficient head has been developed between the
basin and the outer waters, gates are opened and water
allowed to flow out of the basin through turbines.
Flood Tide Sea water flows through sluices
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Flood Tide- Sea water flows through sluicesinto basin
flow ofwater
through
sluices
Open sea Within barrage
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High Tide- Sluices closed to retain water in basin
flow ofwaer
through
sluices
Open sea Within barrage
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Open sea Within barrage
EbbTide(a)- water retained in the basin toallow a useful head to develop
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Ebb Tide(b)- sea water flowing through generators
flow of
water
through
turbines
Open sea Within barrage
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Ebb Generation
generation
hase
water level outside the basi
water level inside
the basinclosure of sluices
opening
of turbine
gatesreopening of
sluices
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Flood Generation Mode
In this alternative to ebb generation, the sluices are are
closed at low water and a head develops during the flood
tide.
Gates are opened once the head is sufficient to drive the
turbines.
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Flood Generation
generation
hase
water level outside the basin
water level inside
the basin
closure of sluices
opening
of turbinegates
reopening of
sluices
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Two Basin Systems
Double basin system have been proposed to allow an
element of storage and to give time control over power
output levels.
Typically, he main basin would behave, essentially like an
ebb generation single basin system.
A proportion of the electricity generated during the ebb
phase would be used to pump water to and from the second
basin to ensure that there would always by a generationcapability.
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Multiple basin systems are unlikely to become popular, as
the efficiency of low-head turbines is likely to be too lowto enable effective economic storage of energy.
The overall efficiency of such low head storage, in terms
of energy out and energy in, is unlikely to exceed 30%.
It is more likely that conventional pump-storage systemswill be utilised.
The overall efficiencies of these systems can exceed 70%
which is, especially considering that this is a proven
technology, likely to prove more financially attractive.
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Two Basin Systems
second
basinmain basin
turbines
turbines
sluices
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Combined Generation and Storage
main basin level
second basin level
generation in
the main basin
and pumping
from the
second basin
generation in
the second
basin
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The Financial Implications of
Tidal Barrage Development Severn Estuary could provide in excess of 8 % of the
UKs requirement for electrical energy .
La Rance took 6 years to complete. No electricity couldbe generated before the total project was completed. This
is a major disincentive for commercial investment.
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Environmental Opposition to
Tidal Barrages Environmental groups, although generally in favour of the
exploitation of alternative energy sources, are suspicious of
the likely environmental changes large estuary based
schemes would produce.
One politician in the UK likened the proposed creation of a
barrage across the Severn Estuary to the formation of a
large stinking lake.
Similar opposition has been voiced against anydevelopment of the tidal resource in the Solway Firth
between Scotland and England. It is anticipated that public
and political opposition will limit the development of tidal
barrage schemes in the short term.
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An ebb generation system will reduce the time tidal sands
are uncovered. This would have considerable influences onthe lives of wading birds and other creatures.
The presence of a barrage will also influence maritime
traffic and it will always be necessary to include locks to
allow vessels to pass through the barrage. This problem will be less problematic for an ebb system,
where the basin is potentially kept at a higher level, than it
would be with a flood generation system, in which the
basin would be kept at a lower than natural level.
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Tidal Currents Typically small in the open ocean.
Local geographical effects can enhance flow speeds.
In the Pentland Firth there is evidence of tidal currents exceeding
7m/s. Other sites, in Europe alone, with large currents include, theChannel Islands and The Straits of Messina.
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In the open ocean tidal currents are typically very small
and are measured in cm/s at most.
Local geographical effects can result in quite massive local
current speeds. In the Pentland Firth to the North of theScottish mainland, for example, these is evidence of tidal
currents exceeding 7m/s. The kinetic energy in such a flow
is considerable.
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It has been estimated in a recent report for the EuropeanCommission Directorate General for Energy (Cenex 1995)
that the European Resource could represent a potential for
48 TWhr annual energy production
If even a small fraction of this potential were exploited it
could represent a major contribution to the European
energy market.
More recent studies studies, including one commissioned
by the Scottish Executive, suggest that the UK resource
alone could exceed 40TWhrs per annum!
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Tidal Current Resource
UK Resource -
36 TWhr/year*
40-50TWhrs/year#
* ETSU 1999
# Bryden 2002
World-wide - 400 TWh/year#
achievable with technology
currently on drawing board
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Tidal Current DevicesMust convert energy in moving water into
mechanical movement
Horizontal axis devices
Vertical axis devicesLinear lift devices
Venturi devices
Must be held in place against fluid loadingFixed to sea bed
Anchored floating
CRE+E
CRE+E
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Tidal Conversion Concepts
Tidal flow
rotational
axisTidal flow
rotational axis
Horizontal axis turbine Vertical axis turbine
Venturi based device Linear lift based device
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Vertical Axis Turbines
The rotational axis of the system is perpendicular to the
direction of water flow.
Tidal flow
rotationalaxis
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A horizontal axis turbine has the traditional form of fan
type system familiar in the form of windmills and wind
energy systems.
