The Application of 3D Blading and Non-Axisymmetric Hub Endwall Contouring in a Dual-stage Axial Flow

International Journal of Energy Science (IJES) Volume 4 Issue 3, June 2014 doi: 10.14355/ijes.2014.0403.04

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The Application of 3D Blading and NonAxisymmetric Hub Endwall Contouring in a Dual-stage Axial Flow Counter-Rotating Compressor Zhiyuan Cao*1, Bo Liu2, Xiaodong Yang3, Min Li4 School of Power and Energy, Northwestern Polytechnical University NO. 159 Mail Box, NO. 127 West Youyi Road, Xi’an, 710072, P. R. China *1

zylast@126.com; 2liubo704@nwpu.edu.cn; 3yangxiaodong1986@163.com; 4limin2749433@163.com

Received 27 August 2013; Accepted 9 September 2013; Published 16 April 2014 © 2014 Science and Engineering Publishing Company

Abstract 3D blading and non-axisymmetric endwall contouring technologies are effective ways to control secondary flows in cascades. 3D blading can effectively reduce the secondary flows near the blade surface, but it has little impact on the endwall region. Non-axisymmetric endwall contouring is widely used in the control of endwall secondary flows in turbines. However, the use of non-axisymmetric endwall contouring in compressors is rarely. The effect of nonaxisymmetric endwall contouring on compressors is not clear.

The research object of the report is an axial flow dual-stage counter-rotating compressor. In order to further improve the performance of the compressor and to explore the method of reducing secondary flow loss, the two rotor blade rows and the hub endwall of the secondary rotor row are redesigned by 3D blading and non-axisymmetric endwall contouring technologies based on optimization algorithm. The flow fields of original compressor and redesigned compressor are also compared. After 3D blading optimization, the secondary flows near the suction surface of the rotor blades are obviously reduced and the efficiency of the optimization point increases. Nonetheless, the secondary flows at the hub endwall improve scarcely any.

Based on the 3D blading optimization, the second row rotor hub endwall are parameterization designed, and nonaxisymmetric endwall contouring is designed by optimization algorithm. After non-axisymmetric endwall contouring optimization, the hub endwall consist of a “hill” near the rotor pressure surface and a “valley” near the suction surface. The contouring reduces the pressure gradient at 0~40% axial chord near the hub. And the secondary flow loss is reduced effectively. This paper successfully combines the advantages of both 3D blading

and non-axisymmetric endwall contouring technologies; the performance of the counter-rotating compressor is improved effectively.

Keywords Counter-rotating Compressor; Three Dimension Optimization Design; Non-axisymmetric Endwall

Blade;

Introduction High efficiency, high stage load are the objectives of the aero turbomachinery designers all the time.

Separation and secondary flows are inevitable as the stage load increases.

The efficiency of turbomachineries decreases as the separation and secondary flows increase.

3D swept and lean blades have been widely used because of its advantages of controlling internal flows and improving the performance of compressors, such as E3E engine, PW4084 and PW6000 [1~2]. In the 1960s, Professor Wang Zhong-qi puts forward the leaned blades, which can effectively weaken the secondary flows in blade tip and hub [3]. Afterwards, researchers found that leaned blades can control the radial secondary flows on the blades and the transverse flows near the endwall. Swept blades are used to weaken shock intensity and to improve the stability margin of the transonic compressors [4]. Recent research demonstrates that the swept blades can also improve the performance and the stability margin of subsonic compressors. C. Xu and R. S. Amano find that swept blade redistributes the flow reducing the secondary loss depending on the baseline, and forward swept can 91

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reduce the tip loading [5]. Reference [6] indicates that swept blades have the similar effects on the endwall flow fields as leaned blades in subsonic compressors.

In 1994, Rose put forward the new concept of nonaxisymmetric endwall [7]. Non-axisymmetric endwall contouring can effectively control the transverse pressure gradient between pressure surface and suction surface near the endwall, hence decreases the secondary loss. Literature [8] investigates the secondary flows in a turbine cascade with and without the implementation of endwall profiling. G. Brennan redesigns the HP turbine of the Trent 500 engine by using non-axisymmetric endwall, and improves the HPT by 0.4% in efficiency [9]. T. Germain designs the endwalls using automatic optimization algorithm, and the results confirm that non-axisymmetric endwall profiling can improve turbine efficiency [10]. Na Zhenzhe optimizaiton designs the non-axisymmetric end wall in a high pressure turbine. The isentropic efficiency increases by 0.456% [11].

