一维建模分析轴流压气机性能

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"这篇论文探讨了一维轴流压气机性能建模的技术，采用近似一维的方法。尽管这种方法对复杂三维流动系统进行了大幅度简化，但因其输入需求简单且收敛速度快，适合在优化程序中使用，例如在克兰菲尔德大学开发的用于优化静叶叶片倾斜角的程序中。目标是开发一种能够简单模拟多级压缩机内部流动的技术，提供包括整体压力比、效率和不同速度下的流量范围在内的性能数据，并提供间隔数据以支持叶片重新排列的优化设计。" 1维轴流压气机性能分析是流体动力学领域中的一个重要主题，它主要关注如何通过简化模型来预测压气机的性能指标。一维方法通常基于平均线性假设，将复杂的三维流动简化为沿轴向的流动，忽略横截面内的流动细节。这种简化处理虽然牺牲了精度，但大大降低了计算复杂度，使得计算快速并能快速收敛。论文作者指出，虽然现代的计算流体动力学（CFD）软件可以更精确地模拟三维流动，但它们的输入要求复杂，计算时间较长，不适合在需要快速迭代和优化的设计过程中使用。因此，一维建模方法在压气机性能预测中仍有其独特优势。在压气机设计和优化中，静叶叶片的排列角度是关键参数之一，它直接影响压气机的效率和工作范围。通过一维模型，工程师可以快速评估不同叶片倾斜角度对整体性能的影响，无需详细计算每个压气机级的详细数据。模型提供的性能数据包括总体压力比，这是衡量压气机增压能力的关键指标；效率则反映了能量转换的效能；流量范围则表明压气机在不同操作条件下的适应性。此外，一维模型还提供了间隔数据，这有助于研究相邻叶片之间的相互作用，以及如何调整叶片角度以改善流动特性，进而提升压气机的效率和稳定运行范围。这种技术在多级压缩机设计中尤为重要，因为各级之间的相互影响会显著影响整个系统的性能。一维轴流压气机性能分析是一种实用而有效的工具，适用于快速评估和优化压气机设计，特别是在需要快速迭代的工程应用中。通过这种技术，工程师能够以较低的成本获得关键的性能指标，为压气机的创新设计和改进提供指导。

The purpose of the present study is to select from the

open literature a set of correlations that collectively give a

good overall performance prediction at design and off-

design conditions for a range of different compressors

with conventio nal blade pro les (pro les with circular or

parabolic camber lines). A quasi-one-dimensional numerical

model will then be developed in the form of a FORTRAN

program. The program will be subsequently coupled to a

surge prediction model also written in FORTRAN and

previously develo ped at Cran eld by Gill and Elder [10]

and Escuret and Elder [11].

It is intended that these two prediction programs will be

 nally incorporated (as subroutines) into an optimization

program for geometry settings. This is mentioned in more

detail later on.

2 CORRELATION REVIEW

There are two basic requirements for the prediction of stage

performance of an axial  ow compressor [12]. The  rst is

knowledg e of the variation in the outlet  ow angle as a

function of the inlet  ow angle, and the second is knowledge

of the variation in the losses or ef ciency, again as a

function of inlet  ow angle. Cetin

et al.

[13] described

work that had been directed towards selecting the most

promising correlations for off-design loss coef cient and

deviation from the literature and improving them to account

for transonic and three-dimensional effects. Miller and

Wasdell [3] and Wright and Miller [4] presented a different

set of correlations that had originated from other sou rces but

subsequ ently improved to account for effects such as

Reyno lds number and compressibility. They were successful

in predicting the off-design performance for a selection of

high-sp eed compressors.

The work described in this p aper required individual

bladerow analysis to ensure that the axia l mismatching

between rotor and stator blades was captured at off-design

condit ions. Moreover, the correlation set had to offer stable

convergence for the whole comp ressor operating range.

Resultin g from these considerations, the moss successful

correlation set suggested in reference [13] was chosen for

comparison with those given in references [3] and [4]. In

each case, the actual method is similar and can be summar-

ized as follows:  rstly, a blade loading parameter is found

such as the equivalent diffusion ratio

at the minimum

loss incidence

. The velocity and  ow angle te rms that

correspon d to th is minimum loss cond ition are estimated by

assuming that

remains constant at inlet and exit to the

bladerow and

1 ml

and

2 ml

are given by the correlations for

and

. The corresponding pro le loss parameter,

p ml

, is then estimated for the minimum loss incidence

condit ion using a co rrelation based upon the classic Lieblein

approach [14]. Secondly, the shock loss

is found for high

inlet Mach numbers, estimated from a simple, normal shock

analysis. Finally, the combined magnitude of

pml

and

corrected for the actual incidence, using a suitable function

that approximates the blade loss c haracteristic. The deviation

is also corrected for the actual incidence. The effects of

endwall lo ss

and blockage

are subseque ntly

introdu ced to give the total loss coef cient

tot

2.1 Selected correlations

Table 1 lists the origin of each set of correlations u sed

within this study. The suggested method for estimating

in reference [13] was the Koch and Smith technique,

presented in detail in reference [15]. The in uences of

streamtube contraction, Rey nolds number, Mach n umber

and blade surface roughness upon the loss were included to

produce an effective model that was found to give agree-

ment with test results for compressors with a wide range of

design parameters. The correlations used to account for off-

design incidence and deviation in set 1 were those of

Creveling [16]. This choice was also based upon the  ndings

given in reference [13], where it was shown th at the equation

set gave the best agreemen t with the available test data.

The shock loss coef cient,

, was estimated from two

different models, one for each set. In set 1, the techniqu e

was again that suggested in reference [13], where the

subson ic but su percritical loss was found with the Jansen

and Moffatt method [17] and the supersonic loss was found

with the Swan method [18]. The second model, used in set 2,

was that of Schwenk

et al.

[19] applied in the same way as

given in reference [4]. This particu lar loss component is a

dif cult mechanism to approximate well, in particular the

interaction of the passage shock wave and the suction

surface boundary layer is a major factor that should be

consid ered. As sonic conditions are approached, the  ow

becomes very sensitive to c hanges in  ow area and a blade-

to-blade description may not be very suitable. Bearing these

facts in mind, the loss model employed within a simple one-

dimensio nal mean-line code such as this is likely to be, at

best, a fair approximation of the magnitude and general

trend of such a complex system. Figure 1, taken from

reference [19], shows a simple representation of the passage

shock mechanism. The position of the bow wave intersec-

tion point with the suction surface is determined, and the

suction surface Mach number is then estimated at that point

using the Prandt–Meyer expansion angle

. The total

pressure loss across the normal shock wave at this point,

¡P

, is then found from the average of the upstream

and suction surface Mach numbers.

The methods given in references [18] and [19] are quite

similar, and both follow the above procedure for supersonic

inlet Mach numbers. Subson ic inlet conditions that have

exceeded a critical level and caused a supersonic patch on

the suction surface result in a weaker shock wave, and this is

estimated in reference [17] by a simple law that increases

increases. Alte rnatively, for set 2, the Schwenk

et al.

method is applied for

1:0 and a linear relationship is

assumed between this loss value and that for the critical

subson ic

1 cr

where the loss is taken to be zero. The actual

A06101 # IMechE 2002 Proc Instn Mech Engrs Vol 216 Part A: J Power and Energy

AXIAL COMPRESSOR PERFORMANCE MODELLING WITH A QUASI-ONE-DIMENSIONAL APPROACH 183

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