aerodynamic investigation of a single-stage axial ... · fig. 1 meridional plane of the compressor...

AERODYNAMIC INVESTIGATION OF A SINGLE-STAGE AXIAL COMPRESSOR WITH A CASING GROOVE AND TIP INJECTION USING FLUID-STRUCTURE

INTERACTION ANALYSIS

Sang-Bum Ma Department of Mechanical Engineering,

Inha University Incheon, Republic of Korea

[email protected]

Man-Woong Heo Department of Mechanical Engineering,


[email protected]

Kwang-Yong Kim Department of Mechanical Engineering,


[email protected]

Jaeho Choi Power Systems R&D Center, Samsung Techwin,

Seongnam-si, Gyeonggi-do, 463-400, Republic of Korea

[email protected]

ABSTRACT

In this paper, a fluid-structure interaction (FSI) analysis was performed for a single-stage axial compressor with casing groove and tip injection using three-dimensional Reynolds-Averaged Navier-Stokes equations. The k-ε turbulence model and hexahedral grids system were used in the analysis. ANSYS solid 186 elements type was used to analyze the solid characteristic. In order to achieve robust stability of the transonic axial compressor, a casing groove was installed with tip injection on rotor tip region. FSI analysis was carried out to predict the deformation of the blades, and the results were compared to those of non-FSI analysis. Validation of the numerical results performed in comparison with experimental data, showed good agreements with experimental data for the adiabatic efficiency and total pressure ratio. It was found that deformation of blades affects the aerodynamic performance of the compressor to some extent. Stability of the axial compressor was enhanced by installing the casing groove with tip injection.

INTRODUCTION In the tip clearance region of an axial compressor, a

complex leakage flow occurs, which is a key feature related to the stability of the compressor. Thus, it’s important to control this tip leakage flow to suppress the stall and surge. Recently, casing treatments and tip injection are being introduced to enhance the stability and aerodynamic performances of the compressors.

Smith and Cumpsty [1] demonstrated a 23 percent drop in

maximum pressure rise and a 15 percent increase in flow coefficient at stall condition with an increase of tip clearance from 1 to 6 percent of the blade chord. Wisler [2] confirmed a 1.5 percent drop in peak efficiency when the tip clearance doubled in a low speed compressor. Rabe & Hah [3] demonstrated that the stall margin and stability range increased with a small depth of circumferential casing grooves in a single-stage axial compressor. Beheshti et al. [4] studied on the performance enhancement of a transonic axial compressor using blade tip injection coupled with a casing treatment, but the efficiency presented was polytropic efficiency that is not the experimental efficiency reported by Dunham [5], and the stall point predicted by numerical simulation was 0.936 of choking mass flow, while that of experimental data was 0.925. Khaleghi et al. [6] presented the effects of various injection angles combined with tip injection and casing groove on the stability enhancement of an axial compressor. Kim et al. [7] investigated the effects of three design parameters; leading edge length, trailing edge length, and height of casing groove combined with tip injection on aerodynamic performance of a transonic axial compressor. Kim et al. [8] suggested the depth and location of a single casing groove combined with tip injection, which maximizes the stall margin and peak efficiency of a transonic axial compressor. Hathaway [9] reported an increase in stall margin and efficiency by reducing the casing endwall blockage with

1 Copyright © 2015 by ASME

Proceedings of ASME Turbo Expo 2015: Turbine Technical Conference and Exposition GT2015

June 15 – 19, 2015, Montréal, Canada

GT2015-42121

Fig. 1 Meridional plane of the compressor with casing groove and tip injection

Table 1 Design specifications for axial compressor

Number of rotor blades 15 Number of stator blades 34

Inflow Total pressure (Pa) 101,325 Inflow Total temperature (K) 288.15

Design flow coefficient 0.2836 Total Pressure ratio 2.3

Ratio of tip clearance to blade chord length of rotor (Tr/C)

0.005

injection and ejection combined in a single transonic fan rotor (NASA Rotor 67). This idea was to eject pressurized fluid from downstream of the rotor and properly inject it upstream.

