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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
7/25/2019 Fluid System 09-Reaction Turbine-Francis and Kaplan
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adial Flow Francis Turbine
adial Flow Francis Turbine
7/25/2019 Fluid System 09-Reaction Turbine-Francis and Kaplan
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Construction of Francis
onstruction of Francis
Turbine
urbine
7/25/2019 Fluid System 09-Reaction Turbine-Francis and Kaplan
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Velocity Triangle
elocity Triangle
Euler Equation:
( )
g
CUCU
mg
WE xx 2211
==
Flow velocities:
11
12 br
QCr
=
22
22 brQCr
=
heightrunnerb =
7/25/2019 Fluid System 09-Reaction Turbine-Francis and Kaplan
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Axial Flow Kaplan Turbine
xial Flow Kaplan Turbine
7/25/2019 Fluid System 09-Reaction Turbine-Francis and Kaplan
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Construction of Kaplan
onstruction of Kaplan
Turbine
urbine
7/25/2019 Fluid System 09-Reaction Turbine-Francis and Kaplan
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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=
7/25/2019 Fluid System 09-Reaction Turbine-Francis and Kaplan
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Installation
nstallation
7/25/2019 Fluid System 09-Reaction Turbine-Francis and Kaplan
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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
7/25/2019 Fluid System 09-Reaction Turbine-Francis and Kaplan
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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 $oss
cc gQhP = draft tubeandcasinginlosshead=ch
"nergy balance beco&es!
( ) srcrrm PqHQhQhgPgQH ++++=
7/25/2019 Fluid System 09-Reaction Turbine-Francis and Kaplan
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$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=
7/25/2019 Fluid System 09-Reaction Turbine-Francis and Kaplan
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Caracteristics Cur#es
aracteristics Cur#es
7/25/2019 Fluid System 09-Reaction Turbine-Francis and Kaplan
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Caracteristics Cur#es
aracteristics Cur#es
omparison of hydraulic turbine efficiencies
7/25/2019 Fluid System 09-Reaction Turbine-Francis and Kaplan
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'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
7/25/2019 Fluid System 09-Reaction Turbine-Francis and Kaplan
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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
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