混流式水轮机叶片流激振动机理的数学描述

诱发混流式水轮机水力振动的机理十分复杂，理论上按振因可将其分为湍流激振、涡激振动、流弹性失稳振动、两相流激振以及平均轴向流诱发振动等因素。这些激振因素可能是单项激励诱发振动，也可能是多因素并存而发振。本文在正交流线坐标系中，使用一般壳体理论及任意拉各朗日一欧拉描述(ALE)，建立了描述混流式水轮机叶片流激振动及其稳定性的数学模型，为从理论上深入分析叶片流激振动的机理及振动特性提供一个分析平台。

Mathematical modeling of fluid-induced vibration of Francis hydro turbine blades

Intrinsically, the mechanisms of induced vibration of blades of a large scaled Francis hydro turbine are sophisticated. From theoretical viewpoints, the vibrating factors are categorized into turbulence-induced vibration, vortex-induced vibration, hydro elasticity instability, two phases flow induced vibration, and vibration induced by mean axial flow in the flowing passage etc.. These factors are possibly an evil behind the vibrations in single or in combination forms. Objectives of this paper are to establish a mathematical model expressing the vibrating mechanisms fluid-induced vibrations of blades in various causing factors and to provide analytical fundamentals of the characteristics of the vibration and stability. To do this, the general shell theory and arbitrary Lagrangian-Eulerian (ALE) formulation are applied in an orthogonal streamline coordinate system.