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Design Analysis of Francis Turbine Runner
P M V SubbaraoProfessor
Mechanical Engineering Department
Provision of Features to Reaction Muscle.…
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Velocity trianglesrri
rre
Uri
Vwi
Vri
Vfi
Vai
Ure
Vwe
Vre
Vfe
Vae
i
i
ee
rU
UU
r
rire
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Inlet Velocity Triangles Vs Ns
Low Specific Speed : Slow Francis Runner
Vwi
Vai
Vfi
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Inlet Velocity Triangles Vs Ns
Low Specific Speed : Normal Francis Runner
Vwi
Vai
Vfi
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Inlet Velocity Triangles Vs Ns
High Specific Speed : Fast Francis Runner
Vwi
Vai
Vfi
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Specifications of Runner
• Slow Runner: Ns=60 to 120 to 250
– Kui = 0.62 to 0.68 to
– B0/Dp=0.04 – 0.033• Normal Runner: Ns = 120 – 180
to 32.50
– Kui = 0.68 to 0.72 – B0/Dp=0.125 to 0.25
• Fast Runner: Ns = 180 to 300 to 37.50
– Kui = 0.72 to 0.76 to
– B0/Dp=0.25to 0.5
min
hpin
s
H
PNN
4/5
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Selection of Exit Velocity Triangle
Exploitation of Reaction Character…..
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Energy of Water Leaving a Francis Runner
RE
TEZreZte
Vte
Vare
HTW
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Hydraulic Energy of Exiting Fluid
TEte
TEREare
RE gzV
pQgzV
pQ 22
22
For frictionless flow through exit tube
For frictional flow through exit tube
draftfTEte
TEREare
RE pQgzV
pQgzV
pQ ,
22
22
For maximum energy recovery
arete VV
tere pp
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draftfTEte
TEREare
RE pgzV
pgzV
p ,
22
22
draftfTEte
twatmREare
RE pgzV
gHpgzV
p ,
22
22
draftfTEtwREteare
REatm pzHzgVV
pp ,
22
2
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Components of Draft Tube
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Geometric Ratios for Draft Tube
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Rsiteat NPSHNPSH
NPSH required
g
Ub
g
VaNPSH refre
R
22
22
15.005.0
15.105.1
b
a
Turbines
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Dimensions of the outlet
g
UbUa
g
Ub
g
VaNPSH reererefre
R 2
tan
22
2222
13o < e < 22o
1,05 < a < 1,150,05 < b < 0,15
Highest value for highest head
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Internal Anatomy of Runner
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Blade Velocity Vs Tangential Component of Fluid Velocity
Ub
UbVw
Va
Vf
gzUUVVVhI bladebladerx 2222
2
1
Vr
In maridional plane at mean radius of rotor
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Runner Design
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Runner Design
The main procedure in design of a new runner includes;
• Use of Classical theory for shaping the blade geometry
• CFD analysis for the tuning of runner geometry
The classical method;
• Design the meridional plan of runner based on available methods
• Obtain the perpendicular view of runner using conformal Mapping.
• Modify using model testing or CFD.
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Runner Design
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Shape of Francis Channel : Meridional Plan
Rr1i
Rr2e
L/Dri
Rr2i
Rr1e
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Real values of Radii
The real value of the outlet tip radius3
1
22
eer
QR
The real value of the intlet root radius3
1
21
1
2
iir h
gHR
28.024.0 2 e 8.165.1 1 ih
Rr2e and Rr1i are only fix two points of the leading and trailing edges and the rest of these curves should be drawn to lead to better efficiency of runner.
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Determination of Inlet & exit edges runner
1i
2i
1e
2e
The form of these edges is two parabolic curves.
Define the non-dimensional specific speed
Q
gH
NN NDs 75.0260
2
For 275.0088.0 NDsN
the leading edge form is a parabolic arcwith the peak in the point by radius of 2.Rr1i-Rr2iwhich passes through the points 1i and 2i,
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1i
2i
1e
2e
and for specific speeds between
its form is also a parabolic arc but with the minimum point in the 1iand the axis is parallel to runner axis.
89.0275.0 NDsN
In the exit area, trailing edge is a parabolic curve which has a minimum point in 1e and also passes through a point such as 2i with a radius of Rr1i/3.