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1、Research of an unattended intelligentized control system of air compressor for supplying constant-pressure airLingen Chen , Jun Luo , Fengrui Sun , Chih Wu Postgraduate School, Naval University of Engineering, Wuhan, 430033, PR China Mechanical Engineering Department, US Naval Academy, Annapolis MN2

2、1402, USAAvailable online 28 November 2007AbstractA 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 in

3、let 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 th

4、e multi-stage compressor. 2007 Elsevier Ltd. All rights reserved.Keywords: Multi-stage axial-flow compressor; Efficiency; Analytical relation; Optimization1. IntroductionThe design of the axial-flow compressor is partially an art. The lack of accurate prediction influences the design process. Until

5、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

6、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 1720. However, it is sti

7、ll 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

8、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 desi

9、gn 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 va

10、riables. 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 compresso

11、r see Fig. 1. Fig. 2 shows the specific enthalpyspecific 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 enthalpyspecific

12、 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 i

13、n 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 fl

14、uid 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.

15、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

16、 stage-stator blade.Fig. 1. Flow-path of a n-stage axial-flow compressorFig. 2. Enthalpyentropy diagram of a n-stage compressorFig. 3. Velocity triangle of an intermediate stageFig. 4. Enthalpyentropy diagram of an intermediate stage.The blade profile loss-coefficients and are functions of parameter

17、s 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 de

18、scribed 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

19、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 c

20、an be obtained from the energy-balance equation for the one-dimensional flow (8) (9)3. Mathematical model for the behaviour of the multi-stage compressorThe compression work required by each stage is. The total compression work required by the multi-stage compressor is . The stagnation isentropic en

21、thalpy 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

22、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 re

23、lative 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 c

24、ompressor 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

25、 Eqs. (19)(21).4. Solution procedureOnce 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 optimiz

26、ation model is a non-linear programming procedure withTable 1Relative areas for the stationsStation ()1234567Relative area 10.9360.8860.8090.7290.7010.647Table 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=0.59549080.589172.685874.911666.5570359049.5045.0045.0

27、045.00549084.133876.343177.5568.2003359049.5045.0045.0045.00549066.41159.708069.058255.7046359049.541845.0045.0046.6157549089.9990.0090.9989.6147031.0891.04591.09131.093031.1481.14741.15491.0798031.4241.39701.39001.2624031.4241.41171,。41981.2624031.5651.53721.60911.3345031.6181.63381.66711.44500.902

28、00.90500.90740.89555. Numerical exampleIn the calculations, , , , n = 3, R = 286.96 J/(kgK), , 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 par

29、ameters 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

30、 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

31、 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-eff

32、iciency 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. ConclusionIn this paper, the efficiency optimization of a multi-stage axial-flow compressor for a fixed

33、 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

34、is a preliminary study. It will be necessary to use multi-objective numerical optimization techniques 1113,20,21,2529 and artificial neural network algorithms 10,19,30,31 for practical compressor optimization.References1 Wall RA. Axial-flow compressor performance prediction. AGARD-LS-83 1976(June):4

35、.14.34.2 Gu C, Miao Y. Blade design of axial-flow compressors by the method of optimal control theory. Trans ASME, J Turbomach1987;109(1):99107.3 Hearsey RM. Numerical optimization of axial compressor design. ASME paper No. 89-GT-14.4 Tuccille R. A proposal for optimized design of multi-stage compre

36、ssors. ASME paper No. 89-GT-34.5 Lim JS, Chung MK. Design-point optimization of an axial-flow compressor stage. Int J Heat Fluid Flow 1989;10(1):4858.6 Massardo A, Statta A. Axial-flow compressor design optimization: Part I-pitchline analysis and multi-variable objective functioninfluence. Trans ASM

37、E, J Turbomach 1990;112(2):339404.7 Massardo A, Statta A, Marini M. Axial-flow compressor design optimization: Part II-throughflow analysis. Trans ASME, JTurbomach 1990;112(2):40511.8 Egorov IN, Fomin VN. Numerical method of optimization of a multi-stage axial compressor. Experimental and Computatio

