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1、基于正交试验的离心压缩机叶轮摩擦损失优化分析庞海英 李 爽 张吉礼/哈尔滨工业大学摘要：推导了叶轮摩擦损失的数学模型，针对与之相关的众多结构参数，采用正交试验的方法，对各影响因素进行优化分析，找出了影响叶轮摩擦损失的关键结构参数，并比较其影响的显著性。关键词：离心式压缩机；叶轮摩擦损失；正交试验中图分类号：TH452 文献标识码：B文章编号：1006-8155（2008）05-0023-04Optimization Analysis on Impeller Friction Losses in Centrifugal Compressor based on Orthogonal Test Ab
2、stract: In this paper, the mathematical model of impeller friction losses is deduced. The method of orthogonal test is applied to optimally analyze all the influencing factors. The key structural parameters influencing impeller friction losses are found out and the significance of its influence is c
3、ompared. Key words: centrifugal compressor; impeller friction losses; orthogonal test0 引言近年来，热泵作为一种既节能又环保的技术越来越受到人们的重视，并且逐步向大型热泵装置的方向发展1。在工业生产中，不但需要大量能源，而且产生和浪费了大量各种形式的余热，特别是低温余热。实践证明，低温余热完全可以作为二次能源来开发和利用，其中采用热泵技术就是重要方法之一。国外热泵技术已成功地应用于许多工业部门，并取得了良好的节能效果2。压缩机作为压缩式热泵的核心部件，其运行的效率、工况范围和安全性能直接影响着整个机组的性能。
4、压缩机级内部的损失主要包括吸气室损失、叶轮入口损失、叶轮流道内的摩擦损失、漏气损失、轮阻损失、无叶扩压器损失、弯道与回流器损失和蜗壳损失(最后一级)。本文主要针对叶轮部分的流道摩擦损失分析，找出对流道摩擦损失影响大的结构参数，为压缩机的设计提供参考。 1 叶轮流道内部的摩擦损失模型建立当气体流经压缩机时，由于粘性作用，在贴近流道壁的地方流速最小，中间主流流速最大，这样将气流分成许多层，层与层之间流速各不相同，因而产生摩擦损失。_收稿日期：2008-01-07 哈尔滨市 150090由文献3摩擦损失为(1)式中 为假想通道是直管时的摩擦损失。(2)式中 为摩擦因数，；为叶片通道平均水力直径，m；
5、为叶片通道平均长度，m；为叶片通道内平均速度，m/s。(3) （4）(5)式中 分别为叶轮进口外径、内径相对速度、出口相对速度m/s；为叶片通道在子午面上的平均曲率半径，m。(6)式中为叶轮出口直径，m；为叶轮出口安装角；分别为叶轮进口外径、内径，m；分别为叶轮进口外径、内径安装角；为叶片出口宽度，m；为叶轮出口叶片数，片；为叶轮轴向长度，m。与叶轮进口截面直径相等，;。2 结构参数优化分析由于离心式压缩机在进行设计时有很多参数都有经验的取值范围，这些参数在其取值范围之内取不同值时对设计结果影响程度有多大，哪些是关键的影响参数，哪些对于关键性影响参数的取值更重要，所以就这些问题用正交设计方法对
6、压缩机结构参数进行优化分析。 叶轮摩擦损失优化分析叶轮摩擦损失计算公式见式 (1)(6)，首先来简化摩擦损失公式。式(1)中的的处理如下，把此分式中的分子、分母同时除以可以得到：(7)(8)同样的方法来处理式(2)中的项：(9)对式(7)(9)代入简化条件：，并进行量级比较，简化为(10)(11)(12)以上公式中各参数的意义详见式(1)(6)。下面来处理式(2)中的摩擦因数和叶片通道内平均速度这两项。(1) 摩擦因数的处理摩擦因数cfb=0.0412Re-0.1925，关键是雷诺数的处理。雷诺数的大小，代表了作用在气体微团上惯性力与粘性力的比值，雷诺数越大，则相比之下粘性力的影响就越小。当雷
7、诺数超过某一定界限时，级的一些气动参数(流动效率、等熵效率、多变效率、能量头系数)就不受雷诺数大小的限制，这种现象称为粘性力的自动模化，而这个界限的数值就是临界雷诺数，对于离心式压缩机的级来说，其临界雷诺数为51065107，实际上经常用的是雷诺数大于临界雷诺数的情况。所以，把雷诺数当作常数并取5107来计算，所以摩擦因数也为一常数。(2) 叶片通道内平均速度的处理叶片通道内平均速度，由，则，将等式两边同时除以，得(13)式(13)中，/是叶轮内相对速度的减速比。此值如果过大则叶片通道内的减速和扩压程度会很大，造成效率的下降；若过小则叶轮效率虽高，但整个级效率会下降，所以它严格控制在1.51.
