Combination of mathematical and hydraulic modeling methods when analyzing unsteady regimes in canals

Conclusions

In a hydraulic substantiation of the designs of channels conveying water to the intakes of diversion hydrostations and having a considerable length and headworks regulation at a gated intake, satisfactory results can be obtained from the combined use of mathematical and hydraulic models.

The final goal of using the mathematical model is to check, on the basis of the allowable values of the hydraulic parameters at control sections, the design proposals on selecting the canal cross sections and to find the optimal agreement of the schedules of operating the intake gates with the operating regimes of the turbines, i.e., to develop the basic principles for creating an appropriate automatic control system. For this purpose a model of unsteady flow based on one-dimensional Saint Venant equations is sufficient.

The hydraulic model of the part of the channel length adjacent to the hydrostation intake or to the headworks intake makes it possible to analyze the initial period of development of unsteady flow during starting and stopping of the turbines with the characteristic undular oscillation of the wave front characteristic for positive surges and to reveal both the three-dimensional character of the wave itself and the effect on it of the three-dimensional forms of the transition structures; plunge pool, stilling basin, etc.

The extreme hydraulic characteristics are determined by the data of both models. As shown for the sample of investigating a diversion channel, the maximum elevation of the level upon stopping the turbines and simultaneous lowering of the gates can be observed either at the time of motion of the undular front of the wave (and then it is recorded on the hydraulic model) or considerably later — at the time of arrival of a wave of the opposite sign at the given control section (and then the data on the increase in the average level on the hydraulic model are extrapolated to the corresponding time determined on the mathematical model). A preliminary estimation of the maximum elevation of the crest of the undular surge above the initial level can be given on the basis of the experimental relations presented in this article.