matching of buckets & wheel optimal number of muscles for this artificial beat……. p m v...
TRANSCRIPT
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Matching of Buckets & Wheel
Optimal number of Muscles for this Artificial Beat…….
P M V SubbaraoProfessor
Mechanical Engineering Department
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The Bucket of A Pelton Wheel
• A Pelton Wheel is a work generating animal (An Elephant).
• Basic diet is Hydro Potential energy (calorific Value).
• Intake System efficiently converts Potential Energy into Kinetic Energy (ATP).
• Bucket convert kinetic energy into shaft energy (The Muacles)
• How to select the size and number of Muscles Required by a Specific Pelton Turbine.
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Geometry of Wheel, Bucket & Jet Interactions
Rpelton
dj,O, Vj,O
Rwheel
A
A’B B’
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Number of buckets
• The number of buckets for a given runner must be determined so that no water particle is lost.
• Minimize the risks of detrimental interactions between the out flowing water particles and the adjacent buckets.
• The runner pitch is determined by the paths of; – the bucket tip (diameter Dpelton), – the Wheel diameter (DWheel).
• and the relative paths of the water particles stemming from the upper (A-A’)and lower (B-B’) generators of the jet.
• The bucket pitch must be selected so that no particle stemming from the lower generator of the jet can escape the runner without encountering any bucket.
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Bucket Duty Cycle
Reference Position
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Zones of Bucket Duty Cycle
• i) Approach of the tip to the jet (θj < −40◦).
• ii) Initial feeding process : (θj = −40◦...−10◦).
• iii) Entire separation of the jet (θj = −10◦...0◦)
• iv) Last stage of inflow (θj = 0◦...15◦)
• v) Last stage of outflow (θj = 15◦...50◦).
• vi) Series of droplets (θj = −50◦...∞).
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Minimum Number of Buckets
1B 1C
Rwheel
Rpelton
Dj,O, Vj,O
1A
1D
Best location of Jet :The axis of the jet falls on Pitch Circle
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Minimum Number of Buckets
1B 1C1E
RwheelR
Pelton
dj,O, Vj,O
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Minimum Number of Buckets
RW
heelRPelton
dO, Vj,O
lj
tj : Time taken bye the jet to travel lj
tb: Time taken by first bucket to travel
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RWRP
dO, Vj,O
lj
sinpeltonj Dl
wheel
wheel
R
U
• tj = lj/Vjet,O
• tb =
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For better working tj < tb
Oj
j
V
l
,
wheel
wheel
Oj
pelton
U
R
V
D
,
sin
Ojwheel
peltonwheel
VR
DU
,
sin
The minimum allowable value of
sin12sin ,
,
wheelvO
wheelu
wheel
pelton
Oj
wheel
Rk
k
R
D
V
U
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RWRP
dO, Vj,O
lj
pelton
Ojetwheel
R
dR
2cos
,
wheel
Ojetwheel
R
dR
2cos
,
wheel
wheel
Ojet
D
D
d
2
1
1
cos
,
wheel
VCjetvturbine
us D
dK
KN wheel ,
14
260
wheel
wheel
Ojet
D
D
d
2
1
1
cos
,
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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
d
Dz
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Bucket Power Distribution
P(j)
1
2
34
5
Total
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Bucket Energy Distribution
Ej,k
gHm
E
water
kk
h
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Non-Orthogonal Jet Bucket Interactions : Entry
Vjet Vrel,jet
Ublade
Vjet
Vrel,jetUblade
Vjet
Vrel,jet
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Non-Orthogonal Jet Bucket Interactions : Exit
Vjet
Vrel,jet
Ublade
VjetVrel,jet
Ublade
Vjet Vrel,jet
Ublade
VjetVrel,jet
Ublade
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Absolute and Relative Paths of Jet : Orthogonal Interactions
e
Vjet
Ublade
Ublade
Vrel,jet,exit
e
Vjet,exit
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U
Vri
Vre
UVri
Vai
Inlet Velocity Triangle
U
VreVae
Exit Velocity Triangle
Vai
Orthogonal Interactions
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U
VriVai
Vre
Vae
iie e
Vai: Inlet Absolute VelocityVri: Inlet Relative VelocityVre: Exit Relative VelocityVae:Exit Absolute Velocity
i: Inlet Nozzle Angle.i: Inlet Blade Angle.e: Exit Blade Angle.i: Exit Nozzle Angle.
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Actual Velocity Triangles: Pelton Bucket
1cos2max, ed k riereb VVUmP
cos
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Influence of the Casing
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Casing with Rectangular dome.
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Casing with cylindrical dome.
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Splash Water Distribution
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Evaluation of Casing Perfromance
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ANALYSIS OF THE LOSSES
• The losses in a Pelton turbine may be split up into the following losses:
• Losses in the jet because of friction, high turbulence, jet-divergence and gravitation.
• Losses in the runner because of friction in the buckets, entrance losses.
• Losses in the casing because of ventilation and splash water falling into the runner and/or the jet.
• Mechanical losses in the generator, bearings,...
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Closing Remarks on Pelton Wheel
• The first scientifically developed concept and also patented product.
• The only one option for high heads (> 600 m)
• Best suited for low flow rates with moderate heads (240m -- 600m).
• A better choice for moderate heads with medium flow rates.
• Easy to construct and develop, as it works at constant (atmospheric) pressure.
• Low rpm at moderate or marginal heads is a major disadvantage.