强耦合流激振动的建模及求解的预测多修正算法

MODELING OF STRONGLY COUPLED FLOW-INDUCED VIBRATION AND SOLVING METHOD ON PREDICTOR MULTI-CORRECTOR ALGORITHM

将基于Lagrangian描述的结构振动问题与基于Eulerian描述的不可压缩粘性流动问题通过流-固系统的功率耗散平衡在广义变分原理的框架下统一,建立了描述强耦合流激振动的有限元控制方程。采用将Newmark法和Hughes预测多修正法相结合的求解策略,提出了基于稳定有限元法求解小变形弹性结构强耦合流激振动的计算方法,用于计算复杂边界条件下的流激振动问题。以三维混流式水轮机叶道为例的数值算例表明,模拟结果与试验实测结果吻合较好。

To describe strongly coupled flow-induced vibration of a slender structure in incompressible viscous flow,this paper establishes Lagrangian-Eulerian formulations based on a generalized variational principle of coupling fluid and solid dynamics with power dissipative balance. The formulations are discretized spatially into multi-linear interpolating functions in the finite element method for fluid and solid structure. Hughes＇ predictor multi-corrector algorithm for flow and Newmark＇s method for vibration are monolithically combined to construct a stabilized computational method of solving the strongly coupled flow-induced vibration with complex geometry. A three-dimensional hydro turbine blade passage is taken as a numerical example to validate the method proposed in this paper. Good agreement between simulations and measurements of the pressure and vibration acceleration indicates that the method is appropriate to analyze the flow-induced vibration of a structure with complex geometry.