基于三维时域Green函数法的船舶在规则波浪中的运动数学模型

在小时间区域采用级数展开法, 在大时间区域采用渐进展开法, 在大、小时间过渡区域采用精细积分法, 对三维时域Green函数进行数值计算; 采用线性叠加原理求解船舶辐射与绕射问题, 构造出船舶在规则波浪中的运动数学模型, 并采用数值方法计算WigleyⅠ型船舶和S60型船舶以Froude数为0.2迎波浪航行时的水动力系数、波浪激励力与运动时间历程。计算结果表明: 由于不规则频率的影响, 当量纲一频率为1.7时, WigleyⅠ型船舶的垂荡附加质量计算结果比试验结果小44%, 当量纲一频率为2.5时, S60型船舶的纵摇阻尼系数计算结果比试验结果小43%;随着入射波频率的增加, WigleyⅠ型船舶和S60型船舶的水动力系数和波浪激励力的大部分计算结果与试验结果的相对误差小于30%, 且二者的变化趋势一致; 对于WigleyⅠ型船舶, 当波长与船长比为1.25时, 采用三维时域方法计算的垂荡幅值响应因子和纵摇幅值响应因子分别比试验值小11.3%和4.8%, 采用三维频域方法计算的垂荡幅值响应因子比试验值大48.4%, 纵摇幅值响应因子比试验值小48.4%, 当波长与船长比为1.50时, 采用三维时域方法计算的垂荡幅值响应因子和纵摇幅值响应因子分别比试验值小3.0%和11.3%, 采用三维频域方法计算的垂荡幅值响应因子比试验值大9.8%, 纵摇幅值响应因子比试验值小23.6%。可见, 采用三维时域方法能准确地仿真船舶在波浪中的运动时间历程。 

Mathematical model of ship motion in regular wave based on three-dimensional time-domain Green function method

The series expansion method was adopted in the short time interval region, the asymptotic expansion method was adopted in the long time interval region, and the precise integration method was adopted in the transitional region between the short and long time interval regions to numerically calculate the three-dimensional time-domain Green function. The radiation and diffraction problems of ship were solved by the linear superposition principle. The ship motion mathematical model in regular wave was formulated. The hydrodynamic coefficients, wave exciting forces and motion time histories of a Wigley Ⅰ hull and a S60 hull were calculated by the numerical method when they sail on the wave with a Froude number of 0.2. Calculation result shows that due to the influence of irregular frequencies, when the dimensionless frequency is 1.7, the numerical result of heave added mass of Wigley Ⅰ hull is 44% smaller than the test result. When the dimensionless frequency is 2.5, the numerical result of pitch damping coefficient of S60 hull is 43% smaller than the test result. As the incident wave frequency increases, for a Wigley Ⅰ hull and a S60 hull, the relative errors of hydrodynamic coefficients and wave exciting forces between most of the numerical results and the test results are less than 30%, and the two have a same variation trend. For a Wigley Ⅰ hull, when the ratio of wave length to ship length is 1.25, the heave response amplitude operator and the pitch response amplitude operator calculated by the three-dimensional time-domain method are 11.3% and 4.8% smaller than the test values, respectively, the heave response amplitude operator calculated by the three-dimensional frequency-domain method is 48.4% larger than the test value, and the pitch response amplitude operator is 48.4% smaller than the test value. When the ratio of wave length to ship length is 1.50, the heave response amplitude operator and the pitch response amplitude operator calculated by the three-dimensional time-domain method are 3.0% and 11.3% smaller than the test values, respectively, the heave response amplitude operator calculated by the three-dimensional frequency-domain method is 9.8% larger than the test value, and the pitch response amplitude operator is 23.6% smaller than the test value. Thus, the three-dimensional time-domain method can accurately simulate the time history of ship motion in wave.