Theory of turbo machinery / Turbomaskinernas teori. Dixon, chapter 9. Hydraulic Turbines

Transkript

1 Theory of turbo machinery / Turbomaskinernas teori Dixon, chapter 9 Hydraulic Turbines

2 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).

3 Hydraulic Turbines Todays topics Introduction; Where and how much Types of turbines Pelton Francis Kaplan

4 Hydraulic Turbines, potential

5 Hydraulic Turbines, production Land Produktion TWh Per capita Andel av elproduktion Kanada 344-1% Kina % Brasilien % USA % Ryssland % Norge % +1% Syrien % Japan 96 +2% Indien 78 +2% Frankrike 67-6% Venezuela % Sverige 65 ~ 50% -6% Förändring mot Wikipedia: Produktion

6 Hydraulic Turbines, large plants Name Country Year of completion Three Gorges Dam Itaipu Guri (Simón Bolívar) Total Capacity (MW) Max annual electricity production (TW-hour) China ,600 (August 2008); 22,500 (when complete) > Brazil/Paragu ay 1984/1991/ , ,350 Venezuela , ,250 Area flooded (km²) De största svenska kraftverken är: Harsprånget i Luleälven (945 MW) Stornorrfors i Umeälven Messaure i Luleälven

7 Sverige Vattentillgången störst tidig sommar Elbehovet i Sverige störst på vintern Reglering-vattnet sparas Energi- eller effektbegränsningar?

8 Hydraulic Turbines Greenpeace (hemsida*): Fler stora vattenkraftsutbyggnader är inte försvarbara ur biologisk och ekologisk synpunkt: 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. 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. *

9 Hydraulic Turbines Regeringen De fyra outbyggda huvudälvarna* ska bevaras STEM Vattenkraft är en ren energikälla som ger stora mängder energi. Att anlägga nya vattenkraftverk orsakar dock stora skador i naturen. Därför byggs inga nya större kraftverk i vårt land. *Nationalälvarna: Torne, Kalix, Pite och Vindelälven

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

11 Main types of Hydraulic Turbines

12 Hydraulic Turbines Ω = s ΩQ ( gh ) 1/2 3/4 Ω = sp Ω ( P / ρ) 5/4 ( gh ) 1/2 Ω sp Ω = s η Ωsp Ω = s η FIG Typical design point efficiencies of Pelton, Francis and Kaplan turbines.

13 Hydraulic Turbines

14 Hydraulic Turbines Operating ranges of the main types of hydraulic turbines (Alvarez)

15 Hydraulic Turbines

16 Hydraulic Turbines Ohakuri Dam Bue Penstocks

17 Pelton Turbines

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

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

20 Pelton Turbines From Eulers turbine equation ΔW = U c U c 1 θ1 2 θ 2 For the Pelton turbine: U1 = U2 = U c = c = U + w θ1 1 1 c = U + w cos β θ and thus Euler becomes cos β 2 < 0 β 2 ( β ) ( β ) ΔW = U U + w U + w cos = U w w cos

21 Pelton Turbines Friction looses are accounted for by relating relative velocities w = kw 2 1 where k is a loss factor less than 1. Introducing this into Eulers eq.: Dividing by the available energy,, yields a runner efficiency: η R U U = 2ΔW c = cos ( 1 cos ) ( )( 1 cos ) ΔW = Uw k β = U c U k β c 1 2 ( k β ) c1 c1

22 Pelton Turbines η U c R,max = ν = 0.5 Cos is a forgiving function: β 2 = 165 cos( 165) = = FIG Theoretical variation of runner efficiency for a Pelton wheel with blade speed to jet speed ratio for several values of friction factor k.

23 Pelton Turbines Surge tank reduces pressure spikes Gross head: HG = zr zn Effective head: H = H H E G F( riction) FIG Pelton turbine hydroelectric scheme.

24 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: N ( ) η = c gh KU 2 E An overall efficiency of the machine (excluding penstock) may be defined: 2 ΔW KU U η0... η = = = N ηr 2K 2 gh E c 1 2

25 Pelton Turbines The subtraction of energy by the U 2 term displaces the optimum blade speed to jet speed ratio FIG Variation of overall efficiency of a Pelton turbine with speed ratio for several values of windage coefficient, K.

26 Pelton Turbines, controle Spear used for slow control Deflector plate causes no hammer FIG Methods of regulating the speed of a Pelton turbine: (a) with a spear (or needle) valve; (b) with a deflector plate.

27 Pelton Turbines, part load Controle by adjustment of needle valve: Hydraulic losses reduced at low load, but FIG Pelton turbine overall efficiency variation with load under constant head and constant speed conditions. bearings and windage losses remain at constant speed

28 Francis Turbines James Bicheno Francis May 18, 1815 September 18, 1892

29 Francis Turbines Reaction turbines Pressure drop takes place in the turbine itself Water flow completely fills all part of the turbine Pivotable 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

30 Francis Turbines Draft tube Shaped as a diffusor to minimize losses Turbine may be placed above tailwater surface FIG Location of draft tube in relation to vertical shaft Francis turbine. Cavitation may be an issue

31 Francis Turbines Flow is through the scroll into guide vanes and onto the runner Volute or scroll: Decreasing diameter => constant velocity

32 Francis Turbines Euler turbine equation ΔW = U c U c 2 θ 2 3 θ 3 If there is no swirl at exit (design point): ΔW = U c 2 θ 2 Slip is present

33 Francis Turbines, control Volume flow rate reduced by guide vanes Blade speed retained Rotor incidence high. Swirl at exit increases losses and risk for cavitation (why?) FIG Comparison of velocity triangles for a Francis turbine for full load and at part load operation.

34 Kaplan Turbines Viktor Kaplan November 27, 1876 August 23, 1934

35 Francis Turbines FIG Part section of a Kaplan turbine in situ.

36 Kaplan Turbines (Voith Siemens) Cross section of a 9.5 m diameter Kaplan runner for the Yacyretá hydropower plant in Argentina Yacyretà, Argentina

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

38 Kaplan Turbines, free vortex Swirling flow at inlet, free vortex: c c θ 2 = x K r = const. Flow angles become: ( ) tan β = U c tanα = Ωr c K rc tan β = U c = Ωr c No swirl at exit 2 x 2 x x 3 x x

39 Hydraulic Turbines, part load FIG Variation of hydraulic efficiency for various types of turbine over a range of loading, at constant speed and constant head.

40 Hydraulic Turbines, cavitation Two types: On the suction side of the runner near outlet On the centerline of the draft tube at off-design operation (Francis) The Thoma cavitation coefficient may be defined as NPSH σ = = H E ( ) ( ρ ) p p g z a υ H E