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ISABE-2015-20059

Aerodynamic Investigation and Optimization of a 5-Stage Axial Flow Compressor

Yin Song1, Chunwei Gu

1, Xiaotang Li

2, Taiqiu Liu

2

1 Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Thermal

Engineering, Tsinghua University, Beijing, China

2 Shenyang Engine Design and Research Institute (SEDRI), Shenyang, China

Abstract

This paper presents numerical and experimental

research on the aerodynamic performance of a 5-stage

compressor, which has been designed for developing a

modern industrial gas turbine. The objective of this

research is to assess the compressor performance,

calibrate the throughflow method as well as CFD

method, and improve the current design using 3D

optimization method based on the above analysis and

verification of numerical methods. The full-scale test

results of the compressor overall performance are

presented, which demonstrate the good performance of

the current design. The test data also shows a slightly

under-prediction of the corrected mass flow rate by the

throughflow code, and a better prediction by the CFD

simulations. Then detailed analysis at design and off-

design points is further carried out. The predictions of

casing wall static pressure and spanwise total pressure

profiles are compared with the test data. At the design

point, the well stage matching and the favorable

internal flowfield are verified by the two methods. At

the near-stall point, CFD results show that significant

separation exists in the last stator, and the throughflow

method also predicts extremely high loading there.

Finally, 3D optimization focused on the spanwise

distribution of blade inlet angle and solidity is carried

out for the last stator, which improves the stall margin

of the 5-stage compressor by 13.4% and maintains the

high design-point efficiency. The optimized stator

shows a C-shape solidity distribution and the effect of

such solidity distribution is discussed with a case study,

in which phenomenon contradictory with traditional

2D theory is observed and it is explained in a three-

dimensional perspective.

Nomenclature

B blockage

C chord length

h enthalpy

i incidence

*i reference incidence

Ma Mach number

2

2

m meridional direction

m massflow

N number of blades

q coordinate which is nearly orthogonal to a

streamline

r distance in the radial direction

s entropy

T static temperature

V velocity

w streamsurface thickness

angle of the quasi orthogonal from the radial

direction

deviation

* reference deviation

angle of the streamsurface from the radial

direction

circumferential direction or camber angle

1 blade inlet angle

density

total pressure loss coefficient

inclination of meridional streamline to the

axial direction

Abbreviations

BC Boundary condition

CDA Controlled Diffusion Airfoil

CFD Computational Fluid Dynamics

DP Design point

IGV Inlet Guided Vane

LE Leading edge

LER Leading Edge Re-camber

MCA Multiple Circular Arc

NS near stall

RANS Reynolds-averaged Navier-Stokes

TE Trailing edge

Subscripts and superscripts

0 stagnation parameter

ew end-wall

ml minimum-loss

leak leakage

opt optimized

ori original

prof profile

tangential component

1 Introduction

The large adverse pressure gradient and blade row

interaction in multistage compressors of modern

aeroengines and heavy-duty gas turbines have led to an

internal turbulent flowfield of high three-

dimensionality and nonlinearity. As a result, the

analysis and control of the three-dimensional flow in

highly-loaded compressors are important and

challenging, and have been the general interest of

engineers and researchers.

Up to now, the throughflow calculation, which is the

major component of the traditional quasi-3D design

system, remains the main tool for aerodynamic design

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and performance prediction of multistage compressors.

The throughflow calculation can give a fast and

reliable solution for predicting the aerodynamic

performance and checking stage matching provided

that it is based on efficient correlation models and

empirical data [1]. Nevertheless, the dependency on

correlation models of throughflow calculation limits its

use in compressor designs beyond the state of the art,

since proper correlation models and empirical data are

unavailable, and the throughflow code should be

calibrated with test-rig data when used in the design or

analysis of compressors with higher loading.

In contrast, with the rapid development of computer

science and computational fluid dynamics, 3-D CFD

has been successfully used to predict the performance

and the detailed flowfield of multistage compressors,

e.g. Rhie [2], Adamczyk [3] and Mansour [4]. Though

there are still limitations existed in today’s CFD

technique [5], the use of CFD has made it possible to

reduce the development cost and time since some

necessary parameter studies in the design process can

be easily performed by CFD, without going through

expensive experiments.