The main objectives of the report are to reduce the radial secondary flows on the rotor blades and the transverse secondary flows near the endwall of the dual-stage axial flow counter-rotating compressor by using 3D blading and non-axisymmetric endwall technologies. The swept law and lean law of the stacking line of the two rotor blade rows are optimized designed firstly. And the hub endwall of the secondary rotor blade row are optimization designed. What’s new in this report is that the 3D blading is found having little effect on the transverse flows near the hub endwall, and the compressor is optimized combined by 3D blading and non-axisymmetric endwall contouring technique. That is rarely found in existing literatures.

Investigated Compressor The dual-stage axial flow counter-rotating compressor is from Northwestern Polytechnical University of China [12]. FIG. 1 shows a picture of the compressor.

The compressor mainly consists of an inlet guide vane row (IGV), a first rotor row (R1), a second rotor row (R2), an outlet guide vane row (OGV). The meridional channel of the counter-rotating compressor is shown in FIG. 2. The external diameter of the compressor is 400mm. The compressor is designed with a rotating speed of 8000rpm, and the mass flow is 6.4Kg/s at the design point and the efficiency is 0.89. Table 1 shows the main parameters of the compressor. In order to save time, the investigation of the report only focuses on the two rotor blade rows.

92

Rotor 1

Rotor 2

OGV

FIG. 1 The picture of the dual-stage axial flow counter-rotating compressor

FIG. 2 The meridional channel of the compressor TABLE 1 MAIN PARAMETERS OF THE COMPRESSOR

IGV

R1

R2

OGV

22

19

20

22

Tip clearance

0.5mm

0.5mm

Hub-tip ratio

0.485

0.641

Design rotatingspeed

8000 （rpm）

-8000 （rpm）

Blade number

Numerical Model The AUTOGRID model in NUMECA FINE/TURBO commercial software package has been employed for grid generation. The total grids number is about 0.71 million. The minimum orthogonality of the mesh is 17.19. The investigation in this paper is based on this mesh. FIG. 3 to FIG. 5 show the mesh of blade and hub endwall surface, S1 surface at the mid span, and the leading edge of R1 hub. This report utilizes FINE/TURBO to compute the flow fields. The FavreReynolds averaged Navier-Stokes equations are discretized by a cell-center explicit finite volume scheme according to Jameson et al. The temporal discretization scheme used for the computation is an explicit multi-stage Runge-Kutta scheme. The spatial resolution is Jameson’s finite volume scheme. The mixing plane is used between the two rotors. Full multigrid technology is used for convergence.

Turbulence effects are modeled using the SpalartAllmaras model. Inlet absolute total pressure, inlet total temperature, inlet flow angle, and outlet static pressure are presented for the boundary conditions.

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1.3

Calculation Experiment

Total Pressure Ratio

1.25

1.2

1.15

1.1

1.05

FIG. 3 The grids of blade and hub endwall surface

1

5

5.5

6

6.5

7

7.5

8

Mass Flow(kg/s)

FIG. 8. Total pressure ratio-mass flow performance

Optimization Design Method Design Methods of 3D Blading

FIG. 4 The grids of S1 surface at the mid span

FIG. 5 The grids of the leading edge of R1 hub

As the experiment was done on the whole compressor, the performance of the whole compressor is numerical simulated firstly with the purpose of verifying the validity of the mesh and the numerical method. The mesh of R1 and R2 is the same with that of FIG. 3. And the numerical method is the same, too. The mesh of the whole compressor is shown in FIG. 6. The results of numerical simulation and experiments at design rotating-speed are provided in FIG. 7 and FIG. 8. The comparison shows that the calculation results agree well with the experiment results. As a result, the numerical model is reasonable and practicable.

The original geometry of the compressor is given by discrete points. But the optimization design is a parameterization optimization design process. The blade sections are firstly parametric fitted by high order Bezier curves of 8 control points. The stacking lines are defined by meridional position (swept) and tangential position (lean). We use leading edge stacking method to stack the S1 blade element. Both swept and lean lines are fitted by high order Bezier curves (7 control points, the control point at the blade hub is fixed), which is shown in FIG. 9. In the optimization design process, individual blade sections, hub line and shroud line remain unchanged. Only 'swept' law and 'lean' law of the stacking lines are modified in the design process.

(a) Swept law FIG. 6 The mesh of the whole compressor 1

Calculation Experiment

Isentropic Efficiency

0.9

0.8

0.7

0.6

0.5

5

5.5

6

6.5

7

7.5

8

Mass Flow(kg/s)

FIG. 7. Isentropic efficiency-mass flow performance

(b) Lean law

FIG. 9 Parametric stacking line

Design Methods Contouring

of

Non-axisymmetric

Endwall

The optimization design object is a single period of the hub endwall. The original hub endwall curved surface is expressed by some simple control parameters. The parameters are adjusted in the design process in order that the non-axisymmetric endwall curved surface is obtained. FIG. 10 shows the method of nonaxisymmetric endwall contouring.

