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Theory of turbo machinery / Turbomaskinernas teori

Dixon, chapter 9

Hydraulic Turbines

Hear ye not the hum of mighty workings? (KEATS, Sonnet No. 14).

The power of water has changed more in this world than emperors or kings.

(Leonardo da Vinci).

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Hydraulic Turbines

Todays topics

Introduction; Where and how muchTypes of turbines

PeltonFrancisKaplan

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Hydraulic Turbines, potential

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Land Produktion TWh

Per capita

Andel av elproduktion

Förändring mot 1995-2000

Kanada 344 -1%

Kina 321 +58%

Brasilien 304 +6%

USA 260 -20%

Ryssland 170 +7%

Norge 121 99% +1%

Syrien 119 +2%

Japan 96 +2%

Indien 78 +2%

Frankrike 67 -6%

Venezuela 66 +12%

Sverige 65 ~ 50% -6%

Wikipedia:

Produktion2000-2005

Hydraulic Turbines, production

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Hydraulic Turbines, large plants

De största svenska kraftverken är:• Harsprånget i Luleälven (945 MW)• Stornorrfors i Umeälven • Messaure i Luleälven

Name Country Year of completion

Total Capacity (MW)

Max annual electricity production (TW-hour)

Area flooded (km²)

Three Gorges Dam

China 2009 17,600 (August 2008); 22,500 (when complete)

>100

90

46

632

Itaipu Brazil/Paraguay

1984/1991/2003 14,000 1,350

Guri (SimónBolívar)

Venezuela 1986 10,200 4,250

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Sverige

Vattentillgången störsttidig sommar

Elbehovet i Sverigestörst på vintern

Reglering-vattnet sparas

Energi- eller effekt-begränsningar?

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Hydraulic Turbines

• Utbyggnaden av kraftverk i älvar och floder får stora konsekvenser för den biologiska mångfalden när stora områden sätts under vatten.

• Lekområden för fisk ödeläggs och vattenorganismer såväl som ett flertal andra växter, fåglar och djur påverkas negativt.

Greenpeace (hemsida*):

Fler stora vattenkraftsutbyggnader är inte försvarbara ur biologisk och ekologisk synpunkt:

* http://www.greenpeace.org/sweden/kampanjer/klimat/losningar/klimatvanlig-energi/vatten

Småskalig vattenkraft å andra sidan fångar flodernas energi utan att ta bort för mycket vatten från deras naturliga flöde. Därför är den småskaliga vattenkraften en miljövänlig energikälla med stor tillväxtpotential.

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Hydraulic Turbines

Regeringen

De fyra outbyggda huvudälvarna* ska bevaras

*Nationalälvarna: Torne, Kalix, Pite och Vindelälven

STEM

Vattenkraft är en ren energikälla som ger stora mängder energi. Attanlägga nya vattenkraftverk orsakar dock stora skador i naturen. Därförbyggs inga nya större kraftverk i vårt land.

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Hydraulic Turbines

3 Gorges Dam

The Three Gorges Project, including a 2,309-meter-long, 185-meter-high dam with 26 power generators, is being built on the middle reaches of the Yangtze, China's longest river.

The project started 1993 and is assumed to be finished 2011, at what time the power output will be 22 500 MW.

Water from upstream is flowing into the reservoir at a rate of 13,200 cubic meters per second.

http://maps.google.com/maps?ll=30.83,111.01&spn=0.01,0.01&t=h&q=30.83,111.01

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Main types of Hydraulic Turbines

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Hydraulic Turbines

sp

s

Ωη

Ω=

FIG. 9.1. Typical design point efficiencies of Pelton, Francis and Kaplan turbines.

sp

s

Ωη

Ω=

( )( )

1/ 2

5/ 4

/sp

P

gH

Ω ρΩ =

( )

1/ 2

3/ 4sQ

gHΩΩ =

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Hydraulic Turbines

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Hydraulic Turbines

Operating ranges of the main types of hydraulic turbines (Alvarez)

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Hydraulic Turbines

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Hydraulic Turbines

Ohakuri Dam Bue Penstocks

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Pelton Turbines

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Pelton Turbines

Lester Allan Pelton (no image)September 5, 1829 –March 14, 1908

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Pelton Turbines

FIG. 9.5. The Pelton wheel showing the jet impinging onto a bucket and the relative and absolute velocities of the flow (only one-half of the emergentvelocity diagram is shown).

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Pelton Turbines

1 1 2 2ΔW U c U cθ θ= −

( ) ( )1 2 2 1 2 2Δ cos cosW U U w U w U w wβ β⎡ ⎤= + − + = −⎣ ⎦

From Eulers turbine equation

For the Pelton turbine:

1 2U U U= =

1 1 1c c U wθ

and thus Euler becomes

= = +

2 2 2cosc U wθ β= +2β

2cos 0β <

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Pelton Turbines

2 1w kw=

where k is a loss factor less than 1.

