题目：高速排水型船
姓名： 学号：
摘要：
船舶的阻力主要由粘性阻力和兴波阻力两部分组成。对于给定航速，粘性 阻力与船舶湿表面面积成正比，但船体湿表面面积受到设计用途和船型参数的 限制不易改变或改变不大，而在一定的弗汝德数范围内，兴波阻力对船型的变 化相当敏感，如适当的修改船体型线，可使兴波阻力显著降低m。因此，用理 论的、实验的以及计算的手段探讨兴波阻力的机理，预估实船的兴波阻力，并 以此改造优良的船型，一直是船舶阻力和性能研究的中心的内容之一。
Abstract：
The ship's resistance is mainly composed of viscous resistance and wave resistance of two parts. For a given speed, viscosity resistance is proportional to the ship wet surface area, but the ship wet surface area is limited to the design purpose and ship type parameter is not easy to change or change is not big, and within a certain range of the RuDe number, the wave-making resistance of ship form is quite sensitive, such as the appropriate modification hull lines, can significantly reduce the wave-making resistance m. , therefore, the use of theory, experiment and calculation method to explore the mechanism of the wave resistance, estimate the testing result of the wave resistance, and excellent form, has always been the center of the ship resistance and performance study of one of the content.
船舶的大型化、高速化是现代水路交通发展的趋势背景： 之一，这是运输业追求 高效率的必然结果。近年来，国内外越来越多的人关注高速船舶产生的尾浪， 高 尾浪不但可能危及水岸附近的人的生命，也会对近岸建筑以及附近的其他船 舶产生安全威胁，同时高 尾浪也会侵蚀堤岸，产生环境危害。如何降低高速
船 的尾浪，已成为船舶工程界及航运部门关注的焦
点之一。航行尾浪小或船行波 波能小己成为限制水 域中高速船舶或大型船舶能够正常营运的必要条件。一方 面，作为追求经济效率必然结果的船舶大型化、 高速化趋势已对航行安全和生 态环境构成威胁，在限制水域中情况更为严重。另一方面，航区限速等 被动措 施对于大型船舶、高速船舶造成的经济效率下降也更为明显。不少国家的政府 和民间机构曾就 高速船尾浪对近岸的沉积物、水质及生态环境的影 响做过大量 的研究a近年来国外(如澳大利亚、荷兰等国）已开始试验、生产低尾浪低冲刷 的高速双 体、多体客船，国内也有人开始着手对此进行研究。试验方法是一种 可信度较高的解决方法，但试验要 求在相当广阔的水域进行，需要花费大量的 人力和物力。由于在船舶设计阶段难以对其尾浪作较准确 的估计，常规设计通 常对此未予考虑。以数值方法
表达船舶的尾浪，可以在一定精度范围内简单高 效
地获取船舶尾浪的相关属性，为船型设计和船型优化提供理论依据和指导， 有助于改善船舶尾浪造成的严重环境问题，并可为相应的护岸问题研究和生态 环境评估提供必要的科学依据。
高速排水型三体船兴波阻力研究
船舶的阻力主要由粘性阻力和兴波阻力两部分组成。对于给定航速，粘性 阻力与船舶湿表面面积成正比，但船体湿表面面积受到设计用途和船型参数的 限制不易改变或改变不大，而在一定的弗汝德数范围内，兴波阻力对船型的变 化相当敏感，如适当的修改船体型线，可使兴波阻力显著降低m。因此，用理 论的、实验的以及计算的手段探讨兴波阻力的机理，预估实船的兴波阻力，并 以此改造优良的船型，一直是船舶阻力和性能研究的中心内容之一。
