Investigation on mode-coupling parametric vibrations and instability of spillway radial gates under hydrodynamic excitation

Abstract

Flow-induced parametric oscillation of the spillway radial gates occurs under hydrodynamic excitation due to flow fluctuation, threatening the hydropower systems’ safety. However, the underlying instability mechanisms of the spillway radial gates are still not clear. In this work, we explore the dynamic instability of spillway radial gates with multiple modes considered during the gate-lifting dynamic process. A numerical method for transferring dynamic instability problem of the gate to the generalized eigenvalue problem is developed by using Galerkin method, Floquet theorem and harmonic balance methods. The results reveal that, the critical gate opening exists during the gate lifting process, and the number and distribution of critical gate openings in dynamic instability regions are the key factors inducing the gate's instability. The presented instability intensity can be used to diagnose the vibration state of the gate. The mode-coupling effect renders the radial gate more dynamically instability, increasing the damping ratio is an effective measure on dynamic instability mitigation. The proposed insights in this work can provide guidelines for evaluating the gate's safety and bring rational decision-making in design and operation stages.