Tidal flow
rotational axis
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Device Location
The energy flux is so high in many locations that the real
engineering challenge is not energy conversion but in
securing the conversion systems against the flow.
Should a system be:
suspended from a floating structure
mounted on the sea bed
How should either the system itself or, in the case of a
moored system, anchors be secured?
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Moored Systems
moored surface system
turbine and generator
This concept has advantages of mobility and accessibility. There
are, however, possible problems concerning the stability of the
surface pontoon and the generator/turbine.
How is the anchor attached?
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Loch Linnhe TurbineSmall floating demonstration device
in the early 1990s
Study conducted by IT Power Ltd
and funded by Scottish Nuclear
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Fixed Systems
vertical support drilled or
piled into the sea bed
Provides a stable platform but the construction and installationcosts could be very much larger.
Technology options:
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Technology options:
holding a turbine in placeShallow water options Deeper water options
CRE+E
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Prototype SystemsENERMAR
Tested in 2000 in the Strait of Messina (between Sicily and theItalian mainland)
A large vertical axis floating generator
CRE+E
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Prototype Devices
SeaFlow (Marine Current Turbines Ltd)
Rated power output of 300kW,
mounted on a vertical pillar fixed into thesea bed.
In Bristol Channel off Lynmouth
Prototype DevicesCRE+E
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Prototype Devices Stingray (The Engineering Business Ltd)
Tested in Yell Sound, Shetland during 2002 to 2003
Uses a unique linear foil system
Novel barge based installation system
Stingray awaiting installation in Yell Sound Artists impression of Stingray
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Prototype Devices Hammerfest Strom
Grid connected, sea bed mounted horizontal axis system
which was installed in Norway in 2003.
Artists impression Installation process CRE+E
S t d d l t
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Systems under development
60kW device being installed
Hydroventuri LtdEnergy extraction system based
upon utilisation of the pressure
differential created in a venturi
Lunar Technology LtdUses a horizontal axis turbine in
a protective/flow enhancing
cowl
1.5MW device concept CRE+E
SeaGEN awaiting
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g
installation in Strangford
Lough
CRE+E
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Systems under development
TiDel (SMD Hdrovision)
Tethered twin horizontal
axis system
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The Sea Snail (my device) Support system for tidal
energy extraction systems
minimal sea bedpreparation
System is prefabricatedrequiring minimal on-siteconstruction
Installation requires the use
of a tug
Easily removed formaintenance, etc.
CRE+E
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Kinetic Energy in Moving Water
A
3
2
1 dA)(UP
A(m2)
U(r)r
is the water density (kg/m3)
A is the cross sectional area of the channel (m2) and
U is the component of the fluid flow velocity (m/s)
3
A2
1 UAP
A
33
A dA)(UUA
where
Influence of Flow Speed on Energy
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Influence of Flow Speed on Energy Flux
0
5
10
15
20
25
30
35
0 1 2 3 4
Flow Speed (m/s)
PowerDen
sity(KW/m2)
0
200
400
600
800
1000
1200
1400
Energy
Flux(MW)
Influence of Flow Speed on Energy
Flux in a Simple Channel
Channel Width 1000m
Channel Depth 40m
Mean consumption: GlasgowMean consumption: Edinburgh
But:Influence of Flow Statistics
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But: Influence of Flow Statistics
0.01.0
2.03.0
0.0
1.0
2.03.0
0
1
2
3
4
5
6
7
8
9
10
kW/m2
Mean Spring Peak(m/s)
Mean NeapPeak(m/s)
Influence of Tidal Statistics on the Mean KineticEnergy Flux
Obviously vital
that the full tidal
statistics are
considered and not
just the spring
peak!
CRE+E
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Tidal Current Energy Flux Density
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What Makes a Good
Site(Hydrodynamics) Sufficient Current Speeds over a full monthly cycle!
(dont rely only on peak spring currents)
Flow stability*
Sufficient Water Depth to allow devices to operate away
from the sea bed and sea surface
Bidirectional flow
It will be very difficult to operate effectively if thecurrent is heavily asymetric
Sheltered from wave influence through either coastal
geography or water depth
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What Makes a Good
Site(environmental and social) Proximity to economic grid connection points
Some design concepts cannot coexist with shipping and
fishing activity- is an exclusion zone acceptable?
Proximity to service capabilities
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Energy Extraction Mechanisms reflect those in wind power
eg formulation of speed power curves
Case 1: Fixed Rotational Speed
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
12.5 4
5.5 7
8.5 10
Tip Speed Ratio
Cp
Turbine Form 1
Turbine Form 2
Turbine Form 3
Speed Power Curves
0
500
1000
1500
0 2 4 6 8 10
Current Speed (m/s)
PowerOutput(kW
Turbine Form 1
Turbine Form 2
Turbine Form 3
Turbine Diameter: 20m; Rotational Period: 8 s
period(s)RotationalT
)Diameter(mTurbineD
later)(more*speed(m/s)waterU
,UT
D
3
p21 AUCP
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Case 2: Variable Speed
In energy conversion term, it would be advantageous if a turbine
could be maintained with a tip speed ratio at the optimal value to
ensure that the power coefficient Cp is kept close to the maximum
possible. As tidal current speeds vary more sedately than wind
speeds, this might be more practical for a tidal turbine than for awind turbine.