The detailed description of the 3D complex

flowfield given by CFD also enables the designers to

achieve a better understanding of internal flowfield,

which significantly promotes the research of 3D blade

features. For example, Denton and Xu [6] investigated

3D flow effects of blade sweep and lean with particular

reference to their use to improve turbomachine

performance. Gallimore et al. [7] developed an

integrated multistage CFD design system and a 3D

design toolkit for the application of 3D features into

multistage compressor blading. The 3D blade effects

are verified by CFD and low-speed and high-speed

compressor test. Vad [8] overviewed the aerodynamic

effect of non-radial blade stacking in low-speed axial

flow rotors. Weingold [9], Gümmer [10], Fisher [11],

Ramakrishna [12] et al. also carried out researches on

the 3D blade effects. In addition to the above 3D

stackline design, the automatic optimization of 3D

blades which incorporates 3D CFD analysis and

optimization algorithms is another kind of 3D blade

design method, e.g. Oyama [13], Benini [14], Luo [15]

and Okui [16]. In such method, the 3D blade geometry

is represented by several parametric curves or a

parametric surface, the aerodynamic performance of

the blade is evaluated by CFD and the optimum

geometry parameters are searched using optimization

algorithm. It should be noted that some researchers

also incorporate the stackline design with optimization

algorithms, e.g. Jang [17] and Samad [18, 19].

The above-mentioned 3D blade features have

already been incorporated in the compressor design

process by the engine manufacturers, though relatively

few literatures have been published to disclose the

detailed 3D blade optimization method applied in the

multistage compressors of actual aeroengines or gas

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turbines. LeJambre [20] introduced bowed stators and

rotor hub contouring into the design of the high-

pressure compressor of PW4000 engine with the help

of multistage CFD, who was the first to publish such

application. Then Dong [21], Steven [22], Gallimore

[23] et al. also used single-row or multistage CFD

method to carry out 3D optimization for multistage

compressors.

In this paper, numerical and experimental research

on the aerodynamic performance of a 5-stage

compressor is presented. The overall performance is

assessed by both numerical and test results, which

prove that the compressor meets the design objectives.

The accuracy of the numerical methods in predicting

the compressor performance is examined by the

detailed test data under design and off-design

conditions. At the same time, stage-matching

characteristics and 3D flowfields are discussed in

details, and recommendations are put forward for

performance improvement. Finally, 3D blade

optimization is carried out to increase the stall margin

of the 5-stage compressor and the corresponding flow-

control mechanism is discussed to offer some guideline

for the design of blades with enhanced loading limits.

2 Overview of the 5-stage compressor

The 5-stage compressor is newly designed for

developing an industrial gas turbine. A schematic view

of its flowpath is shown in Fig. 1. MCA airfoils are

used for the transonic rotor of the first stage, and CDA

profile philosophy is adopted in designing the rest

subsonic blades. 3D design features such as vane bow

are incorporated into the conventional 2D design based

on 3D numerical simulations. The first two stators as

well as the IGV are variable for surge control at part

speed. Recently, full-scale rig test has been performed

in SEDRI, with the overall performance as well as the

static pressure on the casing and the spanwise profiles

in front of the stators measured.

3 Computing Methodology

3.1 Throughflow Method

An in-house throughflow code has been used in the

analysis of the 5-stage compressor. The code is based

on the streamline curvature method, with

empirical/semi-empirical models incorporated to

determine loss, deviation, spanwise mixing, etc. This

throughflow code has been validated by several test

cases of modern compressors including Pratt &

Whitney 3S1, NASA Rotor 1B, GE E3 high pressure

compressor, and several self-designed compressors, as

in Ref. [24].

3.1.1 Governing Equations

The governing equations of the streamline curvature

method include the full radial equilibrium equation and

the continuity equation in the coordinate system as in

Fig. 2, which can be written as:

5

5

2 0

22 2

2

1sin

2

1cos tan

2

mm m

m m

m

h VsV T V

q q q m

V Vr V rV

r q r mr

(1)

casing

hubcosm

mV wdq

N (2)

where 2w rB N .

3.1.2 Empirical Models

Reference Incidence Angle Model

The reference incidence angle is considered as the

incidence at which the stagnation point of the incoming

flow stays at the leading edge of the blade. The

reference incidence model is based on cascade tests

[26] and is given by:

*

0 10i ish ti K K i n (3)

where i shK is the shape correction factor, i t

K is

the thickness correction factor, 0 10i is the basic

value of incidence, is the camber angle and n is

the slope of the variation of incidence with .

Deviation Model

The deviation prediction includes the reference

deviation calculation and off-design deviation

calculation. The reference deviation is calculated using

Lieblein’s model [26], which is given by:

*

0 10sh tK K m (4)

where sh

K is the shape correction factor, t

K

is the thickness correction factor, 0 10 is the basic

value of incidence, and m is the slope of the

variation of deviation with the camber angle. The off-

design deviation correlation used in the code is that of

Creveling [27].