Introducing this into Eulers eq.:

( )21 2

1 1

2Δ c 2 1 1 cosRU UW kc c

η β⎛ ⎞

= = − −⎜ ⎟⎝ ⎠

Dividing by the available energy, , yields a “runner” efficiency:

Friction looses are accounted for by relating relative velocities

21 2c

( ) ( )( )1 2 1 21 cos 1 cosW Uw k U c U kΔ β β= − = − −

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Pelton Turbines

FIG. 9.6. Theoretical variation of runner efficiency for a Pelton wheel with blade speed to jet speed ratio for several values of friction factor k .

2 165β =

,max

1

@

0.5

R

Uc

η

ν= =

Cos is a forgiving function:

( )cos 1650.966

=

= −

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Pelton Turbines

FIG. 9.7. Pelton turbine hydroelectric scheme.

Surge tank reduces pressure spikes

Gross head:

G R NH z z= −

Effective head:

( )E G F rictionH H H= −

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Pelton Turbines

More losses:

• Friction losses in penstock (pipe flow: moody chart)• Nozzle efficiency • Bearing friction and windage, assumed proportional to the

square of the blade speed:

( )21 2N Ec gHη =

2KU

An overall efficiency of the machine (excluding penstock) may bedefined:

22

0 21

... 2N RE

W KU UKgH c

Δη η η⎡ ⎤⎛ ⎞− ⎢ ⎥= = = − ⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

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Pelton Turbines

FIG. 9.9. Variation of overall efficiency of a Pelton turbine with speed ratio for severalvalues of windage coefficient, K .

The subtraction of energy by the U2

term displaces the optimum blade speed to jet speed ratio

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Pelton Turbines, controle

FIG. 9.8. Methods of regulating the speed of a Pelton turbine: (a) with a spear (or needle) valve; (b) with a deflector plate.

Spear used for slow control

Deflector plate causes no “hammer”

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Pelton Turbines, part load

FIG. 9.10. Pelton turbine overall efficiency variation with load under constant head and constant speed conditions.

Controle by adjustment of needle valve:

Hydraulic losses reduced at low load, but

bearings and windagelosses remain at constant speed

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Francis Turbines

James Bicheno FrancisMay 18, 1815 – September 18, 1892

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Francis Turbines

Reaction turbines

Pressure drop takes place in the turbine itselfWater flow completely fills all part of the turbinePivotable guide vanes are used for control (Francis)A draft tube is normally added on to the exit; it is considered an integral part of the turbine

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Francis Turbines

FIG. 9.15. Location of draft tube in relation to vertical shaft Francis turbine.

Draft tube

Shaped as a diffusor to minimize losses

Turbine may be placed above tailwater surface

Cavitation may be an issue

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Francis Turbines

Volute or scroll: Decreasing diameter => constant velocity

Flow is through the scroll into guide vanes and onto the runner

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Francis Turbines

Euler turbine equation

2 2 3 3ΔW U c U cθ θ= −

2 2ΔW U c

If there is no swirl at exit (design point):

θ=

Slip is present

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Francis Turbines, control

FIG. 9.13. Comparison of velocity triangles for a Francis turbine for full load and at part load operation.

Volume flow rate reduced by guide vanes

Blade speed retained

Rotor incidence high.

Swirl at exit increases losses and risk for cavitation(why?)

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Kaplan Turbines

Viktor KaplanNovember 27, 1876 – August 23, 1934

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Francis Turbines

FIG. 9.16. Part section of a Kaplan turbine in situ.

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Kaplan Turbines (Voith Siemens)

Cross section of a 9.5 m diameter Kaplan runner for the Yacyretá hydropower plant in Argentina

Yacyretà, Argentina

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Kaplan Turbines

FIG. 9.17. Section of a Kaplan turbine and velocity diagrams at inlet to and exit from the runner.

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Kaplan Turbines, free vortex

Swirling flow at inlet, free vortex:

2

.x

c K rc constθ ==

Flow angles become:

( )2 2

3

tan tantan

x x x

x x

U c r c K rcU c r c

β α Ω

β Ω

= − = −

= = No swirl at exit

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Hydraulic Turbines, part load

FIG. 9.14. Variation of hydraulic efficiency for various types of turbine over a range of loading, at constant speed and constant head.

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Hydraulic Turbines, cavitation

Two types:

On the suction side of the runner near outletOn the centerline of the draft tube at off-design operation (Francis)

The Thoma cavitation coefficient may be defined as

( ) ( )a

E E

p p g zNPSHH H

υ ρσ

− −= =