近年来，排水型高性能船型的研究趋于活跃，如深V型船、小水线面双体 船以及穿浪双体船等都是研究和实用较多的船型，高速三体船也引起了国内外 广泛的关注。高速三体船水下部分由一个中体(主船体)和两个小侧体(辅船体) 组成，三个船体均为细长片体，中体比普通单体船更加瘦长a/5大约在12到 18之间），侧体排水量不超过中体排水量的10%,连接桥将侧体与中体连接成 一体。
与其它高性能船相比，三体船的研究起步较晚，但三体船具有一系列更为 突出的优点，主要表现在以下几个方面：
(1) 消波性能
三体船最大的特点是消波性能好。在航行时，从首部进入通道内的气流和 水流被限制在两个船体之间，很少自横向溢出和飞溅，气水混合通过船底滑行 船尾冲出。因此船尾波明显下降，在高速时，尤为明显。常规滑行艇、常规单 体船和三体船相比，常规滑行艇无消波作用，兴波很大，常规高速单体船只能 消除一小部分波浪，而三体船不仅兴波小，消波的功能优于前两种船型，而且 耐波性亦好。这一优点不仅改善快速性，提高运输效率而且明显减少波浪对河 岸的冲刷以及。
(2) 宽敞的甲板面积和良好的安全性
三体船甲板宽敞，可为旅客提供较大的人均面积和活动场所。由于船宽较 大，复原力矩大、稳性好、储备浮力大，破舱后不会翻船、沉船危险，抗沉性
1
增加了航道中船员和人员的安全性好。三体船具有三个滑行支撑面，航行时航向稳定性好。
(3) 较好的舒适性和灵活的操纵性
三体船高速航行时，有较好的髙速流动动力性能，波浪中抨击小，垂向加 速度可望减小。由于进入通道内的高速气流喷向船尾，增加了空气的润滑作用， 因此，载逆风航行时，风浪中失速亦小。另外，桨距和舵距较大，舵效好，操 纵性能得到明显改善。三体船在高速回转时仅需4.5-5.5倍船长，而常规滑行艇 需要8-12倍船长。在极低速度下，利用螺旋桨正反转，基本上可实现原地回转。
(4) 优良的耐波性
该船型也具有优良的耐波性，尤其是可避免双体船的“扭摇”（横摇与纵摇 的耦合摇摆)与“急摇”（短周期的横摇)，并可明显减小纵摇和升沉。
(5) 良好的经济性
由于三体船具有良好的阻力性能，在航速相当的情况下，三体船比常规单 体船可较多降低主机功率。在航速相当的情况下，三体船可节约较多的燃油消 耗。
《方尾图谱》重分析与范围扩展
2.1原苏联《方尾图谱》
原方尾图谱是由现代驱逐舰船模实验得到的。与水池拖曳实验结果相比较用该图谱进行高速船
的阻力估算，误差一般在5%以下。方尾图谱基准船
型的横剖面图如图l所示。基准船型的剩余阻力图
谱一共有9幅，对应Fr=0.30~0.70不同的傅汝德数。
其中=0.45的一幅曲线如图2所示。图谱的棱形系
数和修长系数范围分别为Cp=0.58~0.67和！=7.0~
8.5。基准船型的方尾特征参数：尾收缩度
1《方尾图谱》基准船型横剖面 Fig.l Transverse section of norm transom ships
图
bB
，
[2
4]
1/3
阻力等资料,的分析比较时发现，在较高的速度和较高的修长系数！=L/!>O.8O的情况下，原方尾 图谱给出的剩余阻力结果偏高，如图2中虚线所示为有人修正后的结果。同时由于高速排水型船舶航 速的进一步提高，原图谱的傅汝德数范围与长度排水量系数！范围均已不能满足现代船舶设计的 要求。本文作者在对原方尾图谱进行重分析的基础上，综合分析和参考了 MO3、MO7、MO8、M1O、M13、 M15等修长系数！>O.8O以上的系列方尾模型阻力试验数据'并换算到基准模型，以合理地修正原 方尾图谱高速段和修长度高端的剩余阻力值，并向外延伸了图谱的修长度！和傅汝德数fr。新方尾 图谱！=5.O~1.O，Cp=O.58~O.67和=O.3O~1.OO的应用范围，既可适用于
图2方尾基准船型fr=O.45的剩余阻力系数曲线
Fig.2 Norm diagram of residual resistance of transom ships at F,=O.45
基准船型的剩余阻力系数CrO电子图表简化成为和！的函数，即 C. O=/(\"r；!)Cp = O.65 棱形系数&不再是新方尾图谱基准阻力曲线的变化参数，但Cp不同于Cp=O.65时对于剩余阻力 的影响是用基尔斯影响系数曲线'即
65
〜销)'0%，〇.)
来进行修正的。重分析后新方尾图谱的基准船型阻力数据再现曲线如图3所示。 3方尾特征参数0、!/\"和\"/#对剩余阻力的修正
仅由尾板宽度不同于基准值b/B=O.6时，对剩余阻力修正系数为Kb/B=Cr\"/B $CrO\"/B=图4。 O.6 )，见
0.
30 0.40 0.50 0.60 0.70 0.80 0.90
图3重分析后的方尾图谱基准阻力数据曲线 Fig.3 Norm diagram of residual resistance of weightiness analysis transom ships
0.
