规则波中船舶Froude-Krylov力的解析积分计算

Evaluation of a Ship’s Froude-Krylov Forces Using Analytical Integration in Regular Waves

Froude-Krylov力是船舶航行中所受的主要作用力,对Froude-Krylov力的精确计算尤为重要.将船体平均湿表面划分为一定数量的四边形平面面元,在每个面元局部坐标系内,对四边形平面面元的边长坐标进行参数化处理.对于给定的线性入射波波高函数,基于格林定理,推导了Froude-Krylov力在平面面元上的解析压力积分表达式,避免由于数值积分方法计算Froude-Krylov力产生的误差的同时,船体所需划分的面元数量大大减少.研究了水深在不同波长及浪向角下对船体所受Froude-Krylov力的影响,并进一步基于线性时域理论,对绕射力采用三维时域格林函数法进行计算.对具有前进速度的WigleyⅠ型船进行仿真,计算结果表明:水深大于船长的一半时,船体所受的Froude-Krylov力逐渐接近于无限水深所受的Froude-Krylov力;水深无限时,作用在船体上的波浪激励力计算结果与试验值在大部分频率范围内吻合较好.因此,由解析压力积分求取Froude-Krylov力的算法有效性得到验证.

Froude-Krylov(F-K)forces are the main forces acting on a ship’s hull;thus,calculating the F-K forces is crucial.The mean wetted hull surface is discretized into a number of quadrilateral panels,and the coordinates of each side of the quadrilateral panel are parameterized in each local panel coordinate reference.For a given function of linear incident wave elevation,the F-K forces are evaluated exactly on each quadrilateral panel using analytical formulations on the basis of Green’s theorem.Thus,the computational errors of F-K forces are avoided owing to numerical integration methods,and the number of quadrilateral panels required to discretize a ship’s hull is greatly reduced.The influences of water depth on F-K forces acting on the ship’s hull are studied under different incident wavelengths and wave angles.Based on linear theory,the diffraction forces are solved by three-dimensional timedomain Green function.Simulations are conducted for WigleyⅠhull with forward speed.The computational results indicate that the F-K forces acting on the ship’s hull closely approach the indefinite water depth cases when the water depth is larger than half of the ship’s length.When water depth is indefinite,the wave exciting forces acting on the ship’s hull agree well with experimental results in the definitive range of frequency.Thus,the algorithms for F-K force evaluations using analytical pressure integration formulation can be validated.