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畢業(yè)設(shè)計外文資料翻譯
學(xué) 院： 機械電子工程學(xué)院
專 業(yè)： 過程裝備與控制工程
姓 名：
學(xué) 號：
外文出處： Applied Energy 85 (2008)
625—633
附 件： 1.外文資料翻譯譯文；2.外文原文。
指導(dǎo)教師評語：
簽名：
年 月 日
附件1：外文資料翻譯譯文
一維多級軸流壓縮機性能的解析優(yōu)化
Lingen Chen Jun Luo Fengrui Sun Chih Wu
摘要 對多級壓縮機的優(yōu)化設(shè)計模型，本文假設(shè)固定的流道形狀以入口和出口的動葉絕對角度，靜葉的絕對角度和靜葉及每一級的入口和出口的相對氣體密度作為設(shè)計變量，得到壓縮機基元級的基本方程和多級壓縮機的解析關(guān)系。用數(shù)值實例來說明多級壓縮機的各種參數(shù)對最優(yōu)性能的影響。
關(guān)鍵詞 軸流壓縮機 效率 分析關(guān)系 優(yōu)化
1 引言
軸流式壓縮機的設(shè)計是工藝技術(shù)的一部分，如果缺乏準(zhǔn)確的預(yù)測將影響設(shè)計過程。至今還沒有公認(rèn)的方法可使新的設(shè)計參數(shù)達(dá)到一個足夠精確的值，通過應(yīng)用一些已經(jīng)取得新進展的數(shù)值優(yōu)化技術(shù)，以完成單級和多級軸流式壓縮機的設(shè)計。計算流體動力學(xué)（CFD）和許多更準(zhǔn)確的方法特別是發(fā)展計算的CFD技術(shù)，已經(jīng)應(yīng)用到許多軸流式壓縮機的平面和三維優(yōu)化設(shè)計。它仍然是使用一維流體力學(xué)理論用數(shù)值實例來計算壓縮機的最佳設(shè)計。Boiko通過以下假設(shè)提出了詳細(xì)的數(shù)學(xué)模型用以優(yōu)化設(shè)計單級和多級軸流渦輪：（1）固定的軸向均勻速度分布（2）固定流動路徑的形狀分布，并獲得了理想的優(yōu)化結(jié)果。陳林根等人也采用了類似的想法，通過假設(shè)一個固定的軸向速度分布的優(yōu)化設(shè)計提出了設(shè)計單級軸流式壓縮機一種數(shù)學(xué)模型。在本文中為優(yōu)化設(shè)計多級軸流壓縮機的模型，提出了假設(shè)一個固定的流道形狀，以入口和出口的動葉絕對角度，靜葉的絕對角度和靜葉及每一級的入口和出口的相對氣體密度作為設(shè)計變量，分析壓縮機的每個階段之間的關(guān)系，用數(shù)值實例來說明多級壓縮機的各種參數(shù)對最優(yōu)性能的影響。
2 基元級的基本方程
考慮圖1所示由n級組成的軸流壓縮機, 其某一壓縮過程焓熵圖和中間級的速度三角形見圖2和圖3，相應(yīng)的中間級的具體焓熵圖如圖4，按一維理論作級的性能計算。按一般情況列出軸流壓縮機中氣體流動的能量方程和連續(xù)方程,工作流體和葉輪的速度。在不同級的軸向流速不為常數(shù)，即考慮, () 時的能量和流量方程。在下列假定下分析軸流壓縮機的工作:
·相對于穩(wěn)定回轉(zhuǎn)的動葉、靜葉和導(dǎo)向葉片機構(gòu), 氣體流動是穩(wěn)定的；
·流體是可壓縮、無黏性和不導(dǎo)熱的；
·通過級的流體質(zhì)量流量為定值；
·在實際工質(zhì)的情況下, 壓縮過程是均勻的；
·本級出口絕對氣流角為下一級進口角絕對氣流角；
·忽略進出口管道的影響。
在每一級的具體焓如下：
（1）
（2）
第階段的動葉和靜葉的焓值損失總額計算如下：
（3）
（4）
其中是第階段動葉葉片輪廓總損失系數(shù)，是第階段靜葉葉片輪廓總損
失的系數(shù)。
圖1 n級軸流式壓縮機的流量路徑。
葉片輪廓損失系數(shù)和是工作流體和葉片的幾何功能參數(shù)。它們可以使用各種方法及視作常量來計算。當(dāng)和看做工作流體和葉片的幾何功能參數(shù)時，可以使用Ref迭代的方法來計算損失系數(shù)。使用迭代方法解決計算損失系數(shù)：
（1）選擇和初始值，然后計算各級的參數(shù)。
（2）計算的，值，重復(fù)第一步，直到計算值和原值之間的差異足夠小。
第階段理論所需計算得：
（5）
第階段實際所需計算得：
圖2 n級壓縮機的焓熵圖
圖3 中間級的速度三角形
圖4 中間級的焓熵圖
（6）
基元級反應(yīng)度定義為。因此有：
（7）
在這里，視作速度系數(shù),它們的計算為:
和
（8）
（9）
3 級組的數(shù)學(xué)模型
壓縮機各級的比壓縮功為則總的比耗功為， 各級的滯止等熵能量頭為，則級組各級滯止等熵比壓縮功總和為，級組等熵比壓縮功為, 則為壓縮機的重?zé)嵯禂?shù)。根據(jù)定義,多級壓縮機通流部分滯止等熵效率為：
求解確定各級能量頭的分配：
（11）
方程式（11）同樣可以寫作：
….
