2V—0.510型空气压缩机设计【含CAD图纸、说明书、开题报告】
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毕业设计外文资料翻译
学 院： 机械电子工程学院
专 业： 过程装备与控制工程
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学 号：
外文出处： Applied Energy 85 (2008)
625—633
附 件： 1.外文资料翻译译文；2.外文原文。
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附件1：外文资料翻译译文
一维多级轴流压缩机性能的解析优化
Lingen Chen Jun Luo Fengrui Sun Chih Wu
摘要 对多级压缩机的优化设计模型，本文假设固定的流道形状以入口和出口的动叶绝对角度，静叶的绝对角度和静叶及每一级的入口和出口的相对气体密度作为设计变量，得到压缩机基元级的基本方程和多级压缩机的解析关系。用数值实例来说明多级压缩机的各种参数对最优性能的影响。
关键词 轴流压缩机 效率 分析关系 优化
1 引言
轴流式压缩机的设计是工艺技术的一部分，如果缺乏准确的预测将影响设计过程。至今还没有公认的方法可使新的设计参数达到一个足够精确的值，通过应用一些已经取得新进展的数值优化技术，以完成单级和多级轴流式压缩机的设计。计算流体动力学（CFD）和许多更准确的方法特别是发展计算的CFD技术，已经应用到许多轴流式压缩机的平面和三维优化设计。它仍然是使用一维流体力学理论用数值实例来计算压缩机的最佳设计。Boiko通过以下假设提出了详细的数学模型用以优化设计单级和多级轴流涡轮：（1）固定的轴向均匀速度分布（2）固定流动路径的形状分布，并获得了理想的优化结果。陈林根等人也采用了类似的想法，通过假设一个固定的轴向速度分布的优化设计提出了设计单级轴流式压缩机一种数学模型。在本文中为优化设计多级轴流压缩机的模型，提出了假设一个固定的流道形状，以入口和出口的动叶绝对角度，静叶的绝对角度和静叶及每一级的入口和出口的相对气体密度作为设计变量，分析压缩机的每个阶段之间的关系，用数值实例来说明多级压缩机的各种参数对最优性能的影响。
2 基元级的基本方程
考虑图1所示由n级组成的轴流压缩机, 其某一压缩过程焓熵图和中间级的速度三角形见图2和图3，相应的中间级的具体焓熵图如图4，按一维理论作级的性能计算。按一般情况列出轴流压缩机中气体流动的能量方程和连续方程,工作流体和叶轮的速度。在不同级的轴向流速不为常数，即考虑, () 时的能量和流量方程。在下列假定下分析轴流压缩机的工作:
·相对于稳定回转的动叶、静叶和导向叶片机构, 气体流动是稳定的；
·流体是可压缩、无黏性和不导热的；
·通过级的流体质量流量为定值；
·在实际工质的情况下, 压缩过程是均匀的；
·本级出口绝对气流角为下一级进口角绝对气流角；
·忽略进出口管道的影响。
在每一级的具体焓如下：
（1）
（2）
第阶段的动叶和静叶的焓值损失总额计算如下：
（3）
（4）
其中是第阶段动叶叶片轮廓总损失系数，是第阶段静叶叶片轮廓总损
失的系数。
图1 n级轴流式压缩机的流量路径。
叶片轮廓损失系数和是工作流体和叶片的几何功能参数。它们可以使用各种方法及视作常量来计算。当和看做工作流体和叶片的几何功能参数时，可以使用Ref迭代的方法来计算损失系数。使用迭代方法解决计算损失系数：
（1）选择和初始值，然后计算各级的参数。
（2）计算的，值，重复第一步，直到计算值和原值之间的差异足够小。
第阶段理论所需计算得：
（5）
第阶段实际所需计算得：
图2 n级压缩机的焓熵图
图3 中间级的速度三角形
图4 中间级的焓熵图
（6）
基元级反应度定义为。因此有：
（7）
在这里，视作速度系数,它们的计算为:
和
（8）
（9）
3 级组的数学模型
压缩机各级的比压缩功为则总的比耗功为， 各级的滞止等熵能量头为，则级组各级滞止等熵比压缩功总和为，级组等熵比压缩功为, 则为压缩机的重热系数。根据定义,多级压缩机通流部分滞止等熵效率为：
求解确定各级能量头的分配：
（11）
方程式（11）同样可以写作：
….
