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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=0.59549080.589172.685874.911666.5570359049.5045.0045.0
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 633一个用来提供恒定空气压力的无人值守的智能化控制系统的空气压缩机的研究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
49、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
50、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
51、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
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