Introduction to Tidal Power

7/28/2019 Introduction to Tidal Power

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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



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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



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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



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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



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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
http://www.pontediarchimede.com/dyn_pda/images/gallery/00000130_BIG.jpghttp://www.pontediarchimede.com/dyn_pda/images/gallery/00000039_BIG.jpg


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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


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



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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


80/124

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


1100 00

1300.00

1500.00

0 25

0.30

0.35


81/124

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


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


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


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


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


82/124

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


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


83/124

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)


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)


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


84/124

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


85/124

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


86/124

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


87/124

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


88/124

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


89/124

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


90/124

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


91/124

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


92/124

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


93/124

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.


94/124

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


95/124

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


96/124

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


97/124

y

Kinetic Energy in the Channel


98/124

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?


99/124

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


100/124

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


101/124

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


102/124

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


103/124

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


104/124

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:


105/124

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


106/124

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


107/124

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


108/124

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


109/124

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


110/124

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


111/124

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


112/124

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


113/124

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


114/124

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


115/124

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


116/124

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


117/124

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


118/124

Advantages of Tidal Current

Power High energy density

Small devices

Low visibility

Predictable resource

Suitability for energy storage

Marine currents = high energyintensity


119/124

intensity

A tidal current turbine gains

over 4x as much energy per

m2 of rotor as a wind turbine

Visual Impact


120/124

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


121/124

Predictability

Tid l F


122/124

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


123/124

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


124/124

Introduction to Tidal Power

Documents

Tidal Current - Introduction

Sihwa tidal power

Tidal Power plants

Tidal Power - libvolume2.xyzlibvolume2.xyz/.../energyfromtides/energyfromtidespresentation2.pdf · Tidal Power • Tidal power generators derive their energy from movement of the

Tidal Power Projections

Dynamic tidal power

Syllabus for - Rashtrasant Tukadoji Maharaj Nagpur · PDF fileEnergy from Tides: Introduction, basic principles of Tidal power, components of Tidal Power Plants, operation methods

Severn Estuary Tidal Power - National Assembly for Wales · Severn Estuary Tidal Power April 2010 This paper provides briefing on the current situation of tidal power development

TIDAL and WAVE POWER

The tidal power

xxxxxx - Tidal Lagoon Power

Apex Tidal Power Scotland

SEVERN TIDAL POWER - GOV.UK

Tidal Power

Tidal Power Technology Review

Severn Estuary Tidal Power - National Assembly for Wales Documents/Severn... · 2014-06-11 · Severn Estuary Tidal Power 1. Introduction The UK has the potential to generate at least

Marine Power (Tidal and Wave ) - UTKweb.eecs.utk.edu/~kaisun/Backup/ECE421_Fall2014... · Rance Tidal Power Station – the worlds first commercial tidal power plant . Located in

Tidal Power Lucas O’Neil Elec 395 May 30, 2006. Introduction Alternative Energy Sources/Renewable Energy Overview of Tidal Generation -Tides -Basic methods

Severn Estuary Tidal Power Feasibility Study Not just a barrage! Severn Tidal... · Severn Estuary Tidal Power Feasibility Study Not just a barrage! Stuart Easterbrook Severn Tidal

Tidal/Wave generation of power - terpconnect.umd.edumpatel11/sgc/Tidal%2FWave generation of power.… · "Wave & Tidal Energy Technology." Renewable Northwest Environment 360. "Why