As mentioned above, many researches have been performed to investigate the aerodynamic characteristics of axial compressors with casing treatment and tip injection. However, the FSI analysis hardly has been applied to investigation of an axial compressor with casing treatment and tip injection. In this work, aerodynamic analysis of a single-stage axial compressor with a casing groove and tip injection has been carried out by using three-dimensional Reynolds-averaged Navier-Stokes (RANS) equations. And, the FSI analysis has been also performed to investigate the effects of the blade deformation on aerodynamic performance of the compressor.

COMPUTATIONAL DOMAIN Figure 1 shows the meridional plane of the axial

compressor combined with a casing groove and tip injection. The transonic axial compressor considered in this study consists of fifteen rotor blades and thirty four stator vanes. The inflow total pressure and total temperature are 101,325 Pa and 288.15 K, respectively. The ratio of tip clearance to blade chord length of rotor is 0.005. The detailed design specifications are listed in Table 1.

The computational domain considered in this work is shown in Fig. 1. The optimum geometry and location of a

NOMENCLATURE C Rotor blade tip axial chord length D Depth of groove d Displacement FSI Fluid-Structure Interaction L.E. Leading Edge LF Front length of groove LR Rear length of groove m& Mass flow rate PR Total pressure ratio Pt Total pressure RANS Reynolds-averaged Navier-Stokes SM Stall margin Tt Total temperature T.E. Trailing Edge g Specific heat ratio h Adiabatic efficiency σ Stress

Table 2 Design specifications for casing groove

LF/C 0.707 LR/C 0.144 D/C 0.026 ̇ /̇ 0.024 , /, 1.38

casing groove with tip injection was found for single compressor rotor by Kim et al. [8], and the same groove geometry and location was used in this work for the single-stage compressor. The information about the geometry and location of the casing groove is presented in Table 2. Here, LF and LR are the distances from the center of rotor, respectively.

tipm& and cm& are the tip injection and choked mass flow rates of the reference compressor, respectively. , and , are the total pressure of tip injection flow and compressor inflow, respectively. The direction of tip injection is parallel to the axis of rotation.

FLOW ANALYSIS For the aerodynamic analysis, RANS equations were

solved using ANSYS-CFX 15.0, which employs an unstructured grid system as shown in Fig. 2. In the present study, the RANS equations were obtained using time-averaged Reynolds composition. For compressible flows, the averaging is weighted by density (Favre-averaging) [10]. The numerical analysis was carried out through the finite volume method to discretize the RANS equations. Blade profile creation, computational mesh generation, boundary condition definitions, flow analysis, and post processing, were carried out by using Blade-Gen, Turbo-Grid, ANSYS ICEM-CFD, ANSYS Meshing, CFX-Pre, CFX-Solver and CFX-Post, respectively.


(a) Grid system of the fluid domain

(b) Geometry of the compressor with casing groove

Fig. 2 Computational domains and grid systems

The working fluid was considered as an ideal gas and the

average static pressure was set at the outlet boundary for steady-state simulation. The blade surfaces were considered as adiabatic and smooth walls, the periodic boundaries were set at the passage interfaces. The frozen-rotor interface method was used at the interfaces where relative motions exit. A structured grid system was constructed in the computational domain with O-type grids near the blade surface and H/J/C/L grids in other regions, and a grid dependency test was performed in a range of grid number, 1,200,000 ~ 3,200,000. From the results of the test, 2,200,000 was determined as optimal number of grids. The k-e model was employed with the values of y+ at the first nodes from the wall established from 20 to 100 to use empirical wall function.

The criteria proposed by Chen et al. [11] were employed in this work to determine the stall point numerically;

- The inlet mass flow rate variation is less than 0.001 kg/s for 300 steps.

- The difference between the inlet and outlet mass flow rate is less than 0.5%.

- The adiabatic efficiency variation is less than 0.3% per 100 steps.

