Computational Fluid Dynamics – or How to Make a Good Boat Fast David Vacanti The term CFD is showing up more often these days in articles describing the design efforts used tomake Volvo 60 round the world racers and America’s Cup yachts faster. Computational Fluid Dynamics or CFD actually covers a great many engineering specialties and is not the sole domain of boat and ship design. In this article we will review what types of CFD products exist and hopefully provide some understanding of when and how CFD products are best suited to a project. Computational Fluid Dynamics is the application of computers to the modeling of fluid characteristics when either the fluid is in motion or when an object disturbs a fluid. A few examples of a fluid in motion are water or chemical flow in pipes, heating and ventilation systems conducting cooling, heating or fresh air supplies to a building. Fluids in motion also include flame and fire effects in combustion or jet engines. Surprised by these fields of interest? What about examples of an object disturbing a fluid? Examples include stirring paddles submerged in a tank of water and effluent in a waste treatment plant, aircraft of all kinds, cars and trucks at highway or racing speeds and even monohull sailboats, ship, multihull sailboats to name but a few. Obviously, an open mind is important when considering what constitutes a fluid. Fluids can exist in gaseous and liquid states and science has recently found that even some solids can exhibit fluid like characteristics under right conditions. Scientists have found that some of the most spectacular and deadly landslides or rock falls behave as a fluid while the mass of stone and soil or sand is in motion, only to return to a most decidedly solid form when the motion subsides. The general field of fluid dynamics differs from the field of boat design in one critical way. Only boat design deals with a vehicle passing through the two fluids of air and water simultaneously. Our atmosphere is a compressible fluid, though not at yachting or even high-powered boat racing speeds. Air can change in density according to altitude, temperature and humidity. Water is anincompressible fluid that can vary in viscosity according to its salinity and temperature.For most of us, small effects such as variable salinity and temperature are not of concern, but can make the difference between winning and loosing a major international yacht race. How do CFD programs Work? CFD programs are based on the laws of physics, such as the law of conservation of momentum, and special “boundary conditions”. The law of conservation of momentum states
that the total momentum of a system remains constant regardless of how the system may change. A boundary condition limits how and where a fluid can travel. A simple example is that motion of the fluid must emain tangent or parallel to the surface of an object passing through it. Another example is that pressure applied by the fluid against the object must be perpendicular to the surface at all points. These laws and conditions are critical to the development of a CFD program because they allow an aerodynamicist to write equations that describe the system that is being studied. Without the physical laws and boundary conditions there would be no way to write equations that describe fluid motion. The complex equations that result take into account the viscosity, mass and other characteristics of the fluid. The equations are written using integral and differential calculus and require specialized computer techniques to solve them. Typically the programmer writes an algorithm that makes a series of estimates using algorithms that iteratively solve the sets of equations by looking for “balance” in the system of equations. A final answer is obtained when the algorithm converges on a solution with an error that is sufficiently small for the desired accuracy. Once an algorithm has been developed to implement the laws of momentum and boundary conditions, it cannot be applied to the entire surface of the hull and appendages at once. The surface area of the hull, keel and rudder are broken into thousands of small patches (collectively called a mesh) and the algorithm applied to each patch. Each patch in turn influences the fluid flow on the patch area of its neighbors and therefore the solution must account for the conditions surrounding the patch currently being solved. As a result the program must solve and resolve the equations for all of the patches until the solution obeys the physical laws and boundary conditions. Sometimes the complexities of the laws of physics are too difficult to implement all at the same time. As a result the aerodynamicists choose to write programs that make certain limiting assumptions that permit the programming to become more practical and still result in reasonable results. A specific example arises in the case of what actually happens to fluids very near the surface of an object. The boundary layer as it is called experiences shear forces in the objects direction of travel that result in viscous drag. These shear forces are described in a special set of equations called the Navier Stokes relationships. The Navier Stokes equations are sufficiently complex themselves that attempting to include them within every aerodynamics or hydrodynamics program would make the solutions nearly impossible. As a result there are Navier Stokes based programs that specifically address viscous drag and Panel method programs that compute lift,wave drag and induced drag. A complete estimate of the drag encountered by a boat requires the data supplied by both programs.
