Matching of Buckets & Wheel Optimal number of Muscles for this Artificial Beat……. P M V Subbarao Professor Mechanical Engineering Department

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.

Geometry of Wheel, Bucket & Jet Interactions R pelton  d j,O, V j,O R wheel  A A’ B B’

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 D pelton ), –the Wheel diameter (D Wheel ). 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.

Bucket Duty Cycle Reference Position

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◦...∞).

Minimum Number of Buckets 1B 1C R wheel R pelton  D j,O, V j,O  1A 1D  Best location of Jet :The axis of the jet falls on Pitch Circle

Minimum Number of Buckets 1B 1C 1E   R wheel R Pelton  d j,O, V j,O  

Minimum Number of Buckets   R Wheel R Pelton  d O, V j,O ljlj  t j : Time taken bye the jet to travel l j t b : Time taken by first bucket to travel 

  RWRW RPRP  d O, V j,O ljlj  t j = l j /V jet,O t b = 

For better working t j < t b The minimum allowable value of 

  RWRW RPRP  d O, V j,O ljlj 

Maximum allowable angle between two successive buckets Minimum number of buckets Dr Taygun has suggested an empirical relation for z

Bucket Power Distribution P(  j) Total

Bucket Energy Distribution E j,k

Non-Orthogonal Jet Bucket Interactions : Entry V jet V rel,jet U blade V jet V rel,jet U blade V jet V rel,jet

Non-Orthogonal Jet Bucket Interactions : Exit V jet V rel,jet U blade V jet V rel,jet U blade V jet V rel,jet U blade V jet V rel,jet U blade

Absolute and Relative Paths of Jet : Orthogonal Interactions ee V jet U blade V rel,jet,exit ee V jet,exit

U V ri V re UV ri V ai Inlet Velocity Triangle U V re V ae Exit Velocity Triangle V ai Orthogonal Interactions

U V ri V ai V re V ae ii ii ee ee V ai : Inlet Absolute Velocity V ri : Inlet Relative Velocity V re : Exit Relative Velocity V ae :Exit Absolute Velocity  i : Inlet Nozzle Angle.  i : Inlet Blade Angle.  e : Exit Blade Angle.  i : Exit Nozzle Angle.

Actual Velocity Triangles: Pelton Bucket

Influence of the Casing

Casing with Rectangular dome.

Casing with cylindrical dome.

Splash Water Distribution

Evaluation of Casing Perfromance

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,...

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 m). 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.