Speed Power Curves
0
500
1000
1500
0 2 4 6 8
Current Speed (m/s)
PowerOutput(kW)
Turbine Form 1
Turbine Form 2
Turbine Form 3
20 10Optimal Variable Speed Turbines In this case, the power
output simply follows the
cube power law
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Regulated Power Curves
In principle, the output will be regulated so that it rises up
to the Rated Power, then flattens off.
Speed Power Curves
0
100
200
300
400
500
600
0 1 2 3
Current Speed (m/s)
PowerOutput(kW)
Turbine Form 1
Turbine Form 2
Turbine Form 3
Turbine Diameter: 20m; Rotational Period: 6 s
Speed Power Curves
0
100
200
300
400
500
600
0 1 2 3Current Speed (m/s)
PowerOutput(kW
Turbine Form 1
Turbine Form 2
Turbine Form 3
Turbine Diameter: 20m; Rotational Period: 8 s
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Depth Speed Profile
The horizontal speed of water in a tidal flow (U) varies
with depth below the surface. This variation may be
complex in form. It has, however, become common to
represent the variation parametrically as following inpower law of the form:
n1
)H
(ConstU
is the vertical distance above the sea
bed (m)
H is the water depth (m)
n is the power law coefficient
Variation in Current Speed Within the Water
Column
0
5
10
15
20
25
30
35
40
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
m/s
m
Top of Turbine
Bottom of Turbine
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As the power density is proportional to the speed cubed,
the ideal descriptor of current speed is given by the cube
root of the mean speed cube over the swept area
If the turbine is of a horizontal axis type, this is given by:
r
r
dyzyury
ru )(sincos2 0313
31
r is the turbine radius
z0 is the height of the hub above the sea bed.
u() is the flow speed a distance above the sea bed.
I fl f C t S d St ti ti
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Influence of Current Speed Statistics
As with wind power, the mean power can be determined
by using the speed/power curve and the speed probability
density curve, which is given by (u)
du)u()U,P(U
2
1
U
U
x21
So that the probability an instantaneous
measurement of the velocity component ux
would fall between U1 and U2 would be
P(u)du)u(Power
0
And the mean power output is given by:
i d
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Parametric Speed Spectra
It may prove convenient to use a parametric form of thetidal current variation. One of the simplest being of the
form:
)T
2))sin(
T
2Ecos((DF(t)U
and)T
2))cos(
T
2Ccos((BA(t)U
01y
01x
A & F are related to residial current speeds,
B, C, D and E are amplitude terms,
T0 is the period of the semidiurnal variation,
T1 is the period of the Spring-Neap cycle,
Ux(t) represents the E-W current speed and
Uy(t) represents the N-S current speed.
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Examples of Parametrically
Defined Tidal FormsSample Current Speed Probability Density
00.1
0.2
0.3
0.4
0.5
0.6
0 0.2 0 .4 0.6 0 .8 1 1.2 1 .4 1.6 1 .8 2 2.2 2.4 2 .6 2.8 3 3.2 3.4
Current Speed m/s
s/
Distribution A
Sample Current Speed Probability Density
00.1
0.2
0.3
0.4
0.5
0.6
0 0.2 0 .4 0.6 0 .8 1 1.2 1 .4 1.6 1 .8 2 2.2 2.4 2 .6 2 .8 3 3.2 3.4
Current Speed m/s
s/
Distribution B
Spring mean 3m/s
Neap Mean 1.5m/s
Spring Mean 3m/s
Neap Mean 2m/s
Optimal Rotational Speed-
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fixed speed turbine (unregulated)
The optimal rotational
speed of a turbine is a
function of the form of the
CP- curve and the flow
statistics: eg
Power Coefficient
0.0
0.1
0.2
0.3
0.4
0 2 4 6 8 10
Tip Speed Coefficient
Cp
Using the parametric distributions Aand B defined earlier and with a
14m diameter turbine (Optimal is
defined as maximising the mean
power output):
Parametric
Speed
Spectrum A
Parametric
Speed
Spectrum B
OptimalPeriod (s) 5.1 4.9
Mean Power
Output (kW)
114 149
Maximum
Power
Output (kW)
510 540
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Influence of Tidal Statistics on
Energy Conversion Potential If a fixed speed device is utilised, the optimal rotational
speed, which delivers the highest mean power output is
highly dependent upon the nature of the flow statistics.
If is assumed that it is possible to identify this optimalrotation, then it becomes possible to establish a maximum
achievable effective energy conversion coefficient Ceff.
CyclepSpring/NeatheDuringdInterceptePowerIncidentMeanCyclepSpring/NeaaDuringOutputPowerMeanCeff
Ceff is, in effect, the mean effective value of the power
coefficient Cp.