What do CFD programs Calculate? The most obvious calculation that would be of interest in boat design is the determination of drag forces. But drag comes in several forms that can include, wave, viscous, and induced drag.Therefore, a designer must evaluate the effects of his design in each of these drag areas. The second general area of calculation is lift. The term lift arises from its application to aircraft and becomes a bit confusing when applied to the field of boat design. Lift applies to the forces generated by a keel or centerboard to resist the side force of sails and the driving force of the sails themselves. It also applies to the turning forces of a rudder, and the supportive force acting on “foils” to elevate a hydrofoil sail or powerboat above the water surface. There is also a distinction between 2 and 3 dimensional fluid dynamics analysis. Specifically, there are programs that predict the performance of foils as if they existed on a wing of infinite length.Here the term “foil” is used to define the shape of a keel or rudder along the chord from the leading to the trailing edge. Foil shapes are best known by the alphanumerical names given to them such as NACA 63A012. So a 2D fluids program would compute the lift, drag, velocity distribution,turbulence onset and the generation of bubbles similar to cavitation for a 2D shape such as a wing or keel foil, and would not include any 3D information such as keel span or thickness distribution or the presence of a bulb. A 3D fluids program would compute wave and induced drag from a hull,keel and rudder, including the effects of a bulbed keel carrying winglets. CFD codes are critical for more than optimizing the performance of a top-notch America’s Cup class racing yacht. These codes can be of great value to determine loads placed on boat structures of all types and are invaluable when applied to unique marine structures such as oil platforms that are frequently subjected to the world’s worst storms. Lift and drag effects translate directly into loads that must be sustained by the boat or oil derrick if it is to remain intact in its intended operational conditions. For example, several years ago when the race was known as the Whitbread Round The World Race, many boats developed life threatening hull delamination when subjected to the continuous pounding of high speed downwind surfing and upwind beating. While delamination of a boat at sea is definitely related to structural design errors,those errors were caused by a lack of detailed information about the fluid forces experienced by the boats. Knowledge of these forces would have enabled designers to prevent the hull damage in the first place. Therefore, the potential application of CFD to your design project should depend on whether or not the design regime that your vessel will operate in has well understood engineering data available to prevent hull damage in addition to overall performance of the