0.4 0.7
图4修正系数Kb/B fig.4 The cOrrected parameter
3 0.6
0.5
Fr
仅由尾板底斜升角！不同于基准值！=9。时，对剩余阻力的修正系数为&!\"&0!=9。)，见 图5。
0.3 0.4 0.5 0.6
Fr
0.7
图5修正系数％
Fig.5 The corrected parameter
仅由宽吃水比不同于基准值B/T=3.0时，对剩余阻力的修正系数为KB/T=Ct!W\"CT0!W=3.0 )，见
图6。
图6修正系数KB/T
Fig.6 The corrected parameter KBIT
显然，当船型参数为1/B=0.6，B/^3.0，，8=9°基准值时，剩余阻力修正系数
K
b/B=KB/T=K!=1.〇
I /B# BW和！值为任意时，共同对剩余阻力的影响结果为 Cr=Kb/BKB/iK$Cr〇
由于电子计算技术的发展，上述估算过程已毋须再由繁复的手工查图谱和计算来完成。重分析后 新方尾图谱的基准图谱和各影响系数曲线均转化处理为电子图表数据，以
便于用MicrosoftExcel计
算，集成编写方尾船型的快速性预报程序。在作快速性计算时，除了输入船型方案的主尺度与方尾船 型特征参数外，尚需输入主机功率、转速、齿轮箱速比等参数（本文从略），MicrosoftExcel即可自动执行 电子图表程序计算，实时输出与显示计算结果，包括给出完整的阻力曲线、螺旋桨主要参数、能达到的 航速等快速性计算结果。过去原图谱只能进行手工计算，算一条阻力曲线至少需要l~2天的时间，若 计算和比较几组船型方案的快速性则更为困难。改进后的电子数据程序图表使计算效率大大提高，精 度也明显高于手算，同时减小了计算差错率。新方法的电子数据程序图表，适应数字化船舶设计模式 的要求，特别适合对多组设计方案的快速性进行比较计算，其功效和优势更为明显。 较
以某驱逐舰模型M07为算例，其主要参数
[2]
见表1。
表1 M07模型的主要船型参数 Tab.1 Themainship-formparametersofmodelM07
水线长1 设计吃水： 方形系数： 最大横剖面系数：
尾板底部横向斜升角1 Lm=3.00m dm=0.0949m Cb=0.493 CM=0.806 !=4.50
水线宽： 排水量： 棱形系数： 相对尾板宽度：
Bm=0.3l24m !m=0.04397t C； =0.608 bm/Bm=O.84
-6— M07 istffi „„■■■ M07iiW
图7 MO7驱逐舰剩余阻力系数Cr计算值与试验结果比较 Fig.7 Comparison of calculation and experiment results of residual resistance coefficient of MO7 destroyer
[2]
驱逐舰MO7模型的剩余阻力系数见表2，本文新方尾图谱方法的计算结果与中国船舶科学研究 中心的试验结果相当吻合，如图7所示。 5结论
(1)重分析后的单体排水型方尾船图谱的长度排水量系数和航速范围更宽，电子阻力数据不仅 适合高速普通单体船的阻力预报，也适合现代高双速船舶的阻力估算。
表2 M07模型的剩余阻力系数 Tab.2 ResidualresistancecoefficientofmodelM07
0.20 0.22 0.24 0.26 0.28 0.30 0.32 Cr 0.97 1.01 1.06 1.14 1.22 1.25 1.2 0.34 0.36 0.38 0.40 0.42 0.44 0.46 Cr 1.2 1.32 1.59 1.91 2.19 2.43 2.58 0.48 0.50 0.52 0.54 0.56 0.58 0.60 Cr 2.65 2.66 2.64 2.6 2.53 2.45 2.37 0.62 0.64 0.66 0.68 0.70
Cr 2.3 2.23 2.15 2.08 2.01 (2) 整个计算过程直接使用MicrosoftExcel,电子图表方法更适合进行船舶不同尺度方
案的快速 性比较与最佳方案的选取，以及确定高速单体船或高速双体船的总阻力与有效功率曲线，以及所能达 到的航速。
(3) 实际算例与船模试验结果比较表明，本方法是一种实用、高效、灵活、便捷与可靠的计算方 法。其他任何新老形式的阻力图谱都可以适用这种方法进行更新和改造。
(4) 本文方法的普遍意义在于可以激活大量经典的快速性图谱（包括阻力图谱和螺旋桨图谱等） 这些宝贵技术存量资源，实现计算机自动查值计算，扩大计算机辅助船舶设计快速性软件功能的多样 性和增强快速性预报的可靠性与精确性，进一步开发和创造传统阻力图谱的工程应用价值。
数值研究
假定一刚性船体在无限深的理想、不可
压缩的静止流体中以速度 f = (t/Q，o,o)作匀速直线运动。如图2-1取随船运动坐标系U = o平面为未扰动 自由面)，则对于此坐标系，流动为定常。设流动无旋，则存在速度势将总速度势分解为扰动势与来流势即有y =
船舶兴波速度势应满足如下之Laplace方程：
vV = °, z<^{x,y)
自由面形状为：z = <(x，_y)
求解此定常的兴波问题需满足如下各个边界条件:
(2_1)
V v^-vc-t/〇c-^=〇 ^ z=ax,y) i(V^-V^) + ^-L/0^=0, z = i；(x,y) (2-3) (2-4) lim(p=〇 ’ (2-5) 此外，对于稳态船波问题还需要满足辐射条件，即远前方无波条件，条件(2-6) 是无穷远处的自然边界条件，并非辐射条件。 由自由面运动学边界条件(2-3)与动力学边界条件(24)可得如下耦合的线 性化自由面边界条件： = ^(x,y) ^+^=°z 为波数。 式中…壺 由以上方程及相应的边界条件构成的定解问题又称为Neumann-Kelvin问 题。 8 (2-7) 波高< 可由如下线性化的自由面动力学条件求得： (2-8) 2.3船体兴波速度势的表达 2. 3.1 Rankine源法基本方程 本文采用以Rankine源作为Green函数的方法求解船舶兴波。以Rankine源 法作为Green函数求解一般三维物体势流的数值计算，是航空界从20世纪50 年代末、60年代初开始的面元法。1977年后，该方法通过Dowson引入船舶界， 并成为求解船体在静水中航行兴波问题的主流方法。 Rankine源方法Green函数简单，相比Kelvin源方法，虽仅自动满足无处边界条件(2-6)，但易于推广到非线性问题，计算量小。取Laplace方程(2-1) 的基本解(?(/?，^) = 1/4；^(；>,^)作为格林函数，；7为场点，9为源点，/*(/^)为源 点与场点的距离。 船体兴波问题属于无升力问题，采用常用的源汇分布法，直接在船体、自 由面等边界面上布置源汇即可，流场中任何一点的扰动速度势即可求出： f| 3(!ldS (2-9) 5 ^r{p,q) 式中： 其中，上角标为s表示船体表面的有关物理量，/表示自由面有关物理量。由物 面边界条件 (2-2)可以得到积分方程为： g(g) 2 s (2-11) 将式(2-9)和式(2-10)代入式(2-7),可得线性自由面边界条件: 由上可知，只要求得布置在各边界面上奇点的强度1(〖），即可求得流场中 各点的速度势。基于NURBS高阶面元法与一般的低阶面元法和高阶面元法不一 样，在布置源强时，不再将船体划分为一块块的面元，并在每个面元上布置源 汇，而是把船体当做一整块面，其源强也是当成一整块，未知的是整个源强“面” 的控制顶点，布置配置点满足边界条件，即可求出控制顶点，从而求得源强， 从而解决问题。 2.3.2自由面奇点上置 将原本应该布置于自由面面元上的奇点(对船舶兴波问题通常是源汇)置于 自由面上方一定的距离，这种方法最初被引入的目的或许是便于采用“配置点 移动”法数值满足辐射条件。Raven™、Nakos[2l]和高高[22]M先后对自由面奇点 上置的误差、稳定性等问题作了深入的研究。有关研究发现：该方法可以明显 减少离散带來的数值色散误差、提高计算精度。奇点上置的髙度一般取1-3倍的 纵向网格距离为好，既可减少色散误差又不至于使最终求解方程系数矩阵的性 态恶化。 2. 3. 3辐射条件的满足 船舶兴波计算中所谓的“辐射条件”，即为满足远前方无波的条件。Rankine 源不像Kelvin源自动满足辐射条件，所以在具体的计算中，常常采用某些数值 手段以保证辐射条件的满足。对于辐射条件的满足，存在诸多不同的方法。具 体包括不直接引入数值粘性和直接引入数值粘性两大类。本文采用了配置点移 动的方法，将自由面上置的源点与自由面相应的配置点交错一个纵向网格间距， (相当于将配置点向上游移动一个纵向网格间距)，使得辐射条件较好的得到满 足。 参考文献： 1 高速排水型三体船兴波阻力数值计算 2 高速双体船的水动力特征研究 3 高速细长体理论在双体船运动计算中的应用 4 排水型高速船舶尾浪的数值研究 5 预报现代高速排水型船舶阻力性能的新型方尾图谱(1) 6 高速排水型船的运动性能预报 7 高速排水型船支架空化观测 8 排水型船横摇阻尼的理论和试验研究 9 高速排水型舰船加装尾板的节能机理 10 单螺旋桨排水型船的前后体型线设计 Title：High speed semi-displacement vessel Name：Zhang Yitan Number：1340110126 Abstract： Trimarans have many advantages in performances and open up a vast range of prospects for applications. The research on them becomes more active and has made progress recent years. One of the key problems in the hull design and optimization is how to forecast the ship resistance quickly and accurately. With the development of computational fluid dynamics and computer technology, the forecasting precision of ship resistance has increased. The numerical calculation of wave resistance by a raised panel method based on NURBS (Non- Unifonn Rational B-Splines) for high speed ships is discussed, and numerical examples of the