Total Pressure Loss Model

Generally speaking, the total pressure loss in

subsonic cascades can be categorized into profile loss,

endwall loss and leakage loss, which is:

ml prof ew leak (5)

where the endwall loss includes the secondary flow

loss and annulus friction loss, and the leakage loss

includes the unshrouded blade leakage and the

shrouded blade seal leakage loss.

The off-design loss can then be calculated with the

minimum loss, the incidence and the Mach number:

*,ml f i i Ma (6)

For transonic stages, the shock loss must also be

considered. In the present throughflow code, the model

of Boyer [28] is implemented, which is physics-based

and assumes different shock structures under peak

efficiency, near choke and near stall conditions.

Spanwise Mixing

The spanwise mixing of end-wall and main flow is

also modeled in the code to avoid the unrealistic

accumulations of entropy increases in the end-wall

regions, which is especially important for the rear

stages in the multistage compressor. The mixing model

by Gallimore and Cumpsty [29] is commonly used for

the compressor throughflow calculation. Their model

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contains the radial heat transfer and shear stresses in

the axial and circumferential direction, by which the

total temperature distribution at the outlet can be

predicted precisely but the total pressure may not be

well predicted sometimes. So a revised model given by

Howard and Gallimore [30] is used in the present code,

in which the shear force on the annulus walls is taken

into account.

Stall Prediction Model

Koch’s criterion [31] is adopted in the present code

to predict stall. In this criterion, the compressor

cascade flow is assumed to be equivalent of that in a

straight diffuser, and the stalling effective static

pressure rise is correlated with the normalized

diffusion length.

3.2 CFD Method

The 3D CFD computations in the paper are

performed with a commercial CFD software

FINE/Turbo [32]. Steady simulation results are

obtained by second order upwind scheme for spatial

discretization, with a multigrid approach to accelerate

the convergence. Spalart-Allamaras turbulence model

is used to close the RANS equations, and the mixing

plane approach is used as the rotor-stator interface

strategy.

Structural mesh generated using all hexahedral

elements is used for CFD computations, which is

shown in Fig. 3. The total mesh size for all the eleven

blade passages is around six millions. The tip

clearances of rotors and the clearances of variable

stators as well as the inlet guide vane are all taken into

account in the computations.

4 Analysis of the Baseline Compressor

4.1 Overall Performance Results

Both experimental and numerical analysis is made

for the current design, which is also noted as the

baseline compressor in the paper. The measured and

predicted overall performances of the 5-stage

compressor at the design speed are present in Fig. 4,

where all data has been non-dimensionalized by the

design parameters. The test data has proved the high

performance of the current design, which meet the

design objectives with a slightly larger mass flow rate,

though larger stall margin is still required.

Compared with the experimental data, it is found

that the shapes of speedlines predicted by the two

methods are both similar to the test one; the

throughflow calculation under-predicts the mass flow

rate by approximately 1.4%, while the CFD calculation

over-predicts the mass flow rate by approximately

0.4%; the throughflow code predicts a relatively larger

stall margin compared with the test data, whereas CFD

predicts slightly smaller one because of the rigid

boundary conditions which are not suitable for near-

stall condition [33]; the peak efficiencies of the

throughflow and CFD calculations show good

agreement with experimental results, with errors within

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0.5%, though both methods under-predict the drop of

efficiency at higher-pressure-ratio conditions, of which

CFD acts slightly better. To summarize, the

throughflow and CFD methods both predict the overall

performance of this 5-stage axial flow compressor

well, though some errors exist in the off-design

conditions. The predicted flow details under different

operating conditions are further compared with test

data and analyzed in the following sections.

4.2 Design-point Results

In this section, analysis of the flow details is made at

the design operating point. Figure 5 shows the

dimensionless static pressure evolution on the casing

versus axial distance. It is clear that the static pressure

evolutions are well predicted with both throughflow

and CFD methods. The spanwise total pressure profiles

in front of each stator row (from Stator 1 to Stator 5)

are compared in Fig. 6. On the whole, the calculated

profiles agree with the test data, especially in the main-

flow region. Specifically, the calculated total pressure

in front of Stator 1 deviates from the test data at 50%-

100% span, the possible reason of which is the

secondary flow including the interaction between the

tip clearance flow and the main flow as well as the

passage shock in the tip region of the transonic rotor. It

is known that the above tip-leakage related secondary

flow has important effect on the performance of

transonic rotors and is difficult to predict accurately

[34, 35]. It should also be noted that the differences of

CFD results are relatively smaller than those of

throughflow results. Besides, differences also exist at

90% span for other stators, which are affected by the

end-wall boundary layer.