Mean Spring(m/s) Peak
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
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Mean Spring
(m/s)
Peak
Mean Neap
Peak(m/s)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
1 28.4 28.2 27.9 26.8 26.9 26.6 26.3 26.0 25.9 25.9 25.3
1.2 28.2 28.4 27.2 27.8 27.6 27.2 26.9 26.6 26.3 26.1 25.2
1.4 27.9 27.2 28.1 28.3 28.1 27.8 27.3 27.1 26.9 26.6 25.31.6 26.8 27.8 28.3 28.4 28.3 28.2 27.9 27.6 27.3 27.1 25.8
1.8 27.0 27.6 28.1 28.3 28.4 28.3 28.2 28.0 27.7 27.5 26.5
2 26.6 27.2 27.8 28.2 28.3 28.4 28.4 28.2 28.1 26.7 27.1
2.2 26.3 26.9 27.3 27.9 28.2 28.4 28.4 28.4 26.9 27.4 27.7
2.4 26.0 26.6 27.1 27.6 28.0 28.2 28.4 28.4 27.6 27.9 28.1
2.6 25.9 26.3 26.9 27.3 27.7 28.1 26.9 27.6 28.0 28.3 28.3
2.8 25.9 26.1 26.6 27.1 27.5 26.7 27.4 27.9 28.3 28.4 28.4
3 25.3 25.2 25.3 25.8 26.5 27.1 27.7 28.1 28.3 28.4 28.4Table 2: Ceffexpressed as a percentage for Turbine Form 2
Mean Neap
Peak(m/s)
1 26.9 27.6 27.0 26.3 25.7 25.2 23.3 24.4 24.7 24.7 24.7
1.2 27.6 27.8 27.6 27.1 26.7 26.1 23.6 24.6 24.8 24.7 24.7
1.4 27.0 27.6 27.6 27.7 27.3 26.9 24.9 25.5 25.5 25.2 24.9
1.6 26.3 27.1 27.7 27.8 27.7 25.1 26.1 26.5 26.2 25.8 25.5
1.8 25.7 26.7 27.3 27.7 27.8 26.5 27.1 27.2 26.8 26.5 26.1
2 25.2 26.1 26.9 25.1 26.5 27.3 27.7 27.6 27.3 27.0 26.7
2.2 23.3 23.6 24.9 26.1 27.1 27.7 27.8 27.8 27.6 27.4 27.1
2.4 24.4 24.6 25.5 26.5 27.2 27.6 27.8 27.8 27.8 27.6 27.3
2.6 24.7 24.8 25.5 26.2 26.8 27.3 27.6 27.8 27.8 27.6 27.7
2.8 24.7 24.7 25.2 25.9 26.5 27.0 27.4 27.6 27.6 27.8 27.8
3 24.7 24.7 24.9 25.5 26.1 26.7 27.1 27.3 27.7 27.8 27.8
Table 1: Ceffexpressed as a percentage for Turbine Form 1
OptimalU
nregulatedT
urbines
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Influence of Residual Current on
CeffValues Assuming Neap component is 50% of spring component!
Net Veloc
(m/s)
ity
Mean SpringPeak(m/s)
0 .2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
1 26.6 27.0 27.5 27.5 28.6 29.1 29.4 29.5 28.6 29.7 30.0
1.2 26.5 27.0 26.7 27.8 28.2 28.7 29.1 29.3 29.1 29.7 29.8
1.4 26.6 26.1 27.3 27.6 27.8 28.4 28.7 28.1 29.2 29.5 29.6
1.6 25.6 26.9 27.2 27.5 27.8 28.1 27.1 28.5 29.1 29.3 29.4
1.8 26.5 26.9 27.1 27.4 27.6 27.9 27.7 28.5 28.8 29.1 29.0
2 26.6 26.9 27.1 27.3 27.5 27.1 27.9 28.3 28.6 28.9 29.02.2 26.6 26.8 27.0 27.2 26.7 27.5 27.9 28.2 28.4 28.5 28.9
2.4 26.6 26.8 27.0 26.3 27.2 27.6 27.8 28.0 28.2 28.5 28.7
2.6 26.6 26.8 26.0 26.9 27.3 27.5 27.7 27.9 28.1 28.3 28.5
2.8 26.6 25.8 26.7 27.1 27.3 27.4 27.6 27.7 28.0 28.2 28.3
3 25.5 26.4 26.9 27.1 27.2 27.4 27.5 27.7 27.9 28.0 28.2
Table 4: Influence of Net (residual current) velocity on Ceff: Turbine Form 2
Optim
alUnregulatedturbine
Optimisation: Rated Power and Rotational
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Speed in a regulated turbine
The situation is morecomplicated in the
case of a regulated
turbine.
Consider distribution
B; the optimal
rotational speed and
the rated speed is a
function of the rated
power output!
