Numerical Prediction of The Performance Recovery of an Axial ...

Journal of Applied Mathematics, Islamic Azad University of Lahijan

Vol.S, No.l7, Summer 2008

Archive of SID

Numerical Prediction of The Performance Recovery of an Axial Compressor by Inlet-Air-Injection Technique During The Unstable Operations Nima Amanifard* , H. M. Deylami 1 Mechanical Engineering Department, Faculty of Engineering, University of Cui/an, P.O. Box 3756, Rasht, Iran, Tel: +981316690270, Fax: +981316690271,

Abstract The effects of the inlet air-injection on aerodynamic behavior and the characteristics of an axial compressor were numerically investigated. The operation curve was numerically captured at the design operation region of a specified test compressor with no air-injection. The computed results showed good agreements with those obtained from the experiments, to validate the unsteady two-dimensional finite-volume solver which was developed based on Van Leer's flux splitting algorithm in conjunction with TVD limiters and the K-£ turbulence model. At the second step, to show the improvement of the operation curve during the air injection, the operating points were adjusted to the unstable values, and the aerodynamic unstable streamlines and consequently the performance reduction were revealed apparently. Afterwards, the required air-injection at the inlet was imposed numerically, and all unstable flow patterns were removed with a significant recovery of the performance, to present a numerical explanation of the airinjection technique. Keywords: Air-Injection Technique, Numelical Study, Performance Recovery, Axial Compressor.

1 Introduction As the gas turbine engines have become better understood and better designed, substantial performance increase in engine designs have become harder to achieve, especially with passive control method. Axial compressors, because of its adverse pressure gradient is the most sensitive device in gas- turbine engines, and otherwise the majority of the researches about this device are concerned on preventing of aerodynamic instabilities, when trying to a.chieve higher levels of the operating pressure ratios without significant reduction of performance, as well as preventing engine damages. Sine the aerodynamics instabilities such as Rotating Stall (RS) and surge, are the main obstructions of maintaining the efficiency in off-design conditions, the control and removing techniques of flow instabilities have been always the interest of researchers during last two decays. Because of significant difficulties of experimental investigations about the flow visualizations in operating conditions of real axial compressors (Dayet.al. [1], Hoying et. al. [2], moue et. al. [3], Hah et. al. [4], Jahen et.

www.SID.ir 'Corresponding author (associate professor) Email address:[email protected] IM.Sc

1

N. Amanifard

et al

Archive of SID al. [5]), the test compressors became strong research tools for experimental studies. Besides, very expensive and high level techniques of flow visualizations, at mean radiuses during the surge or RS, revealed the great role of CFD studies. A set of numerical studies were prepared about the recognition of RS and surge. The 2-D study He et al. [6] led to more detailed numerical studies of Saxer etal.[7], Nishizava [8], Farhanieh etal [9,10], Amanifard [11], and Gourdain [12]. A set few works were prepared on Control of rotating stall from the modeling and controller design point of view (Murray et al. [13], Amanifard et. aI. [14], and Mahir et. al. [15]), which all of them used the experimental results or other proposed models for controller design or optimization. Because of the lack of the numerical studies of injection system, the present work concerns on presenting a 2-D numerical simulation of the inlet injection technique for test axial compressor to study the required injection values for the recovery of efficiency, a simple restricted model of compressor aerodynamic behavior with and without using the inlet injection system. 2 The Test Compressor The test compressor that is simulated in present work is the one that was used by Murrayet. al. [13] in their experimental studies (The test rig is shown in Figure1). The axial single stage compressor has 14 blades in each row of the rotor and the stator. The compressor is equipped with 6 pressure transducers and three injectors at the inlet, and they are arranged and positioned in the circumferential direction (Figure2). The tip and hub radiuses are 8.5 cm and 6 cm respectively. The blades are of type NACA65 series with a variable stagger angle 300 to 51.60 from tip to hub and the chord length is 3.75 cm, and the solidity is about 1. The gap distance is 12 cm, and the injectors are located 10.4 cm before the rotor. The Rotor frequency is set to 100Hz during the tests. The effects of the air injectors can be roughly characterized by their effects on the static compressor map. The experimental results indicated that the compressor characteristic could be altered by air injection. The experimental operating curves of the test compressor, with and without the injection are shown in figure 3. Figure1 The compressor test rig

PiezostatkRing

f

Disturbance

v~ve

www.SID.ir f- 28em -1

~

79em

1

Journal of Applied Mathematics, Islamic Azad University of Lahijan

Vol.S, No.I7, Summer. 2008

Archive of SID Figure 2 The single stage test compressor ~ 01

If'" ~ollf'" If'" If'" 0 I If'" If'" ~ollf'" If'" If'" 0 I If'" If'" ~ollf'"

in~

""""" .....

I

I' .,.."..

rits

"" "" "" "" "" "" "

~

,...,,,""

(o,IYiew)

I

1

"'" (,;lniew)

Figure 3 The experimental operating curves of the test compressor, with and without the injection [13]

0.'

