Francis turbines Examples Losses in Francis turbines NPSH
Francis turbines • • Examples Losses in Francis turbines NPSH Main dimensions
Traditional runner X blade runner
SVARTISEN P = 350 MW H = 543 m Q* = 71, 5 m 3/S D 0 = 4, 86 m D 1 = 4, 31 m D 2 = 2, 35 m B 0 = 0, 28 m n = 333 rpm
La Grande, Canada P = 169 MW H = 72 m Q = 265 m 3/s D 0 = 6, 68 m D 1 e = 5, 71 m D 1 i = 2, 35 m B 0 = 1, 4 m n = 112, 5 rpm
Outlet draft tube Outlet runner Inlet runner Outlet guide vane Inlet guide vane
Hydraulic efficiency 1
Losses in Francis Turbines Hydraulic Efficiency [%] Draft tube Output Energy Head [m]
Hydraulic Efficiency [%] Losses in Francis Turbines Output Energy Output [%]
Friction losses between runner and covers Friction losses
Gap losses
Friction losses in the spiral casing and stay vanes Guide vane losses Gap losses Runner losses Draft tube losses
Relative path Absolute path without the runner installed Absolute path with the runner installed
Velocity triangles
Net Positive Suction Head, NPSH J 1
NPSH NB: HS has a negative value in this figure.
NPSH required
Main dimensions • Dimensions of the outlet • Speed • Dimensions of the inlet D 1 D 2
Dimensions of the outlet We assume cu 2= 0 and choose b 2 and u 2 from NPSHR: 13 o < 35 < 1, 05 < 0, 05 < b 2 u 2 a b < < 22 o (Lowest value for highest head) 43 m/s (Highest value for highest head) 1, 15 0, 15
Diameter at the outlet Connection between cm 2 and choose D 2 : D 1 D 2
Speed Connection between n and choose u 2 :
Correction of the speed The speed of the generator is given from the number of poles and the net frequency
Example Given data: Flow rate Head We choose: a = 1, 10 b = 0, 10 b 2 = 22 o u 2 = 40 m/s Q = 71. 5 m 3/s H = 543 m
Find D 2 from:
Find speed from:
Correct the speed with synchronic speed:
We keep the velocity triangle at the outlet: u 2 b 2 c 2 K w 2 u 2 K
Dimensions of the inlet At best efficiency point, cu 2= 0
Diameter at the inlet We choose: 0, 7 < u 1 < 0, 75 D 1 D 2
Height of the inlet Continuity gives: We choose: cm 2 = 1, 1 · cm 1
Inlet angle cu 1 c 1 cm 1 b 1 w 1
Example continues Given data: Flow rate Head We choose: hh = 0, 96 u 1 = 0, 728 cu 2 = 0 Q = 71. 5 m 3/s H = 543 m
Diameter at the inlet D 1
Height of the inlet B 1
Inlet angle cu 1 c 1 cm 1 b 1 w 1
SVARTISEN P = 350 MW H = 543 m Q* = 71, 5 m 3/S D 0 = 4, 86 m D 1 = 4, 31 m D 2 = 2, 35 m B 0 = 0, 28 m n = 333 rpm
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