Turbines for very low head

Torbjørn K. Nielsen14.okt 2005

• The oldest known text that mentions a water-powered machine is over 2000 years old

• Norse mills had then already been used for a long time in the mediterraneancountries

Vitruvius mill with gear

Ramelli 1588 Barker 1740Segner 1750

Besson 1568

• 1750 J.A.Segner – reaction turbine• 1750-54 Euler develops the turbine theory• 1827 Forneyron - radial turbine, 30 – 40 hp, D = 0.5 m• 1840 Henschel/Jonval – aksial turbine

Jonval – draft tube• 1849 Francis – Francis turbine

Fink – Load regulation with guide vanes• 1890 Pelton – Pelton turbine, impilse turbine• 1913 Kaplan – Kaplan turbine, propeller

Turbine development – modern time

• 1855: J. B. Francis presents a inward-flow turbine

• Hydraulically well-shaped vanes and blades

• Efficiency equal to Fourneyron and Jonval turbines

• 1873: Voith and Kankelwitz addadjustable guide vanes

Francis turbin

• 1926: First large Kaplan turbineinstalled at Lilla Edet

• Efficiency up to 92,5%• Part load efficiency above 83%• Final break-trough for Kaplan turbines

Kaplan

Pelton turbine – impulse turbine

Fourneyron turbine Jonval-Henschel turbine

The Girard turbine

Thomson

Hydraulic energi

P = ρgQH

kg m m3 mm3 s2 s

[ ]

=Nms = [W ][ ]

H = Gross HeadQ – Flowρ – densityg – gravitation

H

Available from nature

Power transformation

UIMgQH ⇒⇒ ωρ

Hydraulic power

Mechanical rotating power

Electric energy

Turbine Generator

⇒⇒

cu1

cu2c1

c2

o

v1v2

u1

u2

)( 2211 uu cucuQP −= ρ

Velocity components

ω

u – peripheral velocityv – relative velocityc – absolute velocity

vuc +=

u1

v1

v2

c1

c2

u2

Inlet – and outlet velocity triangle

β2

α1 β1

Runner vane

Guide vane

Dimensionless velocities

All velocities are scaled related to the velocity of”Toricellis theorem” - Reduced velocities:

He

e

e

e

gHcv

gHcu

gHcc

2

2

2

=

=

=

egH2

Hydraulic efficiency:

enatur

uu

gQHPcucuQTP

ρρω

=−== )( 2211

naturh P

P=η

e

uu

e

uuh gH

cucugQH

cucuQ )()( 22112211 −=

−=

ρρη

)( 2211 uuhe cucugH −=η

Or:

Introducing reduced velocities:

)(12211 uueh cucu

gH −=η

ee gHgH 21

21

)22

(12

2211

e

u

e

u

e

eh

gHcu

gHcu

ggHH

−=η

( )22112 uuh cucu −=η

Redused flow:

Redused angular speed:

[ ]2

2m

gHQQ

e

=

⎥⎦⎤

⎢⎣⎡=mgHe

12ωω

Then the following equations still applies:

ω=

=

u

cAQ

Speed number – classification of turbinesGeometric similar turbines but different in size, Shall have the same specification – a speed number

Two geometric similarturbines has the same redusedvelocity triangles:

12

22

:1.

1:2.

konstkonstQ

eqinPut

konstDeqFrom

=

=

ω

ω

cm

cmD

2

122

)24

)1

konstDDu

konstDQ

D

Qcm

=⇒=

=⇒=

ωω

π

konstQ =ω

Qω=Ω Speed number

The turbine must be designet optimal for a given operational point defined by:Q, H og w (or RPM) *- denotes BEP :

Q*** ω=Ω

Another classification number is ”spesific speed ”:

4/3HQn

nq =

Ω= *89qn

How the form of a turbine changes with the speed number:

Speed number: Qω=Ωee gH

QgH 22ω

=Ωeller:

2

22

22

2

44 m

m

c

QD

D

Qc ππ =⇒=

D2

cm2

ωω egH

uDDu22

2 111

1 =⇒=

D1

The redused velocities areapproximate constant

B

momo cD

QBcBDQ

11 π

π =⇒=

cmo

Incresed speed number: D2 andB increases

Turbine types

∗Ω=0.1 ∗Ω =0.2 ∗Ω =0.4 ∗Ω =1.0 ∗Ω =2.5

ChoosePelton

To much friction

KAPLAN: ∗Ω = 1.5 − 2.5FRANCIS: ∗Ω = 0.2 − 1.2PELTON: ∗Ω = 0.08 − 0.15

TurbindimensjonerLavtrykks vannkraft:

H 3 3 5 5 m 35 mQ 5 10 10 100 m3/s 80 m3/sPolpar 15 20 14 40 10n 200 150 214,2857 75 RPM 300 RPMeta 0,8 0,8 0,8 0,8 0,8Effekt 117,84 235,68 392,8 3928 kW 21996,8 kW

w 20,94 15,71 22,44 7,85 rad/s 31,42 rad/ssqrt(2gH) 7,67 7,67 9,90 9,90 m/s 26,20 m/s

Qred 0,65 1,30 1,01 10,10 3,05wred 2,73 2,05 2,27 0,79 1,20

Fartstall 2,20 2,34 2,28 2,52 2,09

u2 40,00 40,00 40,00 40,00 m/s 40,00 m/sD2 3,82 5,09 3,57 10,19 m 2,55 m

Turbin i fri strøm

32

VACP RV

P ⋅=ρ

0 5 10 150

1

2

3

4

Rotor radius [m]

Effe

kt [M

W]

3 m/s 2.5 m/s

2 m/s 1.5 m/s

Cp ≈ 0.4

Wells turbinen

• Luftturbin• Roterer samme vei uansett

retning på strømningen• Negativt startmoment

Voith-Schneider propellDarrius turbin

SeawaveSeawave SlotSlot--Cone Cone

• Turbin:1-3 m fallhøyde

• Flertrinns

Turbin

Ledeskovler

SugerørSug

erør

skon

us

Generator Utgangspunkt: Jonval turbin

• Uten sugerøret avløpstap:

• Gjenvinnes i sugerøret

mg

ch 62,062,195,3

2

22

===Δ

• Low head gives– low speed of rotation– huge dimensions on turbine and

generator– High torque

• How to increase head?– Amplification– Displacement pump

Q

t

Peltonturbin

SynkrongeneratorAkkumulator

• En- eller to strålers PeltonH = 155 mQ = 46 l/sP = 5,6 kW

• Turtall 1500• Diameter 340mmEller:• Turtall 3000 o/min• Diameter 170 mm