Design of Pelton turbines

When to use a Pelton turbine

Energy conversion in a Pelton turbineOutletOutlet of the runnerInlet of the runnerOutlet of the needleInlet of the needle

Main dimensions for the Pelton runner

The ideal Pelton runnerAbsolute velocity from nozzle: Circumferential speed: Euler`s turbine equation:

The real Pelton runnerFor a real Pelton runner there will always be losses.We will therefore set the hydraulic efficiency to: The absolute velocity from the nozzle will be: C1u can be set to 1,0 when dimensioning the turbine.This gives us:

From continuity equation: Where:Z=number of nozzlesQ =flow rateC1u=

The size of the bucket and number of nozzlesRules of thumb:B = 3,1 ds1 nozzleB = 3,2 ds2 nozzlesB = 3,3 ds4-5 nozzlesB > 3,3 ds6 nozzles

Number of buckets empirical

Number of buckets

Runner diameter Rules of thumb:D = 10 dsHn < 500 mD = 15 dsHn = 1300 m

D < 9,5 ds must be avoided because waterwill be lostD > 15 ds is for very high head Pelton

Speed number

For the diameter: D = 10 ds and one nozzle:z = 1For the diameter: D = 10 ds and six nozzle:z = 6The maximum speed number for a Pelton turbine today is W = 0,22 The maximum speed number for a Pelton turbine with one nozzle is W = 0,09

Dimensioning of a Pelton turbineThe flow rate and head are given*H = 1130 m*Q = 28,5 m3/s*P = 288 MW

Choose reduced valuesc1u = 1 c1u = 149 m/su1 = 0,48 u1 = 71 m/s

Choose the number of nozzlesz = 5

Calculate ds from continuity for one nozzle

Choose the bucket width B = 3,3 ds= 0,73 m

Find the diameter by interpolation

Calculate the speed:

Choose the number of poles on the generator:

The speed of the runner is given by the generator and the net frequency:

where Zp=number of poles on the generator

The number of poles will be:

Recalculate the speed:

Recalculate the diameter:

Choose the number of buckets

z = 22

Diameter of the turbine housing (for vertical turbines)

Calculate the height from the runner to the water level at the outlet (for vertical turbines)

Given values:

*Q = 28,5 m3/s*H = 1130 m

Chosen values:

c1u = 1u1 = 0,48z = 5B = 0,73 mz = 22Zp = 7

Calculated values:

ds = 0,22 mn = 428,6 rpmD = 3, 16 mHeight = 3,1 mDhousing= 9,4 m*P = 288 MW

GE Hydro*Q = 28,5 m3/s*H = 1130 m*P = 288 MWJostedal, Sogn og Fjordane

Jostedal, Sogn og FjordaneGE Hydro*Q = 28,5 m3/s*H = 1130 m*P = 288 MW

ExampleKhimti Power PlantThe flow rate and head are given*H = 660 m*Q = 2,15 m3/s*P = 12 MW

Choose reduced valuesc1u = 1 c1u = 114 m/su1 = 0,48 u1 = 54,6 m/s

Choose the number of nozzlesz = 1

ExampleKhimti Power PlantCalculate ds from continuity for one nozzle

Choose the bucket width B = 3,2 ds= 0, 5 m

Find the diameter by interpolation

Calculate the speed:

Choose the number of poles on the generator: The speed of the runner is given by the generator and the net frequency:

where Zp=number of poles on the generator

The number of poles will be:

Recalculate the speed:

Recalculate the diameter:

Choose the number of buckets

z = 22