Journal of Thermal Science Vol.18, No.2 (2009) 119−125
DOI: 10.1007/s11630-009-0119-0
Article ID: 1003-2169(2009)02-0119-07
Study on the Effects of End-bend Cantilevered Stator in a 2-stage Axial Compressor Songtao WANG, Xin DU and Zhongqi WANG Harbin Institute of Technology, P.O. BOX 458, Harbin 150001, China
Leading edge recambering is applied to the cantilevered stator vanes in a 2-stage compressor in this paper. Different curving effects are produced when the end-bend stator vanes are stacked in different ways. Stacking on the leading edge induces a positive curving effect near the casing.When it is stacked on the centre of gravity, a negative curving effect takes place. The numerical investigation shows that the flow field is redistributed when the end-bend stators with leading edge stacking are applied. The variations in the stage matching for the mainstream and near the hub have an impact on the performance of the 2-stage compressor. The isentropic efficiency and the total pressure ratio of the compressor are increased near the design condition. The compressor total pressure ratio is decreased near choke and near stall. The maximum flow rate is reduced and the stall margin is decreased.
Keywords: axial compressor; end-bend; blade stacking; stage matching
Introduction In axial compressors the presence of end-wall boundary layers and secondary flows leads to high inlet flow angles close to the wall. In the latter stages of multistage compressors boundary layers get thicker and occupy more passage area which produces high loss and causes stall inception. By improving end-wall flow matching and suppressing corner stall, end-bend has shown an encouraging impact on multistage compressor stability. A comprehensive study of the end-bend mechanism including numerical calculation, theoretical analysis and experimental investigation was processed by Huang [1]. Various forms of end-bend were studied. The results indicated that end-bend caused the redistribution of the whole flow field along span and the characteristic variations in main flow might be a vital factor for the compressor performance improvements. An end-bend with bigger exit blade angle was applied to a HP compressor stator by Cai [2]. The experiment results showed that the
decreased positive incidence at rotor tip and hub caused the delay of flow separation and enhanced surge margin. Li [3] proposed a kind of endwall flow control method called as end-sweep-bend which showed a better performance than end-bend when the endwall flow turning was increased. So far, the applications of end-bend to the compressors with shrouded stators have been studied a lot [4, 5].However, the applications of end-bend to cantilevered stators are still rare [6]. Leading edge recambering was applied to the cantilevered stator vanes in a 2-stage compressor in this paper. It was supposed to match to the high inlet flow angles at the casing and reduce stator flow separations. The curved blade mechanisms were investigated for the end-bend stator vanes with different stacking ways. The effects of the end-bend cantilevered stators in the 2-stage compressor were discussed in the analyses of flow rate characteristics and the studies of flow fields at different working conditions.
Received: October 2008 Songtao WANG: Professor www.springerlink.com
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Nomenclature R
Rotor
2
second stage
S
Stator
P
prototype stator
M
mass flow rate (kg/s)
L
end-bend stator stacking on the leading edge
G
end-bend stator stacking on the centre of gravity
choke
in the working condition near choke
Subscripts 1
first stage
Geometric parameters and numerical method Geometric parameters The main geometric parameters and the structure of the 2-stage compressor are respectively shown in Table 1 and Fig.1. In order to match to the high inlet flow angles at the casing, leading edge recambering was applied to the cantilevered stator vanes. From 85% span out to the casing the increment of the inlet blade angle was linearly increased from 0 degrees to 10 degrees, while the exit blade angle was kept unchanged. Two blade stacking methods were applied to the end-bend stator vanes, stacking on the leading edge (S1L, S2L) and stacking on the centre of gravity (S1G, S2G). The casing profiles of S1P, S1L and S1G are compared in Fig.2. The stator vanes of S1P, S1L and S1G are shown in Fig.3. Numerical method Numeca Fine/Turbo was used for numerical simulation in this paper. The computational grid of the 2-stage compressor had 998834 mesh cells. By increasing mesh points in the boundary layer, the y+ value of the first mesh width was below 3.0 in order to accurately resolve the turbulent boundary layer. FINETM was used to solve the Reynolds-averaged Navier-Stokes equations. In the
S1G S1L S1P
Fig.2 Comparison of profiles at the casing for S1P, S1L and
S1G
Casing
Hub
Fig.3 Comparison of stator vanes for S1P, S1L and S1G
1.36E+06
Rotor 1 Stator 1 Rotor 2 Stator 2 aspect ratio
1.762
2.653
1.744
2.632
blade camber angle at 50% span 17.80 (deg)
22.54
16.57
22.04
blade camber angle at the casing (deg)
23.17
—
22.88
—
Total Pressure
Table 1 Compressor geometric parameters 1.34E+06
1.32E+06
0
0.2
0.4
0.6
0.8
1
Relative Span
Fig.4 Inlet total pressure of 2-stage compressor
Fig. 1 2-stage compressor grid
time direction, the explicit 4-stage Runge-Kutta time stepping was adopted. The Spalart-Allmaras turbulence model was used in this paper. The 2-stage compressor consisted of two latter stages of a multistage compressor. Considering the boundary layer accumulation of the front stages, the boundary layer