wave-making problem for trimarans is presented. This is a high-precision and the generalized high-order panel method. The body surface, free surface and every physical quantities to be solved are expressed as a whole nth-order continuous s urface, or several surfaces if needed, in this method. It is of better numerical characters than conventional panel methods. Raised panels above the free surface combined with collocation-point shifting up-stream are used to satisfy the radiation condition numerically. Full paper： The ship's resistance is mainly composed of viscous resistance and wave resistance of two parts. For a given speed, the viscous resistance is proportional to the ship wet surface area, but the ship wet surface area is limited to the design purpose and ship type parameter is not easy to change or change is not big, and within a certain range of the RuDe number, the wave-making resistance of ship form is quite sensitive, such as the appropriate modification hull lines, can significantly reduce the wave-making resistance m. , therefore, the use of theory, experiment and calculation method to explore the mechanism of the wave resistance, estimate the testing result of the wave resistance, and excellent form, has always been one of the center of the ship resistance and performance research content. In recent years, the displacement of high-performance ship form studies tend to be more active, such as deep V type of ship, wave of catamaran and wear small waterplane area twin hull ships are more research and practical type, such as high-speed trimaran also caused wide attention both at home and abroad. High-speed trimaran underwater by a middle body (main body) and two small side body (auxiliary hull), three are long and thin strip, hull body is more slender than ordinary monohull a / 5 between 12 to 18), lateral displacement does not exceed 10% of the middle body displacement body, connecting bridge connect the side of the body and absorbing into one [2]. Compared with other high performance ship, research of trimaran starts relatively late, but trimaran has a series of more prominent advantages, mainly manifested in the following aspects: (1) wave elimination performance The greatest characteristic of trimaran is absorbing performance is good. In, from the first into the air and water are limited within the channel between two hull, rarely from lateral overflow and splash, mixed gas water slide through the bottom Rushed out of the stern. So the stern wave decreases obviously, at high speed, especially. Conventional glider, compared to conventional single hull and trimaran, regular glider no wave action, wave is very large, conventional high-speed single ships can remove a small part of the wave, and trimaran small wave, not only the function of the wave is superior to the former two kinds of ship type, and wave resistance is also good. The advantages of not only improve the quickness, improve transport efficiency and significantly reduce the waves on the shore of the river erosion and increase the safety of the crew and staff in the channel. (2) the spacious deck area and good security Trimaran spacious deck, can provide larger area per capita and activity places. Restoring moment, because of the large beam is big, good stability and reserve buoyancy, no damage after a vessel capsized, danger, heavy resistance 1 Wuhan university of science and a master's degree thesis Good. Trimaran has three sliding bearing surface, while sailing course stability is good. (3) good comfort and flexible maneuverability Trimaran high-speed, good dynamic performance high speed flow, wave attack small, vertical speed is expected to decrease. Due to enter the channel of high-speed airflow spray to the stern and increased the air lubrication, therefore, load sailed against the wind, the wind and waves in the stall is also small. In addition, the pitch and rudder is bigger, good steering, longitudinal performance is improved significantly. Trimaran in high-speed rotation only 4.5 to 5.5 times the captain, and regular glider need 8 to 12 times the captain. At very low speed, the use of propeller and reversing, basically can be realized in situ rotation. (4) excellent seakeeping The ship also has excellent seakeeping, especially can avoid catamaran torsional wave \"(roll and pitch of coupling swing) and\" shake \"(short cycle rolling), and can obviously reduce the pitch and heave. (5) a good economy Because the trimaran has good resistance performance, under the condition of the speed quite, compared to the conventional single trimaran The ship can