The non-

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axisymmetric endwall region is limited to “Inlet” and “Outlet” shown in the figure. Axisymmetric hub endwall is defined by period boundary curve and tangential profile. Both the period boundary curve and meridional profile are defined by a high order Bezier curve which has 7 control points. Through adjusting the value of the control points, all the superposition of ΔR along radial direction is obtained. Finally, the nonaxisymmetric hub endwall is obtained. All the control points are modified at last.

function and the optimized variables, and uses the genetic algorithm to find the optimal value of target function.

In this report, as the structure changes small, we only consider the aerodynamic performance. There are no mechanical constraints and the throat area is also not considered. The work of the 3D blading and nonaxisymmetric endwall optimization lasted for 21 days in all.

Results and Analysis The surge margin of the compressor is defined as follows:

FIG. 10 Non-axisymmetric endwall contouring method

Optimization Methods The numerical simulation indicates that the radial secondary flows near the blade surfaces and the transverse flows near the hub endwall are obvious at the near stall condition. So we select near stall condition for optimization condition. The optimization object is to improve the efficiency of the whole compressor. In the optimization process, the same condition is defined as with the same boundary conditions described in ‘NUMERICAL MODEL’.

Based on artificial neural network, approximate function and genetic algorithm, the optimization methods of 3D blading design is the same with nonaxisymmetric endwall contouring design. A database is generated before the optimization process by using the ‘DATABASE_GENERATION’ model in NUMECA FINE/TURBO software. This paper utilizes discrete layer sampling method to generate samples. The sampling method divides the geometric constraint into some region in order to guarantee the generating samples having globally representative. Little changes for the values of the objective function are obtained during the process. As a result, a total of 150 samples for 3D blading and 80 samples for non-axisymmetric endwall contouring are generated.

The ‘OPTIMIZATION’ model is employed in the optimization process. The object for the optimization is improving the efficiency of the compressor, with the mass flow not decreasing. The optimization method utilizes artificial neural network technology to establish the relationship between the objective

94

*  π Ks    mas = − 1 ×100% SM  *  π Ko  mao   * m π Ks 、 as —the

total pressure ratio and mass flow at the near surge point; * m π Ko 、 ao —the

total pressure ratio and mass flow at the highest efficiency point.

Results of 3D Blading After 3D blading optimization, the efficiency of the compressor improves by 0.5% and the mass flow sees an increase of 2.84%, while the total pressure ratio remains unchanged. FIG. 11 and FIG. 12 show the shape of R1 and R2 after 3D blading optimization separately. FIG. 13 and FIG. 14 compare the lean law and swept law of the stacking line for R1 and R2 before and after 3D blading optimization.

The performance character of the original compressor and 3D blading optimized compressor are shown in FIG. 15 and FIG. 16. Because we define the same outlet static pressure condition as the same condition during the optimization process, the mass flow after 3D blading optimization increases. So, although the efficiency increases and the total pressure ratio remains unchanged at the same condition, the efficiency character shows little increase, but the total pressure ratio character increases. The mass flow at the near surge point decreases from 5.049kg/s to 4.872kg/s.

The surge margin increases from 27.03% to 30.90%.

FIG. 17 and FIG. 18 show the limited streamlines at the suction surface of the original compressor and 3D blading compressor. The radial secondary flows are

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discovered at the suction surface of R1 and R2 of the original compressor. The area of the secondary flow region is about 25% of the suction surface. The radial secondary flow is one of the main sources of flows loss.

After 3D blading optimization, the area of the radial flow decreases, especially with R2. And it has a positive role to improve the performance of the compressor.

FIG. 15 Isentropic efficiency performance

FIG. 11 3D blading shape of R1

FIG. 16 Total pressure ratio performance

FIG. 12 3D blading shape of R2

Origin Lean law

Swept law

3D blading

FIG. 17 Suction surface limited streamline for R1

FIG. 13 The stacking line of R1

Lean law

Swept law

FIG. 14 The stacking line of R2

Origin

3D blading

FIG. 18 Suction surface limited streamline for R2

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FIG. 19 and FIG. 20 show the limited streamline and static pressure contour at the hub of R1 and R2. The blades' load at the optimization point is high, so the hub of R1 shows transverse flow clearly. But as the bending of R2 is less than R1, the blade load is lower than R1. So the transverse flows of R2 hub are not as obvious as R1. However, because the attack angle of R2 hub is high at the near stall condition, the air flow stagnation point is near the pressure surface, so the static pressure at the leading edge of pressure surface is much higher than that of suction surface. So the pressure gradient at R2 inlet is higher than at the middle and the outlet of the blade passage at R2 hub.