Fig. 3 Procedure of FSI analysis

Table 3 Properties of blade material

Density (kg/m3) 4620 Young’s modulus (Pa) 9.60 x 1010

Poisson’s ratio 0.36 Bulk modulus (Pa) 1.14 x 1011

Shear modulus (Pa) 3.53 x 1010

Tensile Yield strength (Pa) 9.30 x 108

FLUID STRUCTURE INTERACTION ANALYSIS Figure 3 shows the algorithm of FSI analysis. The fluid

force and external force cause deformation of the structural model and this deformation changes the flow. The FSI simulation is achieved by satisfying both the displacement and stress at fluid-solid boundary. [12]

For the FSI analysis, the Arbitrary Lagrange Euler formulation was used, which gives a correct mathematical description for flow problems including moving grid [13]. A continuum motion of steady deformation was analyzed based on the Cauchy’s equation:

∇ + = 0 (1)

where, is the stress tensor and is the external force (i, j = 1, 2, 3 for 3D structures) [10].

The structured hexahedral grids were constructed in the solid domain of rotor and stator, respectively, with 29,000 and 17,900 nodes.

Table 3 represents material properties of blade used in this work. The density, young’s modulus, and Poisson’s ratio of the blade material are 4,620 kg/s, 9.6×1010 Pa, and 0.36, respectively. Bulk and shear moduli, and tensile yield strength are 1.14×1011 Pa, 3.53×1010 Pa, and 9.30×108, respectively.


(a) Head coefficient

(b) Normalized Efficiency

Fig. 4 Validation of the flow analysis for the compressor with smooth casing (experiment by Choi [14])

VALIDATION OF NUMERICAL SOLUTION The numerical results based on k-e turbulence model were

compared with experimental data obtained by Choi [14] for head coefficient and normalized efficiency curves. The locations of inlet and outlet planes for the test and the analysis are shown in Fig. 1. As shown Fig. 1, the locations denoted by A and B are inlet and outlet measurement planes, respectively.

Total pressure and total temperature were measured by a 5-probe rake where the probes are equally spaced. And, the efficiency was obtained with mass-averaged total pressure and mass-averaged total temperature. The validation of numerical results for the axial compressor with smooth casing is presented in the Fig. 4. As shown in Fig. 4, the numerical results based on k-ε turbulence model show quite good agreements with the experimental data. Especially, the peak head coefficient and efficiency values of current calculation are predicted well in comparison with the experimental data.

(a) Head coefficient

(b) Normalized Efficiency

Fig. 5 Comparison between aerodynamic performances with and without FSI analysis and groove

RESULTS AND DISCUSSION The aerodynamic performances of transonic axial

compressor, i.e., total pressure ratio, adiabatic efficiency, and stall margin (SM) are defined as follows:

in,t

out,t

PP

PR = (1)

1

1

-

-

=)

TT

(

γ-1γ

)PP

(η

int,

outt,

int,

outt,

(2)

100%1)mm

( ´-´=peak

stall

stall

peak

PRPR

SM&

& (3)


(a) Smooth casing

(b) Casing groove with tip injection

Fig. 6 Static pressure distributions at 98% span at normalized mass flow of 0.85

(a) Smooth casing

(b) Casing groove with tip injection

Fig. 7 Entropy distributions at 98% span at normalized mass flow of 0.85

Table 4 Results of the numerical analyses

With smooth

casing

With tip casing groove and injection

ηpeak

(%) Without FSI 87.28 89.70

With FSI 87.32 89.57

SM (%)

Without FSI 14.93 20.95 With FSI 14.66 20.84

where, peakm& and stallm& are mass flow rates at peak efficiency and stall point, respectively. PRpeak and PRstall are total pressure ratios at peak efficiency and stall point, respectively. Pt, Tt and g, indicate total pressure, total temperature and specific heat ratio, respectively.

Figure 5 shows the performance curves for normalized efficiency and head coefficient of a transonic axial compressor without and with casing groove and tip injection. And, the performance curves are also compared with those with FSI analysis. As for head coefficient and normalized efficiency, the results with FSI analysis show slightly smaller values than the results without FSI analysis throughout the entire flow rate range. However, the FSI results indicate that the calculated stall margin is extended compared to the case where the fluid-structure interaction is not taken into account. Prediction for the stall point moves from the normalized mass flow, 0.822 to 0.817 in the case with groove, and from 0.855 to 0.850 in the case with smooth casing.

