空氣壓縮機設(shè)計外文翻譯--一維多級軸流壓縮機性能的解析優(yōu)化

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1、　　中文2320字　　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

2、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，如果缺乏準確

3、的預(yù)測將影響設(shè)計過程。至今還沒有公認的方法可使新的設(shè)計參數(shù)達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

4、（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。

5、　　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:

6、　　·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

7、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：　?。?）　?。?）　　第階段的動葉和靜葉的焓值

8、損失總額計算如下：　?。?）　?。?）　　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)。

9、　　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

10、階段理論所需計算得：　?。?）　　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<b&

11、gt;　?。?）　　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 　?。?

12、）　?。?）　　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： &l

13、t;p>　　求解確定各級能量頭的分配：　?。?1）　　方程式（11）同樣可以寫作：　　….　　(12)　　出于

14、方便，一些參數(shù)簡化約束計算做了如下定義：　?。?3）　?。?4）　?。?5）　?。?6）<

15、p>　　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：　?。?7）　　這里

16、（18）　　因此約束條件也可寫作　?。?9）　?。?0）　　（21）　　在這里多級軸流式壓縮機滯止等熵線的效率計算如

17、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

18、;　　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。

19、;　　表1 各級相對面積　　表2 原始數(shù)據(jù)和設(shè)計計劃　　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

20、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)。

21、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

22、法用于分析壓縮機優(yōu)化。　　參考文獻（見原文）　　術(shù)語　　Design efficiency optimization of one-dimensional multi-stage 　　axial-

23、flow compressor　　Lingen Chen , Jun Luo , Fengrui Sun , Chih Wu　　Postgraduate School, Naval University of Engineering, Wuhan, 430033, PR China　　Mechanical Eng

24、ineering Department, US Naval Academy, Annapolis MN21402, USA　　Available online 28 November 2007　　Abstract　　A model for the optimal design

25、 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 i

26、nlet 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

27、 to illustrate the effects of 　　Keywords: Multi-stage axial-flow compressor; Efficiency; Analytical relation; Optimization　　1. Introduction　　The design of th

28、e 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 quantiti

29、es 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

30、development of computational fluid-dynamics 　　2. Fundamental equations for elemental-stage compressor　　Consider an-stage axial-flow compressor – see Fig. 1. Fig. 2 shows the spec

31、ific 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.

32、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<

33、;p>　　? 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.

34、;　　? 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 jt

35、h 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 s

36、tation are as follows　　（1）　?。?）　　The total profile losses of the jth stage rotor and the stator are calculated as follo

37、ws:　　（3）　?。?）　　Whereis the total profile loss coefficient of jth stage rotor-blade and is that of jth stage-stator blad

38、e.　　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 intermedi

39、ate 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 geomet

40、ry. 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 me

41、thod 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 t

42、he 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.</p&g

43、t;　　The work required by the jth stage is　?。?）　　The work required by the jth rotor is:　?。?）<p

44、>　　The degree of reaction of the jth stage compressor is defined as . Hence, one has　?。?）　　Where， are the velocity coefficients, and they are defined as: an

45、dThe constraint conditions can be obtained from the energy-balance equation for the one-dimensional flow　?。?）　?。?）　　3.

46、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 stagnati

47、on 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

48、 isentropic efficiency of the multi-stage axial-flow compressor is　?。?0）　　The total energy-balance of a n-stage compressor gives:

49、　　（11）　　Eq. (11) can be rewritten as　　….　　(12)　　For convenience, in order to make the co

50、nstraints dimensionless, some parameters are defined:　　（13）　?。?4）　?。?5）

51、;　?。?6）　　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

52、 flow coefficient. Introducing the isentropic coefficient used by Boiko [23] ,one has　?。?7）　　Where （18）

53、;　　Therefore, the constraint conditions can be rewritten as：　　（19）　?。?0）　　（21）

54、　　and the stagnation isentropic efficiency of the multi-stage axial-flow compressor can be rewritten as　　（22）　　Where is isentropic work coefficient o

55、f 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 cons

56、traints 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 dete

57、rmine 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

58、1Relative areas for the stations　　Table 2Original and optimal design plans　　5. Numerical example　　In the calculations, ,, , , n = 3, R = 286.96 J/(kg·K)

59、, , 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

60、 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

61、 and 7　　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

62、. The universal characteristic relation of the compressor behaviour is obtained. Numerical examples are presented. The results can provide some guidance as to the performance analysis and optimization of the multi-stage

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空氣壓縮機設(shè)計外文翻譯--一維多級軸流壓縮機性能的解析優(yōu)化

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