Kaplan turbine

Jebba, Nigeria

*Q = 376 m3/s*H = 27,6 m*P = 96 MW

D0 = 8,5 mDe = 7,1 mDi = 3,1 mB0 = 2,8 m

Machicura, CHILE

*Q = 144 m3/s*H = 36,7 m*P = 48 MW

D0 = 7,2 mDe = 4,2 mDi = 1,9 mB0 = 1,3 m

Outletdraft tube

Outletrunner

Inletrunner

Outletguide vane

Inletguide vane

Hyd

raul

ic e

ffic

ien c

y η h

Flow rate Q

Runner blade angleφ = constant

Hydraulic efficiency

Hill chart

c1

v1

u1

c2 v2

u2

Hgcucu 2u21u1

h ⋅⋅−⋅

=η

Pressure distribution and torque

LiftLift

DragDrag

Torque

Arm

LL

DD

c

LChord4

α

FLift

FDragv

AVCF

AVCF

DD

LL

⋅⋅⋅⋅=

⋅⋅⋅⋅=

2

2

21

21

ρ

ρ

Blade profile data

L

D

CC

Angle of attack

Angle of attackAngle of attack

Average relative Average relative velocityvelocity

δv∞

Pressure distribution and torque

Pressure side

Suction side

Cord length, l0,24 · l

Single profile

Cascade

The pressure at the outlet is lower for a cascade than for a single profile. The cavitation performance will therefore be reduced in a cascade.

Radial distribution of the blade profile

CL =Lift coefficient for a cascade

CL1 =Lift coefficient for a single profile

The ratio t/l influences the lift coefficient in a cascade. The cord length for a blade will therefore increase when the radius becomes increase

Radial distribution of the blade profile

Flow in the axial plane

The figure shows blades with two different design of the blade in radial direction. This is because it will influence the secondary flow in the radial direction

Main dimension of a Kaplan turbine

no Q⋅ω=Ω

1.5

Cml =0.12 + 0.18 0

Cm

l

2.00

0

0.5

(tilnærmet)

1.0

2.5 3.0

( )

m1

n

m1

22

n

c4Q

D

c4

dDQ

⋅Π

⋅=

⇓

⋅−⋅Π

=

Diameter of the runner

Ω

Ω

Height of the guide vanesand runner diameter

0.4

0.3300 400

ns

B /D0

d/D

d/D

, B

/D0

500 700600 800 900

0.5

0.6

0.7

45n

s HPnn ⋅=

Gap between hub and ring and the runner blades

Gap between the blade and hub

Gap between the blade and ring

Spalteåpning x =1000s/D

Virk

ning

sgra

d

00.80

0.85

0.90

1

s = x 10 d-3

2 3 4 5 6

Effic

ienc

y

Gap

Runaway speed

ϕ2

ϕ3

ϕ1

ϕ6

02

2.2

2.4

2.6

0.5 1.0 2.0 3.0σ

ϕ5

ϕ4

kavitasjonskoeffisient

Rus

ning

stal

l/nor

mal

turta

ll

Voit h

Cavitation coefficient

Run

away

spee

d

HH10 S−

=σ

The figure shows different runaway speed at different runner blade openings. The runaway speed is dependent of the cavitation as shown in the figure

Hill chart

Example

P = 16,8 MWH = 16 mQn = 120 m3/sn = 125 rpm

• Find the dimensions D, d and Bo

• Given data:

93,178,674,0Qn

o =⋅=⋅ω=Ω

sm7,171682,92Hg2 =⋅⋅=⋅⋅

srad1,13

602125

602n

=Π⋅⋅

=Π⋅⋅

=ω

1m74,0s

m7,17s

rad1,13

Hg2−==

⋅⋅ω

=ω

2

3

nm78,6

sm7,17

sm120

Hg2QQ ==⋅⋅

=

Speed number:

Diameter, D:

467,018,012,01 =Ω⋅+= omc

mc

QD

m

n 3,4467,0

478,64

1

=⋅Π

⋅=

⋅Π

⋅=

Diameter, d:

59016

22826125 4545 =⋅=⋅=

mHp

rpmHPnnn

s

0.4

0.3300 400

ns

B /D0

d/D

d/D

, B

/D0

500 700600 800 900

0.5

0.6

0.7

m9,145,0Dd45,0Dd

=⋅=⇒=

Height, B:

0.4

0.3300 400

ns

B /D0

d/D

d/D

, B

/D0

500 700600 800 900

0.5

0.6

0.7

m76,141,0DB41,0DB

OO =⋅=⇒=

Number of vanes, z:

95,0tl=

5z =

Num

ber o

f bla

des

z