The above analysis has validated the ability of both

methods in predicting the compressor performance,

and then the calculation results are analyzed in details

to look deeper into the flow field of this compressor.

Figure 7 illustrates the predicted adiabatic efficiency

of each stage, from Stage 1 to Stage 5. The stage

efficiencies calculated by both throughflow and CFD

are almost the same, and the efficiencies of different

stages are all at a high level around 90%, with minor

decreases along the axial direction. The high stage

efficiencies indicate that the stages are well matched at

the design point. The 3-D flowfield calculated by CFD

is checked by the limiting streamlines on the suction

side of each blade in Fig. 8. The limiting streamlines

have confirmed the absence of corner separation or any

remarkable flow deflects, which proves that the three-

dimensional flow in the compressor is successfully

controlled at the design point.

Figure 7 also compares the total pressure ratios of

different stages. CFD has predicted a smooth axial

distribution of stage pressure ratio, which decreases

gradually from the first stage to the last stage. For

Stage 3-5, the pressure ratios predicted by the

throughflow calculation are almost the same with CFD

results, while for Stage 1 and 2 they are much different.

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Throughflow results show a lower pressure ratio of the

first stage and a higher pressure ratio of the second

stage, forming an unusual axial total-pressure-ratio rise

in the front stages. Referred to Fig. 6 which indicates

that the pressure ratio of Stage 1 is under-predicted and

Fig. 4 which compares the calculated overall

performances, it is believed that CFD gives a more

realistic distribution of stage pressure ratio. The reason

of the drop of total pressure ratio for Stage 1 in

throughflow results is thought to be related to the

transonic characteristics of Rotor 1. The flowfield

within the transonic rotor is strongly three-dimensional,

and it is difficult for the 2D throughflow code to

predict accurately. The detailed reason of the error of

the throughflow results is further analyzed as follows.

Since the blade loading is directly related to the

incidence and the inlet Mach number, Fig. 9 compares

the spanwise distributions of flow angles and the inlet

Mach number for Rotor 1. The throughflow-predicted

inlet and outlet flow angles are very close to the CFD

results, while Mach numbers at 50%-100% span are

obviously smaller than the CFD predictions, with the

maximum difference at the blade tip. So it can be seen

that the incidences as well as the deviations have been

well predicted, but the blockage in the tip region

caused by the complex three-dimensional shock-

leakage interaction is not accurately predicted by the

throughflow code, which causes the under-prediction

of the inlet Mach number and thus the blade loading.

Moreover, contours of relative Mach number at span

of 99% in Fig. 10 illustrate the shock wave structure of

the transonic rotor. It is found that a strong normal

shock wave appears near the leading edge of the rotor

blade, interacting with the suction surface of the

adjacent blade. This single-normal-shock structure is

similar with the structure assumed by Miller [36], but

differs from the design-point dual-shock structure in

Boyer’s model used in the throughflow code, the

advantage of which lies in prediction for highly

transonic fans, and which may not be suitable for the

present transonic rotor for industrial compressor. The

difference between actual and model-assumed shock

structure may cause the discrepancy in shock loss,

which might be another reason of the under-prediction

of the total pressure ratio of Rotor 1.

4.3 Near-stall Results

In this section, analysis is made about the flow

details at a near-stall operating point (NS1 in Fig. 4).

Again, the static pressure on the casing is well

predicted by both throughflow and CFD methods, as in

Fig. 11.

Compared with the design-point condition, the

streamwise variations of stage pressure ratio at near-

stall point (Fig. 12) show increased loading for the rear

stages, and the distributions of stage efficiency at the

near-stall point show an obvious efficiency decrease in

the last stage, especially in the CFD results. It should

also be noted that the CFD predicts a much lower

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efficiency in Stage 5 than that by the throughflow

method. The limiting streamlines on the suction side of

different blades are presented in Fig. 13 to show the

reason for the low efficiency in the last stage. Large

separation region near the suction side of Stator 5 can

be found from the streamlines, which causes the

obvious efficiency decrease in Stage 5 and may induce

stall of the compressor.

The spanwise distributions of loss coefficient in Fig.