Rated Power
(kW)
Rated Speed
(m/s)
Optimal
RotationalPeriod (s)
200 2.1 6.44
300 2.5 5.76
400 2.7 5.32
500 3.0 4.99
0
0.5
1
1.5
2
2.5
3
3.5
200 300 400 500
Rated Power(kW)
Ra
tedSpee
d(m
/s)
0
1
2
3
4
5
6
7
Optimal Rotational Period(s)
Rated Speed (m/s)
Optimal Rotational
Period (s)
Power Performance Curve
1100 00
1300.00
1500.00
0 25
0.30
0.35
Power Performance Curve
1100 00
1300.00
1500.00
0 25
0.30
0.35
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Influence of
Rated Power
on the form ofthe optimal
power curve in
a fixed speed
turbine
-100.00
100.00
300.00
500.00
700.00
900.00
1100.00
1
1.
3
1.
6
1.
9
2.
2
2.
5
2.
8
3.
1
3.
4
3.
7 4
Current Speed(m/s)
Power(
kW(
0.00
0.05
0.10
0.15
0.20
0.25
Cp
Power
Effective Cp
Optimal Unregulated Fixed Speed Turbine: CurrentDistribution A
-100.00
100.00
300.00
500.00
700.00
900.00
1100.00
1
1.
3
1.
6
1.
9
2.
2
2.
5
2.
8
3.
1
3.
4
3.
7 4
Current Speed(m/s)
Power(
kW(
0.00
0.05
0.10
0.15
0.20
0.25
Cp
Power
Effective Cp
Optimal Unregulated Fixed Speed Turbine: CurrentDistribution B
Power Performance Curve
0.00
200.00
400.00
600.00
800.00
1000.00
1200.00
1
1.
3
1.
6
1.
9
2.
2
2.
5
2.
8
3.
1
3.
4
3.
7 4
Current Speed(m/s)
Power(
kW(
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
Cp
Power
Effective Cp
20m Optimal Fixed Speed Turbine rated at1000kW: Distribution A
Power Performance Curve
0.00
200.00
400.00
600.00
800.00
1000.00
1200.00
1
1.
3
1.
6
1.
9
2.
2
2.
5
2.
8
3.
1
3.
4
3.
7 4
Current Speed(m/s)
Power(
kW(
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
Cp
Power
Effective Cp
20m Optimal Fixed Speed Turbine rated at1000kW: Current Profile B
Power Performance Curve
0.00
200.00
400.00
600.00
800.00
1000.00
1200.00
1
1.
3
1.
6
1.
9
2.
2
2.
5
2.
8
3.
1
3.
4
3.
7 4
Current Speed(m/s)
Power(
kW(
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
Cp Power
Effective Cp
20m Optimal Fixed Speed Turbine rated at 500kW:
Current Profile A
Power Performance Curve
0.00
200.00
400.00
600.00
800.00
1000.00
1200.00
1
1.
3
1.
6
1.
9
2.
2
2.
5
2.
8
3.
1
3.
4
3.
7 4
Current Speed(m/s)
Power(
kW(
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
Cp Power
Effective Cp
20m Optimal Fixed Speed Turbine rated at 500kW:
Current Profile B
Influence of Rated Power/Speed for an
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optimal variable speed turbinePower Performance Curve
0.00
200.00
400.00
600.00
800.00
1000.00
1200.00
1
1.
3
1.
6
1.
9
2.
2
2.
5
2.
8
3.
1
3.
4
3.
7 4
Current Speed(m/s)
Power(
kW(
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
Cp
Power
Effective Cp
20m Optimal Speed Turbine rated at 1000kW
Power Performance Curve
0.00
200.00
400.00
600.00
800.00
1000.00
1200.00
1
1.
3
1.
6
1.
9
2.
2
2.
5
2.
8
3.
1
3.
4
3.
7 4
Current Speed(m/s)
Power(
kW(
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
Cp
Power
Effective Cp
20m Optimal Speed Turbine rated at 500kW
Figure10: Influence of Rated Speed on the Turbine Speed/Power Curves for an Variable Speed
Turbine (Turbine Form 1)
The value of Cp remains at the peak value of the Cp- curve until the rate
power is achieved and then falls off rapidly to ensure a constant power
output by reducing the efficiency of energy conversion
Influence of Rated Power on Average
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Power OutputFixed Rotational Speed
0
50
100
150
200
250
100
200
300
400
500
600
700
800
900
1000
Rated Power(kW)
AveragePower
output(kW)
0
0.5
1
1.5
2
2.5
3
3.5
RatedSpeed(m/s)
P(av)
U(R)
Influence of Rated Power on Average Power
Generation in Flow Regime A:
Variable Rotational Speed
0
50
100
150
200
250
300
100
300
500
700
900
1100
1300
Rated Power(kW)
AveragePower
output(kW)
0
0.5
1
1.5
2
2.5
3
3.5
RatedSpeed(m/s)
P(av)
U(R)
Influence of Rated Power on Average Power
Generation in Flow Regime A:
Fixed Rotational Speed
0
50100
150
200
250
300
350
100
200
300
400
500
600
700
800
900
1000
Rated Power(kW)
Ave
ragePower
output(kW)
0
0.51
1.5
2
2.5
3
3.5
Rated
Speed(m/s)
P(av)
U(R)
Influence of Rated Power on Average PowerGeneration in Flow Regime B:
Variable Rotational Speed
0
50
100
150
200
250
300
350
400
100
300
500
700
900
1100
1300
Rated Power(kW)
Ave
ragePower
output(kW)
0
0.51
1.5
2
2.5
3
3.5
RatedSpeed(m/s)
P(av)
U(R)
Influence of Rated Power on Average Power
Generation in Flow Regime B:
Figure 11: Influence of Rated Power Upon The Average Power Output and Rated Speed in two
tidal regimes (Turbine Form 1)
Observations of Conversion
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Observations of Conversion
Effectiveness in an Optimised
Turbine The mean Ceffis closely related to the value in the peak of
the Cp- curve
A well matched unregulated turbine should achieve a Ceffof more than 75% of the peak value in the Cp- curve
The size of the rated power only influences the Ceffif the
rated power is much less than 75% of the maximum
unregulated power output at which there should be lessthan a 10% reduction with respect to the unregulated case.
