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

3. 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.

4. 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.

5. Shape variations of Buckets

7. 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.

8. Number of Geometrical Options for Bucket Each evaluation is a combination of length, width and depth.

9. Optimization of Bucket Geometry

10. 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.

13. Sequence of Jet Bucket Interactions         V jet U blade V jet U blade V jet U blade

14. V jet U blade V rel,jet,in V rel,jet,exit

17. Distribution of Reaction Measure of Reaction: Local Pressure Coefficient

18. Driving Force

19. Instantaneous Driving Force during Bucket Duty Cycle

20. Cutout Leakage Losses

21. Jet Diameter Vs Losses

22. Minimization of Losses

24. Empirical Geometry of Bucket Shape A B C 2i2i ee S I IV II III V DWDW

25. Empirical Relations for Bucket Geometry A = 2.8 d jet,VC to 3.2 d jet,VC B = 2.3 d jet,VC to 2.8 d jet,VC C= 0.6 d jet,VC to 0.9 d jet,VC  i = 5 0 to 8 0  e is varied from section I to section V I: 30 0 to 46 0 II: 20 0 to 30 0 III: 10 0 to 20 0 IV: 5 0 to 16 0 V: 0 0 to 5 0

26. Matching of Buckets & Wheel Matching of Organs of a Pelton Wheel.…….

27. 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.