Design of stay vanes and spiral casing Revelstoke, CANADA Guri-2, VENEZUELA Aguila, ARGENTINA Sauchelle-Huebra, SPAIN Three Gorges Turbine, GE Hydro The spiral casing will distribute the water equally around the stay vanes In order to achieve a uniform flow in to the runner, the flow has to be uniform in to the stay vanes. Flow in a curved channel Streamline The pressure normal to the streamline can be derived as: Newton 2. Law gives: 1 m The Bernoulli equation gives: Derivation of the Bernoulli equation gives: 2 Equation 1 and 2 combined gives: Free Vortex 2 1 Inlet angle to the stay vanes ii cmcm cucu Plate turbine Find the meridonial velocity from continuity: B R0R0 Find the tangential velocity: ByBy R0R0 R Example ByBy Flow RateQ=1,0m 3 /s VelocityC=10 m/s Height B y =0,2m RadiusR 0 =0,8m Find:L 1, L 2, L 3 and L 4 L1L1 C L3L3 L2L2 L4L4 R0R0 R Example ByBy Flow RateQ=1,0m 3 /s VelocityC=10 m/s Height B y =0,2m RadiusR 0 =0,8m L1L1 C L3L3 L2L2 L4L4 R0R0 R Example ByBy Flow RateQ=1,0m 3 /s VelocityC=10 m/s Height B y =0,2m RadiusR 0 =0,8m We assume C u to be constant along R 0. At =90 o, Q is reduced by 25% L1L1 C L3L3 L2L2 L4L4 R0R0 R Example ByBy Flow RateQ=0,75m 3 /s VelocityC u =12,9 m/s Height B y =0,2m RadiusR 0 =0,8m L1L1 C L3L3 L2L2 L4L4 R0R0 R Example ByBy Flow RateQ=0,75m 3 /s VelocityC u =12,9 m/s Height B y =0,2m RadiusR 0 =0,8m L1L1 C L3L3 L2L2 L4L4 R0R0 R L 2 =0,35m L 3 =0,22m L 4 =0,10m Find the meridonial velocity from continuity: R0R0 B k 1 is a factor that reduce the inlet area due to the stay vanes Find the tangential velocity: Spiral casing design procedure 1.We know the flow rate, Q. 2.Choose a velocity at the upstream section of the spiral casing, C 3.Calculate the cross section at the inlet of the spiral casing: 4.Calculate the velocity C u at the radius R o by using the equation: Spiral casing design procedure 5.Move 20 o downstream the spiral casing and calculate the flow rate: 6.Calculate the new spiral casing radius, r by iteration with the equation: Outlet angle from the stay vanes cmcm cucu Weight of the spiral casing Stay Vanes Number of stay vanes Design of the stay vanes The stay vanes have the main purpose of keeping the spiral casing together Dimensions have to be given due to the stresses in the stay vane The vanes are designed so that the flow is not disturbed by them Flow induced pressure oscillation Where f = frequency [Hz] B = relative frequency to the Von Karman oscillation c = velocity of the water [m/s] t = thickness of the stay vane [m] Where A = relative amplitude to the Von Karman oscillation B = relative frequency to the Von Karman oscillation