【文章內(nèi)容簡介】 orthwhile significance to calculate, using onedimensional flowtheory, the optimal design of pressors. Boiko [23] presented a detailed mathematical model for the optimal design of single and multistage axialflow turbines by assuming (i) a fixed distribution of axial velocities or (ii) a fixed flowpath 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 singlestage axialflow pressor by assuming a fixed distribution of axial this paper, a model for the optimal design of a multistage axialflow pressor, 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 pressor stage are obtained. Numerical examples are provided to illustrate the effects of various parameters on the optimal performance of the multistage pressor 2. Fundamental equations for elementalstage pressor Consider a nstage axialflow pressor – see Fig. 1. Fig. 2 shows the specific enthalpy–specific entropy diagram of this pressor. For a nstage axialflow pressor, there are (2n + 1) section stations. The stage velocity triangle of an intermediate stage (. jth stage) is shown in Fig. 3. The corresponding specific enthalpy–specific entropy diagram is shown in Fig. 4. The performance calculation of multistage pressor is performed using onedimensional flow theory. The analysis begins with the energy and continuity equations, and the axialflow velocities of the working fluid and wheel velocities at the different stations in the pressor are not considered as constant, that is, ijuu?,ijcc? (ij? ), 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 pressible, nonviscous and adiabatic. ? The massflow rate of the working fluid is constant. ? The pression 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 j*22 j i 2 ji= 1 /2i i h c? ? ?? （ 1） j*22 j+ 1 1 i 2 j+ 1i1 /2i i h c?? ? ?? （ 2） The total profile losses of the jth stage rotor and the stator are calculated as follows: ? ? ? ?? 222r j r j 2 j 1 2 j 1 2 j 1 2 j 1 2 j 1 2 j 1 2 j 1 r j / 2/ 2 / /h w G F u G c tg F? ? ? ? ?? ?? ? ? ?? ? ? ? ? ?? ? ? ? ? （ 3） ? ? ? ?222r j s j 2 j 2 j 2 j 2 j s j/ 2 / 1 / 2h c G F c tg? ? ? ???? ? ? ????? （ 4） Where ri? is the total profile loss coefficient of jth stage rotorblade and sj? is that of jth stagestator blade. Fig. 1. Flowpath of a nstage axialflow pressor Fig. 2. Enthalpy–entropy diagram of a nstage pressor Fig. 3. Velocity triangle of an intermediate stage Fig. 4. Enthalpy–entropy diagram of an intermediate stage. The blade profile losscoefficients ri? and sj? 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 ri? and sj? 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 ri? and sj? and then calculate the parameters of the stage. (2) Secondly, calculate the values of ri? and sj? , 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 j 2 j u , 2 j 2 j 1 u , 2 j 1 2 j 2 j 2 j 1 2 j 12 j 2 j 2 j 1 2 j 1GGh u c u c u c tg u c tgFF????? ? ? ? （ 5） The work required by the jth rotor is: 2 2 2 22 j1 2 j 2 j 2 j1rj 22w w u uh ???? （ 6） The degree of reaction of the jth stage pressor is defined as rj j/hh?? . Hence, one has ? ? ? ?? ?u ,2 j2 2 2a ,2j 2 j 2j 1ja ,2j 2j 2 j 11112k c t g c t gk k c t g c t g? ? ?????? ? ???? ? ?? （ 7） Where u,ik ， ? ?a,i 12k i n?? are the velocity coefficients, and they are defined as: a ,i a ,i a ,1 1 1 i i//k c c F F????and u,i i 1/k u u? The constraint conditions can be obtained from the energybalance equation for the onedimensional flow ? ? ? ?j 2*22 j 1 1 2 j i 2 j 2 j 2 ji = 1 / 1 / 2 0A i i h G F c tg????? ? ? ? ? ???? （ 8） ? ? ? ?j 22 j 1 2 j + 1 i 2 j + 1 2 j 1 2 j + 1i1 / 1 / 2 0A i i h G F c tg???? ??? ? ? ? ? ???? （ 9） 3. Mathematical model for the behaviour of the multistage pressor The pression work required by each stage is ? ?j 1h j n?? . The total pression work required by the multistage pressor is ncjj=1hh??. The stagnation isentropic enthalpy rise o