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1、基于二次流能量法的最小阻力船型研究张 宝 吉（上海海事大学，上海 201308）摘要：船体尾部流场速度场的横向和垂向分量是导致粘性阻力增加的根本原因，为了获得最小总阻力船型，以船体尾部区域为优化设计对象，以YZ方向的二次流能量最小为目标函数，以样条函数的参数为设计变量，在保证排水量为基本约束条件下，根据实际情况附加其它约束条件来控制尾部形状的变化，采用非线性规划法进行优化设计。通过集装箱船的优化算例，证实了采用该方法进行船型阻力优化的可靠性。关键词：二次流能量；Hess-Smith法；Rankine源法；非线性规划法中图分类号：U661.1 文献标识码：A 文章编号：1005-9962(201
2、0) 02-0021-04Abstract: The transverse and vertical components of the velocity field in the stern area are the prime source of resistance increasing. In order to obtain the minimum resistance hull form, tanking the stern shape as the optimization objective, the energy of secondary flow of the y and z
3、 directions as the objectives function, the parameters of B-spline function as the design variables, the appropriate displacement as the basic constraints and the allowable variation of stem shape as an additional constraint, the design is optimized with nonlinear programming (NLP). The optimization
4、 examples for full-scale container ships are provided, which confirm that the resistance is reduced distinctlyby this optimal design method.Key words: secondary flow energy; Hess-Smith method; Rankine source method; nonlinear programming0 引 言最小阻力船型的确定通常是船舶设计者孜孜以求的目标，而常规的做法是基于兴波阻力理论的船型改型研究，即在保持尾部线型不变
5、的情况下，优化船体首部或前半体形状，这种方法对中高速船型很有效，但对于一些受形状影响较大的中低速肥大船型其效果未必可靠，因为这些船型的粘性阻力在总阻力中占有主要份额，特别是尾部区域1,2。因此，必须从降低粘性阻力的角度去优化此船型，从而达到总阻力最小的目的。近年来，随着计算流体力学（CFD）理论的不断深入发展，采用CFD进行数值模拟和船型优化逐渐成为可能。然而，如果将CFD和最优化技术结合起来进行船型设计需要花费太长的计算时间。众所周知，船舶在运动过程中，尾部区域速度势的横向分量和垂向分量是船体尾部产生压力的根本原因，再加上尾部线型的复杂多变，有时还会产生舭涡和粘性分离现象，导致粘性阻力明显增
6、加，控制尾部流场速度势分量的流向是问题的关键。可以作者简介：张宝吉，男，博士，讲师。1979年生，大连理工大学船舶与海洋结构物体设计制造专业毕业。现主要从事船舶与海洋结构物设计制造研究和从事教学工作。根据叠模流周围的势流解来选择船体尾部的线型。本文在参照文献3，4的基础上，采用非线性规划法，在确保排水量为基本约束条件下，以尾部YZ剖面上的二次流能量最小为目标函数进行优化设计，以此来获得最小阻力船型。1 最小二次流能量法叠模船体坐标系可以表示成图1的形式，轴、轴取在未扰动的静水面上，轴沿着均匀来流指向船尾，轴垂直向上。船尾任意剖面的二次流能量可以定义为下列形式。YUZX图1 叠模坐标系 (1)式
7、中，流体质量密度；叠模速度势。可通过Hess-Smith法和Rankine源法求得。 1) Hess-Smith法5求： 该方程所满足的物面条件如下，即 (3)式中，场点 (x , y, z)与源点之间的距离；叠模船体表面；船体的外法线方向。2) Rankine源法6,7求： (4) 式中，场点 (x , y, z)与源点 (x, y, z)之间的距离； 静止水面。物面条件 (7)自由面条件在上 (8)二次流能量密度可以表示成下列形式，即 (9)2 船型优化数学模型2.1 目标函数以二次流能量密度最小为优化目标，则目标函数可以表达成下列形式： (10)2.2 设计变量和船型修改函数优化设计范围
8、取船体尾部区域，从第0站到第10站，且设计范围的水线处、船底、船尾和船体的端部为固定，如图2所示。A.P.设计变量区域固定不变区域0 1 2 3 4 5 6 7 8 9 10图2 优化设计范围设计船的船型函数可以表达成母型船船型函数和相对于母型船的变化量函数之和的形式8，即 (11) 将沿着型深方向的z固定，这样各单位变化函数只表示x的函数，然后将各单位变化函数多项式沿着x方向展开，即 式中，参数是被展开的各单位变化函数的参数。如果参数给定，则各个单位变换函数的值就能够确定下来，因此各条水线位置沿方向的船宽变化量就可以求出来。其次，已知各水线位置各单位变化函数的值就可以通过3次样条插值函数求出
9、任意水线位置的单位变化函数。这个插值函数是以为基底的函数，沿着型深方向进行插值。 (14)式中，和是标准B-Spline函数，是修改范围内和方向的内部节点（端点除外）的个数，是B-Spline函数的阶数。在这里取=4，3，2以B-Spline函数的参数为设计变量，则设计变量的个数一共是12个，如表1所示。表1 B-Spline函数参数作为设计变量Ciji=1234567j=60.00.00.00.00.00.00.050.00.00.00.00.00.00.040.00.01.01.01.00.00.030.00.01.01.01.00.00.020.00.01.01.01.00.00.010
10、.00.01.01.01.00.00.03 船型优化过程船型优化计算的流程如图3所示，首先输入初始船型型值文件，该文件包括：初始船型主要要素和型值、设计范围、设计变量个数、设计航速、优化计算的初始参数等；通过Rankine源法和Hess-Smith法计算其二次流能量，然后将二次流能量系数作为目标函数并结合基本约束条件，通过NLP法进行优化计算，判断优化结果是否收敛，如果不收敛，则返回初始状态，附加约束条件，重复上面的操作；如果收敛，则优化计算结束，得到最小总阻力船型。母型船Rankine源+Hess-Smith法的势流解目标函数CDJ优化方法（NLP）约束条件附加约束条件最小阻力船型收敛No图
11、3 程序框图4 算 例以908箱集装箱船为例，对其后半体形状进行优化设计。其主要参数如表2所示，选择2种不同的设计方案进行优化计算，如表3所示；优化计算结果汇总于表4；优化过程中的收敛历程如图4所示；优化前后船型的二次流能量系数比较如图5所示；2种方案的优化结果横剖线比较如图6、图7所示。表2 集装箱船主要参数船长/ m型宽/ m设计吃水/ m方形系数傅氏数125.023.45.50.740.24表3 船型优化方案设计方案目标函数设计变量约束条件傅氏数优化范围1（Hess-Smith法求）B-Spline函数参数0.24船体后半体2（Rankine源法求）B-Spline函数参数0.24船体后