(12)
出于方便，一些參數(shù)簡化約束計算做了如下定義：
（13）
（14）
（15）
（16）
這里 是氣動力函數(shù)，在這里的是滯止聲速相對應(yīng)的，且 是相對面積，是相對密度，是葉片高 是流量系數(shù)。
通過Boiko的論文引入等熵線系數(shù)，一個是：
（17）
這里 （18）
因此約束條件也可寫作
（19）
（20）
（21）
在這里多級軸流式壓縮機滯止等熵線的效率計算如下：
（22）
這里是多級壓縮機的等熵工作系數(shù)，每一級的等熵工作系數(shù)是。
現(xiàn)在的優(yōu)化問題是尋找和的最佳值，來找出在方程（19~21)約束下的目標(biāo)函數(shù)的最大值。
4 結(jié)論
一旦這些系統(tǒng)和定義的常數(shù)按目標(biāo)實現(xiàn)自己系統(tǒng)功能，在他最理想的環(huán)境下達(dá)到預(yù)計函數(shù)最大的程度。其呈現(xiàn)的并非是一個線性的而是一階梯函數(shù)。本優(yōu)化模型是（2n +1）約束功能和一個n級軸流壓縮機（4n + 1）變量的非線性規(guī)劃程序。例如改善外部法或SUMT法，對于這樣的問題Powell采用在無約束極小化技術(shù)與一維最小的拋物線插值方法。人們已經(jīng)發(fā)現(xiàn)是非常有作用的。
表1 各級相對面積
級 () 1 2 3 4 5 6 7
相對面積
1
0.936
0.886
0.809
0.729
0.701
0.647
表2 原始數(shù)據(jù)和設(shè)計計劃
參數(shù)
上限
下限
原始數(shù)據(jù)
最佳數(shù)據(jù)
=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 數(shù)值計算例子
在計算中，做，，，，，,則為0.04, 為0.025和為0.02的設(shè)置。表1列出了在每個級的相對面積。應(yīng)當(dāng)指出會有一些優(yōu)化目標(biāo)的關(guān)系與這些量綱的影響是工作流體參數(shù)的功能和流動路徑的幾何參數(shù)設(shè)置。然而，得到的關(guān)系不會改變流體性質(zhì)。對于3級壓縮機中，有13個設(shè)計變量和7個約束條件。此外，較低上限約束的13個設(shè)計變量的值也應(yīng)考慮在計算中。優(yōu)化變量的上限和下限，原來的設(shè)計方案中優(yōu)化不同流量系數(shù)和工作系數(shù)的結(jié)果列于表2。由此可以看出，優(yōu)化程序是有效和實用的。
計算結(jié)果表明，最佳停滯等熵效率是隨工作系數(shù)和流量系數(shù)的遞減而遞減的函數(shù)。工作系數(shù)影響最佳停滯等熵效率的作用大于流量系數(shù)。各值流量系數(shù)和工作系數(shù)，最優(yōu)的最后一級輸出絕對角度總是接近。
6 結(jié)論
在本文中在研究固定流形的多級軸流壓縮機的效率優(yōu)化中使用一維流體理論研究。根據(jù)壓縮機普遍特性和特征間關(guān)系。由展示的數(shù)值量其結(jié)果可以為多級壓縮機的性能分析和優(yōu)化提供一些指導(dǎo)。這是一個初步的研究將其不可避免的使用多目標(biāo)數(shù)值優(yōu)化技術(shù)和人工神經(jīng)網(wǎng)絡(luò)算法用于分析壓縮機優(yōu)化。
參考文獻(xiàn)（見原文）
術(shù)語
聲音速度 (m/s) c 絕對速度 (m/s)
F 過流面積 f 相對面積
G 空氣質(zhì)量流量 h 焓
i 焓比 k 速度系數(shù)
l 葉片升度 n 級數(shù)
p 壓力 R 理想氣體常數(shù)
s 特定熵 T 溫度
u 輪線速度 W 相對速度
y 相對密度
希臘符號
絕對氣流角, 相對氣流解,
氣動力系數(shù) 效率
流量系數(shù) 熱率參數(shù)
量綱速度 氣體密度,
反動度 氣動力系數(shù)
能量頭系數(shù) 損失系數(shù)
下標(biāo)
軸向 重?zé)嵯禂?shù)
臨界 第級
第階段
理想的 動葉
靜葉 等熵過程
切向速度
1 動葉入口點 2 動葉的出口點
3 靜葉出口點 * 滯止參數(shù)
附件2：外文原文（復(fù)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
參數(shù)
上限
下限
原始數(shù)據(jù)
最佳數(shù)據(jù)
=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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