These observations aid in the assessment of likely power
outputs, even in the absence of detailed technical
descriptions of the technology!
f l i
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Assessment of Energy Flux at a Site
Level Necessary to consider temporal variation over the
semi-diurnal and spring/neap cycles
Also necessary to consider the variation in currentflow spatially
In some sites, Energy Hot Spots may move
between flood and ebb tides
Need to identify regions of spatial stability fordevice installation
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Identifying Limits to Extraction
Influence of Energy Extraction on Current
Speed
0%
1%
2%
3%
4%
5%
6%
7%
0% 5% 10% 15% 20% 25%
Proportion of Natural Energy Flux Extracted
SpeedReduction
Based on a simple 1 dimensional channel model
The extraction of energy from a
tidal flow will alter the
underlying hydraulic nature of
a tidal environment.
This will set limits to how
much energy can be extracted
without causing unacceptable
changes
What those limits are will
depend upon the site
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Influence of Energy Extraction
Hypothesis
The extraction of energy from a tidal flow will alter theunderlying hydraulic nature of the flow
This may, depending upon the nature of the tidalenvironment, reduce the underlying flux
It may have environmental consequences
It may have design consequences
It may also have financial consequences
The Simple Static Channel
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hinhout
dh
x
h(x)
Side View
b(x)
Top View
Horizontal channel bed Linking 2 infinite oceans
Flow driven by a known head dh
Ignore, for now, dynamic effects
The Simple Static Channel
0er32
2
23
2
Pgbh
1
bgh
Q
x
b
x
h
bh
Q1
g
UC
g 2
20 Q is the discharge rate(m3/s)
g is the acceleration due to gravity(m/s2)
Per is the wetted perimeter (m) =b+2h
0 is the bed sheer stress(kg/m/s2),
C is the Chezy friction coefficient
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Natural Boundary Stress Calculation
The boundary stress can be determined in terms of
the Chezy coefficient. But in the UK it is common
to use the Manning Friction coefficient:
n
RC
61
n is the Manning roughness factor (sm-1/3)R is the hydraulic radius (m)
2hbA
perimeterwettedareasectionalCrossR
3
1
R
nUg
22
0 The natural boundary stress equation can bewritten, therefore as:
Energy Extraction Hypothesis
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Energy Extraction Hypothesis
In the presence of the artificial extraction of energy, flowin a channel will experience retarding forces resulting from
the natural boundary friction and from the artificial
extraction processes themselves.
The forces resulting from extraction can be considered, incases where vertical flow structure can be neglected, as
resulting from an additional component of the boundary
stress, so that the net effective shear would be:
add 0eff
Calculating the additional stress
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Calculating the additional stress
UPF nretardatio
Consider a flow with longitudinal velocity component U passing
through a cross sectional area A. There will be a retarding force,
resulting from the extraction of P (Watts), which is equal to:
This can be modelled as an equivalent boundary stress, add, given by:
er
nretardatio
add xP
F
x is the length over which the energy is
being extracted and Peris the wettedperimeter
b h Per=b+2h
er
xPU
P
add
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Boundary Conditions
Upstream
There is an initial drop in the elevation head as
a result of flow accelerationThis drop in elevation can be related to the
speed of flow just downstream from the
entrance to the channel:
g2
Uh
2
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Boundary Conditions
Downstream
Assume that the jet output from the channel
does not rapidly mix with the ambient watersA condition of velocity continuity is assumed. Mixing will, of course, occur eventually but this three dimensional
effect will manifest itself outside of the channel constraints and
will not be considered here.
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Solving the Equations
By integrating the flow equation from the known depth at
the downstream boundary, establish the upstream depth as
a function of the discharge rate, Q.
Establish an iteration to determine the value of discharge,Q, compatible with chosen upstream and downstream
water depth
This allows a the determination of depth and speed
between the upsteam and downstream boundary.