.. ..251'.

.

..f \\

..,51-

."

"

,

"

/

",

~,"''''''\

..OS l

\ \

0'0

0..

..

0.3

.

..

0.5

,

...

3 Numerical Procedure The governing equations in conservative fonn are transfonned to a computaional space for a structured grid finite-volume solution. Hence, they are as following: aQ aEE aFE aEv aFv -+-+-=-+a-z- aq aTJ aq aTJ -

(1)

Q is the prernitive variables matrix, EE and FE are the transformed convective flux

matricies in Sand 11directions respectively, and Ev and F v are the transformed viscous matrices in Sand 11directions respectively. T is the dimensionless time variable.

The equation (1) is rearranged to its discrete fonn, the time www.SID.ir derivative is approximated by a first-order backward differencing quotient and the remaining tenns are evaluated at time level n+1. Thus:

N. Amanifard

et al

Archive of SID

-n + 1 -n Q -Q ! of the simulated stage are those used by Murray et.al. [13]. Five blades were selected for the 2-D numerical study for each row of rotor and stator (Figure 4). The number of blades was selected upon the conclusions of Farhanieh et. al. [9], and some numerical pre-tests between 3 to 7 blades for the required capturing of the RS vortices (The validation are presented in future pages). The grid system is composed of O-type grids structured grids around the blades, unstructured grid near the cascade, and the H-type at the inlet and the outlet zones. The grid resolution is chosen upon grid dependency studies (Figure 4a to 4c). Figure 4 The Schematic shape of the selected geometry of the compressor stage.

I

I

~

~I~ %I~

Figure 4a The structured mesh used around the airfoils.

www.SID.ir

Journal of Applied Mathematics, Islamk Azad University of Lahijan

Vol.s, No.17, Summer 2008

Archive of SID Figure 4b The orthogonality and clustering over the leading and trailing edges.

Figure 4c The mesh used for the 5-blade model of the compressor stage.

The number of structured meshes around the rotor and stator blades, and at the inletoutlet region is 96000 and 20000, respectively. The number of unstructured meshes between the blades is set to 80000. The mesh dependency study and code assurance are performed in previous works of Amanifard [9-11], in which the required descriptions were presented. 5 Boundary Conditions Inlet: For the inlet flow the fixed total pressure and I temperature with a zero inlet angle were used. The inlet length was set to four times of the chord. Outlet: The static pressure was set to required variable conditions to set the operating point of the compressor. The outlet length size from the stator cascade to exit boundary was set to three times of the chord. Solid boundaries: The no-slip boundary condition was assumed for all blade surfaces. The periodic boundary condition: The upper and the lower bounds of the computational domain were set aswww.SID.ir the periodic boundaries.

N. Amanifard

et al

Archive of SID Inteiface: At the interface between rotor and stator cascades, a sliding mesh technique was exploited, to simulate rotor movement against the stator cascade. The position averaging of flow characteristics with required relative velocity corrections, as well as, the consecutive mesh generating were employed in this technique. 6 Discussion of Results

The explicit time marching method with a high order upwind scheme for the convection terms and the second order central difference derivation for diffusion terms is exploited for the discritisized equations. By using coupling of pressure and velocity field with the adequate relaxation factors a relatively rapid convergence occurs. The solution is followed until the errors reach in a period way to 10-5for the continuity equation and to 10-6for the momentum equation. The numerical solution is started at the conditions given in table 1, similar to that used for the test compressor. To obtain other points of the operating curve, the boundary condition outlet pressure is changed. In five time intervals during a complete rotation of the rotor, the outlet pressure, inlet pressure, flow coefficient and the head coefficient are determined with a time averaging in a

specifiedpoint. The flow coefficientis defined to be m1pAP

r'

wheren; is the mass

flow rate through the compressor,p is the density of air, Aa is the cross sectional area of the annulus, Uris the rotor blade speed at midspan. The head coefficient is defined to be b.Pl(pU}) , in which b.Pis the pressure rise across the compressor. Table 1 The Solution step

Time step

P2

105 110 115 120 125

101880 102006 101987 102002 102034

PI 101132 101150 101135 101167 101180

b.P 882 856 852 835 854

IJf

310/0 345/0 343/0 337/0 344/0

7 Numerical Results

The comparison between the experimental and the numerical operating curves with or without injector are shown in different figures (6) and (7), which illustrates the www.SID.ir required assurance of the computations for further studies. However, to show the injection effect on operating conditions the numerical operating curves are compared in figure 8.

Vol.S, No.I7, Summer 2008

Journal of Applied Mathematics, Islamic Azad University of Lahijan

Archive of SID Figure 6 The comparison of Numerical and experimental operating curves without injection. --- Numerical

-

I: 0.41 ~ 0.3 i .2

~0

0.2

~

i

" , m 0.1j :I: 0-10 0.1 0.2

Experimental

0.3 0.4

0.5

0.6

0.7

Row coefficient

Figure 7 The comparison of Numerical and experimental operating curves without injection.