Songtao WANG et al. Study on the Effects of End-bend Cantilevered Stator in a 2-stage Axial Compressor
thickness at inlet was taken into account. The spanwise distribution of the inlet total pressure was obtained by a numerical simulation of the whole multistage compressor. The result is shown in Fig.4. The maximum inlet total pressure is 1364560.0 Pa. The inlet total temperature was set to 675.6 K and the inlet flow angle to 40.81 degree. The radial-equilibrium equation was solved at outlet and the compressor speed-line was obtained by adjusting outlet static pressure at mid-span. Stator flow field at design condition The limiting streamlines on the suction surface and casing of S1P, S1L and S1G at design condition are presented in Fig.5. A large-scale flow separation starting from 50% chord-wise occurred in the suction-casing corner of S1P. In S1L the large-scale flow separation was eliminated and the flow separation start point was delayed to 80% chord-wise. However the flow separation length of S1G was enlarged both on the suction surface and on the casing, and the flow separation starting point moved upstream.
S1P
S1L
S1G
Fig.5 Comparison of limiting streamlines on the suction surface and casing at design condition for S1P, S1L and S1G
It was assumed that for a given turning of the flow an over-cambered blade performed better than a profile at high positive incidence. For both S1L and S1G the inlet blade angles were increased at the casing so as to decrease positive incidence. At design condition the flow separation in the suction-casing corner was obviously controlled in the former, but in the latter it was strengthened on the contrary. Then a question came out that why the flow separation could be controlled for S1L, while it could not for S1G. As the blade angle varied, blade shape altered and blade force direction changed. Compared with S1P, the casing blade profile of S1L offset along the positive direction of circumferential velocity (shown in Fig.2), which formed an obtuse angle between the suction surface and the casing. Similar to the positive curved blade definition, the blade force on the suction surface had a component towards mid-span. It was obvious that the positive curving effect was strengthened gradually along the chord-
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wise direction. In the presence of positive curving effect, the low energy fluid was driven away from the suction-casing corner so that the flow separation was delayed and the flow separation length was diminished. With the improvement of flow behavior in the suction-casing corner, the flow capacity and axial velocity were increased near the casing, and the local inlet flow angle was diminished. The under-turning near the casing was of benefit to delay flow separation. Compared with S1L, a negative curving effect occurred at the leading edge of S1G. The low energy fluid migration to the casing caused a thicker boundary layer in the suction-casing corner. The flow separation start point then moved upstream and the flow separation was enlarged. The flow capacity and axial velocity were decreased near the casing producing an increase of inlet flow angle. The over-turning near the casing would also promote flow separation. Although a positive curving effect took place at the trailing edge of S1G, it was relatively weak compared with S1L. The low energy fluid had separated off the blade surface at the trailing edge so it was hard for the blade force to control the separated flow. As far as S1G was concerned, it was the negative curving effect at the leading edge that dominated the flow performance. The concept of end-bend, which was originally used to solve three-dimensional flow problems e.g. for flow separations, was based on a two-dimensional approach. In this paper, combined with blade stacking, end-bend formed a three-dimensional approach to deal with flow separations. For each stator in the prototype compressor there was high positive incidence near the casing and the aerodynamic loading was out of the attached flow limit. Applying the end-bend with leading edge stacking could decrease the high positive incidence and form a positive curving effect to change the distribution of the low energy fluid and control the flow separation. The design method called as “static state design” in end-bend was increasing inlet blade angle by θ degrees in order to decrease positive incidence by θ degrees. As mentioned above, when the flow performance was improved at endwall e.g. for S1L, the inlet flow angle would be diminished and the desired end-bend extent would be smaller than that of the "static state design". In addition, when the flow performance got worse at endwall e.g. for S1G, the desired end-bend extent would be larger than that of the "static state design". In these cases, in order to find out the exact end-bend extent, iterative retrofits and simulations might be necessary, which would cost lots of time and turn to be ineffective. In this paper, for each stator in the retrofit compressor the inlet blade angle was
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increased by 10 degrees a little smaller than the positive incidence in the prototype compressor. The simulation at design condition indicated that the incidence near the casing in S1L was decreased to around 0 degrees. Since the end-bend stator 1 with leading edge stacking had shown an encouraging performance improvement, its effects on a 2-stage compressor with cantilevered stators would be discussed below.
