Fluid System 09-Reaction Turbine-Francis and Kaplan

7/25/2019 Fluid System 09-Reaction Turbine-Francis and Kaplan

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Dr. Ir. Harinaldi, M.EngMechanical Engineering Department

Faculty of Engineering University of Indonesia

Reaction turbines


2/18

adial Flow Francis Turbine

adial Flow Francis Turbine


3/18

Construction of Francis

onstruction of Francis

Turbine

urbine


4/18

Velocity Triangle

elocity Triangle

Euler Equation:

( )

g

CUCU

mg

WE xx 2211

==

Flow velocities:

11

12 br

QCr

=

22

22 brQCr

=

heightrunnerb =


5/18

Axial Flow Kaplan Turbine

xial Flow Kaplan Turbine


6/18

Construction of Kaplan

onstruction of Kaplan

Turbine

urbine


7/18

Velocity Triangle

elocity Triangle

Euler Equation:

( )g

CCU

mg

WE xx 21

==

For zero whirl at exit:

gUCE x1=

( )1

11

cot

180cot

a

oax

CU

CUC

+=

=

( )g

UCUE a 1

2 cot +=

arr CCC == 21

( )22114

dD

QCCC arr

===

Flow velocities:

diameterhubd

tipbladetodiameterD

=

=)(diametermeanatevaluateis mDU

Note:

( ) 2dDDm += ( ) 60NDU m=


8/18

Installation

nstallation


9/18

Net Head Across Turbine

et Head Across Turbine

Net head (H) is the different in the

total head between the inlet flange

and the tail water level Net head (H) is not equal to Gross

head (H1)

Total ead across turbine

( ) ( ) ( )( ) gVZgVgpH

ZgaugepZZgVVgppH

22

0;)(0;2

2

30

2

00

3330

2

3

2

030

++=

==++=

gVhHH fp 22

31 =

elation! net ead and gross ead

"nergy gi#en to te runner

rgd hhhHmgWE ==

energykineticresidual2

runnerinlossheadfrictional

draft tubeinlossheadfrictional

vanesguideinlossheadfrictional

ielineinlossheadfrictional

23 =

=

=

=

=

gV

h

h

h

h

r

d

g

fp


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$osses and "fficiency

osses and "fficiency

"nergy balance troug te turbine

slcrm PPPPPP ++++=

Ps= shaft power output P

c= casing and draft tube loss

Pm= mechanical loss P

l= leakage loss

Pr= runner loss P = water power available

unner $oss

rrr hgQP =

qQQr =runnerthroughrateflo!=rQ

leakagerateflo!=q

runnerinlossheadfrictional=rh

$ea%age $oss

rl gqHP = runnertheacrossheadtotal=rH

Casing and draft tube $oss

cc gQhP = draft tubeandcasinginlosshead=ch

"nergy balance beco&es!

( ) srcrrm PqHQhQhgPgQH ++++=


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$osses and "fficiency

osses and "fficiency

Overall Efficiency

gQH

Pso

==flangeinletatavailableo!erfluid

o!eroututshaft

( )

gQH

PP msH

+

==

flangeinletatavailableo!erfluid

runnerbyreceivedo!er

Hydraulic efficiency

For maximum efficiency

gQH

CU xH

11=


12/18

Caracteristics Cur#es

aracteristics Cur#es


13/18

Caracteristics Cur#es

aracteristics Cur#es

omparison of hydraulic turbine efficiencies


14/18

'raft Tube

raft Tube

Bring the water ressure bac! to the ressure of the tailrace "e#ove the !inetic energ$ still existing at the runner outlet

( ) ( )

( )[ ] adsada

a

d

pphgVVHgpgp

hgVVZgpgp

gpgpZ

hZgVgpZgVgp


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Ca#itation in Turbine

a#itation in Turbine


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"xa&ple

xa&ple

! Francis turbine has an inlet diameter of "#$ m and rotates at $%& rpm# 'ater

enters the runner without shocks with a flow velocity of (#) m*s and leaves

the runner without whirl with an absolute velocity of + m*s# ,he difference

between the sum of the static and potential heads at entrance to the runnerand at the exit from the runner is -. m# /f the turbine develops ". .)& k' and

has a flow rate of ". m%*s of water when the net head is "") m0 find

1a2 ,he absolute velocity at entry to the runner and angle of inlet guide vane

1b2 3unner blade entry angle

1c2 Head loss in runner

4olution:5iven: D

1= "#$ m6N= $%& rpm6Cr1= (#) m*s6 C2= + m*s6P = "..)& k'6 H= "")

m6 Q = ". m%*s 6 Cx2

= &

1a2 /nlet velocity and inlet guide vane angle

( ) ( )( )( ) m"s#$31604304$16011 === NDU

3unner tip speed

7ower

given to

runner

( )( )( )m"s4$32

#$311210

10$122#03

3

1

1

112211

===

=

=

QU

PC

CQUg

CUCUgQP

x

xxx


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"xa&ple

xa&ple

m"s8$334$32#$% 22212

11 =+=+= xr CCC

1b2 3unner blade entry angle

!bsolute inlet velocity

/nlet guide vane angle

o

x

r

C

C3$16

4$32

#$%arctanarctan

1

11 =

=

=

o

x

r

UC

C6$84

#$314$32

#$%arctanarctan

11

11 =

=

=

1c2 Head loss in runner

Head loss in runner = total head across runner 8 head transferred to runner

,otal head across runner = ( )2122

2121

2ZZ

g

CC

g

pp+

+

Head transferred to runner =g

CU x11


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"xa&ple

xa&ple

( ) m622121 =+

ZZ

g

pp

However0

( )g

CUZZ

g

CC

g

pph xr

11

21

2

2

2

121

2+

+

=

Head loss in runner

,hus0

( ) ( )

( )( )m6%$13

81$%

4$32#$31

81$%2

&8$3362

262

22

11

2

2

2

1

=

+=

+=

g

CU

g

CCh xr

Fluid System 09-Reaction Turbine-Francis and Kaplan

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