Matching of Bucket to Jet in Pelton Wheels

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Matching of Bucket to Jet in Pelton Wheels
P M V Subbarao Professor Mechanical Engineering
Department
Satisfying the Concerns of Pelton.
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A Set of Relations

• A jet of finite velocity needs to have a relation
  with peripheral velocity of wheel.
• A jet of finite area need to have a relation with
  dimensions of bucket.
• A bucket of finite dimensions and shape should
  have a relation with wheel.

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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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Shape variations of Buckets
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Shape variations of Buckets
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Optimum bucket design

• At first, various combinations of the free design
  variables are tested with the optimization
  method.
• This helps in assessing the relative importance
  of each one, as well as to determine their
  variation ranges.
• Hydraulic efficiency depends more on the main
  bucket dimensions (length, width and depth), than
  on the shape of the outer part of its rim or on
  the lateral surface curvature.
• The optimization has to be carried out for all
  the free design variables simultaneously.
• This practice enhances the time of design
  optimization, but at the same time ensures that
  the resulting optimum design is acceptable.
• The creation of evaluations using Artificial
  Intelligence Tool is an option of the method to
  achieve faster convergence.

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Number of Geometrical Options for Bucket
Each evaluation is a combination of length, width
and depth.
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Optimization of Bucket Geometry
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Parametric studies

• The developed methodology also facilitates the
  investigation of the effect of any design
  parameter on the runner efficiency, as well as
  the prediction of the turbine behaviour at
  various operation conditions (e.g. different head
  or rotation speed).
• Two important parametric studies are
• In the first study the bucket size is varied by
  increasing or reducing its main dimensions
  (length, width, depth) at the same degree, so as
  the modified shapes remain similar to the initial
  one.

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Sequence of Jet Bucket Interactions
Dq50
Dq250
Dq350
Dq150
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Vjet
Vrel,jet,in
Vrel,jet,exit
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Distribution of Reaction
Measure of Reaction Local Pressure Coefficient
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Driving Force
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Instantaneous Driving Force during Bucket Duty
Cycle
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Cutout Leakage Losses
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Jet Diameter Vs Losses
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Minimization of Losses
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Empirical Geometry of Bucket Shape
C
2bi
DW
S
A
be
B
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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
• bi 50 to 80
• be 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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Matching of Buckets Wheel
Matching of Organs of a Pelton Wheel..
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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.