【摘要】 基于有限差分法对Navier-Stokes方程进行数值离散,建立纵荡与升沉耦合激励下流体晃荡三维数值模型,自由液面采用具有二阶精度的流体体积法进行追踪。基于势流理论推导出纵荡与升沉耦合激励下理想流体晃荡解析解,用于验证已建立的数值模型与响应规律分析。该模型也与文献结果进行对比分析,表明该模型能准确地模拟耦合激励下的非线性晃荡问题。理论与数值结果表明:即使单自由度纵荡与升沉激励无法激发明显的波动,即非共振,当激励频率的和值或差值接近流体系统自然频率时,耦合激励也可以激发共振晃荡波;耦合晃荡波与激励频率的关系也通过两组扫频分析得到。更多还原

【Abstract】 A three-dimensional Navier-Stokes model based on the finite difference method was applied to investigate the coupled surge and heave sloshing, and the free surface was captured by the second-order volume-of-fluid method. Based on the linearized potential theory, an analytical solution for the coupled sloshing was derived and applied to validate the present numerical model as well as analyze the free surface response. Rather good agreement was guaranteed through comparison with the available results in literatures. According to the analytical and numerical results, it can be found that the coupled resonant sloshing is triggered when the sum or difference of the two excitation frequencies is close to the system′s natural frequencies even though any single-degree-of-freedom excitation cannot excite resonant wave motion individually. The relationship between the wave height of the coupled sloshing and excitation frequency is obtained through two groups of sweeping tests.更多还原