14 also show higher loss at 10%-50% span caused by

the separation in CFD results, and the throughflow

code predicts a relatively lower loss because the 3-D

separations cannot be accurately predicted by the 2-D

throughflow method. Despite the disability of the

present throughflow code in predicting separation, it

should be claimed that the code also indicates the

serious working condition of the last stator, which can

be seen from the diffusion factor distributions

predicted by the throughflow method as in Fig. 15. The

diffusion factors of the rear stages rise distinctly from

the design point to the near-stall point, and the root

section of Stator 5 exhibits the largest diffusion factor,

which also indicates the possible separation or stall in

Stator 5.

Furthermore, the streamlines at the tip region of the

rotors predicted by CFD are checked, and in this paper

only the streamlines of Rotor 1 and Rotor 5 are

presented as in Fig. 16, for simplicity. As in Ref. [37],

the alignment of the interface between the incoming

flow and tip clearance flow with the rotor leading edge

plane is a typical feature of the rotor spike stall. It is

found in the figure that the interfaces are far from

being aligned with the leading edge plane, which

indicates that the flow limit of the rotors has not been

reached. So it is believed that optimization or redesign

of the last stator will benefit in improving the stall

margin, which will be the focus of the next section.

5 Optimization of the Baseline Compressor

On the basis of the evaluation of the baseline

compressor, the target of the optimization is set at

increasing the stall margin by 10% while maintaining

its efficiency. Considering that the baseline compressor

has shown relatively good performance in its first-build

rig test, the optimization is required to be a retrofit

with major constraints for risk and cost reduction,

which means, the mean-line and axis-symmetric design

as well as the structural design will not be changed and

only the geometry of some blade rows will be

optimized. As indicated by the above analysis, the flow

instability at the large-pressure-ratio condition is

caused by the high load and the consequent separation

of Stator 5, and it becomes the focus of the

optimization.

5.1 Compressor Performance with Re-staggered

Stator 5

It is shown in Fig. 17 that incidences larger than 5

degree exist in Stator 5 along the full span, which is

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highly related to the suction-side separation. Stator re-

staggering is a commonly and easily used method to

adjust the working conditions of blades in multistage

environment, as in Ref. [21, 38], so at first Stator 5 is

re-staggered (closed) by 3 degree to improve the

incidences and multistage CFD analysis is carried out

to check whether the stall margin can be improved.

In Fig. 18 the calculated overall performances of the

re-staggered compressors are compared with those of

the baseline compressor. It can be found that by re-

staggering Stator 5 the stall margin increases by 5.6%

and the design-point efficiency also increases slightly

(0.05%) at the same time.

In order to show the reason of the stall margin

improvement, the streamlines around Stator 5 in the

baseline and re-staggered compressor at the point NS1

are compared in Fig. 19. For the baseline compressor,

Stator 5 works with very high incidences at point NS1,

which causes evident separation at the suction side and

induces stall, whereas no separation exists near the

suction side at larger stagger angle because the

incidence is significantly reduced, which helps to

reduce loss and prevent stall.

To investigate the reason of the increase of design-

point efficiency, spanwise profiles of relevant

parameters at the design point including the inlet total

pressure, the total pressure loss coefficient, the inlet

flow angle and the outlet flow angle are shown in Fig.

20. The inlet total pressures and flow angles in front of

Stator 5 remain the same when the stator is re-

staggered, which indicates that re-staggering Stator 5

does not change the stage matching of the baseline

compressor and the stall-margin increase is only

induced by the improvement of incidences. The loss

profiles show that the loss of Stator 5 is also reduced

slightly at the design point. The explanation is that the

minimum loss of Stator 5 occurs at small negative

incidence, and Stator 5 is a little over-loaded in the

original design even at the design point.

Since re-staggering Stator 5 has shown clear but not

enough improvement in the stall margin, it is therefore

necessary to find out how to further increase the stall

margin to meet the optimization target of 10%. The

possible methods can be categorized into three

following ways.

The first way is to increase the re-stagger angle, i.e.,

make Stator 5 work in a more choked condition. Since

the above 3 degree re-staggering has led to larger stall

margin and slightly higher adiabatic efficiency, it is

reasonable to believe that larger re-stagger angle will

further increase the stall margin while maintaining the

design-point efficiency. The reason that re-stagger

angle larger than 3 degree is not adopted is of the

outlet flow angle. It can be seen from Fig. 20(d) that

the outlet angle also increases by approximately 3

degree with re-staggering. Unlike the middle-stage re-

staggering, in which the alternation of outlet flow

angles is used to adjust the incidence of the

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downstream rotor and thus to improve the axial stage

matching, the increase of the last stator’s outlet flow

angle means the underturning of the outlet flow. The

underturning of the outlet flow will cause additional

loss and may be harmful for the operation of the

combustor, so the re-stagger angle is limited below 3

degree to prevent too serious outlet underturning.