And the transverse flows are more obvious at the leading edge of R2 hub. As the lean law and sweep law changes small in the hub region, the 3d-blading in this paper has little influence in the hub region.

Origin 3D blading FIG. 19 Hub endwall limited streamline/static pressure contours of R1

96

Origin 3D blading FIG. 20 Hub endwall limited streamline/static pressure contours of R2

FIG. 21 and FIG. 22 show the static pressure distribution of R1 and R2 with original compressor and optimized compressor. 3D blading has little influence on the hub and middle blade span of R1 and R2. The distribution curves of original and optimized compressor are almost the same. 3D blading has more influence on the tip span static pressure distribution.

The static pressure in the suction surface decreases in 0~20% axial chord of R1, and static pressure in the pressure surface increases in 0~10% axial chord of R1.

Thus the load decreases at the leading edge of R1. But at about 15%~100% axial chord of R1, the blade load increases. The static pressure of R2 is similar to R1, while the load increases higher at about 10%~100% axial chord of R1.

(a) R1 hub

(b) R1 mid FIG. 21 Static pressure distribution of R1

(c) R1 tip

(a) R2 hub

(b) R2 mid FIG. 22 Static pressure distribution of R2

(c) R2 tip

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FIG. 23 compares the radial distribution of efficiency for original and 3D blading compressor. After 3D blading optimization, the efficiency at 0~20% and 60%~90% span of R1 improves, while the efficiency of other span remains the same. The efficiency at 0~60% span of R2 decreases, while the efficiency at 60%~100% span increases.

FIG. 24 compares the radial distribution of total pressure ratio for original and 3D blading compressor.

After 3D blading optimization, the total pressure ratio at 0~30% of R1 decreases, while the total pressure ratio of other span increases. The total pressure ratio at 0~40% and 86%~100% span of R2 decreases, while the total pressure ratio at 40%~86% span increases. The reason that the efficiency of the whole compressor increases is that the load redistributes along the blade span.

optimization design, the efficiency of the whole compressor improves by 0.343% than 3D blading compressor, and is 0.843% higher than original compressor. FIG. 25 shows the contour of R2 nonaxisymmetric hub. The non-axisymmetric endwall hub is similar with common literatures [7~10], with a "hill" near the pressure surface and a "valley" near the suction surface.

FIG. 25 NON-AXISYMMETRIC HUB ENDWALL CONTOURING OF R2

The performance character of the original compressor, 3D blading compressor, and non-axisymmetric endwall compressor are shown in FIG. 26 and FIG. 27.

The efficiency of the non-axisymmetric endwall compressor is higher than that of the original compressor in most of the efficiency performance curve at design speed. The total pressure ratio is higher than that of the 3D blading compressor and original compressor. Surge margin is almost the same with the original compressor.

R1 R2 FIG. 23 Efficiency radial distribution

R1

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FIG. 26 ISENTROPIC EFFICIENCY PERFORMANCE

R2

FIG. 24 Pressure ratio radial distribution

Results of Non-axisymmetric Endwall Contouring The 3D blading of R1 and R2 has little influence on the transverse flows of the hub. Thus, in order to further improve the flow fields of the rotor hub and to improve the efficiency of the compressor, the author designs the R2 hub contouring by non-axisymmetric endwall contouring technique based on 3D blading compressor.

After

non-axisymmetric

endwall

contouring

FIG. 27 PRESSURE RATIO PERFORMANCE

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FIG. 28 and FIG. 29 compare the suction surface limited streamline of 3D blading compressor and nonaxisymmetric hub endwall compressor. The figures show little variation after non-axisymmetric endwall optimization. Non-axisymmetric hub endwall has little effect on improving the radial secondary flows near the blade suction surfaces.

3D blading

Non-axisymmetric hub

FIG. 28 Suction surface limited streamline for R1

3D blading

Non-axisymmetric hub

FIG. 29 Suction surface limited streamline for R2

FIG. 30 and FIG. 31 compare limited streamline/static

3D blading

pressure contour near the hub endwall of 3D blading compressor and non-axisymmetric hub endwall compressor. The flow fields of R1 show little variation.