Compressor flow rate characteristics The flow rate characteristics at design speed are compared for the prototype compressor and the retrofit compressor in Fig.6. The isentropic efficiency and the total pressure ratio of the retrofit compressor were increased near the design condition (m/mchoke=0.8407). The peak isentropic efficiency of the retrofit compressor was 0.176 % higher than that of the prototype compressor. The maximum flow rate was diminished and the stall margin was decreased due to a reduced operating range of the retrofit compressor.
As the stators were located at the downstream of rotor 1, rotor 1 was limited affected by any geometry variation of the stators. Qualitatively the performance of rotor 1 was scarcely changed in the retrofit compressor (it was validated in the numerical simulations). The flow rate characteristics at design speed of rotor 2 are compared for the prototype compressor and the retrofit compressor in Fig.7. The total pressure ratio of rotor 2 decreased from its maximum while that of the compressor still increased. Then it was assumed that stall might start from rotor 2. The isentropic efficiency and the total pressure ratio of rotor 2 were increased near design condition, decreased near stall and near choke in the retrofit compressor. The pressure loss coefficient of each stator is compared for the prototype compressor and the retrofit compressor in Fig.8. The operating range of stator 2 with low loss coefficient was smaller than that of stator 1. The loss coefficient of each stator near choke was higher in the retrofit compressor than in the prototype compressor, while it was lower near stall. The decreased loss of each stator near stall made up the increased loss of rotor 2 in
(a) (a)
0.92 0.91 0.9 0.89 0.88 0.78
0.8
0.82
0.84
0.86
(b) (b)
Fig.6 Flow rate characteristics of 2-stage compressor at design speed
Fig.7 Flow rate characteristics of Rotor 2 at design speed
Songtao WANG et al. Study on the Effects of End-bend Cantilevered Stator in a 2-stage Axial Compressor
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Inlet axial velocity
95 90 85
R2 - Prototype R2 - Retrofit
80 75 0
0.1
0.2
0.3
0.4
0.5
0.6
Relative Span
0.7
0.8
0.9
1
(a)
Fig.8 Pressure loss coefficient of each stator at design speed
the same condition. So there were few differences in the isentropic efficiency between the retrofit compressor and the prototype compressor near stall.