12、半体其中：y(i, j)为船体表面坐标值；, 0分别为改良船型和初始船型的排水体积。从优化过程中的收敛记录可以看到，HessSmith法的收敛速度要比Rankine源法快得多，但二次流能量降低程度较低；从图5和表4中也可以看出，在设计航速点，改良船型的二次流能量都有了明显的降低；从优化计算结果的横剖线比较中可以看出改良船型横剖线的变化情况，而且基于Rankine源法的二次流能量优化获得改良船型线型变化趋势更加明显。.W.L 方案2 初始船型 改良船型 .AP.5.55.04.03.02.01.00.0方案1 方案2CDJ/CDJ00 2 4 6 8 10 12 14 16迭代次数1.000.9
13、60.920.880.840.80图4 优化过程中收敛记录母型方案1方案2CDJ1030.0 0.1 0.2 0.3 0.4 0.51.00.90.80.70.60.50.40.30.20.10.0图5 集装箱船分布的比较表4 基于Rankine源法和Hess-Smith法的优化计算结果方案10.961.0021.00120.881.0111.004.W.L 方案1 初始船型 改良船型 .AP.5.55.04.03.02.01.00.0图6 方案1的优化结果横剖线比较4 结 语本文研究了基于二次流能量法的最小阻力船型优化设计，分别把不带有自由面影响的HessSmith法和带有自由面影响的Ran
14、kine源法计算的图7 方案2的优化结果横剖线比较二次流能量作为目标函数，以B-Spline函数的参数为设计变量，在保证必要的排水量为基本约束条件下，再考虑附加约束条件，采用非线性规划法进行优化设计，获得的改良船型降阻效果明显。证实了采用该方法进行船体尾部形状优化的可行性，也可以为船体的整体线型优化设计提供有益的借鉴。由于中高速船型粘性阻力占有很大的比例，对于方形系数在0.70.8左右，在0.20.3之间的较肥大船型采用该方法进行优化效果会更好。为了证实理论优化的可靠性，需要对母型船和改良船型分别做船模试验，来验证该方法的实用性，这些工作有待于今后进一步研究。【 参 考 文 献 】1 王言英，
15、王清霞. 实际流体中船体绕流流场的理论计算J. 大连理工大学学报，1995,35(5): 685-689.2 张怀新，刘应中，缪国平. 带自由面三维船体周围粘性流场的数值模拟J. 上海交通大学学报，2001,35(10): 1429-1432.3 SUZUKI K., KAI H. and KASHIWABARA S. Studies on the optimization of stern hull form based on a potential flow solverJ. Journal of Marine Science and Technology, 2005, 10 (2): 6
16、1-69.4 Asano S. A consideration on the energy of secondary flow around a ship section (in Japanese). J Kansai Soc Nav Archit Jpn,1979,174:6975.5 张宝吉. 船体线型优化设计方法及最小阻力船型研究D. 大连：大连理工大学，2009.6 张宝吉，马 坤，纪卓尚. 基于Rankine 源法的兴波阻力数值计算研究J. 大连理工大学学报，2009，49（6）：872-875.7 Zhang Bao-ji, Ma Kun, Ji Zhuo-shang. The o
17、ptimization study for hull form of minimum wave making resistance based on Rankine source method J. Journal of Hydrodynamics, Ser. B. 2009,21(2):277-284. 8 http:/www.j-Editors note: Judson Jones is a meteorologist, journalist and photographer. He has freelanced with CNN for four years, covering seve
18、re weather from tornadoes to typhoons. Follow him on Twitter: jnjonesjr (CNN) - I will always wonder what it was like to huddle around a shortwave radio and through the crackling static from space hear the faint beeps of the worlds first satellite - Sputnik. I also missed watching Neil Armstrong ste
19、p foot on the moon and the first space shuttle take off for the stars. Those events were way before my time.As a kid, I was fascinated with what goes on in the sky, and when NASA pulled the plug on the shuttle program I was heartbroken. Yet the privatized space race has renewed my childhood dreams t
20、o reach for the stars.As a meteorologist, Ive still seen many important weather and space events, but right now, if you were sitting next to me, youd hear my foot tapping rapidly under my desk. Im anxious for the next one: a space capsule hanging from a crane in the New Mexico desert.Its like the se
21、t for a George Lucas movie floating to the edge of space.You and I will have the chance to watch a man take a leap into an unimaginable free fall from the edge of space - live.The (lack of) air up there Watch man jump from 96,000 feet Tuesday, I sat at work glued to the live stream of the Red Bull S
22、tratos Mission. I watched the balloons positioned at different altitudes in the sky to test the winds, knowing that if they would just line up in a vertical straight line we would be go for launch.I feel this mission was created for me because I am also a journalist and a photographer, but above all