vessel. For example, the last few years have seen the development of high-speed hydrofoil sailboats for the consumer market.These top performance boats experience not only significant speeds and loads, but the potential for unstable characteristics could make it highly dangerous to ride in one. However, the judicious use of field-testing and computer analysis has produced a crop of very exciting hydrofoil sport boats that are a joy to fly in. Finally, several years ago a multihull sailboat arrived in port after participating in a trans-Atlantic race. When the centerboards were raised in the outer hulls of the trimaran, the skipper was shocked to learn that the boards had been sheered off just below hull depth and he had not had their use for some indeterminate time during the later portion of the race. Clearly, the structuraldesign of the boards had not taken into account the true forces of lift, drag or perhaps cavitation that would be experienced at sea. CFD programs do not calculate how fast a boat of any type will pass through the water or predict the time to complete a course around the buoys. Predicting speed on a racecourse is the domain of another class of programs called Velocity Prediction Programs or VPP. The VPP makes use of lift and drag numbers calculated in a CFD program to estimate the speed about will sail a course given the sail drive forces and the stability or righting moment of the hull. The VPP is a closed loop simulation continuously varies estimated speed and resulting lift, drag and righting forces until retarding and driving forces are balanced and a stable speed results. A CFD program on the other hand is an open loop simulation that simply states that given an angle of heel and speed for a specified hull and appendage configuration, here are the forces that will result for that instant in time. No consideration is given to how the vessel achieved that speed or sailing condition. In summary then, CFD programs not only calculate lift and drag forces of a hull with appendages,they can also be used to compute pressure loads due to waves and wave impact at speed. The forces of lift, drag and pressure can be translated into structural requirements and provide the means to optimize a hull working in concert with its appendages to produce lift in the most efficient manner possible while satisfying the needs for stability. Predictions of lift and drag at various speeds can be used to develop a mathematical model needed to accurately close the analysis loop of a velocity prediction program. When is a CFD Computer Program Required? CFD codes are not always required or justified however, when simpler means of estimating the forces involved are available. In the case of a typical sailboat design, the forces generated by the keel and rudder can be easily estimated if the keel lacks a bulb and if the keel and rudder shape are essentially straight leading and trailing edges. It is possible to make use of analytical methods that are easily implemented on personal computers. A simple example is
