Home > Documents > Design of stay vanes and spiral casing - IV - NTNU of the stay vanes • The stay vanes have the...

# Design of stay vanes and spiral casing - IV - NTNU of the stay vanes • The stay vanes have the...

Date post: 10-Apr-2018
Category:
Author: dinhdieu
View: 213 times
Embed Size (px)
of 33 /33
Design of stay vanes and spiral casing Revelstoke, CANADA
Transcript
• Design of stay vanes and spiral casing

• 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:

dbdsdnnpdbdsdn

nppdbdspdFn

=

+=

• Newton 2. Law gives:

StreamlineStreamline

Rc

np

n

21=

=

Rca

2

n =

1

m

• The Bernoulli equation gives:

.const2cp 2=+

Derivation of the Bernoulli equation gives:

0ncc

np1

=+

2

• Equation 1 and 2 combined gives:

.constcR

0)Rc(d

0dRcdcR

Rc

nc

=

=

=+

=

Free Vortex

Rc

np 21=

0ncc

np1

=+

2

1

• Inlet angle to the stay vanes

icm

cu

=

u

mi c

ctana

• Plate turbine

• Find the meridonial velocity from continuity:

BR2Q

AQc

cAQ

0m

m

==

=B

R0

• Find the tangential velocity:

=

==

=

=

00y

u

0y

R

Ry

R

Ry

u

R

Ry

RRlnRB

Qc

RRln.constB

rdr.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

QC

y

u 9,12ln

00

=

=

mBCQL

y

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

RRconstBQ

=

=

=

• 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

AQc

cAQ

==

=R0B

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

2yB

• Find the tangential velocity:

Rcc

.constcRc

Tu

Tu

=

==

=

=+

drRcrQ

dRcBQ

tT

u

rR

Ry

t

cossin

2

2

2

0

R0B R0B

drdRrRR

rB

T

y

==

=

sincos

sin2

2yB

• =

dcosrR

sinr2

Qc

T

22

T

R0B R0B

=

dcosrR

sinr2R

Qc

T

22

u

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:

=CQr

=

dcosrR

sinr2R

Qc

T

22

u

• 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

=

drRcrQ tT cos

sin2

2

2

• Outlet angle from the stay vanes

cm

cu

=

u

m

cctana

.constRcu =

kBR2Q

AQcm ==

• 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 1,6

Speed Number

Num

ber o

f Sta

y Va

nes

• 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

+=tcBf

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

Recommended