more reduce the host power. Under the condition of the speed quite, trimaran can save more fuel consumption. The wave-making resistance of the current research status of numerical calculation method Put forward the famous idea of ship resistance in the 19th century Froude divided assume that laid the foundation of modern theories of ship resistance [4]. He also built the world's first ship model towing tank, actual and feasible model is given a testing result of the conversion method. He will ship total resistance can be divided into two parts, viscous resistance and residual resistance assumes that both each other. Viscous resistance is determined by \"a tablet\mainly the wave-making resistance of residual resistance to compare rates. Using the modern theory of ship resistance, the division is not strict, calculate method is not perfect. However, the contemporary theory of ship resistance is still within this framework. Because of the viscous drag force and the hull is proportional to the wet surface, and hull wet surface area is difficult to change, unless the surface of the conventional, measures, viscous resistance is difficult to reduce. And the wave-making resistance obviously along with the change of Froude number, the wave-making resistance force curve convex and concave, within a certain range of Froude number, sensitive to the change of ship wave making resistance. If the appropriate change form, it is possible to reduce the wave-making resistance significantly. Therefore, study the mechanism of the wave resistance, test method and the calculation method of wave resistance, accurate prediction of the testing result of wave-making resistance, 3 To guide the ship design, has been the core issue of ship resistance research. Now popular at home and abroad the wave-making resistance of potential flow calculation is based on the boundary element method. In a uniform flow as the basic flow of the linear wave theory, such as michelle integral method, the new theory of slender, Noblesse Neumann - Kelvin problems such as the use of green's function is the so-called mobile xing waves (also called Kelvin source or Havelock source), it is a fundamental solution of Laplace equation, linear free surface condition and the radiation of the parts, only need to move the xing waves distribution profile or objects in the object's surface, does not need to be decorated at the boundary of the flow field of wave source. But compared with the test result is found from the result of calculation, the calculation method is only applicable to thin ship and simple mathematical form, get the wave-making resistance curve only in medium and high speed close to experimental results, the low Froude number is not desirable. For obese type, because there is no guarantee that linear free surface condition, the calculation results are not ideal. The likelihood - Gilloton and Dowson [5] for the thin ship theory, put forward the weakly nonlinear theory, under certain conditions and the influence of some nonlinear term, weak nonlinear theory is always in a certain basic flow of perturbation, thin ship theory, the basic flow is uniform uniform flow requirements relative to the uniform flow The disturbance is small. The basic flow of the method, by contrast, Dawson is the stack mold flow around hull, the hull waterline For solid surface, according to the image method of fluid mechanics, ideas on the water surface, based on the principles of symmetry plays back a ship model, in the \"whole space\" to solve free surface, the flow of fluid around pile modulus, the flow dynamic can accurately meet the surface conditions, including the tail end of the first, this avoids the original theory of thin ship first disturbance not small problems. Assumes that the hull wave relative to the stack mold flow is small, more natural, the corresponding free surface condition can also be linearized. As a limiting case, speed is zero, fold mode solution is accurate solution, low speed and remember and wave, Dawson method is reasonable, to fold the mold flow around as the basic flow is one of the characteristics of Dawson method. Dawson method is another characteristic is the basic source of the Rankine source for the green's function, the source function is very simple, it besides Laplace equation, other conditions can not meet the needs of any specific, such as free surface condition, radiation condition, water conditions, etc., and all that is based on Laplace party control equation of the problem, both steady and unsteady problems, linear or nonlinear problems can use it, which makes the