The second way is to modify the stage matching.

The above analysis shows that Stator 5 is over-loaded

in the original design, so modification of the stage

matching to reduce the load of Stator 5 will certainly

be helpful for increasing the stall margin. This method

has also not been put into effort because of the required

major constraints of the present optimization as

mentioned above.

Then the last and adopted way comes to

optimization of the geometry of Stator 5 to increase its

load limit and the optimization is presented and

discussed in the next section.

5.2 Three-dimensional Optimization of Stator 5

In this section, three-dimensional optimization is

carried out for Stator 5, with aim to further increase the

stall margin. Bowed-type stackline has been adopted

for Stator 5 in the original design, and it has been

found by case study that further variation of the

stackline shape does not show obvious benefits in

improving stability, so the stackline of Stator 5 is kept

unchanged, and solidity distribution optimization and

leading-edge re-camber are used as the approach for

optimization. The use of LER is inspired by the fact

that re-staggered stator improves the stall margin, and

it should be noted that LER is used along the whole

span in the present research, unlike the usually referred

LER such as in Ref. [7] which is only used in the end-

wall region. The optimization of solid distribution is

adopted because it is an effective way to enhance the

blade load limits.

In the currently used blade design system, the 3D

blade geometry is represented by 21 blade profiles and

each sectional profile is defined by a mean camber line

and a thickness distribution. Unlike those published

optimization method, in which the sectional profiles

are represented by parametric curves and the curve

parameters are used as optimization variables, in the

present optimization the spanwise distribution of

solidity and inlet metal angle are parameterized using

two B-spline curves with 6 control points respectively,

and new camber lines at different spanwise locations

are built from the corresponding LER angles and chord

lengths. New blade profiles are then rebuilt with the

new camber lines and the original thickness

distributions. Thus the new 3D blade geometry is

represented by only 12 parameters. A schematic flow

chart of the optimization process is shown in Fig. 21.

The benefit of this kind of parameterization lies in

two aspects. Firstly, it reduces the optimization

parameters under the guidance of previous

aerodynamic analysis, which makes it easier to get an

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optimum design. Secondly, the fixed thickness

distribution helps to maintain favorable mechanical

characteristics.

Further, the optimization objective function is

defined as:

min obj NSF (7)

where NS is the total pressure loss of Stator 5 at the

near-stall boundary conditions corresponding to the

point NS1, which is evaluated by single-row CFD

analysis.

And the following geometrical and aerodynamic

constraints are adopted:

1 11opt ori (8)

2/opt ori oriC C C (9)

3opt oriDP DP (10)

Constraint (8) is used to prevent too large re-

camber angle, constraint (9) must be fulfilled because

the chord length of the blade is limited by the original

structural design, and constraint (10) is used to

prevent significant drop in design-point efficiency. The

value of 1 , 2 and 3 are 15, 0.15 and 0.01,

respectively. In addition, the choked mass flow is not

considered in the optimization constraints because the

flow rate of the original compressor is not limited by

Stator 5 and the above constraints in re-camber angle

and chord length have prevented the choked mass flow

of Stator 5 from varying too much.

The value of the solidity or angle of the above B-

spline control points is optimized by a combination of

Sequential Quadratic Programming method and Mixed

Integer Optimization method with the above

optimization objective and constraints required. Since

the optimization problem is single-objective and the

number of optimization parameters is not large, which

is relatively simple, the detailed algorithm and the

optimization process will not be described here for

simplicity, and the optimization results are presented as

follows.

The resulted blade shape and the corresponding

distributions of solidity and blade inlet angle are shown

in Fig. 22 and Fig. 23, and the original blade is also

plotted for comparison. In the single-row CFD

analysis, the optimized blade shows loss reduction of

approximately 50% at point NS1 and the suction-side

separation is completely eliminated. Then multistage

CFD calculation is performed with the optimized stator

to check the improvement in overall performance. The

calculated overall performances are shown in Fig. 24.

It can be found that by the stator optimization the stall

margin of the 5-stage compressor has been

significantly increased by 13.4% and the calculated

efficiency drop at the design point is less than 0.05%,

so the optimization target has been achieved.

