On the Stability Models for the Surge Tanks in Hydraulic Plants

Since the work of Allievi on water hammer and the thesis of D. Thoma on surge tanks at the beginning of the XXth century, the stability analysis of the surge tanks has become a permanent task in hydraulic engineering. A possible explanation might be as follows. The surge tank is a control and feedback stabilizing construction for water hammer and a simple engineering philosophy states that a stabilizer has to be stable itself in order to avoid e.g. ignition of self sustained oscillations in the feedback system.The standard model for stability studies of the surge tanks is a nonlinear system of ordinary differential equations obtained under the assumption of lumped parameters and of the inference of a constant flow load resulting from the neglecting the load dynamics. Here we start from the standard model with distributed parameters and obtain a more complete model resulting from the time scale analysis and from the reduction of certain distributed parameters to lumped ones. For the model with lumped parameters we focus on the stability by the first approximation which is considered beyond the common model for surge tank stability studies.