the program I wrote called LOFT that makes use of analytical methods developed by NASA and the US Air Force for initial performance prediction of wing designs. However, while simple programs like LOFT can adequately address typical bulb-less keels and rudders they cannot analyze the performance of an America’s Cup racing keel with bulb and winglets. Only 3D CFD programs can address that complex task. Who can operate a CFD program? While CFD programs can be of tremendous value, getting accurate and meaningful results is not typically within the reach of amateur and many professional boat designers. A degreed Naval Architect or a fluids dynamicist is required to generate the key initial input to a CFD program called a mesh. The mesh is a mathematical description of the hull and appendages that are to be analyzed. It is not sufficient or even possible to use standard stations, waterlines and buttocks as inputs to a CFD program. The detailed shapes of the hull and appendages must be defined by a mesh of square patches that adjoin one another and whose dimensions are chosen according to the local curvature of the hull or appendage or by the occurrence of the intersection of the hull and a keel,rudder or lifting strut of a hydrofoil. The generation of a mesh is a science unto itself and can require iterations by the analysts running successive trials to be sure that the mesh is sufficiently dense in critical areas. Some meshing can be done automatically and then refined by hand. Typically the developers run complex 3D CFD programs or those trained in their use and as result are not really meant for use by the rest of us. However, 2D fluids programs designed for the analysis and development of 2D air or hydrofoil shapes (recall the 63A010 example) are sufficiently easy to use for a designer with basic mathematics skills and general knowledge of airfoil characteristics. Analytical programs such as Vacanti Yacht Design’s FOIL program can aero / hydrofoil lift, drag, turbulence onset and bubble formation characteristics for anyone with basic computer skills and a working knowledge of basic foil design. What CFD Programs Exist? Panel Method and Navier Stokes programs are two general classes of CFD programs that apply to the issues of boat design. The most commonly used and most available are Panel Method programs. Panel methods allow the prediction of wave drag, free surface effects and induced drag due to lift generated by a keel or rudder but they do not account for viscous drag. Programs using panel methods assume that there are only forces normal to the surface of the hull within the fluid.However, due to viscosity, the fluid is subject to forces in shear – more or less parallel to the hull surface that causes turbulence. Therefore the panel programs are referred to as “inviscid” analysis methods. As a result they compute wave and induced drag but not the effects of viscous drag.Viscous drag computations are computed by specialized