(12)
出于方便，一些参数简化约束计算做了如下定义：
（13）
（14）
（15）
（16）
这里 是气动力函数，在这里的是滞止声速相对应的，且 是相对面积，是相对密度，是叶片高 是流量系数。
通过Boiko的论文引入等熵线系数，一个是：
（17）
这里 （18）
因此约束条件也可写作
（19）
（20）
（21）
在这里多级轴流式压缩机滞止等熵线的效率计算如下：
（22）
这里是多级压缩机的等熵工作系数，每一级的等熵工作系数是。
现在的优化问题是寻找和的最佳值，来找出在方程（19~21)约束下的目标函数的最大值。
4 结论
一旦这些系统和定义的常数按目标实现自己系统功能，在他最理想的环境下达到预计函数最大的程度。其呈现的并非是一个线性的而是一阶梯函数。本优化模型是（2n +1）约束功能和一个n级轴流压缩机（4n + 1）变量的非线性规划程序。例如改善外部法或SUMT法，对于这样的问题Powell采用在无约束极小化技术与一维最小的抛物线插值方法。人们已经发现是非常有作用的。
表1 各级相对面积
级 () 1 2 3 4 5 6 7
相对面积
1
0.936
0.886
0.809
0.729
0.701
0.647
表2 原始数据和设计计划
参数
上限
下限
原始数据
最佳数据
=0.732
=0.732
=0.732
=0.6
=0.59
=0.59
=0.49
=0.59
54
90
80.5891
72.6858
74.9116
66.5570
35
90
49.50
45.00
45.00
45.00
54
90
84.1338
76.3431
77.55
68.2003
35
90
49.50
45.00
45.00
45.00
54
90
66.411
59.7080
69.0582
55.7046
35
90
49.5418
45.00
45.00
46.6157
54
90
89.99
90.00
90.99
89.6147
0
3
1.089
1.0459
1.0913
1.093
0
3
1.148
1.1474
1.1549
1.0798
0
3
1.424
1.3970
1.3900
1.2624
0
3
1.424
1.4117
1,。4198
1.2624
0
3
1.565
1.5372
1.6091
1.3345
0
3
1.618
1.6338
1.6671
1.4450
0.9020
0.9050
0.9074
0.8955
5 数值计算例子
在计算中，做，，，，，,则为0.04, 为0.025和为0.02的设置。表1列出了在每个级的相对面积。应当指出会有一些优化目标的关系与这些量纲的影响是工作流体参数的功能和流动路径的几何参数设置。然而，得到的关系不会改变流体性质。对于3级压缩机中，有13个设计变量和7个约束条件。此外，较低上限约束的13个设计变量的值也应考虑在计算中。优化变量的上限和下限，原来的设计方案中优化不同流量系数和工作系数的结果列于表2。由此可以看出，优化程序是有效和实用的。
计算结果表明，最佳停滞等熵效率是随工作系数和流量系数的递减而递减的函数。工作系数影响最佳停滞等熵效率的作用大于流量系数。各值流量系数和工作系数，最优的最后一级输出绝对角度总是接近。
6 结论
在本文中在研究固定流形的多级轴流压缩机的效率优化中使用一维流体理论研究。根据压缩机普遍特性和特征间关系。由展示的数值量其结果可以为多级压缩机的性能分析和优化提供一些指导。这是一个初步的研究将其不可避免的使用多目标数值优化技术和人工神经网络算法用于分析压缩机优化。
参考文献（见原文）
术语
声音速度 (m/s) c 绝对速度 (m/s)
F 过流面积 f 相对面积
G 空气质量流量 h 焓
i 焓比 k 速度系数
l 叶片升度 n 级数
p 压力 R 理想气体常数
s 特定熵 T 温度
u 轮线速度 W 相对速度
y 相对密度
希腊符号
绝对气流角, 相对气流解,
气动力系数 效率
流量系数 热率参数
量纲速度 气体密度,
反动度 气动力系数
能量头系数 损失系数
下标
轴向 重热系数
临界 第级
第阶段
理想的 动叶
静叶 等熵过程
切向速度
1 动叶入口点 2 动叶的出口点
3 静叶出口点 * 滞止参数
附件2：外文原文（复印件）
Design efficiency optimization of one-dimensional multi-stage axial-flow compressor
Lingen Chen , Jun Luo , Fengrui Sun , Chih Wu
Postgraduate School, Naval University of Engineering, Wuhan, 430033, PR China
Mechanical Engineering Department, US Naval Academy, Annapolis MN21402, USA
Available online 28 November 2007
Abstract
A model for the optimal design of a multi-stage compressor, assuming a fixed configuration of the flow-path, is presented.The absolute inlet and exit angles of the rotor, the absolute exit angle of the stator, and the relative gas densities at the inlet and exit stations of the stator, of every stage, are taken as the design variables. Analytical relations of the compressor elemental stage and the multi-stage compressor are obtained. Numerical examples are provided to illustrate the effects of various parameters on the optimal performance of the multi-stage compressor. 2007 Elsevier Ltd. All rights reserved.