38、nalAerothermodynamics of Internal Flows. World Publishing Corporation; 1990, p. 495503.9 Tuccille R. Optimal design of axial-flow compressor. ASME IGTI 1990;5:22733.10 Geoge H, Stuart B. Preliminary design of axial compressors using artificial intelligence and numerical-optimization techniques.ASME

39、paper No. 91-GT-334.11 Chen L. A brief introduction of multi-objective optimization for an axial-flow compressor-stage. Gas Turbine Technol 1992;5(1):113in Chinese.12 Egorov IN, Krekinin GV. Multi-criterion stochastic optimization of an axial compressor. ASME IGTI 1992;7:56370.13 Egorov IN. Optimiza

40、tion of multi-stage axial compressor in a gas-turbine engine system. ASME paper, 92-GT-424 1992.14 Chen L. Some new developments on the optimal design of turbomachinery during the past decade. J Eng Thermal Energy Power1992;7(4):21421 in Chinese.15 Egorov IN. Deterministic and stochastic optimizatio

41、n of a variable axial-compressor. ASME paper No. 93-GT-397.16 Sun J, Elder RL. Numerical optimization of a stator vane setting in multi-stage axial-flow compressors. Proc Inst Mech Eng1998;212(A4):24759.17 Calvert WJ, Ginder RB. Transonic fan and compressor design. Proc Inst Mech Eng 1999;213(C5):41

42、936.18 Gallimore SJ. Axial-flow compressor design. Proc Inst Mech Eng 1999;213(C5):43749.19 Li J, Satofuka N. Optimization design of a compressor cascade airfoil using a NavierStokes solver and genetic algorithms. Proc InstMech Eng 2002;216(A2):195202.20 Benini E. Three-dimensional multi-objective d

43、esign optimization of a transonic compressor rotor. AIAA J Propul Power2004:55965.21 Chen L, Sun F, Wu C. Optimal design of subsonic axial-flow compressor stage. Appl Energy 2005;80(2):18795.22 Chen L, Luo J, Sun F, Wu C. Optimized efficiency axial-flow compressor. Appl Energy 2005;81(4):40919.23 Bo

44、iko AB. Optimal Design for Flow-Path of Axial Turbines. Harkov: Higher Education Press; 1982 in Russian.24 Casey MV. A mean-line prediction method for estimating the performance characteristics of an axial- compressor stage. Proc ImechE1987, Turbomach Efficiency Predict Improv 1987:14555.25 Chen L,

45、Wu C, Blank D, Sun F. Preliminary design optimization of a marine dual tandem gear. Int J Pow Energy Syst1997;17(3):21822.26 Chen L, Wu C, Ni N, Cao Y, Sun F. Optimal design of centrifugal compressor stages. Int J Pow Energy Syst 1998;18(1):125.27 Chen L, Wu C, Blank D, Sun F. The multi-objective op

46、timal design method for a radial-axial flow turbine with the criteria of optimaltwist at the outlet of blade. Int J Pow Energy Syst 1998;18(1):1620.28 Chen L, Zhang J, Wu C, Blank D, Sun F. Analysis of multi-objective decision-making for marine steam turbine. Int J Pow EnergySyst 1998;18(2):96101.29

47、 Chen L, Zhou S, Wu C, Sun F. Preliminary design optimization of a steam generator. Energy Convers Manage 2002;43(13):165161.30 Lin BJ, Hung CI, Tang EJ. An optimal design of axial-flow fan blades by the machining method and an artificial neural-network.Proc Inst Mech Eng 2002;216(C3):36776.31 Qin X

48、, Chen L, Sun F, Wu C. Efficiency optimization for an axial-flow steam-turbine stage using genetic algorithm. Appl Therm Eng2003;23(18):230716.L. Chen et al. / Applied Energy 85 (2008) 625633 633一個(gè)用來提供恒定空氣壓力的無人值守的智能化控制系統(tǒng)的空氣壓縮機(jī)的研究Lingen Chen Jun Luo Fengrui Sun Chih Wu摘要 對(duì)多級(jí)壓縮機(jī)的優(yōu)化設(shè)計(jì)模型,本文假設(shè)固定的流道形狀以入口和