codes known as Navier Stokes programs.These programs are difficult to use and apply and are best left to a professional skilled in their use. When a designer has a task that justifies the use of CFD programs, he should be using design tools that that can export true 3D surface shapes in the form of common Computer Aided Design (CAD) file formats. Designing in a typical CAD program such as AutoCAD using lines and polylines, even though in 3D are not sufficient for use with CFD programs. True surface definitions such as Non-Uniform Rational B-spline (NURB) surfaces are required. Most professional versions of the commonly known yacht design programs (AeroHydro, AutoShip, Maxsurf, New Wave,PROLINES) all provide this kind of file exchange. Licensing costs or consulting time is available from the companies or sources listed below. Company Name Aerologic Analytical Methods Inc Fluent South Simulations Vacanti Design Virginia Technical Several University CFD Online Free simple http://www.aoe.vt.edu/aoe/faculty/ Compiler marchman/software programs-Code may be required Very extensive links to http://www.cfd-online.com many suppliers of CFD programs of every possilble type Specialized consulting companies include: Bruce Rosen South Bay Simulations 44 Sumpwams Ave Babylon, NY 11702 631 587 3770, firstname.lastname@example.org
Program(s) Cmarc,Postmarc VSAERO,FSWAVE FLUENT
Wed Address http://www.aerologic.com/dwt.htm l http://www.am-in.com http://www.fluent.com/solutions/m arine/index.htm http://www.panix.com/~brosen http://www.vacantisw.com
Bay SPLASH Yacht FOIL 97
Joe Laisoa Fluid Motion Analysis Consulting, Inc. 3062 Queensberry Dr. Huntingtown, MD 20639, 410 535 0307 X3351, email@example.com Conclusion CFD programs are best applied when there are either significant engineering unknown effects or load levels or where design optimization for a specific application in specific conditions are essential to the goal. For instance, there are many books of scantlings or building standards for typical sailboat or powerboat designs intended for inland cruising. But an attempt at the world record speed sailing at the “ditch” in France at speeds approaching 50 knots clearly calls for specialized analysis to prevent catastrophic failure that could risk lives or incur that last bit of drag that could prevent success in inching the speed record that much higher. Some CFD codes are only usable in the hands of a skilled practioner and others are designed and intended for use by those with reasonable technical skills and willingness to do a bit of reading or research to help them understand the results and limitations of their modeling efforts. CFD and analytical programs are very important to the development of high performance vessels from the perspective of optimization for speed and safety. High speed sailing craft and those destined for offshore use can benefit the most from