23、 I live for taking a leap of faith - the feeling of pushing the envelope into uncharted territory.The guy who is going to do this, Felix Baumgartner, must have that same feeling, at a level I will never reach. However, it did not stop me from feeling his pain when a gust of swirling wind kicked up a
24、nd twisted the partially filled balloon that would take him to the upper end of our atmosphere. As soon as the 40-acre balloon, with skin no thicker than a dry cleaning bag, scraped the ground I knew it was over.How claustrophobia almost grounded supersonic skydiverWith each twist, you could see the
25、 wrinkles of disappointment on the face of the current record holder and capcom (capsule communications), Col. Joe Kittinger. He hung his head low in mission control as he told Baumgartner the disappointing news: Mission aborted.The supersonic descent could happen as early as Sunday.The weather play
26、s an important role in this mission. Starting at the ground, conditions have to be very calm - winds less than 2 mph, with no precipitation or humidity and limited cloud cover. The balloon, with capsule attached, will move through the lower level of the atmosphere (the troposphere) where our day-to-
27、day weather lives. It will climb higher than the tip of Mount Everest (5.5 miles/8.85 kilometers), drifting even higher than the cruising altitude of commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere. As he crosses the boundary layer (called the tropopause), he can expect a
28、lot of turbulence.The balloon will slowly drift to the edge of space at 120,000 feet (22.7 miles/36.53 kilometers). Here, Fearless Felix will unclip. He will roll back the door.Then, I would assume, he will slowly step out onto something resembling an Olympic diving platform.Below, the Earth becomes
29、 the concrete bottom of a swimming pool that he wants to land on, but not too hard. Still, hell be traveling fast, so despite the distance, it will not be like diving into the deep end of a pool. It will be like he is diving into the shallow end.Skydiver preps for the big jumpWhen he jumps, he is ex
30、pected to reach the speed of sound - 690 mph (1,110 kph) - in less than 40 seconds. Like hitting the top of the water, he will begin to slow as he approaches the more dense air closer to Earth. But this will not be enough to stop him completely.If he goes too fast or spins out of control, he has a s
31、tabilization parachute that can be deployed to slow him down. His team hopes its not needed. Instead, he plans to deploy his 270-square-foot (25-square-meter) main chute at an altitude of around 5,000 feet (1,524 meters).In order to deploy this chute successfully, he will have to slow to 172 mph (27
32、7 kph). He will have a reserve parachute that will open automatically if he loses consciousness at mach speeds.Even if everything goes as planned, it wont. Baumgartner still will free fall at a speed that would cause you and me to pass out, and no parachute is guaranteed to work higher than 25,000 f
33、eet (7,620 meters).It might not be the moon, but Kittinger free fell from 102,800 feet in 1960 - at the dawn of an infamous space race that captured the hearts of many. Baumgartner will attempt to break that record, a feat that boggles the mind. This is one of those monumental moments I will always remember, because there is no way Id miss this.
