摘 要：垂荡板因其具有增大水动力阻尼及附加质量的优点而广泛应用于海洋工程领域。将分形理论应用于垂荡板的结构设计，提出一种具有分形特征孔的垂荡板，运用Fluent的自定义函数并结合动网格技术对不同垂荡板模型进行数值模拟，研究其水动力特性。对比分析了不同振幅下实心、不同分形阶数（透空率）以及规则孔垂荡板的水动力特性，得到了不同垂荡板垂向力时间历程曲线、附加质量系数 Cm 和阻尼系数 Cd 以及涡量云图。结果表明：振动周期不变时，随振幅的增大，各垂荡板Cd值随之减小，最终趋于平稳，而Cm值随之增大；比较不同分形阶数时，Cm 值随分形阶数增加而减小，Cd 值随分形阶数增加而先增大后减小，在分形阶数为二阶时，Cd值最大；相同透空率时，分形孔和规则孔垂荡板Cm值大致相等，分形孔Cd值较规则孔有较大提升，最大提升为17.83%，平均为14.74%。由此可见，较之普通开孔垂荡板，分形特征垂荡板具有优越的性能。

Abstract:The heave plate is widely used in marine engineering field because of its advantages in increasing hydrodynamic damping and additional benefits.In this paper,the fractal theory was applied to the design of the heave plate,and a heave plate with fractal features was proposed.Numerical simulations were carried out for different heave plates,by employing the dynamic mesh method and user defined functions in Fluent.The influences of motion amplitudes,fractal order (void ratio),regular hole and fractal hole on the hydrodynamic performance of the heave plate were analyzed.The time history curve of vertical force,added mass coefficient Cm,damping coefficient Cd and the vortex contours were obtained.The results showed that at a constant vibration period, Cd decreases with the oscillation amplitude,and eventually it flattens out.While Cm increases with the oscillation amplitude.As fractal order increases, Cm decreases ,but Cd increases first and then decreases.,with the maximum at the second fractal order.For a same void ratio, Cm is approximately the same for both fractal pore and regular hole,while Cd increases largely for the fractal pore,,with the maximum increase of 17.83% and average of 14.74%.This indicates that compared to the heave plate with the ordinary opening,the heave plate with the fractal characteristics has better performance.

TK83

国家自然科学基金（51676131，51176129）