Keywords: Multi-stage axial-flow compressor; Efficiency; Analytical relation; Optimization
1. Introduction
The design of the axial-flow compressor is partially an art. The lack of accurate prediction influences the design process. Until today, there are no methods currently available that permit the prediction of the values of these quantities to a sufficient accuracy for a new design. Some progresses has been achieved via the application of numerical optimization techniques to single- and multi-stage axial-flow compressor design [1–22].Especially with the development of computational fluid-dynamics (CFD), many more accurate methods of calculating have been presented in many references in which the techniques of CFD have been applied to two- and three-dimensional optimal designs of axial-flow compressors [17–20]. However, it is still of worthwhile significance to calculate, using one-dimensional flow-theory, the optimal design of compressors. Boiko [23] presented a detailed mathematical model for the optimal design of single- and multi-stage axial-flow turbines by assuming (i) a fixed distribution of axial velocities or (ii) a fixed flow-path shape, and obtained the corresponding optimized results. Using a similar idea, Chen et al. [22] presented a mathematical model for the optimal design of a single-stage axial-flow compressor by assuming a fixed distribution of axial velocities.In this paper, a model for the optimal design of a multi-stage axial-flow compressor, by assuming a fixed flow path shape, is presented. The absolute inlet and exit angles of the rotor, the absolute exit angle of the stator, and the relative gas densities at the inlet and exit stations of the stator, of each stage, are taken as the design variables. Analytical relations of the compressor stage are obtained. Numerical examples are provided to illustrate the effects of various parameters on the optimal performance of the multi-stage compressor 2. Fundamental equations for elemental-stage compressor Consider a n-stage axial-flow compressor – see Fig. 1. Fig. 2 shows the specific enthalpy–specific entropy diagram of this compressor. For a n-stage axial-flow compressor, there are (2n + 1) section stations. The stage velocity triangle of an intermediate stage (i.e. jth stage) is shown in Fig. 3. The corresponding specific enthalpy–specific entropy diagram is shown in Fig. 4. The performance calculation of multi-stage compressor is performed using one-dimensional flow theory. The analysis begins with the energy and continuity equations, and the axial-flow velocities of the working fluid and wheel velocities at the different stations in the compressor are not considered as constant, that is, , (), where i denotes the ith station and j denotes the jth stage. The major assumptions made in the method are as follows
• The working fluid flows stably relative to the vanes, stators and rotors, which rotate at a fixed speed.
• The working fluid is compressible, non-viscous and adiabatic.
• The mass-flow rate of the working fluid is constant.
• The compression process is homogeneous in the working fluid.
• The absolute outlet angle of the working fluid, in jth stage, is equal to the absolute inlet angle of the working fluid in (j+1)th stage.
• The effects of intake and outlet piping are neglected.
The specific enthalpies at every station are as follows
（1）
（2）
The total profile losses of the jth stage rotor and the stator are calculated as follows:
（3）
（4）
Whereis the total profile loss coefficient of jth stage rotor-blade and is that of jth stage-stator blade.
Fig. 1. Flow-path of a n-stage axial-flow compressor
Fig. 2. Enthalpy–entropy diagram of a n-stage compressor
Fig. 3. Velocity triangle of an intermediate stage
Fig. 4. Enthalpy–entropy diagram of an intermediate stage.
The blade profile loss-coefficients and are functions of parameters of the working fluid and blade geometry. They can be calculated using various methods and are considered to be constants. When and are functions of the parameters of the working fluid and blade geometry, the loss coefficients can be calculated using the method of Ref. [24], which was employed and described in Ref. [21]. The optimization problem can be solved using the iterative method:
(1) First, select the original values of and and then calculate the parameters of the stage.
(2) Secondly, calculate the values of and , and repeat the first step until the differences between the calculated values and the original ones are small enough.
