Jets & Buckets for Pelton Wheels

Means to Complete the Second Law of Power Retrieval…….

P M V SubbaraoProfessor

Mechanical Engineering Department

Geometrical Relations for Nozzle

dO

2dO – 2.4dO

5dO – 9dO

0.8dO – 0.9dO

1.2dO – 1.4dO

1.1dO – 1.3dO

Numerical Computation of Total Pressure Variation

gHKV vactualVCjet 21:, 99.098.0 1 vK

Jet carrying a discharge of Q to deliver a power P

gHKdQ vVCjet 24 1

2,

To generate a discharge of Q, we need a least jet diameter of

gHK

Qd

v

VCjet2

4

1

,

QgHP turbine

Acceptable Performance of Nozzle

Diameter of the Jet at the outlet, do

gHKdQ voo 24

2

83.081.0 vOK

It is important to find out the VC and outlet jet diameters/areas

The Diameter of Jet before Reaching Bucket

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.

Jet Vs Mean Diameter of Pelton Runner

Mean diameter or Pitch circle diameter:Dwheel

Circumferential velocity of the wheel, Uwheel

gHU wheel 2

gHKUwheeluwheel 2

Dwheel

Jet Power & Conditions for Maximum Power

ei

bijetbbijetb

UVkUVUmP

180coscos

coscos

e

i

jet

bi

bjet

bi

jet

bVU

kV

U

V

UmP

180cos

cos

cos

cos

Define, Blade Speed Ratio asjet

bb V

UC

ei

bibbib

CkCCmP

180cos

cos

coscos

0

bC

P

602.max

wheelwheelpoweruwheel

NDgHKU

wheel

wheel

uwheel D

gHKN wheel

260

4 5gH

PN

Nwheel

s

gHKdQ vVCjet 2

4 12

,

QgHP turbine

Implication of Maximum Power Condition

jet

wheelpowerforb V

UC max,

turbinevVCjet gHKdgHP 24 1

2,

4 5

12

, 24260

gH

gHKdgH

D

gHK

N

vVCjetturbine

wheel

u

s

wheel

12

,42

260vVCjetturbine

wheel

us Kd

D

KN wheel

wheel

VCjetvturbine

us D

dK

KN wheel ,

14 52

60

2

,

2

12

VCjet

wheels

vturbine d

DN

KK

C

wheelu

For maximum efficiency

Optimal values of Wheel diameter to jet diameter

Ns

jet

wheeld

D

Experimental values of Best values of Wheel diameter to jet diameter

Dwheel /djet,VC 6.5 7.5 10 20

Ns (rpm) 35 32 24 10

turbine 0.82 0.86 0.89 0.90

45

H

PNN s P in hp, H in meters and N in rpm

Essential to have a minimum of 10 for acceptable turbine efficiency.

The highest ratio used in the world is 110 (Kt. Glauraus Power House in Switzerland).

Specifications of this Pelton wheel are:

Power 3000HP (2.24MW) Speed: 500 rpmDwheel= 5.36m djet,VC=48.77mmHead =1,650 m

6.2

1650

30005004 54 5

gH

PN

Nwheel

s

Extreme Engineering Conditions

The Second Relation : Jet Vs Bucket

External stroboscopic flow visualization

Runner with Advanced Buckets

Bucket Displacement Diagram

• A notch made near the edge of the outer rim of each bucket is carefully sharpened to ensure a loss-free entry of the jet into the buckets,

• i.e., the path of the jet is not obstructed by the incoming buckets.

BUCKET GEOMETRIC DEFINITIONS

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.