Design of stay vanes and spiral casing

Revelstoke, CANADA

Guri-2, VENEZUELA

Aguila, ARGENTINA

Sauchelle-Huebra, SPAIN

Sauchelle-Huebra, SPAIN

Three Gorges Turbine, GE Hydro

The spiral casing will distribute the water equally around the stay vanes

In order to achieve a uniform flow in to the runner, the flow has to be uniform in to the stay vanes.

Flow in a curved channel

Streamline

StreamlineStreamline

The pressure normal to the streamline can be derived as:

dbdsdnn

pdbdsdnn

ppdbdspdFn

=

+=

Newton 2. Law gives:

StreamlineStreamline

Rc

n

p

adbdsdndbdsdnn

pn

21=

=

Rc

a2

n =

1

m

The Bernoulli equation gives:

.const2cp 2

=+

Derivation of the Bernoulli equation gives:

0n

cc

n

p1=

+

2

Equation 1 and 2 combined gives:

.constcR

0)Rc(d

0dRcdcR

Rc

n

c

=

=

=+

=

Free Vortex

Rc

n

p 21=

0n

cc

n

p1=

+

2

1

Inlet angle to the stay vanes

icm

cu

=

u

m

ic

ctana

Plate turbine

Find the meridonial velocity from continuity:

BR2Q

AQ

c

cAQ

0m

m

pi==

=

B

R0

Find the tangential velocity:

=

==

=

=

00y

u

0y

R

Ry

R

Ry

u

R

Ry

RRlnRB

Qc

RRln.constB

r

dr.constBQ

drr

.constBQ

drcBQ

0

0

0

By

R0 R

Example

By

Flow Rate Q = 1,0 m3/sVelocity C = 10 m/sHeight By = 0,2 mRadius R0 = 0,8 m

Find: L1, L2, L3 and L4

L1

C

L3

L2

L4

R0R

Example

By

Flow Rate Q = 1,0 m3/sVelocity C = 10 m/sHeight By = 0,2 mRadius R0 = 0,8 m

L1

C

L3

L2

L4

R0R

sm

RRRB

QCy

u 9,12ln

00

=

=

mBC

QLy

5,01 =

=

Example

By

Flow Rate Q = 1,0 m3/sVelocity C = 10 m/sHeight By = 0,2 mRadius R0 = 0,8 m

We assume Cu to be constant along R0.

At =90o, Q is reduced by 25%

L1

C

L3

L2

L4

R0R

Example

By

Flow Rate Q = 0,75 m3/sVelocity Cu = 12,9 m/sHeight By = 0,2 mRadius R0 = 0,8 m

L1

C

L3

L2

L4

R0R

00

00

0

ln

ln.

RCBQ

uy

y

uyeRR

RRRCBQ

RR

constBQ

=

=

=

Example

By

Flow Rate Q = 0,75 m3/sVelocity Cu = 12,9 m/sHeight By = 0,2 mRadius R0 = 0,8 m

L1

C

L3

L2

L4

R0R

00

RCBQ

uyeRR =

L2 = 0,35 mL3 = 0,22 mL4 = 0,10 m

Find the meridonial velocity from continuity:

10m

m

kBR2Q

AQ

c

cAQ

pi==

=R0B

k1 is a factor that reduce the inlet area due to the stay vanes

2yB

Find the tangential velocity:

Rc

c

.constcRc

Tu

Tu

=

==

=

=

+

pi

o

drRcrQ

dRcBQ

tT

u

rR

Ry

t

cos

sin2

2

2

0

R0B R0B

drdRrRR

rB

T

y

=

=

=

sincos

sin2

2yB

=

pi

d

cosrRsin

r2

Qc

T

22

T

o

R0B R0B

=

pi

d

cosrRsin

r2R

Qc

T

22

u

o

2yB

Spiral casing design procedure1. We know the flow rate, Q. 2. Choose a velocity at the upstream section of the spiral

casing, C3. Calculate the cross section at the inlet of the spiral casing:

4. Calculate the velocity Cu at the radius Ro by using the equation:

pi=

CQ

r

=

pi

d

cosrRsin

r2R

Qc

T

22

u

o

Spiral casing design procedure5. Move 20o downstream the spiral casing and calculate the

flow rate:

6. Calculate the new spiral casing radius, r by iteration with the equation:

totalo

o

new QQ = 36020

=

pi

o

drRcrQ tT cos

sin2

2

2

Outlet angle from the stay vanes

cm

cu

=

u

m

c

ctana

.constRcu

=

kBR2Q

AQ

cmpi

==

Weight of the spiral casing

Stay Vanes

Number of stay vanes

16

18

20

22

24

26

28

30

0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6Speed Number

N

u

m

b

e

r

o

f

S

t

a

y

V

a

n

e

s

Design of the stay vanes

The stay vanes have the main purpose of keeping the spiral casing together

Dimensions have to be given due to the stresses in the stay vane

The vanes are designed so that the flow is not disturbed by them

Flow induced pressure oscillation

56.09.1

+=

t

cBf

Where f = frequency [Hz]B = relative frequency to the Von Karman oscillationc = velocity of the water [m/s]t = thickness of the stay vane [m]

Where A = relative amplitude to the Von Karman oscillationB = relative frequency to the Von Karman oscillation