The numerical results for peak adiabatic efficiency (ηpeak) and stall margin (SM) of the transonic axial compressors with and without casing groove and injection, and also with and without FSI analysis are represented in Table 4. The numerical result of peak adiabatic efficiency for the transonic axial compressor with smooth casing without FSI analysis is smaller by 0.04% than that with FSI analysis.

While, as for the axial compressor with casing groove and injection, the peak adiabatic efficiency without FSI is larger by 0.14% than that with FSI analysis. The numerical results for the stall margin of the compressor show that the stall margins with FSI are smaller by 0.53% and 1.8%, respectively, than those without FSI analysis for both of the axial compressors with and without casing groove and injection.

Figure 6 shows the static pressure distributions at 98% span from hub at normalized mass flow of 0.85. A narrow region of low pressure locates from the leading edge on the suction surface to the center of the passage in the case with smooth casing. This low pressure region is shifted to the blade surface in the case with casing groove and tip injection. And, it is found that the static pressure on the pressure surface near the blade leading edge is increased by installing the casing groove with tip injection.

Static entropy distributions at 98% span from hub at normalized mass flow of 0.85 are shown in Fig. 7. It is


(a) Choked condition

(b) Peak adiabatic efficiency condition

(c) Near stall condition

Fig. 8 Blade deformation contours for axial compressor (smooth casing) observed that the entropy generation at tip region is reduced by using casing groove and injection.

Figures 8 and 9 show the blade deformation contours on the rotor blade and stator vane of the axial compressor with and without casing groove and tip injection, respectively. As shown in these figures, the deformation is largest at the blade tip on leading edge and the deformation increases as mass flow rate decreases. In the case with casing groove and tip injection, the deformation is increased uniformly on the rotor and stator compared to the case with smooth casing.

(a) Choked condition

(b) Peak adiabatic efficiency condition

(c) Near stall condition

Fig. 9 Blade deformation contours for axial compressor with casing groove and tip injection

Circumferentially averaged static entropy distributions at the leading edges of rotor and stator at the near stall point are shown in Fig. 10. The results of numerical analysis with and without FSI analysis for the transonic axial compressor with casing groove and tip injection are presented in Fig. 10. It is found that the static entropy generation is increased by the deformation, especially near the blade tip at the leading edge of rotor blade, and near the middle at the leading edge of stator vane. Figure 11 shows pressure coefficient distributions on the rotor blade surface in spanwise direction at near stall point.


(a) Leading edge of rotor blade

(b) Leading edge of stator vane

Fig. 10 Circumferentially averaged entropy distributions at the near stall point

(a) Total pressure ratio

(b) Total temperature ratio

Fig. 12 Profiles of circumferentially averaged total pressure ratio and temperature ratio at near stall point

(a) 98% span

(b) 70% span

(c) 50% span

Fig. 11 Pressure coefficient on the surface of rotor blade at near stall point The distributions obtained by CFD with and without FSI analysis are almost same at 50 and 70% span sections. The difference was observed near the tip, where the blade deformation was relatively large.

Figure 12 presents profiles of circumferentially averaged total pressure ratio and temperature ratio in spanwise direction at near stall point. The analysis with FSI shows the values of total pressure ratio smaller than those of the analysis without FSI. And, the higher total temperature ratios were predicted beyond 40% span by introducing FSI analysis.

Static pressure distributions at 98% span from hub at near stall point are shown in Fig. 13. The results with FSI analysis shows higher static pressure at the leading edge near the pressure side (denoted by A) compare to the results without FSI analysis. But, the static pressure upstream of the rotor is rather


(a) Without FSI analysis

(b) With FSI analysis

Fig. 13 Static pressure distribution of 98% span at near stall point smaller in the case with FSI analysis.

Figure 14 represents the Mach number distributions at a location of 5% chord length from leading edge. In the numerical results with FSI analysis, high Mach number widely distributes near the blade tip region.

