Stability analysis of the Vlugter gate

Abstract

Experiments on the Vlugter gate are executed to clarify uncertainties that resulted from the mathematical modeling of the gate, for mathematical model validation purposes and to investigate the influence of the downstream water level. A Vlugter gate structure was designed for the experiments. The structure had a variable angle from 35 up to 55 degrees. Since it was expected that the mass moment of inertia of the gate is important in resonance phenomenon, the structure was designed so that its mass moment of inertia could be changed without changing the upstream set point or the angle . The hinge design prevented rotation friction to avoid damping of gate oscillations and to simplify the mathematical modeling of the gate (damping caused by rotation friction in the hinge is difficult to quantify). Experiments on the Vlugter gate acting as a Begemann gate (downstream water level well below weir crest) gave results similar to experiments executed by Vlugter on the Begemann gate. But for a angle of 55 degrees and small flow rates the channel-gate system could become unstable. The characteristic resonance frequencies of this behavior are found using a Fourier analysis on the measured data. Using a simple analytical formula for resonance in channel pools, it was found that the frequencies encountered during the experiments could very well represent resonance frequencies of the upstream channel pool. Experiments on the Vlugter gate under submerged flow conditions showed that an increase of the downstream energy head up to a certain limit decreased the upstream energy head. For small flow rates and high downstream energy heads, the upstream energy headcould be decreased below the design water level. This decrease was larger for larger angles. Experiments also showed that the channel-gate system could become unstable for angles of 45 and 55 degrees. These findings are in accordance with those of van Asperen and Riekerk. They concluded that the channel-gate system could become unstable for angles exceeding 35 degrees. A Fourier analysis on the measured data resulted in one dominant frequency that could not be explained by resonance in the upstream or downstream channel pools separately. An explanation of this behavior was in the interaction between the upstream and downstream channel pools when these act as communicating vessels. To gain insight in the unstable channel-gate behavior, steady state and dynamic mathematical models were developed for the Vlugter gate. M.Sc. researcher Hof developed a dynamic mathematical model for the channel system. A frequency analysis of the coupled channel-gate system was executed by linking these dynamic gate- and channel models. The steady state mathematical model of the Vlugter gate acting as a Begemann gate (downstream water level well below the weir crest) was tested for angles of 35, 45 and 55 degrees. The model gave quite accurate results for flow rates up to 60% of the maximum discharge. The steady state mathematical model of the Vlugter gate operating under high downstream water levels was tested for a angle of 35 degrees. The model gave quite accurate results for flow rates up to 54% of the maximum discharge. An explicit conclusion on the state (stable/unstable) of the coupled channel-gate system could not be drawn from the dynamic mathematical models, because the channel resonance peaks are overestimated. The coupled channel-gate system could be unstable according to these dynamical models, where it was stable during the experiments. A simplified stability criterium was derived for the channel-gate system. This criterium is used to gain insight in the stability issue. Situations where oscillations were encountered during the experiments were compared to stable ones. Using the criterium and the developed mathematical models it could be seen why the channel-gate