Furthermore, an analysis of the optimized stator is

carried out to seek the reason of the prominent stall

margin improvement, which may offer some guidelines

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for the design of blades with large stall margin. At first

the optimized inlet angle is analyzed. It can be seen

from Fig. 23 that the optimized blade has a larger blade

inlet angle at the whole span, with the increase of inlet

angle more significant at the end-wall region. The

larger blade inlet angle aligns the leading edge more to

the flow direction at near-stall conditions and reduces

the suction-side separation, the effect of which is

similar with that of re-staggered stator.

About the blade solidity, the optimization blade

shows a C-shape distribution of solidity, that is, the

solidity at the middle of the blade is reduced (50%-

80% span for the present case) and the solidity near the

hub and casing is increased. In fact, this kind of

solidity distribution is not new for the blade design.

Similar solidity distribution has been used in the

compressor design even with the traditional quasi-3D

design process, such as in Ref. [39]. For the two-

dimensional cascade flow, larger solidity helps to

increase the load limit but will cause additional friction

loss near the design incidence. Thus in a two-

dimensional view, the benefits of such C-shape solidity

distribution can be explained as follows. The boundary

layer on the blade sections in the end-wall region tends

to be easier to separate because of the inlet pressure

loss caused by the viscous forces exerted on the flow

by the endwalls and the increased inlet flow angle, so

the solidity in the end-wall region should be increased

to suppress separation and to delay the flow instability.

However, for the middle sections of the blade where

the load is more moderate compared with the end-wall

sections, the solidity should be minimized so that the

friction loss can be minimized and the design-point

efficiency can be retained. Hence, the high solidity

near the end wall and the low solidity at the middle

form the above C-shape solidity distribution.

However, in this paper the author intends to explain

the effect of such solidity distribution in a different

perspective with the help of CFD, especially with

concentration on the effect of the low solidity at the

middle of the blade.

To show clearly the three-dimensional effect of

reduced mid-span solidity, a stator with higher mid-

span solidity is built and its aerodynamic performance

evaluated by the single-row CFD analysis is compared

with that of the above optimized stator. Fig. 25 shows

the solidity distribution of this high-solidity stator,

which has the same solidity as the optimized stator at

the end-wall region and higher solidity at the middle of

the blade. It should be noted that the other blade

parameters such as the blade angles are all the same as

the optimized stator.

Based on the above two-dimensional analysis, this

high-solidity stator should show better flow stability in

spite of higher design-point loss compared with the

optimized one. However, the CFD analysis for the two

stators at the same high-pressure-ratio condition

corresponding to point NS2 in Fig. 24 shows that this

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high-solidity stator leads to poor flow stability and

smaller stall margin instead. The iso-surface of axial

velocity for the two stators which shows the reversed

flow region in the passage is presented in Fig. 26. It

can be found that a small reversed flow region exists

around the mid-span for the optimized stator, whereas

for the high-solidity stator a much larger reversed flow

region exists at the corner of the blade suction surface

and the end-wall, which forms the so-called “hub-

corner stall”. The corner stall will cause major passage

blockage and is thought to be a major reason of

compressor instability [40, 41], which leads to the

smaller stall margin of the high-solidity stator.

Such difference in the size and location of separation

can be explained with the pressure distribution on the

blade suction surface, which has been shown in Fig.

27. For the optimized stator, the load limit of near-hub

blade sections is higher than that of the mid-span

sections. The difference in blade load limit forms an

upward radial pressure gradient (denoted by the arrow

in the figure), which induces the migration of the end-

wall low stagnation pressure fluid onto the mid-span

suction surface and forms separation at the mid span.

However, for the high-solidity stator, the radial

pressure gradient becomes downward because of the

increased mid-span solidity, which causes the

accumulation of low stagnation pressure fluid near the

suction surface hub corner and forms serious corner

stall. The above analysis has shown that the C-shape

solidity distribution has introduced 3D flow control

effects in addition to the traditional 2D effect. It should

also be noted that its mechanism is similar to the flow-

control mechanism of dihedral or bowed stators.

6 Conclussion

1. The 5-stage compressor shows good performance

in the full-scale rig test, and has met the design

objectives with a slightly larger corrected mass flow

rate, though the demand for larger stall margin still

requires a revision of the current design.

2. The shape of the speedline as well as the peak

efficiency is well predicted by the in-house

throughflow code, but the mass flow rate is under-

predicted by approximately 1.4%, and the stall margin

as well as the near-stall efficiency is over-predicted.

