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1、专业好文档基于叶片弯掠技术的优化设计李杨 欧阳华 杜朝辉（上海交通大学涡轮机实验室，上海200030）(13817108103，)摘要：在三维粘性流场的数值计算程序平台上，利用BP神经网络和遗传算法，通过叶片弯掠技术对一轴流风机的转子叶片的周向弯曲角度进行寻优，以使风扇的气动性能进一步提高。通过对比优化前、后的叶轮发现，优化之后的叶片呈现明显的周向前弯曲特征。测试结果显示，其全压和气动效率分别提高了3.56和1.27，失速裕度大幅度拓宽36以上，上、下端部的损失进一步降低。关键词：周向前弯叶片，人工神经网络，遗传算法，优化设计中图分类号：TH432.1 文献标识码：AOptimization
2、Design Based on Skewed and Swept Blade TechniqueLI Yang OU YANG-Hua DU Zhao-Hui(Turbomachinery Laboratory of Shanghai Jiaotong University, Shanghai 200030, China)Abstract: Based on a program for solving 3D viscous flow fields, an aerodynamic optimization design was conducted to the rotor blade (arch
3、etypal rotor blade) of an axial flow fan with back-propagation neural network and genetic algorithm. By skewed and swept blade technique, the optimized rotor blade having better aerodynamic performance is obtained. The results show that the optimized rotor blade is circumferential forward-skewed bla
4、de. Compared with the archetypal rotor blade, the total pressure rise and the total pressure efficiency of the optimized rotor are increased by 3.56% and 1.27% respectively. Its stall margin is greatly extended by more than 36%. At the same time, the loss in the upper and lower endwalls of the fan i
5、s reduced further.Key words: Circumferential forward-skewed blade; Artificial Neural Network (ANN); Genetic Algorithm (GA); Optimization design1前言随着计算机技术和各种寻优算法的不断发展，在叶轮机械领域，利用某些算法进行叶片的优化设计来提高叶轮的性能已经成为可能。许多学者利用遗传算法、模拟退火法、梯度法、响应面法等对各种叶轮的静子和转子叶型进行了优化设计，结果显示，通过一些优化方法可以进一步地提高叶轮的效率，改善叶片表面的压力分布，降低了边界层的流动损
6、失，同时也缩短了设计周期【17】。然而，当前的优化设计多是针对改进二维叶型，对于能够减小叶轮的内部流动损失、提高气动效率最为重要的手段之一的弯掠叶片技术【810】，在叶片优化计算中应用的公开报告还比较少。本文利用雷诺平均N-S方程组数值计算程序，基于人工神经网络BP算法和遗传算法的数值优化程序，基于叶片弯掠技术对一轴流风扇转子叶片进行了优化设计，通过寻找合适的周向弯曲角度，来获得具有最优气动性能的风扇叶片，并对优化前、后的叶片在叶片形状、气动性能以及出口流场进行了对比分析。2研究模型所研究的原始叶轮是被广泛应用的低压轴流风扇T35系列5号叶轮的改进型。其叶片的重心积迭线由直线段+圆弧段构成，它
7、们的分界点位于0.4倍叶高处。如图1中的曲线ABR，其中AB为直线段，BR为圆弧段。AB与RO的夹角约为1.27。其叶片可以近似看作径向叶片。原始叶轮的主要设计参数见文献【11】。图1 原始叶片与优化叶片积迭线形状的比较Fig.1 Stacking line shape comparison between archetypal rotor blade and optimal rotor blade3网格划分和计算方法本次优化过程中的网格划分、流场计算以及后处理是利用Numeca公司的CFD软件完成的。在叶轮流场的优化计算中，对原始叶轮采用结构化网格。计算网格分别位于叶片主流区和顶部间隙区，如
8、图2。由于I型网格受到叶片形状的影响较大，进而影响优化过程中数据库样本，因此，主流区只采用H型网格。主流区网格点数分布为：主流方向叶展方向跨叶片方向=1297365，顶部间隙区采用H型网格加O型网格，网格点数为651713和1611313，即在叶顶间隙高度方向和叶片厚度方向分别取13个点。1. 轮毂 2. 叶轮出口 3. 外罩 4. 叶片 5. 周期性边界 6. 叶轮进口 7. 叶顶间隙图2 计算网格Fig.2 Computational mesh由于在建立数据库过程中，设计变量是在上、下限之间随机选取的，因此，如果网格质量不高，很容易出现负网格，从而影响整个优化的顺利进行。本次优化过程的网格
9、质量较高，如网格的最小夹角超过了20，在优化过程中未出现负网格。计算流场为三维不可压缩粘性流动，采用时间平均法求解控制方程组加湍流方程的数值模拟方法。选用Spalart-Allmaras一方程湍流模型来封闭上述方程组。采用守恒形式的有限体积法，中心差分格式进行空间离散。时间推进采用四步Runge-Kutta法。利用多重网格和隐式残差均化对流动实施加速收敛，同时也节约了整个优化设计的时间。4参数化叶片本文对叶片的参数化表达主要包括：不同叶高位置叶型的参数化，积迭点在二维叶型上的选取，参数化三维叶片积迭线。原始叶片由八个叶高位置的二维叶型叠加而成，它们分别位于0、25、38、50、63、75、87
10、和100径向叶高。二维叶型中弧线采用了二阶Bezier曲线进行控制。叶型轮廓线的压力边和吸力边都采用了三阶Bezier曲线进行控制，二维叶型的前、后缘都采用圆头形式。积迭点选位于叶型的重心（重心积迭线）。通过重心积迭线来实现对三维叶片在圆周方向和掠向的控制。在圆周方向上，积迭线的形状采用直线+三阶Bezier曲线的组合形式；在掠方向上，积迭线的形状采用二阶Bezier曲线形式，如图3所示。 (a) 叶片的周向控制 (b) 叶片的掠向控制图3 叶片的重心积迭线的控制Fig.3 Parameterized blade stacking line5优化算法和设计过程本文的数值优化方法采用人工神经网络