8、6范围内。/取1.5，取200m/s，可得=250 m/s。2.2 正交试验的建立经以上分析与简化，叶轮流道内的摩擦损失只与叶轮的结构参数有关。影响叶轮流道内摩擦损失的因素有：（1）叶轮进出口直径比；（2）叶轮宽径比；（3）叶片进口角；（4）叶片出口角；（5）叶片数；（6）叶轮出口轴径比。每个因素设5个水平，不考虑交互作用。进行六因素五水平多目标正交仿真设计。为便于书写，以上6个因素分别用符号A、B、C、D、E、F来表示，它们的取值范围分别是A=0.50.6，B=0.020.075，C=3035，D=1560，E=628，F=0.60.74，并各取5个水平。摩擦损失所选因素水平表示见表1。表1
9、 摩擦损失因素水平表水平ABCDEF123450.50.5250.550.5750.60.020.0330.0460.060.075303132343515263749606121824280.60.6250.650.6750.7用表1中的因素和水平设置，用来计算仿真，摩擦损失的仿真结果见表2。表2 摩擦损失仿真结果所在列123456因素D1/D2b2/D21A2AZ2L2/D2hsf仿真10.50.0230待添加的隐藏文字内容31560.685.36仿真20.50.0333126120.62562.42仿真30.50.0463237180.6552.23仿真40.50.063449240.6
10、7546.15仿真50.50.0753560280.741.73仿真60.5250.023137240.790.11仿真70.5250.0333249280.666.93仿真80.5250.046346060.62543.01仿真90.5250.063515120.6552.71仿真100.5250.0753026180.67545.88仿真110.550.023260120.67580.88仿真120.550.0333415180.778.19仿真130.550.0463526240.663.52仿真140.550.063037280.62553.31仿真150.550.075314960.
11、6531.67仿真160.5750.023426280.65100.54仿真170.5750.033353760.67555.18仿真180.5750.0463049120.746.23仿真190.5750.063160180.642.84仿真200.5750.0753215240.6567.79仿真210.60.023549180.62586.11仿真220.60.0333060240.6562.95仿真230.60.0463115280.67583.68仿真240.60.06322660.738.64仿真250.60.0753437120.638.04从表2看出，仿真结果摩擦损失hsf大部
12、分数值都在3090范围内，其最小值是31.67，而最大值是100.54。但从此表看不出哪个是影响结果的主要因素，分别用直观分析法(极差)和方差分析法来找出主要影响因素。2.3 正交试验的结果分析2.3.1 直观分析法 直观分析法是通过对每一个因素的平均极差来分析问题的。所谓极差就是平均效果中最大值和最小值的差。有了极差，就可以找到影响指标的主要因素，并可以找到最佳因素水平组合。直观分析的具体做法如下。(1) 首先计算各因素每个水平的平均效果和极差。一般用罗马数字表示水平效果，用大写的R表示极差，因素用角标表示，具体计算为A=（85.36+62.42+52.23+46.15+41.73）/5=5
13、7.578A=（90.11+66.93+43.01+52.71+45.88）/5=59.728A=（80.88+78.19+63.52+53.31+31.67）/5=61.514A=（100.54+55.18+46.23+42.84+67.79）/5=62.516A=（86.11+62.95+83.68+38.64+38.04）/5=61.884RA=62.51657.578=4.938用同样的方法可得摩擦损失影响因素B、C、D、E、F的水平效果和极差，结果见表3。(2) 对仿真结果进行分析，分析各因素的主次一般来说，各列的极差是不相等的，这就说明各因素的水平改变对仿真结果的影响是不相同的。极
14、差越大，说明这个因素的水平改变对仿真结果的影响也越大，极差最大的那一列因素，就是因素水平改变对仿真结果影响最大的因素，也就是最主要因素。表3 摩擦损失直观分析表所在列123456因素D1/D2b2/D21A2AZ2L2/D2hsf仿真111111185.36仿真212222262.42仿真313333352.23仿真414444446.15仿真515555541.73仿真621234590.11仿真722345166.93仿真823451243.01仿真924512352.71仿真1025123445.88仿真1131352480.88仿真1232413578.19仿真1333524163.5
15、2仿真1434135253.31仿真1535241331.67仿真16414253100.54仿真1742531455.18仿真1843142546.23仿真1944253142.84仿真2045314367.79仿真2151543286.11仿真2252154362.95仿真2353215483.68仿真2454321538.64仿真2555432138.04均值157.57888.658.74673.54650.77259.338均值259.72865.13462.14462.256.05661.213均值361.51457.73461.29457.77461.0561.315均值462.
