基于傅汝德-克雷洛夫力非线性法的规则波浪中船舶运动数学模型

为准确预报规则波浪中船舶的运动, 提出基于四叉树划分的自适应网格法, 以生成船舶瞬时湿表面, 在船舶瞬时湿表面上计算傅汝德-克雷洛夫(F-K)力与静恢复力; 对于与波面相交的面元, 由于F-K力在波面处剧烈波动, 采用四叉树划分法进一步细分面元; 基于线性理论, 采用瞬时自由面格林函数在船舶平均湿表面上计算扰动力; 为避免瞬时自由面格林函数在自由液面处剧烈波动产生严重数值误差, 舍去扰动势所满足边界积分方程中的水线项, 并对迎浪前进速度为傅汝德数0.2的WigleyⅠ型船舶进行数值计算。计算结果表明: 对低于瞬时波面以下的船体部分, F-K力非线性法所需面元数更少, 为细网格法的1/4~1/8;除不规则频率外, 舍去与未舍去水线项所得水动力系数与试验值的相对误差分别小于33.4%、54.8%, 因此, 舍去水线项所得水动力系数更接近试验结果; 当入射波波幅为0.018 m, 波长与船长比为1.25时, 采用F-K力非线性法与线性法所得纵摇幅值响应因子的计算结果分别比试验值低3.2%、17.0%, 波长与船长比为2.00时, 采用F-K力非线性法与线性法所得纵摇幅值响应因子的计算结果分别比试验值低6.7%、13.5%, 可见, 采用F-K力非线性法能够准确地仿真规则波浪中船舶的运动。 

Mathematical model of ship motions in regular waves based on Froude-Krylov force nonlinear method

To accurately predict the ship motions in regular waves, the adaptive mesh method based on the quad-tree division was proposed to generate the instantaneous wet hull surface. The Froude-Krylov(F-K) force and hydrostatic restoring force were calculated on the instantaneous wet hull surface. For the F-K force fluctuating violently at the wave profile, the quad-tree division method was adopted to further divide the panels interacted with the wave profile. Based on the linear theory, the perturbation forces were calculated on the mean wet hull surface by using the instantaneous free surface Green function. To avoid the serious numerical error caused by the violent fluctuation of instantaneous free surface Green function near the free liquid surface, the waterline integral term of boundary integral equation satisfied by the perturbation potential was excluded. The numerical computation was carried out for the Wigley Ⅰ hull with a forward speed against waves at a Froude number of 0.2. Calculation result shows that for the hull under the instantaneous wave profile, the quantity of panel required by the F-K force nonlinear method is less, being 1/4-1/8 of the fine mesh method. Except for irregular frequencies, the relative errors of hydrodynamic coefficients obtained by the methods with and without waterline term are less than 33.4% and 54.8%, respectively, comparing with the experimental result. Therefore, the hydrodynamic coefficient computational result obtained with the waterline term is closer to the experimental result. When the incident wave amplitude is 0.018 m, and the ratio of wave length to ship length is 1.25, the pitch response amplitude operators obtained by the F-K force nonlinear method and the linear method are 3.2% and 17.0%, respectively, lower than the experimental value. When the ratio of wave length to ship length is 2.00, the pitch response amplitude operators obtained by the F-K force nonlinear method and the linear method are 6.7% and 13.5%, respectively, lower than the experimental value. Thus, the F-K force nonlinear method can accurately simulate the ship motions in regular waves.