Dr. Ir. Harinaldi, M.EngMechanical Engineering Department

Faculty of Engineering University of Indonesia

impulse turbines -Pelton wheels

Construction and ComponentConstruction and Component

ConstructionConstruction

Multi Jet

Single Jet

InstallationInstallation

Velocity TriangleVelocity TriangleEuler Equation:

Assume no loss of relative velocity, W1 = W2

For maximum E dE/dU = 0

Velocity TriangleVelocity TriangleIn practice :Surface friction of the bucket W2≠ W1

Losses and EfficiencyLosses and EfficiencyPipeline transmission efficiency pipeline losses, hf

11

1

reservoirat availableenergy pipeline of endat energy

HH

HhH f

trans

Nozzle efficiency nozzle losses, hin

HH

HhH

hHhhH in

f

infN

'inlet nozzleat energy outlet nozzleat energy

1

1

Energy available in jet at nozzle outlet : gCH 2' 21

Nozzle velocity coefficient

gHCCv 2inlet nozzleat ty jet veloci ltheoretica

outlet nozzleat ty jet veloci actual 1 2vN C

Hydraulic efficiency

gCE

HE

H 2'outlet nozzleat jet in availableenergy nsferredenergy tra

21

Losses and EfficiencyLosses and EfficiencyOverall Efficiency

gQHP

o

inlet nozzleat availablePower turbineby the developedPower

Turbine discharge, Q

1

21 4

outlet nozzleat ty jet veloci actual nozzleareaCdAC

Q

d = nozzle diameter

ExampleExampleA Pelton turbine develops 2000 kW under a head of 100 m and with an overall efficiency of 85%. The coefficient of velocity for the nozzle is 0.98. Determine: (a) The theoretical velocity of the jet ?(b) The actual velocity of the jet ?(c) The flow rate ?(d) The diameter of the nozzle

Solution:Given: P = 2000 kW; H = 100 m; ηo = 0.85 ; Cv= 0.98Let : d = diameter of the nozzle ; Q = discharge flow rate of the turbine

(a) The theoretical velocity of the jet

m/s 3.44)100)(81.9(22 gHCtheo

(b) The actual velocity of the jet

smCCgHCC

gHCC

theovv

v

/ 4.433.4498.02

2

1

1

ExampleExample(c) The flow rate

smgH

PQ

gQHP

o

o

/ 4.285.010081.910

10.2000 33

3

(d) The diameter of the nozzle

m

CQd

CdACQ

265.04.43

4.244

4

1

12

1

Design of Pelton WheelsDesign of Pelton Wheels

Pelton wheel is designed to find out the following data:1. Diameter of the wheel (D)2. Diameter of the jet (d)3. Size (i.e. width and depth) of the buckets4. Number of buckets (z)

Pelton wheel is designed with the following input:1. Head of water2. Power to be developed3. Speed of the runner

Pelton wheel is usually designed with the following assumption:1. Overall efficiency, ηo between 80% and 87% 2. Coefficient of velocity, Cv as 0.98 to 0.993. Ratio of peripheral velocity to the jet velocity, U/C1 as 0.43 to 0.48

Design of Pelton WheelsDesign of Pelton WheelsSize of the buckets

16 to11

2.1 to8.0

4 to3

3 to2

dDdTdBdL

Number of the buckets (z)Theoretical :

oz 360

26.05.0cos

DRdRdR

where:

Empirical :

dDz2

15

Characteristics CurvesCharacteristics Curves

Efficiency and jet speed ratio Efficiency vs speed at various nozzle setting

Power vs speed at various nozzle setting Variation of efficiency with load

Load ChangesLoad ChangesIn practice :U must remain constant when the load changes to maintain maximum efficiency U/C1 must stay the same change the input of water power change in Q change in nozzle area A

Load Control : spear valve and deflector plate

Load ChangesLoad Changes