Diffusion factor
0.55
0.5
R2 - Prototype R2 - Retrofit 0.45
0.4
0.35
Compressor flow field
0
0.1
0.2
0.3
0.4
0.5
0.6
Relative Span
0.7
0.8
0.9
1
(b)
The limiting streamlines on the suction surface for stator 1, rotor 2 and stator 2 at design condition are shown in Fig.9. The flow separations in the suctioncasing corners in the prototype compressor were reduced by the positive curving effect of the end-bend stators in the retrofit compressor. The flow separation length for rotor 2 was basically unchanged. The reduced casing blockages induced the spanwise redistribution of flow capacity. The spanwise distribution of inlet axial velocity for rotor 2 is shown in Fig.10 (a). Near the casing as the flow behavior was improved the inlet axial velocity was increased and then the local inlet flow angle was diminished, so that the aerodynamic loading was decreased. In the mainstream and near the hub the decreased inlet axial velocity caused the inlet flow angle to be increased, and then the aerodynamic loading was enhanced. Hence, the aerodynamic loading of rotor 2 was increased. The spanwise distribution of diffusion factor for rotor 2 at design condition is shown
in Fig.10 (b), which was decreased at the tip and increased below 72% span, consistent with the above analyses. As the compressor aerodynamic loading increased, the flow separations for each stator and rotor 2 were strengthened near stall in the prototype compressor as shown in Fig.11. The flow separations in the suction-casing corners were well controlled in the retrofit compressor. It was noticed that the flow separation length of rotor 2 was increased in the retrofit compressor. The spanwise distribution of inlet axial velocity for rotor 2 near stall is shown in Fig.12 (a). As the casing blockage was enlarged near stall than that of the design condition, a notable increase of flow capacity occurred near the casing when the casing blockage was reduced
Fig.9 Limiting streamlines on the suction surface for Stator 1, Rotor 2 and Stator 2 at design condition
Fig.11 Limiting streamlines on the suction surface for Stator 1, Rotor 2 and Stator 2 near stall
Fig.10
Spanwise distributions of (a) inlet axial velocity and (b) diffusion factor for Rotor 2 at design condition
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in Fig.14 (a). Compared with the prototype compressor, the diffusion factor of rotor 2 was decreased below 88% span in the retrofit compressor as shown in Fig.14 (b). Hence the aerodynamic loading of rotor 2 was diminished in the retrofit compressor.
Inlet axial velocity
90 85 80 75
R2 - Prototype R2 - Retrofit
70 65 60
0
0.1
0.2
0.3
0.4
0.5
0.6
Relative Span
0.7
0.8
0.9
1
(a)
Diffusion factor
0.9 0.8
R2 - Prototype R2 - Retrofit
0.7 0.6
Fig.13 Limiting streamlines on the pressure surface for Stator 1, Rotor 2 and Stator 2 near choke
0.5 0.4 0.2
0.3
0.4
0.5
0.6
Relative Span
0.7
0.8
0.9
1
(b)
Fig.12 Spanwise distributions of (a) inlet axial velocity and (b) diffusion factor for Rotor 2 near stall
in the retrofit compressor. The inlet axial velocity of rotor 2 was remarkably increased at the tip in the retrofit compressor. It was decreased below 83% span and more decrement was shown near the hub due to the increased hub blockage in rotor 2. As shown in Fig.12 (b), the diffusion factor was decreased above 28% span and increased near the hub. The decrement of the diffusion factor indicated that the aerodynamic loading of rotor 2 was decreased. The increased aerodynamic loading near the hub enlarged the blockage in rotor 2 which resulted in an early stall in the retrofit compressor. Because of the negative incidence near choke flow separations occurred in the pressure-casing corners as shown in Fig.13. In the presence of positive curving effect, low energy fluid was migrated to the pressure-casing corner, the flow separation start point moved upstream and the flow separation length was increased for each stator in the retrofit compressor. The enlarged casing blockage in stator 2 was responsible for an early choke in the retrofit compressor. The flow behavior near the casing got worse in the retrofit compressor which induced the spanwise redistribution of flow capacity. It was different from the design condition that the flow capacity was decreased near the casing, increased in the mainstream and near the hub. Therefore the spanwise redistribution of inlet axial velocity was opposite to that of the design condition as shown
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Inlet axial velocity