11、（Artificial Neural Network，简称ANN）的反向误差传播（back-propagation，简称BP）算法与遗传算法（Genetic Algorithm，简称GA）相结合，其基本原理参见文献【12-13】。选取叶片积迭线周向控制参数中的两个量作为本次优化的设计变量，如图3(a)所示的和，而其它参数不变。换句话说，原始叶片重心积迭线中直线段AB（如图1）的形状在本次优化设计中始终保持不变，而只改变圆弧段的形状。接下来，建立数据库样本。本次优化共建立20个样本。利用随机的方式进行样本的采集，即对每一个样本，两个设计变量在其范围内进行随机取值。这样，得到20个具有不同积迭线周
12、向弯曲角度的叶片。对这些样本分别进行网格划分，在这个过程中剔除出现负网格的叶片样本。然后，对剩余的每个样本分别进行数值计算，对计算结果未收敛或未达到收敛标准的样本进行剔除。最后得到真正用于优化设计的数据库样本。本次优化的所有20个样本全部通过网格划分和数值计算，都为可以利用的有效样本。本次优化设计的目标函数为最大化叶轮的效率和压比，同时对流量的变化加以约束以保持工况点基本不变。目标函数表达式如下 （1）其中，为计算中强加的叶轮全压比，它通常要远大于叶轮的实际值；为参考全压比，为了方便起见，这里取；为叶轮全压比计算值；和为权值，它们的数值大小取决于气动效率和全压升在本次优化设计中的相对重要性，在
13、这里都取1.0；值取2.0。6结果分析6.1叶片形状对比对比优化前、后叶片重心积迭线形状（图1）。图中O点是叶轮的轴心，A点是轮毂与叶片重心积迭线的交点，B点为重心积迭线直线段与圆弧段的交点，R和Y点分别为原始叶片和优化叶片重心积迭线与叶顶的交点。可以看出，优化之后的叶片沿圆周方向带有明显顺叶轮旋转方向弯曲的特征，在这里称之为周向前弯。图4给出了原始叶片和优化叶片的三维图。 (a) 原始叶片 (b) 优化叶片图4 原始叶片与优化叶片的比较Fig.4 Comparison between archetypal blade and optimal blade6.2气动性能分析表1给出了原始叶片与优
14、化叶片主要性能参数的对比。可以看出，叶片经过在周向上的适当弯曲，主要性能指标有了进一步的提高，其中，峰值全压效率提高了1.27，全压提高了3.56，而流量没有明显变化。另外，经过优化之后，叶轮的失速裕度也得到明显拓宽，大约增加了36，这进一步增加了叶轮在变工况下的稳定性。表1 原始叶片与优化叶片的气动性能参数比较Table1 Aerodynamic performance comparison between archetypal blade and optimal blade原始叶片优化叶片全压系数0.06750.0699全压效率（）76.2577.52流量系数0.24650.2484失速裕
15、度（）19.8727.116.3出口流场分析图5-7给出了两个叶轮出口气动参数沿叶高分布的试验测量与数值计算结果。如图所示，计算结果与试验结果吻合得很好，表明计算结果能够反映流场的实际情况。图5给出了出口总压损失系数沿叶高分布。与原始叶轮相比，优化之后的叶轮在上、下端壁附近区域的总压损失都明显减小，而中部叶高的损失有所增加。由于优化叶片的重心积迭线在上半叶高向叶轮旋转方向明显弯曲（如图1），造成该位置指向转轴方向的叶片径向力明显增大，从而削弱了旋转离心力的作用，导致叶顶区域的低能量流体向中部叶高区域迁移，减小了叶顶附近的损失。对于叶轮的下半叶高位置，由于叶片重心积迭线形状并未改变，因此叶根附近
16、的低能量流体向中部叶高处迁移，造成中部叶高区域的损失有所增加。经过计算发现，优化叶轮的总损失要小于原始叶轮。这说明，叶片经过适当的周向弯曲能够使流动损失沿叶高方向分布更加合理，从而减小整个流场的损失，提高风扇叶轮的气动效率。 (a) 原始叶轮 (b) 优化叶轮图5 原始叶片与优化叶片出口总压损失系数沿叶高分布Fig.5 Distribution of total pressure loss coefficient at outlet of archetypal blade and optimal blade图6给出了出口全压升沿叶高分布。从具体分布情况来看，原始叶轮的最高压力点位于上半叶高，接
17、近叶顶区域；而优化叶轮的最高压力点下移，位于中部叶高附近。由于原始叶轮沿整个叶高主要是受到离心力的控制，造成上半叶高的承载量增加；对于优化叶轮，由于叶片径向力的作用，造成上半叶高的离心力削弱，在下半叶高主要作用力未发生明显变化的情况下，最终导致中部叶高的载荷能力增加。经过计算发现，整个叶高的全压升，优化叶轮要高于原始叶轮。 (a) 原始叶轮 (b) 优化叶轮图6 原始叶片与优化叶片出口全压沿叶高分布Fig.6 Distribution of total pressure rise at outlet of archetypal blade and optimal blade图7给出了出口轴向速
18、度沿叶高分布。与两个叶轮出口全压分布相似，原始叶轮流道内的最大流量集中在上半叶高区域，优化叶轮的最大流量集中在中部叶高附近。在叶根附近，优化叶轮的流速更大，这对于扩大叶轮的失速裕度创造了有利条件。以上结果也反映了叶片的周向弯曲能够影响流道内流量沿叶高的分布。 (a) 原始叶轮 (b) 优化叶轮图7 原始叶片与优化叶片出口轴向速度沿叶高分布Fig.7 Distribution of axial velocity at outlet of archetypal blade and optimal blade7结论（1） 基于叶片弯掠技术，利用人工神经网络BP算法和遗传算法对轴流风扇转子叶片进行了优
19、化设计，寻找到具有更优气动性能的周向弯曲叶片。在设计工况下与原始叶轮相比，优化叶轮全压效率提高了1.27，全压升提高了3.56，失速裕度拓宽了36以上。（2） 与原始叶轮相比，优化叶轮的内部流动得到进一步改善。在整个叶高区域，叶片的载荷能力增强，端部损失明显减小，而中部叶高损失略有增加。（3） 优化叶轮的试验测量结果与优化设计结果相一致，说明了本文所采用的优化计算程序在实际应用中是完全可行的。参考文献1. 丰镇平, 李军, 沈祖达. 遗传算法及其在透平机械优化设计中的应用J. 燃气轮机技术, 1997, 10(2): 13-22.2. 樊会元, 王尚锦, 席光. 透平机械叶片的遗传优化设计J.
20、 航空学报, 1999, 20(1): 47-51.3. MENGISTU T, GHALY W. Single and multipoint shape optimization of gas turbine blade cascades R, Collection of Technical Papers -10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, 2004. 1652-1662.4. VASCELLARI M, DENOS R, VANDEN B R. Design of a transo