49、出口的動(dòng)葉絕對(duì)角度,靜葉的絕對(duì)角度和靜葉及每一級(jí)的入口和出口的相對(duì)氣體密度作為設(shè)計(jì)變量,得到壓縮機(jī)基元級(jí)的基本方程和多級(jí)壓縮機(jī)的解析關(guān)系。用數(shù)值實(shí)例來說明多級(jí)壓縮機(jī)的各種參數(shù)對(duì)最優(yōu)性能的影響。關(guān)鍵詞 軸流壓縮機(jī) 效率 分析關(guān)系 優(yōu)化 1 引言軸流式壓縮機(jī)的設(shè)計(jì)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(jì)過程。至今還沒有公認(rèn)的方法可使新的設(shè)計(jì)參數(shù)達(dá)到一個(gè)足夠精確的值,通過應(yīng)用一些已經(jīng)取得新進(jìn)展的數(shù)值優(yōu)化技術(shù),以完成單級(jí)和多級(jí)軸流式壓縮機(jī)的設(shè)計(jì)。計(jì)算流體動(dòng)力學(xué)(CFD)和許多更準(zhǔn)確的方法特別是發(fā)展計(jì)算的CFD技術(shù),已經(jīng)應(yīng)用到許多軸流式壓縮機(jī)的平面和三維優(yōu)化設(shè)計(jì)。它仍然是使用一維流體力學(xué)理論用數(shù)

50、值實(shí)例來計(jì)算壓縮機(jī)的最佳設(shè)計(jì)。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(jì)單級(jí)和多級(jí)軸流渦輪:(1)固定的軸向均勻速度分布(2)固定流動(dòng)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(gè)固定的軸向速度分布的優(yōu)化設(shè)計(jì)提出了設(shè)計(jì)單級(jí)軸流式壓縮機(jī)一種數(shù)學(xué)模型。在本文中為優(yōu)化設(shè)計(jì)多級(jí)軸流壓縮機(jī)的模型,提出了假設(shè)一個(gè)固定的流道形狀,以入口和出口的動(dòng)葉絕對(duì)角度,靜葉的絕對(duì)角度和靜葉及每一級(jí)的入口和出口的相對(duì)氣體密度作為設(shè)計(jì)變量,分析壓縮機(jī)的每個(gè)階段之間的關(guān)系,用數(shù)值實(shí)例來說明多級(jí)壓縮機(jī)的各種參數(shù)對(duì)最優(yōu)性能的影響。2 基元級(jí)的基本方程考慮圖1所示由n級(jí)組成的軸流壓縮

51、機(jī), 其某一壓縮過程焓熵圖和中間級(jí)的速度三角形見圖2和圖3,相應(yīng)的中間級(jí)的具體焓熵圖如圖4,按一維理論作級(jí)的性能計(jì)算。按一般情況列出軸流壓縮機(jī)中氣體流動(dòng)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(jí)的軸向流速不為常數(shù),即考慮, () 時(shí)的能量和流量方程。在下列假定下分析軸流壓縮機(jī)的工作: 相對(duì)于穩(wěn)定回轉(zhuǎn)的動(dòng)葉、靜葉和導(dǎo)向葉片機(jī)構(gòu), 氣體流動(dòng)是穩(wěn)定的; 流體是可壓縮、無黏性和不導(dǎo)熱的; 通過級(jí)的流體質(zhì)量流量為定值;在實(shí)際工質(zhì)的情況下, 壓縮過程是均勻的;本級(jí)出口絕對(duì)氣流角為下一級(jí)進(jìn)口角絕對(duì)氣流角;忽略進(jìn)出口管道的影響。 在每一級(jí)的具體焓如下: (1) (2)第階段的動(dòng)葉和靜葉的焓值損失總額計(jì)算如下: (3) (4)其中是第階段動(dòng)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(jí)軸流式壓縮機(jī)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(jì)算。當(dāng)和看做工作流體和葉片的幾何功能參數(shù)時(shí),可以使用Ref迭代的方法來計(jì)算損失系數(shù)。使用迭代方法解決計(jì)算損失系數(shù):(1)選擇和初始值,然后計(jì)

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