16、51646.7361.18655.41866.10462.354均值561.88445.02259.8554.28269.23858.98极差4.93843.5783.39819.26418.4663.374通过仿真的结果比较极差大小。从表中数据结果：RA=4.938，RB=43.578，RC=3.398，RD=19.264，RE=18.466，RF=3.374，可知因素B极差最大，并远大于其他几项的极差；因素D和因素E的极差值相当，位于次之；因素A、C、F的极差最小相对来说是最小的。这说明当因素B水平改变时，对摩擦损失的影响是最大的，并且远大于其他几项因素对摩擦损失的影响，而因素D和因素E水
17、平改变时，对摩擦损失的影响次之，而相比较来说，因素A、C、F的水平改变时，对摩擦损失的影响最小。由此可以根据极差的大小顺序排出因素的主次：BDEACF，即叶轮宽径比对摩擦损失的影响是最大的；其次是叶片出口角和叶片数；对摩擦损失的影响最小的是叶轮进出口直径比、叶片进口角和叶轮出口轴径比。叶轮宽径比水平变化时，对摩擦损失的影响是最大的。摩擦损失影响因素B的水平从1变化到5时，摩擦损失呈减小趋势，尤其在水平3、4、5时，摩擦损失减小趋势更明显。因素B叶轮宽径比的水平变化范围可限制在0.0460.075。2.3.2 方差分析 利用正交表对试验结果进行方差分析的思想：先将数据（仿真结果）的总偏差平方和分
18、解为各因素以及误差的偏差平方和，然后求出F值，再用F检验法。具体步骤如下：若用正交表Ln(rt)，总的仿真次数为n，仿真结果为y1，y2，yn，则数据的总偏差平方和ST为(14)其中 ，。因素A所引起的偏差平方和为(15)其中r为因素A的水平数，为因素的水平Ai所对应的结果的平均值。计算SA的公式也可用来计算误差e的偏差平方和Se。F检验：检验因素A、B、C对试验结果有无显著影响。(16)其中，称为(或因素A)的自由度，有=因素A的水平数1，称为(或误差)的自由度，有=(n1)各因素的自由度之和。给定显著性水平=0.05进行F检验，方差分析表见表4。表 4 摩擦损失方差分析表因素偏差平方和自由
19、度F比F临界值显著性D1/D280.19140.0552.780b2/D26239.06244.2872.780*1A35.99640.0252.7802A1224.52940.8412.780Z21111.69740.7642.780L2/D240.98740.0282.780误差8732.4624由上表可知，在=0.05时，只有因素B显著，即因素B取不同水平对结果有显著影响。3 结论通过直观分析法可以得出：极差的大小顺序排出因素的主次为叶轮出口宽径比叶片出口角叶片数叶轮进出口直径比叶片进口角叶轮出口轴径比。通过方差分析可以得出：在=0.05时，只有因素B显著，即叶轮出口宽径比取不同水平对结
20、果有显著影响。通过两种分析方法均得出叶轮出口宽径比对叶轮流道摩擦损失的影响最大，是关键性因素。对于关键性因素在其取值范围中的取值尤为重要，所以在进行叶轮部分设计时，应细化其取值，关键性因素的取值在满足设计要求的同时，尽可能使得流道摩擦损失最小，从而使得流道内产生的摩擦损失最小，为二元离心式压缩机的结构设计提供了理论参考。参 考 文 献1 赵力. 高温热泵在我国的应用及研究进展J. 制冷学报, 2005(2):8-13.2 Gerdi Breembrook. Retrofitting with heat pump in buildings. The 7th International Energ
21、y Agency Conference on Heat Pump Technologies. 2002:685-693.3 吴宝海, 席光, 王尚锦. 离心式压缩机性能预测模型研究J. 风机技术，1993(3):5-9.4 张亚立. 污水水源中高温热泵机组模拟及区域供热技术经济分析D. 哈尔滨工业大学硕士论文，2002:33-34.Editors note: Judson Jones is a meteorologist, journalist and photographer. He has freelanced with CNN for four years, covering sever
22、e 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 step
23、 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 to
24、 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 set
25、 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 St
26、ratos 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
27、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 an
28、d 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
29、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 plays
30、 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-d
31、ay 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 l
32、ot 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
33、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 exp
34、ected 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 st
35、abilization 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 (277
36、 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 fe
37、et (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 r
38、emember, because there is no way Id miss this.5为了不影响您真情的挥洒，这里我就不给出模板了。J写不写都行。不写的话就删除这章好了。仅“同等学历”的同学需要写这个。什么是“同等学历”？我也不懂。L千万不要删除行尾的分节符，此行不会被打印。不要在此行和下页的注释之间填写任何内容下面的内容是参考文献，通过“插入”“引用”“脚注和尾注”，插入尾注到“文档结尾”后，word会自动生成序号。双击序号能自动定位。移动引用位置会自动重新编号。还可以插入“交叉引用”，实现对一篇文献的多次引用。因为本人能力所限，不能将其自动放入前面的“参考文献”章节内，也不能去掉接下来的这半条直线，所以就只能麻烦您这么做了：打印前，备份文档，然后将下面的内容copy & paste到“参考文献”内，并要手工修改序号。注意！copy前一定要备份！以后再做修改时，要修改备份文档。