More specifically, the throughflow method predicts a

lower transonic-rotor loading because of the

discrepancy in blockage prediction and shock structure

assumption, which indicates that the blockage and

shock loss model for transonic blades in the present

code should be adjusted.

3. CFD has given good prediction of the compressor

performance except for the discrepancy in the near-

casing total pressure in front of Stator 1. Both CFD and

throughflow calculations indicate that the stall of the

compressor is initiated by the separation in the last

stator. So the revised design aiming at improving the

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stall margin should focus on the optimization or

redesign of the last stator.

4. Re-staggering Stator 5 by 3 degree has resulted in

a 5.6% increase in the stall margin and slightly increase

in the design-point efficiency for the 5-stage

compressor, which indicats that Stator 5 is a little over-

loaded in the original design. Larger re-stagger angle

which may further improve the stall margin is not

adopted because of the resulted outlet underturning.

5. Finally, the last stator is optimized with spanwise

distributions of blade inlet angle and solidity. The

optimized stator which is characterized by larger blade

inlet angle and a C-shape solidity distribution has

resulted in a 13.4% improvement in the stall margin of

the 5-stage compressor without loss of design-point

efficiency. By comparing with a high-solidity stator,

the effect of the C-shape solidity distribution of the

optimized stator is then investigated in a three-

dimensional perspective, and phenomena which are

contradictory with the traditional 2D aerofoil theory

are observed. The results show that such solidity

distribution has introduced 3D flow control effects in

addition to the traditional 2D effect, that is, upward

migration of low-energy fluid is induced by the

spanwise difference of load limits caused by the

solidity distribution.

Acknowledgments

The authors wish to thank SEDRI for permission to

publish this paper.

Funding

This work was supported by Shenyang Engine

Design and Research Institute (SEDRI); Collaborative

Innovation Center of Advanced Aero-Engine; and the

National Natural Science Foundation of China [grant

number 51136003].

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Fig. 1 Schematic view of the compressor flow path

(a) Meridional plane (b) View along axis

Fig. 2 Streamline curvature coordinate system [25]

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Fig. 3 Mesh for CFD computations

Fig. 4 Measured and predicted overall performances

Fig. 5 Measured and predicted static pressure on the

casing

Fig. 6 Spanwise total pressure profiles in front of each

stator

Fig. 7 Stage performance at the design point

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Fig. 8 Limiting streamlines on the suction side of each blade

(a) Relative inlet flow angle (b) Relative outlet flow angle (c) Inlet Mach number (Relative)

Fig. 9 Spanwise parameter distributions of Rotor 1

Fig. 10 Relative Mach number contours at 99% span of Rotor 1 by CFD

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Fig. 11 Measured and predicted static pressure on the casing at the near-stall point

Fig. 12 Stage performance at the near-stall point

Fig. 13 Limiting streamlines on the suction side of each blade at the near-stall point

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Fig. 14 Spanwise distributions of the total pressure loss of Stator 5 at the near-stall point

Fig. 15 Streamwise distributions of diffusion factors

(a) Rotor 1 (b) Rotor 5

Fig. 16 Streamlines at the tip region of Rotor 1 and Rotor 5

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Fig. 17 Incidences of different stators at near-stall point NS1 (Predicted by CFD)

Fig. 18 Overall performances of the baseline and re-staggered compressors

(a) Baseline stator (b) Re-staggered stator

Fig. 19 Streamlines at 30% span of Stator 5 at NS1

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(a) Inlet total pressure (b) Inlet flow angle

(c) Total pressure loss (d) Outlet flow angle

Fig. 20 Spanwise profiles of original and re-staggered Stator 5 (Predicted by CFD)

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Start

Specify the control points

Calculate the spanwise distribution of

solidity and blade inlet angle

Calculate the chord lengths and re-camber

angles for the 21 blade sections

Build blade geometry

Generate mesh

Do CFD analysis with BC corresponding to

the design-point and near-stall conditions

Has the optimization

objective been reached?

Stop

Modifiy the control points

Yes

No

Fig. 21 Schematic flow chart of the optimization method

(a) Baseline (b) Optimized

Fig. 22 Shapes of the baseline and optimized stator

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(a) Solidity (b) Blade inlet angle

Fig. 23 Profile parameters of the baseline and optimized stator

Fig. 24 Overall performances of the optimized compressor

Fig. 25 Solidity distribution

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(a) Optimized stator (b) High-solidity stator

Fig. 26 Iso-surface of axial velocity (-0.5 m/s) for the optimized and high-solidity stator

Fig. 27 Pressure distribution at the suction surface of different stators