MINI PROJECT
An Academic Project submitted by
JAGANNATH.C I.Mech.E., A.M.I.Mech.E (I).
CHARTERED ENGINEER (INDIA)
MEM.NO ME/KH/272870IME
THE INSTITUTION OF MECHANICAL ENGINEERS (INDIA)
CHENNAI.
• Examples
• Losses in Francis turbines
• NPSH
• Main dimensions
Francis turbines
X blade runnerTraditional runner
SVARTISEN
P = 350 MWH = 543 mQ* = 71,5 m3/SD0 = 4,86 mD1 = 4,31mD2 = 2,35 mB0 = 0,28 mn = 333 rpm
P = 169 MWH = 72 mQ = 265 m3/sD0 = 6,68 mD1e = 5,71mD1i = 2,35 mB0 = 1,4 mn = 112,5 rpm
La Grande, Canada
Outletdraft tube
Outletrunner
Inletrunner
Outletguide vane
Inletguide vane
Hydraulic efficiency
n
uuh Hg
ucuc
2211
3
23
31
21
1
3
23
31
21
1
z2c
hgz2c
hg
lossesz2c
hgz2c
hg
1
Losses in Francis Turbines
Draft tube
Output Energy
Head [m]
Hyd
raul
ic E
ffic
ienc
y [%
]
Losses in Francis TurbinesH
ydra
ulic
Eff
icie
ncy
[%]
Output Energy
Output [%]
Friction losses between runner and covers
Friction losses
Gap losses
Gap losses
Gap losses
Friction losses in the spiral casingand stay vanes
Guide vane losses
Friction losses
Runner losses
Draft tube losses
Relative path
Absolute path with the runner installed
Absolute path without the runner installed
Velocity triangles
Net Positive Suction Head, NPSH
1
g
cz
g
chhz
g
ch b
222
23
3
23
32
22
2'22 hhh b
23
23
3 2zz
g
chHs
g2
czHhz
g2
ch
23
2sb2
22
2
J
JHhg2
ch sb
22
2
NPSH
vasb hJg
cHhh
2
22
2
NPSH
s2b HhhNPSH
NB:HS has a negative value in this figure.
AsvabR NPSHHhhNPSH
NPSH required
g
ub
g
caNPSH m
R
22
22
22
25.0b2.015.0b05.0b
0.2a6.115.1a05.1a
PumpsTurbines
Main dimensions
D1
D2
• Dimensions of the outlet
• Speed
• Dimensions of the inlet
Dimensions of the outlet
g
ubua
g
ub
g
caNPSH m
R
2
tan
22
22
222
22
22
We assume cu2= 0 and choose 2 and u2 from NPSHR:
13o < 2 < 22o (Lowest value for highest head)
35 < u2 < 43 m/s (Highest value for highest head)
1,05 < a < 1,150,05 < b < 0,15
Diameter at the outlet
222m tanuc
D1
D2
22
4
mc
QD
22
2m2m
22
D
4Qcc
4
DQ
Connection between cm2and choose D2 :
Speed
Connection between n and choose u2 :
2
222 D
60un
60
nDu
Correction of the speed
The speed of the generator is given from the number of poles and the net frequency
Hz50fforz
3000n
p
ExampleGiven data:
Flow rate Q = 71.5 m3/sHead H = 543 m
We choose:a = 1,10b = 0,102 = 22o
u2 = 40 m/s
m8,22
g2
401,022tan401,1NPSH
22
R
Find D2 from:
2222 tan
44
u
Q
c
QD
m
m37.222tan40
5,714D2
Find speed from:
rpmD
un 322
37.2
604060
2
2
Correct the speed with synchronic speed:
rpm3339
3000n9zchoose
3.9n
3000z
Kp
p
We keep the velocity triangle at the outlet:
u2
w2c2
c2K
u2K
2
mn
DnD
DnDn
Dn
DQ
Dn
DQ
u
c
u
c
KK
KK
KK
K
K
mKm
35.2333
322373.2
60
4
60
4
tan
33
32
2
32
32
2
22
2
22
22
22
Dimensions of the inlet
2u21u12u21u1
h cucu2Hg
cucu
At best efficiency point, cu2= 0
1u11u1
h cu2Hg
cu96,0
11
h1u u2
96,0
u2c
We choose: 0,7 < u1 < 0,75
Diameter at the inlet
D1
D2
n
60uD
2
D
60
2n
2
Du
11
111
Height of the inlet
22m11m AcAc
Continuity gives:
We choose: cm2 = 1,1 · cm1
4
D1.1DB
22
11
01 BB
Inlet angle
u1
w1c1
1
cu1
cm1
11
11tan
u
m
cu
c
Example continuesGiven data:
Flow rate Q = 71.5 m3/sHead H = 543 m
We choose:h = 0,96
u1 = 0,728cu2 = 0
66,0728,02
96.0
22
1111
uccu huuh
Diameter at the inlet
smhguu 15,7554381,92728,0211
mn
uD 31,4
333
6015,756011
D1
Height of the inlet
B1
mD
DB 35,0
31,44
35.21,1
4
1,1 2
1
22
1
Inlet angle
u1
w1c1
1
cu1
cm1
sms
mm
m
ucc 9,13
1,1
9,4022sin
1,1
sin
1,1222
1
135,054381,92
9,13
hg2
cc 1m
1m
9.62659,0728,0
135,0arctanarctan
11
11
u
m
cu
c
SVARTISEN
P = 350 MWH = 543 mQ* = 71,5 m3/SD0 = 4,86 mD1 = 4,31mD2 = 2,35 mB0 = 0,28 mn = 333 rpm
THANK YOU
I AM THANKFULL TO MY H.O.D AND FRIENDS WHOSE TIMELY ASSISTANCE MADE ME TO
ACCOMPLISH MINI PROJECT THIS
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