Zero Energy Extraction
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gy
Variation in Current Speed and Water Depth
2.89
2.90
2.91
2.922.93
2.94
2.95
2.96
2.97
2.98
2.99
0
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
2400
2600
2800
3000
3200
3400
3600
3800
4000
Distance(m)
Sp
ee
d(m/s)
38.8
39.0
39.2
39.4
39.6
39.8
40.0
40.2
D
ep
th(m)
Velocity(m/s)
Depth(m)
Abrupt drop in water depth at entrance to the channel
Associated with a sharp increase in flow speed
Decrease in depth along the channel
Acceleration of flow along the channel
10% Kinetic Energy Flux Extraction
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gy
2.81
2.82
2.83
2.842.85
2.86
2.87
2.88
2.89
2.90
2.91
0
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
2400
2600
2800
3000
3200
3400
3600
3800
4000
38.6
38.8
39
39.2
39.4
39.6
39.8
40
40.2
Speed(m/s)
Depth(m)
Influence of Energy Extraction
Distance Along Channel(m)
m/s m
Downstream Upstream
Location of Conversion Devices
Substantial head drop over the extraction vicinity
Overall flow speed reduced by 2.6% in the extraction vicinity
Speed increase downstream of energy extraction
Sensitivity to Extraction
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y
Kinetic Energy in the Channel
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Kinetic Energy in the Channel
This shows the consequences of extracting 25% of the raw kinetic flux from achannel of length 4000m, width 200m, assuming a manning coefficient of
0.035m-1/3s
Note the head drop over the zone of extraction and the INCREASE in kinetic
flux!
If the only energy in the system is kinetic, then this would be impossible!
Where does the energy come from?
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gy
Compare the charts for 25% extraction and
zero extraction
Notice that the kinetic flux is much higher in the zero case than in the exploited
case!The extracted energy is being drawn from the whole flow environment and not
simple removed from the kinetic flux!
A full understanding requires consideration of potential energy and frictional losses,
some researchers have even suggested the concept of Total Flux, which includes
potential energy, frictional energy and pressure
Simplifying the 1D Analysis
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p y g y
effg
er32
2
23
2
Pgbh
1
bgh
Q
x
b
x
h
bh
Q1
In the case of a constant width channel (b=const), this can
be rewritten in the form
gA
P
x
h
hg
U1 effer
2
I have also written the equation interms of U (m/s), the longitudinal
component of the flow velocity rather
than the discharge Q(m3/s)
The effective boundary stress, once again is
the sum of the natural stress: 31
R
nUg22
0
And an artificial term representing the energy extraction:
erxPU
P
add
Simplifying the 1D Analysis
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p y g y
If the flow speed and depth along the channel is
assumed to be constant and the artificial energy
extraction distributed along the entire length, L,then:
hg
U1
gbh
L
h2channel
efferP
This can be further simplified if U2/hg
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p y g y The Total head drop is give, therefore, by:
gRL
2gU
gbhLP
2gUh
2
er
2
total
effeff
In the absence of artificial energy extraction, this can be written as
34
34
R
ng212
U
R
LnU
2g
U
gR
L
2g
Uh22
022
02
002
0total
L
g
Hence:
3
4
R
L2gn1
h2gU 220
Uo is theunexploited flow
speed
Flow Speed in the Exploited Channel
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gR
L
2g
U
gbh
LP
2g
Uh
2
cer2
ctotal
effeff
gR
L
gR
L
2g
U
h
0
2
c
total
add
L
U
LPU
AU
LPU
P2
c21
erc
3
c21
erc
Rffadd
The equation relating the channel speed, Uc, to the total head drop, h
Can be written to include the extraction:
If P is related to the kinetic flux:
The total head drop in the exploited channel can be written:
f
gf
34
34
R
Ln21
2g
U
g2
U
R
LUn
2g
Uh
22
c
2
c
2
c
22
ctotal
Flow Speed in the Exploited Channel
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p p
f
gg
34
34
R
Ln21
2g
U
R
Ln21
2g
Uh
22
c
22
ototal
3
4
R
gLn21
B2
f
By equating the head drop in the exploited and unexploited
channel, we can write:
This can be rewritten as:
B1
R
Lgn211
R
Ln2
1
R
Ln21
U
U
34
34
34
22
2
2
c
2
0
f
g
fg
2
1
)1(
11
U
U
0 B
ALSO:
Suggest a new key parameter:
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gg y p
3
4
R
gLn21
B2
f
-14
-12
-10
-8
-6
-4
-2
0
0 0.05 0.1 0.15 0.2 0.25
B*
ProportionalSp
eedChange(%)
Based upon a
simplified form of the
1d model, but is
starting to look
significant in the 3dresults
Influence of Flow Change on SystemDesign
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Design If a system is designed to operate in the unexploited flow, then large
changes in the flow speed resulting from exploitation will result in reducedsystem performance
The mechanical power output of a system should be expected to be
dependent upon flow speed and device power coefficients
Flow speed reduction will result in requirements for changes in the turbine
control system to maintain optimal power characteristic, in effect to
maintain a appropriate values of the turbine power coefficient i.e. how to
keep the operation close to the peak of the Cp- curve
A
3
2
1 dA)(UCpP(U)
That is the subject of another study!
