Download - Design of Pelton Wheel: Tuesday Group
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Design & Analysis of Pelton Wheel Turbine
P M V SubbaraoProfessor
Mechanical Engineering Department
Internal Details of the Machine….
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Koyna Hydro Electric Project
Koyna Dam from the catchment area of about
891.78 Sq. Km
•Koyna river rises in the Mahabaleshwar, a famous hill station in the hill range of Sahyadri. •It flows in a north - south direction almost parallel to the Arabian Sea coast for a distance of 65 Kms.
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Details of Koyna Hydro Electric Project
• Number of units: 4• Capacity of each unit=250MW• Head
– Normal Head=415m– Maximum Head=510m
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Creation of Reservoir
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MORE ADAPTED TYPE OF TURBINA IN FUNCTION OF THE SPECIFIC SPEED.
Specific Speed in r.p.m. Turbine type Jump height in m
Until 18 Pelton of an injector 800 From 18 to 25 Pelton of an injector 800 to 400 From 26 to 35 Pelton of an injector 400 to 100 From 26 to 35 Pelton of two injectors 800 to 400 From 36 to 50 Pelton of two injectors 400 to 100 From 51 to 72 Pelton of four injectors 400 to 100
Specific speed in rpm4
5H
PNN s
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Selection of Speed of A Turbo Machine
Hzfforz
Np
503000
Zp : Number of pairs of poles of the generator
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Questions to be Answered
• Is it possible to change number of units in Stage IV?
• What is the allowable speed of the generator for each unit, if number of units is 2, 5, 6 or 7?
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Design of Any Selected Pelton Wheel Unit
• Different capacities for each sub-group.• Design for Normal Head.• Assume an overall efficiency: 90 – 94%• Calculate the required flow rate.
HgQP pelton
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General Layout of A Hydro Power Plant
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THE CONDUIT SYSTEM
• Water from the storage is diverted into the main conduit system through a 3,370ft long intake channel and an intake tower, trash racks and two intake gates each 21ftX8ft.
• The head race tunnel is 12,000ft long and 21ft in diameter. • It is concrete lined for the whole of the length expect for
the last 1600ft at the surge end where 17ft diameter steel lining is provided.
• The diameter of the tunnel, in the stretch of steel lining is reduced on ground of economy
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Open Channel Gravity Flow
hgDfVS
24 2
0
Channel Bed Slope
PADh
4
Pipe Material Absolute Roughness, emicron
(unless noted)drawn brass 1.5drawn copper 1.5commercial steel 45wrought iron 45asphalted cast iron 120galvanized iron 150cast iron 260wood stave 0.2 to 0.9 mm
concrete 0.3 to 3 mm
riveted steel 0.9 to 9 mm
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Design of Penstock
2
4 penstockpenstock dVQ
gHVpenstock 2In general
But maximum allowable value is 10 m/sMaximum allowable head loss in Penstock =2 to 4% of available head
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General Design of Under Ground Power Tunnels/Penstocks
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penstock
penstockfriction gd
fLVHxh
24 2
gHkV penstockvpenstock 2,
Speed) Specific toalproportion(inversly 0.15 to2.0:, pestockvk
2
9.0Re74.5
7.3log
0625.0
hDk
f
Pipe Material Absolute Roughness, emicron
(unless noted)drawn brass 1.5drawn copper 1.5commercial steel 45wrought iron 45asphalted cast iron 120galvanized iron 150cast iron 260wood stave 0.2 to 0.9 mm
concrete 0.3 to 3 mm
riveted steel 0.9 to 9 mm
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Design of Penstock
Group No. Unit SizeMW
Qp Dp Head loss
1. 500
2. 333.3
3. 200
4. 166.7
5. 142.85
6. 125
7. 111.1
8. 100
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Distributor : Only for multi jet Wheel
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Design of Distributor
Q2
4 penstockpenstock dVQ
Penstock
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The Nozzle and Jet : A Key Step in Design
d0djet,VC
Free Surface Shape for Maximum Power
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Initial guess for Diameter of the Jet at the outlet, do
gHKdQ voo 24
2
83.081.0 vOK
It is important to find out the VC and outlet jet diameters/areas
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Geometrical Relations for Nozzle
dO
2dO – 2.4dO
5dO – 9dO
0.8dO – 0.9dO
1.2dO – 1.4dO
1.1dO – 1.3dO
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Performance Analysis of Nozzle-Spear Valve
Ideal Nozzle-spear Valve:
constant2
2
gzV
p
Along flow direction
frictiontotal ΔppVp -constant2
2
Real Nozzle-spear Valve:
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penstock
penstockfriction d
fLVp
24 2
2
9.0Re74.5
7.3log
0625.0
hDk
fPipe Material Absolute Roughness, e
micron(unless noted)
drawn brass 1.5drawn copper 1.5commercial steel 45wrought iron 45asphalted cast iron 120galvanized iron 150cast iron 260wood stave 0.2 to 0.9 mm
concrete 0.3 to 3 mm
riveted steel 0.9 to 9 mm
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Numerical Computation of Total Pressure Variation
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Efficiency of Spear Nozzle Valve
1001
inlettot
exittotinlettotvalvespear p
pp
Acceptable Range: 97.5% -- 99%
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Design of Penstock
Group No. Unit SizeMW
djet Head loss
1. 500
2. 333.3
3. 200
4. 166.7
5. 142.85
6. 125
7. 111.1
8. 100
valvespear
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Geometrical Relations for Nozzle
The values of α varies between 20 to 30° whereas β varies from 30 to 45°.