nonlinear wave resistance to be calculated. Phase than Kelvin source method, also need not be complicated oscillation points, To solve problems of wave drag surface conditions. The fully nonlinear theory must meet the following conditions [6] : free surface condition including all of the nonlinear term; Free surface conditions set on the real freedom; Hull surface conditions should meet in an actual ship wet surface. To consider while sailing trim and heave of absence made on the wave-making resistance. To deal with the transom. Nonlinear wave resistance calculation there are two main methods: time step-by-step method and constant iterative method, for calculation of wave resistance often adopt constant iterative method. On the basis of the linear wave resistance calculation, and the influence of nonlinear free surface, will obtain the linear solution as the basic flow, a new perturbation, relative to the new basic flow make the free boundary conditions on the surface of the linearization, and satisfied, on the surface of the newfound freedom in accordance with the time and so on, until completely satisfy nonlinear free surface conditions, each iteration are suitable for the new wave, mesh back into line. The calculation on the free distribution of non-point source distance and the distribution of the non-point source from the surface descend within a surface, the method of improved discrete calculation error. Although it's theory of convergence has not been proved, but has been confirmed by many computing practice, and for all receive by the wave resistance calculation of researchers, is currently one of the most widely This paper studies the main content of the main content and innovation 1.3.1 In this paper, based on national 863 project \"key techniques of high-speed trimaran\means of numerical calculation, the technology route and verified with the experimental data for the research combining numerical calculation and experimental data. Big part of the work, this article is based on Visual c + + software program, to hull modeling, numerical computation and graphical calculation results. In this paper, based on the NURBS surface of generalized high order element method numerical calculation the wave-making problem of high-speed displacement trimaran, its main content is as follows: (1) this paper introduces the basic principle of NURBS, NURBS curve curved surface are calculated by use of a more efficient algorithm, the method of using masked hull surface modeling. 5 (2) of the ship wave making problem the corresponding mathematical model is established, based on the Rankine source method are discussed emphatically the basic principle of solving the wave-making problem of ship, gives a method to satisfy the radiation condition, and the transom boundary conditions and the processing of the shallow water boundary conditions were discussed. (3) is deduced based on NURBS generalized higher-order panel method to calculate the ship's mathematical expression, the wave-making problem and calculate the monomer, catamaran, and transom boundary condition and boundary of the shallow water wave resistance of ships and wave shape. (4) simply discusses the trimaran in domestic and overseas research situation and results of calculating the Wigley trimaran and other mathematical form of wave drag and wave shape, forecast the transom trimaran wave-making resistance. (5) of this article summarizes the research work, analyzes the shortcomings, this paper studies also for more further research in the future. determination of NURBS node vector Node vector is one of the important parameters of NURBS decision, how to select is a vital problem. Normally we have focused on two aspects: first, the heavy node (i.e., nodes overlap) problem; The second is a node interval length distribution. In order to study the effect of heavy node of NURBS, here give a concept: first we call r nodes in sequence of coincidence for the degree of the nodes can be reused r r heavy or the node (1 g). Heavy node to the influence of NURBS is mainly the following several aspects: (1) the use of heavy node can produce sharp point and Angle on the NURBS. Many ship form with Angle, for example, using the node method, a NURBS surface will be used to express hull, don't block 9 Wuhan university of science and a master's degree thesis To represent. (2) when the NURBS curve surface domain with k (curve surface for k times, similarly hereinafter) heavy node, then the curve surface interpolation points corresponding control vertex overlap. (3) when the endpoint is k + 1 time node, the nature