However, the transverse flows near the R2 leading edge is reduced after non-axisymmetric endwall optimization. The static pressure near the pressure surface of R2 decreases and the flow fields are better.

FIG. 32 and FIG. 33 compare the static pressure distribution of different spans of 3D blading compressor and non-axisymmetric hub endwall compressor. The figures indicate that the nonaxisymmetric hub endwall has little effect on R1 and the upper blade span of R2 static pressure distribution.

The static pressure of R2 hub is influenced much by non-axisymmetric hub endwall. The static pressure gradient decreases at about 0~40% axial chord, and increases at about 40%~100% axial chord. The change of static pressure is corresponding with that of the flow fields in FIG. 28.

FIG. 34 shows the efficiency radial distribution of original compressor, 3D blading compressor and nonaxisymmetric hub endwall compressor. After nonaxisymmetric endwall contouring, the efficiency distribution of R1 varies little compared with 3D blading compressor. The efficiency of 20%~70 span of R2 increases, while at other spans remain the same with 3D blading compressor.

Non-axisymmetric hub

FIG. 30 Hub endwall limited streamline/static pressure contours of R1

(a) R1 hub

98

3D blading

Non-axisymmetric hub

FIG. 31 Hub endwall limited streamline/static pressure contours of R2

(b) R1 mid FIG. 32 Static pressure distribution of R1

(c) R1 tip

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(a) R2 hub

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(b) R2 mid FIG. 33 Static pressure distribution of R2

R1

(c) R2 tip

R2 FIG. 34 Efficiency radial distribution

R1

R2 FIG. 35 Pressure ratio radial distribution

FIG. 35 shows the total pressure ratio radial distribution of original compressor, 3D blading compressor and non-axisymmetric hub endwall compressor. The total pressure ratio at all different R1 span of non-axisymmetric endwall compressor decreases compared with that of 3D blading compressor, and at 20%~100% R1 span of nonaxisymmetric endwall compressor decreases compared with that of original compressor. The reason why the total pressure ratio of R1 decreases is that the mass flow increases after non-axisymmetric hub optimization. So the load decreases when the mass flow increase. However, because of the influence of non-axisymmetric hub, the distribution of R2 is not the same with R1, and the total pressure ratio of R2 increases instead. The total pressure ratio at all different R2 span of non-axisymmetric endwall compressor increases compared with that of 3D

blading compressor, while at 0~90% R2 spans of nonaxisymmetric endwall compressor increases compared with that of original compressor. Non-axisymmetric hub endwall can not only improve the flow fields of R2 hub, but also redistribute the aerodynamic parameter along the rotor span.

Conclusions The report optimization designs the 'swept' law and 'lean' law of the stacking line of R1 and R2 separately at the near stall condition. The effect of 3D blading on the compressor performance and flow fields are investigated. 3D blading optimization design indicates that 3D blading have little influence on the hub flow fields. So the hub endwall of R2 is optimization designed by non-axisymmetric endwall technique based on optimization algorithm with the purpose of 99

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further improving the compressor performance.

Experimental study is to be done on the platform in order to verify the optimization methods of 3D blading and non-axisymmetric contouring. The conclusions are as follows, (1) 3D blading can significantly improve the performance of the dual-stage axial flow counterrotating compressor, the efficiency of the compressor improves by 0.5%, the mass flow sees an increase of 2.84%, and the surge margin increases from 27.03% to 30.90%. The radial secondary flows are reduced by 3D blading effectively. However, 3D blading has little effect on the transverse flows near the hub endwall, which is rarely found in existing literatures.

(2) 3D blading increases the load at the tip of R1 and R2. But the load of the lower span of R1 and R2 varies little. Efficiency and total pressure ratio distribution along R1 and R2 radial are influenced by 3D blading.

And the reason that the performance of compressor improves is the redistribution of aerodynamic parameter along the rotor span.

(3) After non-axisymmetric endwall contouring optimization design, the efficiency of the whole compressor improves by 0.343% than 3D blading compressor. The transverse flows at the hub of R2 improve significantly, and the loss near the hub reduces.

(4) The static pressure distribution of R2 hub endwall varies after non-axisymmetric endwall contouring.

The static gradient at about 0~40% axial chord decreases, while at about 40~100% axial chord increases. Non-axisymmetric endwall contouring can not only improve the flow fields of R2 hub, but also redistribute the aerodynamic parameter along the rotor span. However, R2 non-axisymmetric hub endwall has little effect on the static pressure distribution of R1 and upper span of R2.

ACKNOWLEDGMENT

The work is funded by the natural science foundation of China. The fund number is 51236006.

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