computer analysis methods. One final key point here is that we have only discussed vessels in displacement mode and have not referred to high performance planning powerboats. The prediction of planning vessel performance is an art unto itself and is the domain of yet another class of programs. I refer those of you who wish to know more about that subject area to research the Society of Naval Architects and Marine Engineers (www.sname.org) web site.
计算流体力学-或怎样做一个又快又好的船 大卫·文森提 CFD 这个词这些天经常出现在文章中,它用来描述如何努力设计来使沃尔沃 60 周游 世界赛车和美洲杯游艇游行地更快。计算流体动力学或 CFD 实际上涵盖了很多了工科领 域，且它也不是船和船舶设计的唯一领域。在本文中，我们将回顾产品存在什么类型的 CFD，并且希望提供一些见解关于 CFD 产品何时以及怎样做最适合应用于一个项目。 计算流体力学是用计算机对正在运动的流体或当一个对象扰乱流体时的特征进行 建模的一个应用程序。几个流体正在运动的例子如水流体，在管道里的化学流体、加热 和通风系统正在进行冷却的流体，加热或新鲜空气正供应于一个建筑的流体。流体运动 还包括火燃烧时对喷气发动机的影响。惊讶于这些领域并感兴趣？ 一个什么样的对象可以扰乱流体？例子包括搅拌棒在水箱里搅拌，废物处理工厂排 出废水，各类飞机、汽车、卡车在高速公路或赛车跑道上行驶，甚至单体帆船、船、多 体船帆船等等，不一而足。 显然，开放性思维是非常重要的，当他在考虑什么构成一个流体时。流体可以存在 于气体和液体状态中，科学最近还发现，甚至一些固体在合适的条件下也可以表现出流 体的特点。科学家们发现，一些最壮观的且致命的山体滑坡或岩石爆布，当它们其中大 规模的石头和土或砂运动时，它们的特征就像流体一样，只有当它们变成最明显的固体 形态时，运动才减弱。 流体动力学的一般领域与船设计领域在一些关键的方法上是不相同的。只有当船的 设计要同时处理空气和水两种流体时才相同。我们的大气层是一个可压缩的流体，尽管 它不是在游艇甚至用来比赛的高性能划船的速度之上。空气可以根据高度、温度和湿度 来改变密度。水是不可压缩流体，它的粘度可根据盐度和温度而改变。盐度和温度的改 变对于我们大多数人来说影响很小，不必担忧，但对于重大的国际帆船竞赛来说，可以 在胜利和失败之间产生很大的作用。 CFD 程序如何工作? CFD 程序是基于物理定律的，比如动量守恒定律和特殊的“边界条件” 。动量守恒定 律，是指不管系统发生怎样的变化，系统表面的总动量保持不变， 。边界条件则限制流 体如何流动以及流到什么地方。一个简单的例子是，运动的流体必须保持切线或平行于 物体表面流动。另一个例子是，压力必须是流体垂直于物体的表面。 这些定律和条件对于 CFD 技术的发展至关重要，因为它们允许一个空气动力学家通 过写方程就可以描述其正在研究的系统。没有这些物理定律和边界条件，他们是不可能 通过写考虑了粘度、质量和其他特性的流体的复杂方程来描述流体的运动的。这些方程
需要积分和微分知识，以及专门的计算机技术来求解。求解的时候一般使用迭代算法来 对方程组进行平衡。得到的最终答案是当方程收敛于错误达到足够小的精度时。 一旦一个算法已用来求解动量定律和边界条件时，它就不能被应用于船体和附件的 整个表面。船体、龙骨和舵的表面分解成成千上万的小补丁（统称为一个网格） ，再把 算法应用到每一个网格上。每一个网格反过来会影响其周围的网格区域内的流体运动， 因此，对网格的求解必须考虑周围的网格。作为一个结果，程序必须解决方程的所有网 格，直到解决方案遵循物理定律和边界条件。 有时候复杂的物理定律在同一时间内难以实现。因此，空气动力学家选择某些限制 的假设条件，这样可以使程序更加实用，也可以导致合理的结果。一个具体的例子是当 离物体的表面很近时流体会突然发生什么情况。在流体移动方向上产生剪切力的边界层 可以对流体产生粘性阻力。这些剪切力在一组特殊的方程中被描述为纳维-斯托克斯关 系。纳维-斯托克斯方程是如此的复杂，以至于它解决试图包括每一个空气动力学和流 体动力学的问题几乎是不可能的。因此，出现了一些以纳维-斯托克斯为基础的地址粘 性阻力程序和计算升力、波阻力和诱导阻力的面板方法程序。当对整条船所遇到的阻力 进行估计时须提供这两个程序的数据。 CFD 程序怎么算? 在船的设计中最明显的且最感兴趣的计算是如何决定阻力。但阻力有几种形式，可 以包括波阻力、粘性阻力和诱导阻力。因此，设计师必须评估他的设计在每一个阻力领 域内的影响。第二个一般计算领域是升力。术语升力源自于对飞机的应用，但当应用于 船的设计领域时变得有点让人摸不着头脑。升力也适用于由龙骨或活动船板抵制侧向力 和驱动力时的帆船本身。它还适用于船舵的旋转，它所受的力量可以用来提升一个水翼 帆或机动船高于水面。 还有一个2维和3维流体力学分析的区别。具体来说，有预测阻力性能的程序就像存 在一个有无限长度的翼。这里的术语“阻力”用来定义龙骨或舵的形状沿弦从导致机翼 后援的力。阻力最为人所熟悉的字母数字名字是给他们命名为 NACA 63A012。所以一个 2D 流体程序将计算升力、阻力、速度分布，出现的湍流，和与翼或龙骨箔的2D 形状相 似的泡沫，但并不包括如龙骨跨度或厚度分布或一个灯泡的任何3D 信息。一个3D 流体 程序将计算波浪和来自船体、龙骨和舵的诱导阻力，其中包括一个球状龙骨由于携带翼 的影响。 CFD 代码对于一个一流的美洲杯赛车游艇的性能优化是很重要的，这些代码对于确 定放在各种结构类型的船上的负载具有很大的价值，但应用到独特的海洋结构如石油平 台就没有啥价值了，因为它们经常受到世界上最严重的风暴的影响。 升力和阻力的影响直接转化为负载，必须靠船或井架在其预期的操作条件下依然保 持完好无损。例如，几年前当比赛被称为惠特布莱德环球竞赛时，许多船体在经受连续 高速重击和殴打时严重威胁生命。而把一艘船分层设计在海上是绝对的结构设计错误，
