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**Design of Pelton turbines**

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**When to use a Pelton turbine**

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**Energy conversion in a Pelton turbine**

Outlet Outlet of the runner Inlet of the runner Outlet of the needle Inlet of the needle

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**Main dimensions for the Pelton runner**

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**The ideal Pelton runner**

Absolute velocity from nozzle: Circumferential speed: Euler`s turbine equation:

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The real Pelton runner · For 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:

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**From continuity equation:**

Where: Z = number of nozzles Q = flow rate C1u =

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**The size of the bucket and number of nozzles**

Rules of thumb: B = 3,1 · ds 1 nozzle B = 3,2 · ds 2 nozzles B = 3,3 · ds 4-5 nozzles B > 3,3 · ds 6 nozzles

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Number of buckets empirical

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Number of buckets

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**Runner diameter Rules of thumb: D = 10 · ds Hn < 500 m**

D < 9,5 · ds must be avoided because water will be lost D > 15 · ds is for very high head Pelton

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Speed number

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**For the diameter: D = 10 · ds**

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

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**Dimensioning of a Pelton turbine**

The flow rate and head are given *H = 1130 m *Q = 28,5 m3/s *P = 288 MW Choose reduced values c1u = 1 c1u = 149 m/s u1 = 0,48 u1 = 71 m/s Choose the number of nozzles z = 5 Calculate ds from continuity for one nozzle

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**Choose the bucket width**

B = 3,3 · ds= 0,73 m

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**Find the diameter by interpolation**

D/ds Hn [m] 10 15 400 1400

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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:

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**Recalculate the speed:**

Recalculate the diameter: Choose the number of buckets z = 22

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**Diameter of the turbine housing (for vertical turbines)**

Calculate the height from the runner to the water level at the outlet (for vertical turbines) K z 8 9 1 6 4

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Given values: *Q = 28,5 m3/s *H = 1130 m Chosen values: c1u = 1 u1 = 0,48 z = 5 B = 0,73 m z = 22 Zp = 7 Calculated values: ds = 0,22 m n = 428,6 rpm D = 3, 16 m Height = 3,1 m Dhousing= 9,4 m *P = 288 MW

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**Jostedal, Sogn og Fjordane**

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

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**Jostedal, Sogn og Fjordane**

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

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**Example Khimti Power Plant**

The flow rate and head are given *H = 660 m *Q = 2,15 m3/s *P = 12 MW Choose reduced values c1u = 1 c1u = 114 m/s u1 = 0,48 u1 = 54,6 m/s Choose the number of nozzles z = 1

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**Example Khimti Power Plant**

Calculate ds from continuity for one nozzle Choose the bucket width B = 3,2 · ds= 0, 5 m

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**Find the diameter by interpolation**

D/ds Hn [m] 10 15 400 1400

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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:

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**Recalculate the speed:**

Recalculate the diameter: Choose the number of buckets z = 22

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