进动圆筒内液体流动不稳定的非线性特征  

NONLINEAR CHARACTERISTICS OF HYDRODYNAMIC INSTABILITY IN A PRECESSING CYLINDER

作　　者：李磊[1] 任业军[1] 蔡斌[1] 王照林[1] 

机构地区：[1]清华大学工程力学系,北京100084

出　　处：《力学学报》2005年第1期64-72,共9页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金(19702022).~~

摘　　要：在建立进动充液圆筒内液体偏差流动方程的基础上，结合液体惯性波和轴向二次流动线性解，通过对定常二次流动的线性稳定性分析，提出了函数空间表达的流动不稳定性非线性分岔分析方程．对非惯性坐标系下液体流动的 Navier-Stokes 方程进行了数值求解，并对惯性波发生破裂(实验提供的3种主模态下得出的共振破裂现象)时的压力时间序列进行分析，得出了液体流动不稳定的基本非线性特征。Based on governing equations of liquid deviated flow in a precessing liquid-filled cylinder,thebifurcation equation in functional space is derived by the linear solutions of liquid inertial wave and axialsecondary flow and linear stability analysis of steady secondary flow.Then,the Navier-Stokes equations ofliquid flow under non-inertial coordinates are directly solved by numerical methods.When inertial wave breaksdown,numerical solutions can also be obtained to reproduce three types resonant breakdown phenomena atprimary mode observed in experiments.The nonlinear time series of average pressure by numerical solutionsof inertial wave's breakdown are analyzed.Some nonlinear characteristics of hydrodynamic instability can bederived by foregoing analysis.

关 键 词：惯性波 轴向二次流动 对称破缺分岔 进动共振失稳 时间序列 自旋充液系统 

分 类 号：O317[理学—一般力学与力学基础]