这些错误是由于缺乏详细的对船所经受的流体影响的信息。这些阻力的知识可以使设计 师设计的船体避免损坏。 因此，CFD 的潜在应用是你设计项目时应该十分清楚船的所有工程数据，这样才可 以防止船体损坏。 例如， 在过去的几年里我们见证了高速水翼帆船在消费市场里的发展。 这些顶级性能船尽管具有显著的速度和负载，但潜在的不稳定性可能使它变得非常危 险。然而，明智地使用实地测试和计算机分析可以产生一批非常激动人心的能快乐飞行 的游艇。 最后，几年前一个多体船帆船抵达港口后参与了一个跨大西洋的比赛。当活动龙骨 板从三体帆船的船体外升起时， 船长才惊讶的发现那些木板已经从低于船体深度的地方 躲开了，在以后的部分比赛中，他对在一些不确定的时间里并没有使用它们。显然，船 体的结构设计并未考虑到升力、阻力或将在海上经历的空穴现象的真正力量。 CFD 程序不计算任何类型的船通过水面时有多快或预测完成一条路线的时间。在赛 马场上预测速度是另一个称为速度预测程序或 VPP 的领域。VPP 在 CFD 程序中通过充分 利用数字来计算升力和阻力，因而可以给帆船评估速度。VPP 是一个闭环仿真程序，它 可以对不断变化的情况进行速度评估。但 CFD 程序只是一个开环仿真程序，它只有在给 定一个倾斜角和速度的条件下才可以说明船体和附件配置的位置，且它的结果也只是瞬 时的，对船舶在一定条件和速度下如何航行没有给予充分考虑。 总结一下，CFD 程序不仅可以计算船体的升力和阻力的力量，而且它们也可以被用 来计算在波速度的影响下的压力。升力、阻力和压力的力量大小可以作为成结构设计的 要求，通过它们提供手段可以用来优化一个船体，这样它就可以在最有效的方式下产生 升力，同时满足稳定的需要。升力和阻力在不同的速度下的预测可以用来开发一个数学 模型，这样可以准确的关闭速度预测程序的分析循环。 什么时候是一个 CFD 电脑程序必需的 CFD 代码并不总是必需的或合理的， 然而， 当估算涉及力量的简单方法时是可用的。 在一个典型的帆船设计中， 当龙骨没有球部且龙骨和舵的形状基本上是直导和尾随边缘 时， 龙骨和舵所产生的动力很容易地被估算。 在个人电脑上充分利用分析方法是可能的。 一个简单的例子是我写的一个叫 LOFT 的程序，她充分利用美国国家航空航天局和美国 空军研制的对翼设计所采用的首次性能预测分析方法。然而，尽管像 LOFT 这样的简单 程序可以充分解决典型的球部很少的龙骨和方向舵问题，但他们不能分析参加美洲杯比 赛的有球部和小翼的龙骨的性能问题。只有三维 CFD 程序才可以解决这些复杂的任务。 谁能操作 CFD 程序 虽然 CFD 程序具有很大的价值，但获取准确的和有意义的结果通常不是许多业余和 专业的船设计师所能做到的。 一个海军建筑师或流体动力学家对一个称为网格的 CFD 程 序获取关键输入是必要的。网格是一个对船体进行分析的数学描述。它甚至可以使用标 准站、水线和龙骨臀部作为 CFD 程序的输入。船体和它的附件的具体形状必须由一平方
的网格所定义，且这些网格之间彼此邻接，网格的维度是由船体及船体与龙骨、舵或起 支柱作用的水翼的交叉处的曲率所决定的。生成一个网格本身就是一门科学，它需要进 行连续运行试验的迭代分析以确保在关键领域形成足够致密的网状。有一些网格可以自 动完成，然后由人工确认。通常，由开发人员运行复杂的三维 CFD 程序，且这些开发人 员必须经过训练，因此，这些复杂的三维 CFD 程序对于我们其他人来说是很难使用的。 然而， 一个只掌握了基本数学技能和机翼特性常识的设计师就可以很方便的使用二维流 体程序来分析和发展二维空气或水翼形状（见63A010例子） 。如文森提游艇设计的箔项 目分析程序，对于任何一个具有基本的计算机技能和基本箔设计的工作知识的人来说， 都可以很容易的了解航空或水翼的升力、阻力、湍流和泡沫的形成特点。 CFD 程序存在什么 面板程序和纳维-斯托克斯程序是适用于船设计问题的两类基本CFD程序。最常用的 和最可用的是面板方法程序。面板方法可以预测波阻、自由表面效应和由于龙骨或舵产 生升力时的诱导阻力，但它不能计算粘性阻力。使用面板方法程序是因为假设在流体状 态下只有船体的表面存在力。然而，由于粘度，流体受剪切力的影响--在平行于船体表 面流体或多或少的会引起动荡。因此，面板程序被称为“粘”的分析方法。他们只能计 算不受粘性阻力影响的波阻力和诱导阻力。粘性阻力计算是由称为纳维-斯托克斯的专 业程序完成的。因为这些程序很难使用和应用，所以最好是由专业且熟练的技术人员来 使用。当一个设计师有一个利用CFD程序的任务时，他应该使用由常见的计算机辅助设 计(CAD）的文件格式作为来描绘真实的3D表面形状的设计工具。设计一个典型的CAD程 序如AutoCAD使用线条和折线，即使在3D里也不足以用CFD程序。真正的表面定义如非均 匀有理样条（NURB）表面是必需的。众所周知的游艇设计程序（AeroHydro, AutoShip, Maxsurf, New Wave,PROLINES)的最专业的版本都提供这样的文件交换。许可成本或咨 询时间可以从以下列出的公司或来源得到。 公司名称 航空物流 分析方法公司 Fluent 南湾模拟 文森提游艇设计 弗吉尼亚大学 CFD 在线 程序 Cmarc,Postmarc VSAERO,FSWAVE FLUENT SPLASH FOIL 97 单程序代码编译器 网址 http://www.aerologic.com/dwt .html http://www.am-in.com http://www.fluent.com/soluti ons/marine/index.htm http://www.panix.com/~brosen http://www.vacantisw.com culty/marchman/software
一些可能需要的免费的简 http://www.aoe.vt.edu/aoe/fa 非常广泛的链接到许多能 http://www.cfd-online.com
提供每一种 CFD 程序类型 的供应商 专业咨询公司包括： 布鲁斯·罗森 南湾模拟 44 Sumpwans大街 巴比伦, NY 11702 631 587 3770, firstname.lastname@example.org 乔Laisoa 流体运动分析咨询公司 3062 昆斯伯里博士 Hunting镇, MD 20639, 410 535 0307 X3351, email@example.com 结论 当需要重要的工程未知效果或负载级别时，或在特定条件下对目标至关重要的一个 特定应用程序进行优化设计时，CFD程序是最好的应用。例如，有很多关于典型帆船的 构件尺寸或建筑标准设计的书，或用于内陆巡航的机动船设计的书。但是，当试图挑战 在法国速度航行接近50海里/小时的世界纪录时，就清楚地需要专门的分析来防止导致 生命危险的灾难性故障或避免在接近成功时招致的最后一丁点儿的阻力。 一些CFD代码只适用于一个熟练的实践人员和一些掌握了合理的技术技能并且愿意 做一点阅读或研究来帮助别人理解他们建模工作的结果和限制性因素的人。CFD和分析 程序对于船舶的速度和安全的角度分析的发展是非常重要的。高速的帆船和那些注定海 上使用的船可以最大程度地受益于计算机分析方法。最后，关键的一点是，我们只讨论 了在位移模式下的船舶，但没有提到怎么规划高性能的汽艇。船性能规划的预测本身是 一门艺术，是另一类程序的领域。我建议那些希望知道更多关于这个领域的人去研究造 船工程学会(www.sname.org)网站。