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25、ery, 1998,120(3): 454-464.10. BELIER M G, CAROLUS T H. Computation and measurement of the flow in axial flow fans with skewed blades J. Journal of Turbomachinery, 1999, 121(1): 59-66.11. 欧阳华, 李杨, 杜朝辉, 等. 周向弯曲方向对弯掠叶片气动-声学性能影响的实验研究J. 航空动力学报, 2006, 21(4): 668-674.12. 李敏强. 遗传算法的基本理论与应用M. 北京: 科学出版社, 2002
26、.13. 程相君. 神经网络原理及其应用M. 北京: 国防工业出版社, 1995.Editors note: Judson Jones is a meteorologist, journalist and photographer. He has freelanced with CNN for four years, covering severe weather from tornadoes to typhoons. Follow him on Twitter: jnjonesjr (CNN) - I will always wonder what it was like to huddle
27、 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 step 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 fas
28、cinated 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 to reach for the stars.As a meteorologist, Ive still seen many important weather and space events, but right now, if you were si
29、tting 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 set 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 unim
30、aginable 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 Stratos Mission. I watched the balloons positioned at different altitudes in the sky to test the winds, knowing that if they wou
31、ld 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 I live for taking a leap of faith - the feeling of pushing the envelope into uncharted territory.The guy who is going to do th
32、is, 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 and twisted the partially filled balloon that would take him to the upper end of our atmosphere. As soon as the 40-acre balloon,
33、 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 wrinkles of disappointment on the face of the current record holder and capcom (capsule communications), Col. Joe Kittinger. H
34、e 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 plays an important role in this mission. Starting at the ground, conditions have to be very calm - winds less than 2 mph, with no p
35、recipitation 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-day weather lives. It will climb higher than the tip of Mount Everest (5.5 miles/8.85 kilometers), drifting even higher than th
36、e 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 lot of turbulence.The balloon will slowly drift to the edge of space at 120,000 feet (22.7 miles/36.53 kilometers). Here, Fearl
37、ess 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 the concrete bottom of a swimming pool that he wants to land on, but not too hard. Still, hell be traveling fast, so despite t
38、he 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 expected 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
39、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 stabilization parachute that can be deployed to slow him down. His team hopes its not needed. Instead, he plans to deploy his 27
40、0-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 (277 kph). He will have a reserve parachute that will open automatically if he loses consciousness at mach speeds.Even if everythi
41、ng 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 feet (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.14.