The work required by the jth stage is
（5）
The work required by the jth rotor is:
（6）
The degree of reaction of the jth stage compressor is defined as . Hence, one has
（7）
Where， are the velocity coefficients, and they are defined as: andThe constraint conditions can be obtained from the energy-balance equation for the one-dimensional flow
（8）
（9）
3. Mathematical model for the behaviour of the multi-stage compressor
The compression work required by each stage is. The total compression work required by the multi-stage compressor is . The stagnation isentropic enthalpy rise of every stage is . The sum of the stagnation isentropic enthalpy rise of each stage is, while the stagnation isentropic enthalpy rise of the multi-stage compressor is . One has,The stagnation isentropic efficiency of the multi-stage axial-flow compressor is
（10）
The total energy-balance of a n-stage compressor gives:
（11）
Eq. (11) can be rewritten as
….
(12)
For convenience, in order to make the constraints dimensionless, some parameters are defined:
（13）
（14）
（15）
（16）
Where are the aerodynamic functions, and , where is the stagnation sound velocity and ，is the relative area, is the relative density, where l is the height of the blade, and is flow coefficient. Introducing the isentropic coefficient used by Boiko [23], one has
（17）
Where （18）
Therefore, the constraint conditions can be rewritten as：
（19）
（20）
（21）
and the stagnation isentropic efficiency of the multi-stage axial-flow compressor can be rewritten as
（22）
Where is isentropic work coefficient of the multi-stage. The isentropic work coefficient of each stage is defined as .Now the optimization problem is to search the optimal values of and for finding the maximum value of the objective function under the constraints of Eqs. (19)~(21).
4. Solution procedure
Once the system variables, the objective function, and the constraints are defined, a suitable method has to be adopted to determine the values of the design variables that maximize the objective function while satisfying the given constraints. The present optimization model is a non-linear programming procedure with
Table 1Relative areas for the stations
Station ()
1
2
3
4
5
6
7
Relative area
1
0.936
0.886
0.809
0.729
0.701
0.647
Table 2Original and optimal design plans
参数
上限
下限
原始数据
最佳数据
=0.732
=0.732
=0.732
=0.6
=0.59
=0.59
=0.49
=0.59
54
90
80.5891
72.6858
74.9116
66.5570
35
90
49.50
45.00
45.00
45.00
54
90
84.1338
76.3431
77.55
68.2003
35
90
49.50
45.00
45.00
45.00
54
90
66.411
59.7080
69.0582
55.7046
35
90
49.5418
45.00
45.00
46.6157
54
90
89.99
90.00
90.99
89.6147
0
3
1.089
1.0459
1.0913
1.093
0
3
1.148
1.1474
1.1549
1.0798
0
3
1.424
1.3970
1.3900
1.2624
0
3
1.424
1.4117
1,。4198
1.2624
0
3
1.565
1.5372
1.6091
1.3345
0
3
1.618
1.6338
1.6671
1.4450
0.9020
0.9050
0.9074
0.8955
5. Numerical example
In the calculations, ,, , , n = 3, R = 286.96 J/(kg·K), , and are set. The relative areas at every station are listed in Table 1. It should be pointed out that there will be some influence on the relation of the optimization objective with these dimensionless parameters if are functions of the working fluid parameters and geometry parameters of the flow-path configuration. However, the relation obtained will not change qualitatively. For a 3-stage compressor, there are 13 design variables and 7 constraint conditions. Besides, the lower and upper limit value constraints of the 13 design variables should also be considered in the calculations. The lower and upper limits of the optimization variables, the original design plan, and the optimization results for different flow coefficients and work coefficients are listed in Table 2. It can be seen that the optimization procedure is effective and practical. The calculations show that the optimal stagnation isentropic efficiency is an increasing function of the work coefficient and a decreasing function of the flow coefficient. The effect of the work coefficient on the optimal stagnation isentropic-efficiency is larger than that of the flow coefficient. Also for various values你of the flow coefficients and work coefficients, the optimal absolute exit-angle of the last stage always approaches .
6. Conclusion
In this paper, the efficiency optimization of a multi-stage axial-flow compressor for a fixed flow shape has been studied using one-dimensional flow-theory. The universal characteristic relation of the compressor be haviour is obtained. Numerical examples are presented. The results can provide some guidance as to the performance analysis and optimization of the multi-stage compressor. This is a preliminary study. It will be necessary to use multi-objective numerical optimization techniques [11–13,20,21,25–29] and artificial neural network algorithms [10,19,30,31] for practical compressor optimization.
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