of the endpoint and k times bezier curve surface properties are the same. So easy to curve surface has better control endpoint behavior. To the problem of node interval length usually can be divided into homogeneous, uniform and non-uniform. Vector in (1) uniform node along the parameters for the uniform shaft or equidistant distribution, all nodes interval length is constant. Although uniform node vector calculation and simple and convenient handling, but there is no retain bezier curve surface endpoint endpoint in nature, at the end of the first (surface corresponding boundary) epidemic and control vertices. Less so in practice Use. (2) vector quasi homogeneous node degree of two endpoints can be reused in k + 1, while the rest of the node length is evenly distributed. In calculation and processing, than uniform node vector is more complex, but the bezier endpoint geometry. (3) the non-uniform node vector also has two endpoints repeatability (k + 1, but in the other node length is not evenly distributed. The value of the node length within a certain good is directly related to the formation of NURBS quality, this is one of the difficult points of NURBS curve surface. Therefore, many scholars put forward all kinds of methods, such as Riesenfeld method, Hartley - Judd method, etc., in the actual design, can according to different mood Condition was chosen. 2 _2. 3 NURBS curves and fast calculation NURBS curve surface is generated, a large number of numerical calculations involved in the design of dynamic, especially when the curve of large curved surface or shape is complex, must use a lot of control vertices to describe, microcomputer limited memory resources and slow speed makes such surface modelling design to become a big problem. Fortunately, however In a normal curve and curved surface building usually adopt surface twice or three times a NURBS curve, because the order number is lower, so you can calculate all the (3.2), the expression into the twice or three times a number type. For a given node vector, the basic properties of b-spline basis function local support (NURBS), the quadratic b-spline basis function only three nonzero continuous basis function, namely % a. a. _22, And M, 2 (M), and three times the b-spline basis function only four non-zero continuous basis function, namely the % _3 > 2 (M), & (2200), and then got the formulas below. The masked method introduction With above through the given data dot matrix inversion control vertex curved surface interpolation, masked method is to generate a bunch of curve surface. This method is traditionally known as the \"loft\ Through the generation of surface were used. Skin, in short, the task is to give a bunch of cross section curve of skeleton cast a layer of smooth skin. The masked method usually used in interactive CAD system. In order to make the masked method become a useful method in interactive CAD application, face how to solve the cross section curve in 3 d space interaction problem. Fortunately, many CAD application permits the cross section curve on the flat surface curve is used for the description of the initial model, the aim is mainly makes the definition and the dimensions of the interaction of surface Reduced from 3 d object space to two dimensional screen plane. Thus it can be finished in the same display plane into the design of the cross section curve. Then use a so-called ridge line guide section curve transformation to the three dimensional space. Next, in turn, generate the cross section curve interpolation curved surface. The following specific masked method the process of generating b-spline surfaces. 1. The design of cross section curve Because all cross section curve is a plane curve, can design plane which shows the plane coordinate system Righteousness all curves. Can be implemented as follows: (1) the initial generation of cross section curve of the b-spline curve is adopted, and the node number vector is not necessarily the same. (2) the number of unified, usually will increase frequency curve of low order method and unified to the highest number of times. (3) domain parameter transformation, make all the section curve of a unified domain. (4) insert node, each cross section curve node vector into the other section curve node values by different nodes in the vector. Insert node yes all cross section curve is the result of the unified node vector. 