Abstract
One of the main sources of vibration in Francis turbines is thought to be pressure-wave disturbances generated from the impeller and interference impulses between impeller vanes and guide vanes.
A theory is developed which explains the occurrence of severe vibrations caused by the elasticity of the water as a resonance phenomenon between the disturbing impulses and normal modes of vibration in the space between the impeller and the guide wheel.
The wave propagation in the fluid, which is assumed to be uniform with no steady flow, is thought to satisfy the well-known sound-wave differential equation without any damping effects. The natural frequencies for one- and two-dimensional pressure-wave oscillations are calculated.
The calculations, based on prior knowledge of the velocity of sound-wave propagation, show that a simple theory of one-dimensional oscillations interpreted as rotating sound waves in the annular space is sufficient to predict critical speeds of the turbine.
Measurements carried out on a laboratory model Francis turbine for a head of 4.5 m and a capacity of about 1.0 m3/s confirmed the presence of free oscillations and indicated the occurrence of a resonance phenomenon in the annular space.
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