Natural mode splitting of a rotating disc in water at different wall distances as a model for high-head francis runners

•Enhanced the analytical model for disc frequency splitting.•Hydraulic damping splits concurrently with frequency.•Damping for both waves increases with rotation speed, especially the forward wave.•Smaller wall distance correlates with increased frequency and damping splitting. Francis turbines are essential equipments in the realm of sustainable energy production. However, their complex dynamics, particularly in the presence of fluid-structure interaction, pose significant challenges to optimising design and enhancing performance. This study focuses on the phenomenon of frequency splitting of a simplified rotating disc submerged in water, serving as a representative model for high-head Francis runners. The primary objective is to gain a deep understanding of how proximity to surrounding walls affects modal parameters of the rotating runner. This research employs both analytical and numerical methods. For cases characterised by significant asymmetry in wall distances on either side of the disc, we have refined the analytical model for frequency splitting based on the assumed mode method and potential flow theory. Additionally, we have developed a numerical model for predicting modal parameters of underwater rotating discs, building upon the imposed modal motion approach. These methods are validated using existing experimental results, demonstrating excellent consistency. The research indicates that for underwater rotating discs, frequency splitting occurs simultaneously with damping splitting. In general, as wall distances decrease, the degree of splitting increases, and the sensitivity of splitting to changes in wall distance also rises. This comprehensive study provides profound insights into the dynamic behavior of high-head Francis runners, highlighting the pivotal role played by wall proximity in shaping their vibrational behavior.