0.1
120 115 110
R2 - Prototype R2 - Retrofit
105 100
0
0.1
0.2
0.3
0.4
0.5
0.6
Relative Span
0.7
0.8
0.9
1
0.9
1
(a) 0.1
Diffusion factor
0
R2 - Prototype R2 - Retrofit
0.08 0.06 0.04
0.02
0
0.1
0.2
0.3
0.4
0.5
0.6
Relative Span
0.7
0.8
(b)
Fig.14
Spanwise distributions of (a) inlet axial velocity and (b) diffusion factor for Rotor 2 near choke
Conclusion Leading edge recambering was applied to the cantilevered stator vanes in a 2-stage compressor in this paper. It was found out that a positive curving effect occurred in the end-bend stator vanes with leading edge stacking and when it was stacked on the centre of gravity a negative curving effect took place. In the retrofit compressor the variations of the flow behavior near the casing induced
Songtao WANG et al. Study on the Effects of End-bend Cantilevered Stator in a 2-stage Axial Compressor
redistribution of the flow field. The flow rate characteristics of rotor 2 were changed with that which had an important effect on the performance of the retrofit compressor. A spanwise redistribution of aerodynamic loading for rotor 2 was produced near the design condition in the retrofit compressor. The aerodynamic loading of rotor 2 was increased. The loss of each stator was decreased due to the reduced flow separations in the suction-casing corners. So the isentropic efficiency and the total pressure ratio of the retrofit compressor were increased near the design condition. As the compressor aerodynamic loading increased, the differences in the spanwise distribution of aerodynamic loading for rotor 2 between the retrofit compressor and the prototype compressor were increased at the tip and hub. The hub blockage length was enlarged for the increased aerodynamic loading of rotor 2 which resulted in an early stall in the retrofit compressor. The flow separations in the pressure-casing corners near choke were increased in the presence of positive curving effect in the retrofit compressor. The enlarged casing blockage in stator 2 was responsible for an early choke in the retrofit compressor. The application of cantilevered end-bend stators improved the compressor performance at the design condition while the stall margin was reduced at the same time. There were two ways to improve the compressor stall margin. 1. Applying leading edge recambering coupled with leading edge stacking to the rotor root. However it might be restricted by the rotor intensity problem at high rotating speed. 2. It was possible to improve the flow matching at hub by controlling stator clearance leakage flow [7-9], which was necessary to be investigated further.
Acknowledgment The authors acknowledge the financial support of the National Basic Research Program of China (No. 2007CB210104) for this work.
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References [1] Huang Lixi, Wei Xinglu, and Peng Zeyan: Approach to Blade End-bend Mechanism, Journal of Aerospace Power, Vol.3, No.3, pp.219−222, (1988). [2] Cai Yunjin, Zhong Yuling, Qian Luhong: Application of End-bend Blade for Enhancing Surge Margin, Journal of Aerospace Power, Vol.3, No.3, pp.215−218, (1988). [3] Li Xihong, Wu Guohua, Peng Zeyan: An Experimental Investigation of Endwall Flow Control in a Compressor Plane Cascade Wind Tunnel, Journal of Aerospace Power, Vol.8, No.2, pp.143−147, (1993). [4] Wu Guohua, Ren Liyun, Peng Zeyan, Yan Ming: Experimental Investigation on the Flow through a Compressor End-bending Cascade, Journal of Aerospace Power, Vol.5, No.3, pp.257−260, (1990). [5] Tao Deping, Peng Zeyan, Wei Xinglu: Study on the Sec-
[6]
[7]
[8]
[9]
ondary Flow and Its Control in Compressor, Journal of Aerospace Power, Vol.5, No.3, pp.251−256, (1990). Woollatt, G., Lippett, D., Ivey, P.C., Timmis, P., Charnley, B.A.: The Design, Development and Evaluation of 3D Aerofoils for High Speed Axial Compressors, Part 2: Simulation and Comparison with Experiment, ASME Paper, GT2005−68793, (2005). Dong, Y., Gallimore, S. J., Hodson, H. P.: Three-Dimensional Flows and Loss Reduction in Axial Compressors, ASME Journal of Turbomachinery, Vol.109, pp.354−361, (1987). Swoboda, M., Ivey, P. C., Wenger, U., Gümmer, V.: An Experimental Examination of Cantilevered and Shrouded Stators in a Multistage Axial Compressor, ASME Paper, 98-GT-282, (1998). Compobasso, M.S., Mattheiss, A., Wenger, U., Arnone, A., Boncinelli, P.: Complementary Use of CFD and Experimental Measurements to Assess the Impact of Shrouded and Cantilevered Stators in Axial Compressors, ASME Paper, 99-GT-208, (1999).