2. Design ridges Ridge line is to control the surface longitudinal lines, either for plane curve can also be used for 3 d B spline curve, parameterized ridge line should correspond to the section curve of vertical distribution. Can the number of ridges and cross section curve of order is the same, can also be different 3. The transform section curve to the three dimensional space Taken by through translation, rotation section curve points and the target point in three-dimensional space, and the osculating plane perpendicular to the ridge line. According to the B spline curve surface geometric invariance, all of the translation, rotation change only in to operate the control vertices can be. 4. The generated surface Using described above B spline surface is calculated, it can be obtained by the above each of the cross section of b-spline control vertices back calculation of b-spline surface control vertices. 2.3.2 hull fitting Most of hull surface for free-form surface, can't use a simple analytical expression, how to use mathematical method to express the more reasonable ship surface shape, is particularly important. The hull surface Computer three-dimensional modeling, in addition to the function of visual display and demo, the final purpose is to hope to be able to realize of surface ship design, performance analysis and hull hull surface building automation, so as to improve the design quality and production quality, shorten the production cycle, ultimately achieve the goal of improve business efficiency. After mathematical expression and the hull surface with the aid of a computer can solve the problem of a large number of practical applications, such as hydrostatic calculation, hydrodynamic calculation, structure design and production design, etc. [12]. Hull surface geometry representation usually can be divided into two categories [13] : (1) curve method. Curve method is composed of a set according to the change regularity of parallel plane curve as a ship body surface, expressed by the curve equations. Plane curve (such as cross-cutting line, line) and polynomial function is often adopted by the polynomial chain, trigonometric functions and other transcendental function. Because the curve method is to use a certain function to the table Lines, compared to express lines in spline, its inflection point in the control line number, inflection point position, piece rate changes evenly and UV, etc is easy to control. In recent years, there are still some scholars expression of hull surface is studied in this way. (2) the surface method. Surface method with curved surface equation to describe the hull surface directly. Need according to the calculation of mathematical surface modeling tools, to determine the hull surface subdivision. If using the Bezier surface, need to ship body surface is divided into a few pieces surface, then according to the position successive, tangent plane continuity conditions of joining together and get the hull surface. If using the method of b-spline and NURBS method, the hull surface does not need to shard. Today, the NURBS method as used for curve surface description of the most popular technology, it is very proper expression of hull surface. Hull design is often given in section type value, therefore take masked method described above to hull surface fitting is suitable for [14, 15]. Can be used for convenience, the section curve of hull transverse profile, but masked method need cross section curve has the same number, the same node vector and the parameters of the same domain, in the design of transverse profile Waiting to meet. Described above if taken up order and unity of node vector method, which will result in cross section curve integral is too close, not only increase the storage space, and waste of time, so must use other ways to solve this problem. This article adopt the cross section curve reconstruction means more satisfactorily solves this problem. Specific method is to use the same number, the same node vector and the parameters of the same domain of b-spline curve fitting again cross section curve, which saves a lot of trouble. In general, the transverse profile of the curvature is not large, in not much control point can be well fit the original cross section curve. It is important to note that when calculated by the new cross section curve, satisfy the equation of uniform length direction along the original cross section curve usually select a better fitting effect, in some cases, may along the vertical uniform selection. For a simple form, by this method is very effective. Due to the transverse profile (cross section curve) perpendicular to the horizontal plane, and there is no bend, ridge line desirable level straight line, therefore, from stem to stern. 因篇幅问题不能全部显示，请点此查看更多更全内容