Matching of Buckets & Wheel

Optimal number of Muscles for this Artificial Beat…….

P M V SubbaraoProfessor

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

Rpelton

dj,O, Vj,O

Rwheel

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 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.

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

Rwheel

Rpelton

Dj,O, Vj,O

1A

1D

Best location of Jet :The axis of the jet falls on Pitch Circle

Minimum Number of Buckets

1B 1C1E

RwheelR

Pelton

dj,O, Vj,O

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

RWRP

dO, Vj,O

lj

sinpeltonj Dl

wheel

wheel

R

U

• tj = lj/Vjet,O

• tb =

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

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

,

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

Bucket Power Distribution

P(j)

1

2

34

5

Total

Bucket Energy Distribution

Ej,k

gHm

E

water

kk

h

Non-Orthogonal Jet Bucket Interactions : Entry

Vjet Vrel,jet

Ublade

Vjet

Vrel,jetUblade

Vjet

Vrel,jet

Non-Orthogonal Jet Bucket Interactions : Exit

Vjet

Vrel,jet

Ublade

VjetVrel,jet

Ublade

Vjet Vrel,jet

Ublade

VjetVrel,jet

Ublade

Absolute and Relative Paths of Jet : Orthogonal Interactions

e

Vjet

Ublade

Ublade

Vrel,jet,exit

e

Vjet,exit

U

Vri

Vre

UVri

Vai

Inlet Velocity Triangle

U

VreVae

Exit Velocity Triangle

Vai

Orthogonal Interactions

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.

Actual Velocity Triangles: Pelton Bucket

1cos2max, ed k riereb VVUmP

cos

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 -- 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.