Design of stay vanes and spiral casing Revelstoke, CANADA

Guri-2, VENEZUELA

Aguila, ARGENTINA

Sauchelle-Huebra, SPAIN

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: m 1

The Bernoulli equation gives: Derivation of the Bernoulli equation gives: 2

Equation 1 and 2 combined gives: Free Vortex

Inlet angle to the stay vanes cm ai cu

Plate turbine

Find the meridonial velocity from continuity: B

Find the tangential velocity: R0 R By

Example C L4 Flow Rate Q = 1,0 m3/s Velocity C = 10 m/s Height By = 0,2 m Radius R0 = 0,8 m Find: L1, L2, L3 and L4 L1 q L3 R0 R L2 By

Example C L4 Flow Rate Q = 1,0 m3/s Velocity C = 10 m/s Height By = 0,2 m Radius R0 = 0,8 m L1 q L3 R0 R L2 By

Example C L4 Flow Rate Q = 1,0 m3/s Velocity C = 10 m/s Height By = 0,2 m Radius R0 = 0,8 m We assume Cu to be constant along R0. At q=90o, Q is reduced by 25% L1 q L3 R0 R L2 By

Example C L4 Flow Rate Q = 0,75 m3/s Velocity Cu = 12,9 m/s Height By = 0,2 m Radius R0 = 0,8 m L1 q L3 R0 R L2 By

Example C L4 Flow Rate Q = 0,75 m3/s Velocity Cu = 12,9 m/s Height By = 0,2 m Radius R0 = 0,8 m L1 q L3 R0 R L2 L2 = 0,35 m L3 = 0,22 m L4 = 0,10 m By

Find the meridonial velocity from continuity: B k1 is a factor that reduce the inlet area due to the stay vanes

Find the tangential velocity:

Spiral casing design procedure We know the flow rate, Q. Choose a velocity at the upstream section of the spiral casing, C Calculate the cross section at the inlet of the spiral casing: Calculate the velocity Cu at the radius Ro by using the equation:

Spiral casing design procedure Move 20o downstream the spiral casing and calculate the flow rate: Calculate the new spiral casing radius, r by iteration with the equation:

Outlet angle from the stay vanes cm a cu

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