Modal analysis of a spinning disk in a dense fluid as a model for high head hydraulic turbines

TL;DR

This paper develops simplified analytical and CFD-based modal analysis methods to predict the dynamic behavior of spinning disks in dense fluids, aiding the design of high head hydraulic turbines by accurately estimating natural frequencies and mode splitting.

Contribution

It introduces a novel simplified modeling approach combining analytical and CFD methods for predicting rotor dynamics in turbines, addressing limitations of existing computationally expensive FSI techniques.

Findings

Both methods predict natural frequency split within 7.9% of experimental data.

The models explain mode split and drift due to added mass dependence on fluid velocity.

The approach provides a practical tool for turbine design and life prediction.

Abstract

In high head Francis turbines and pump-turbines in particular, Rotor Stator Interaction (RSI) is an unavoidable source of excitation that needs to be predicted accurately. Precise knowledge of turbine dynamic characteristics, notably the variation of the rotor natural frequencies with rotation speed and added mass of the surrounding water, is essential to assess potential resonance and resulting amplification of vibrations. In these machines, the disk-like structures of the runner crown and band as well as the head cover and bottom ring give rise to the emergence of diametrical modes and a mode split phenomenon for which no efficient prediction method exists to date. Fully coupled Fluid-Structure Interaction (FSI) methods are too computationally expensive; hence, we seek a simplified modelling tool for the design and the expected-life prediction of these turbines. We present the development of both an analytical modal analysis based on the assumed mode approach and potential flow theory, and a modal force Computational Fluid Dynamics (CFD) approach for rotating disks in dense fluid. Both methods accurately predict the natural frequency split as well as the natural frequency drift within 7.9% of the values measured experimentally. The analytical model explains how mode split and drift are respectively caused by linear and quadratic dependence of the added mass with relative circumferential velocity between flexural waves and fluid rotation.