CONCLUSIONS Aerodynamic analysis using three-dimensional RANS

equations and FSI analysis was performed to investigate aerodynamic characteristics of a transonic axial compressor with casing groove and tip injection. The numerical results for the efficiency and head coefficient of the transonic axial compressor with smooth casing, agree well with the corresponding experimental data. The efficiency and stall margin of the transonic axial compressor were improved by

` (a) Without FSI analysis

(b) With FSI analysis

Fig. 14 Mach number distributions at 5% chord length from leading edge. installing casing groove with tip injection. The FSI analysis for the axial compressor with smooth casing, which takes account for the effects of the deformations of blades and vanes in the aerodynamic analysis, improves the predictions by increasing the peak adiabatic efficiency by 0.04% and decreasing the stall margin by 1.8% compared to the results without FSI analysis. And, for the axial compressor with casing groove and tip injection, both the peak adiabatic efficiency and stall margin are decreased by 0.13% and 0.11%, respectively, with the FSI analysis.

ACKNOWLEDGMENTS The authors would like to thank ADD and Samsung

Techwin for their support with the advanced core technology project and their kind permission to publish this paper.


REFERENCES [1] Smith, G. D. J., and Cumpsty, N. A., 1984, “Flow

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[2] Wisler, D. C., 1985, “Loss reduction in axial flow compressors through low-speed model testing,” ASME J. Turbomach., Vol. 107, pp. 354-363.

[3] Rabe, D. C., and Hah, C., 2002, “Application of casing circumferential grooves for improved stall margin in a transonic axial compressor,” Proceedings of the ASME turbo expo 2002, Amsterdam, Netherlands, GT2002-30641.

[4] Beheshti, B. H., Farhanieh, B., Ghorbanian, K., Teixeira, J. A., and Ivey, P. C., 2005, “Performance Enhancement in Transonic Axial Compressors Using Blade Tip Injection Coupled with Casing Treatment,” Proceedings of Institution of Mechanical Engineers, Part A: Journal of Power and Energy, Vol. 219, No. 5, pp.321-331.

[5] Dunham, J., 1998, “CFD validation for propulsion system components,” AGARD advisory report no. 355, Advisory Group on Aerospace Research and Development, North Atlantic Treaty Organization, ISBN 92-836-1075-X.

[6] Khaleghi, H., Texeria, J. A., Tousi AM, Boroomand, M., 2008, “Parametric study of Injection Angle Effect on Stability Enhancement of Transonic Axial Compressor,” Journal of Propulsion and Power, Vol. 24, No. 5, pp. 1100–1107.

[7] Kim, D. W., Kim, J. H., and Kim, K. Y., 2013, “Parametric Study on Aerodynamic Performance of a Transonic Axial Compressor with a Casing Groove and Tip Injection”,

Applied Mechanics and Materials, Vol. 284-287, pp. 872-877.

[8] Kim, J. H., Kim, D. W., and Kim, K. Y., 2013, “Aerodynamic optimization of a transonic axial compressor with a casing groove combined with tip injection,” Proceedings of The Institution of Mechanical Engineers, Part A-Journal of Power and Energy, Vol. 227, pp. 869-884.

[9] Hathaway, M. D., 2002, “Self-Recirculating Casing Treatment Concept for Enhanced Compressor Performance,” Proceedings of ASME Turbo Expo 2002, GT-2002-30368.

[10] Anon. ANSYS CFX-slover theory guide. Canonsburg, PA: ANSYS, Inc.; 2010; 724-46.

[11] Chen, H., Huang, X. D., and Fu, S., 2006, “CFD Inverstigation on Stall Mechanisms and Casing Treatment of a Transonic Compressor,” 42nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, Sacramento, USA, AIAA-2006-4799.

[12] N.I. Ismail, A.H. Zulkifli, M.Z. Abdullah, M.Hisyam Basri, Norazharuddin Shah Abdullah, 2012, “Computational aerodynamic analysis on perimeter reinforced (PR) – compliant wing,” Chinese Journal of Aeronautics, Vol. 26, No. 5, pp. 1093-1105.

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[14] Choi, J. H., 2003, “Technical Report on the Development of an Highly-Loaded Axial Compressor (in Korean),” Samsung Techwin Co.


aerodynamic investigation of a single-stage axial ... · fig. 1 meridional plane of the compressor...

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