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Industrial Correlations for Jet Area variation with stroke
Optimal value of Outlet jet area, ao
2BsAsao
s is the displacement of spear
sinsin2 orA
2
2
sinsinsinsinB
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Computation of Variation Jet Area with stroke
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Mean Diameter of Pelton Runner
Mean diameter or Pitch circle diameter:Dwheel
Circumferential velocity of the wheel, Uwheel
gHU wheel 2
gHKUwheeluwheel 2
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Experimental values of Wheel diameter to jet diameter
Dwheel /djet,VC 6.5 7.5 10 20
Ns (rpm) 35 32 24 10
turbine 0.82 0.86 0.89 0.90
4 5H
PNN wheels
99.098.0 1 vK gHKQd
vVCjet 2
4
1,
Higher ratios are preferred for better efficiency.Modern wheels for high heads use ratios as high as 30!
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Optimal values of Wheel diameter to jet diameter
Ns
jet
wheeld
D
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Group No. Unit SizeMW
1. 500
2. 333.3
3. 200
4. 166.7
5. 142.85
6. 125
7. 111.1
8. 100
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Geometric Details of Bucket
The hydraulic efficiency depends more on the main bucket dimensions (length (A), width (B) and depth (C)).The shape of the outer part of its rim or on the lateral surface curvature also has marginal effect on hydraulic efficiency.
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Empirical Geometry of Bucket Shape
A
B
C
2i
e
S
I
IVII
III
V
DW
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Empirical Relations for Bucket Geometry
• A = 2.8 djet,VC to 3.2 djet,VC
• B = 2.3 djet,VC to 2.8 djet,VC
• C= 0.6 djet,VC to 0.9 djet,VC
i = 50 to 80
e is varied from section I to section V• I: 300 to 460
• II: 200 to 300
• III: 100 to 200
• IV: 50 to 160
• V: 00 to 50
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RWRP
dO, Vj,O
lj
wheel
wheel
Ojet
D
Dd
21
1cos
,
sin12,
wheelvO
wheelu
Rkk
Number of Buckets
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Maximum allowable angle between two successive buckets
2
Minimum number of buckets 360
z
Dr Taygun has suggested an empirical relation for z
155.0,
VCjet
wheel
dDz
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Group No. Unit SizeMW
1. 500
2. 333.3
3. 200
4. 166.7
5. 142.85
6. 125
7. 111.1
8. 100
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Absolute and Relative Paths of Jet : Orthogonal Interactions
e
VjetUblade
Ublade
Vrel,jet,exit
e
Vjet,exit
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1
coscoscos2
2
eaii
aid i
kVU
VU
2
1coscoscos2
ai
eiai
d Vi
kUVU
Define Blade Speed Ratio,
1
coscoscos2
ik e
id
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Approximate Velocity Triangles: Pelton Bucket
1cos2max, ed k riereb VVUmP
cos
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Start of Jet Bucket Interactions
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Sequence of Jet Bucket Interactions
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Bucket Duty Cycle
• Compute angles of onset and close of interactions.
• Select few locations during bucket jet interaction.• Compute mass of jet intercepted by the bucket and
corresponding blade exit angles.• Numerically integrate the work done by a bucket
per rotation.• Compute Average Power developed by bucket
and efficiency.