Here we will assume the control is being
appropriately handled and look at the energy flux
itself
Influence of Flow Change of RequiredSystem Size
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System SizeAssuming a horizontal axis turbine design, the power
conversion is
32
p21 U
4
DCP
rawedex URU 1Consider a flow speed reduction:
Uexis the flow speed after exploitation
Uraw is the undisturbed flow speed
Red is the proportional flow speed reduction
Assuming that the turbine controlstrategy could maintain a constant
value of the power factor, the
diameter of the device would need to
be increased
23
1 ed
apparent
actual
R
DD
Dactual is the diameter the turbines actually need to be
(m2)
Dapparent is the diameter suggested by considering the
unexploited flow speed only (m2)
Example: The 100MW
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Example: The 100MW
Farm 50 devices each designed to deliver 2MW at 3m/s This corresponds to a peak in the Cp- curve of 0.4
Each turbine needs to have a diameter of 21.5m
If the channel flow speed is reduced by 10%, thenthe turbine diameter would need to be increased to25m, with obvious economic consequences!
Beyond the simple channel
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The simple channel gives some insight into the complexity of
extracting energy from free surface flow but real tidal flows aregenerally multiply connected and exhibit long wave form properties
More sophisticated analysis requires solution of the shallow water
momentum flux equations (in 2 dimensions):
0
3
1
222
h
VUUgn
xghVhf
y
UVh
x
UUh
t
Uhc
0
3
1
222
h
VUVgn
yghUhf
y
VVh
x
UVh
t
Vhc
Associated with the continuity equation
0)()(
y
Vh
x
Uh
t
Cell
chosen forextraction
Extensions of the Shallow water
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Extensions of the Shallow water
Equation
Inclusion of Artificial Energy Extraction
Inclusion of Depth effects
yxVUPFR ,
Retarding force over an area
xy in the [U,V] direction
hdz
Introduction of a transformed
vertical dimension and thensolution of the governing equations
on a layer by layer, defined by ,
basis
The Simple Island ModelSimulation Domain
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Simulation Domain
Initially a 2 dimensional simulation but capable of extension to 3 dimensions
A 3.5m M2 tidal wave, was run from a cold start up to of the tidal period,
The inlet and outlet boundary conditions were then maintained in a steady state.
The extraction planes were one cell width with an extraction figure of 6MW per cell.
Exploitation of the Northern Channel
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Note reduction in flow speed in the northern channel 67m2/s (1.75m/s at a waterdepth of 38.3m)) to approximately 50m2/s (1.31m/s at a water depth of 38.2m). andcorresponding increase in the southern channel
Influence on Energy Extraction in Three
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Dimensions
This shows the reduction in flow speed along the central stream line of the
extraction zone
As expected, the simulation predicts the presence of a reduced flow speed
wake
Influence on Energy Extraction in ThreeDimensions
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Dimensions
This shows the increased flow in the vicinity of the sea bed
The energy extraction zone is, not unexpectedly, resulting in flow diversion
under the zone and (not shown here) around and above
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Resource Assessment
The most recent, and most reliable, assessment wasconducted by Black and Veitch in 2004 and
concluded that the UK potential was equivalent to
22TWhr/annum (6% of UK consumption) Resource is small in comparison with wind
But is concentrated in sites with very high energy
densities, offering the prospect of compact highoutput developments
CRE+E
Specific Technical Issues- Tidal
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Specific Technical Issues Tidal
Current
Installation
High energy flux densities and minimal slack
water periods Intervention and maintenance
Maintain in-situ or return to base?
Erosion and corrosionIncreases the maintenance problem
CRE+E
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Environmental Concerns
Tidal Current
Impact and entanglement with marine life
Flow impedance modification Habitat disturbance, especially during installation
Interaction with other users of the sea (fishing, leisure, transport)
CRE+E
Advantages of Tidal Current
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Advantages of Tidal Current
Power High energy density
Small devices
Low visibility
Predictable resource
Suitability for energy storage
Marine currents = high energyintensity
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intensity
A tidal current turbine gains
over 4x as much energy per
m2 of rotor as a wind turbine
Visual Impact
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p
50 to 100MW / km2
(I challenge these figures!)
10 to 20 MW / km2
marine current farm
wind farm
...and a low visual impact
P di bili
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Predictability
Tid l F
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Tidal Farms
It is likely that, if tidal currents are to be commerciallyexploited, the generators will have to be mounted in
clusters (tide farms?).
If this is done, then, as with wind turbines, the devices will
have to be sufficiently spread to ensure that the turbulencefrom individual devices does not interfere with others in
the cluster.
turbine wakes
tidal currents
Tidal Farms
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Top View
Commercial Development will require tidal energy conversion
systems to be grouped in clusters (tide farms)
Problems will include wake interactions and the influence of
energy extraction on the local and regional environment
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