纵摇容器中液体晃荡的非线性数值模拟

Nonlinear numerical simulation of liquid sloshing in a container subjected to pitch excitation

在海洋工程领域,液体晃荡是一种普遍存在的物理现象。对于船舶而言,转动比平动有着更重要的影响。该文针对纵摇容器中的液体晃荡问题,采用高阶边界元方法建立自由水面满足完全非线性边界条件的时域数学模型。通过大地坐标系和随体坐标系之间的坐标变换,使得计算域仅控制在随体坐标系内。求解中采用半混合欧拉—拉格朗日方法追踪流体瞬时水面,运用四阶龙格库塔方法更新下一时间步的波面和速度势。通过与已发表试验和数值结果的对比,验证了建立模型的准确性。进而开展大量数值试验研究容器纵摇运动频率、纵摇转动中心和容器中布置一竖直隔板对晃动波面与荷载的影响。

In the field of marine engineering, liquid sloshing is a kind of universal physical phenomenon.For the ship, the rotation has a more important influence than translation. Therefore, a time-domain numerical model is developed by higher-order boundary element method to solve the liquid sloshing in a tank subjected to pitch motion, in which the fully nonlinear boundary conditions satisfied on the free surface. With the coordinate exchanged between the global and local coordinates, the computational domain can be governed only in the local coordinates. In the solving process, a semi-mixed Eulerian-Lagrangian technique is applied to track the transient free surface and the 4th-order Runge-Kutta method is used to refresh wave elevation and velocity potential on the free surface at each time-step. The proposed numerical model was testified by comparison with the other published experimental and numerical results. On the base of validation, lots of numerical experiments are carried out to investigate the effect of pitch motion frequency, rotational center and a vertical baffle mounted on the container bottom on the sloshing surface and loads on the container.