Simplified Non-Uniform Models for Various Flow Configurations in Open Channels
Résumé
In this paper, simplified models, derived from well-known infinite-dimensional Saint-Venant equations, are proposed to represent transfer functions from boundary discharges to water flow rates or heights at any point between the two boundaries. The approximation procedure enables to catch different flow configurations. Results are shown for three typical open channels: the first one is short with a small slope, the second one is long with a strong slope, and the third one is long with a small slope. A particular emphasis is given to the third case which corresponds to a typical hydroelectric open channel configuration. Frequency responses of the proposed transfer functions are compared to those numerically computed from linearized Saint-Venant equations. The new Integrator-Delay-Zero models obtained from low frequency analysis represent well the system behaviour for the studied frequency range.