---

Numerical --

0.4 C .S!0.3

~

~

~" 0.2

i

-g ., 0.1' :I: o. 0

Experimental

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Row coefficient

Figure 8 The comparison of Numerical operating curves with and without injection

-c

Wrthout

air inlection

0.4,

~ ~" 0.2

0.11

0.J 0

With air injection

~

~ 0.3 i

~ :I:

--

, 0.1

0.2 0.3 0.4 0.5 0.6 0.7 Row coefficient

The stall cells and the instability movements are shown by the fluctuation of the axial velocity traces. which are captured at the interface zone. To have a movement imagination, 3 probes are considered at the interface of between rotor and stator, and to illustrate three separate curves, they are shifted by constant value. In figure 9, the stall cells are obviously shown by the axial velocity fluctuations with respect to the normal fluctuations related to the rotor movements. Comparing figures 9 and 10, all the stall www.SID.ir cells are nearly removed by inlet air injection. The numerical flow patterns for the five time steps during a complete rotation of the rotor with and without air injection are shown in figures 11.

N. Amanifard et al

Archive of SID

Figure 9 Ve10citytrace between rotor and stator without injection. --Sensor1 ~Sensor2 --Sensor3 200 180 160 ::140 c; 120

~

~1gg ::;- 60 x 40 20 0

0 1 2 3 4 5 6 7 8 9 10 11 lIT

Figure 10 Velocity trace between rotor and stator with injection. --Sensor1 35 30 :: 25 'g 20 ~ 15

x

-o-Sensor2 ---Sensor3

~ ~

10

~

5 0

0

2

3

4

5

6

7

8

9

tIT

Figure]] a Flow pattern of unstable and stable condition without and with injection at time stepl.

Figure 1Ib Flow pattern of unstable and stable condition without and with injection at time step2.

www.SID.ir

Journal of Applied Mathematics, Islamic Azad University of Lahijan

Vol.S, No.17, Summer 2008

Archive of SID Figure lIe Flow pattern of unstable and stable condition without and with injection at time step3.

Figure lid .

Flow pattern of unstable and stable condition without and with injection at time step4.

Figure lie Flow pattern of unstable and stable condition without and with injection at time stepS.

In all five steps the stall cells are considerably removed and cause the reduction of www.SID.ir the velocity fluctuations. However some minor vortices are captured after injection and the performance recoveries.

N. Amanifard

et al

Archive of SID 7 Conclusions

1-

234-

The results and the discussions can give the following conclusion remarks: An experimental high cost observation is numerically simulated, during a simplification of the geometry in the manner of cascade length reduction (number of blades are reduced), and 2-D observation, to minimize the CPU costs and overall study costs. The numerical simulation is compared with obtained from experimental observations and gave the required assurance for further observations. The curves 9-10 obviously could show the effect of injection technique on stall removal and the performance recoveries. The flow visualizations in figures lla to lle, not only gave an obvious imagination during the stall propagation, but also provided a step by step study of the injection effects on flow pattern and consequently the performance recovery. However, such step by step flow pattern study is very difficult or very high cost in experimental observations.

Nomenclature 't

EE

Time in transformed coordinate (time step) Horizontal axis of transformed coordinate Density Load coefficient Flow coefficient Vertical axis of transformed coordinate lnviscid transformed flux vector

Ev

Viscous transformed flux vector

Vx

Axial velocity

S P \If

T\

Subscript

~ T\

Superscript n n+1

partial derivative with respect to ~ partial derivative with respect to T\ www.SID.ir previous time level current time level

Journal of Applied Mathematics, Islamic Azad University of Lahijan

Archive References

Vol.5, No.17, Summer 2008

of SID

[1] Day, 1. J., Breuer, T., Escuret, J., Cherrett, M., and Wilson, A., Stall Inception and the Prospects for Active Control in Four High-Speed Compressors, ASME Journal of Turbo machinery, Vol. 121, 1999, pp. 18-27. [2] Hoying, D. A., Tan, C.S., and Greater, E.M., Role of Blade Passage Flow Structures in Axial Compressor Rotating Stall Inception, Journal of Turbo machinery, Trans. ASME, Vol. 121, NO.4, 1999, pp.181-188. [3] Inoue M., Kuroumaru M., Tanino T., Yoshida S. and Furukawa M., Comparative Studies on Short and Long Length-Scale Stall Cell Propagating in an Axial Compressor Rotor, ASME Paper 2000GT-0425, 1999. [4] Hah, c., Schulze, R., Wagner, S. and Hennecke D. K., Numerical and Experimental Study for Short Wavelength Stall Inception in a Low-Speed Axial Compressor, Proc. 14th Int. Symposium Air Breathing Engines, Florence, Italy, Sep. 1999, ISABE 99-7033. [5] Jahen, W., Peters, T., and Fotter, L., An Experimental Flow Investigation of an HP Five-Stage, Compressor Exihibition Rotating Stall due to Distored Inlet Flow Conditions, Unsteady Aerodynamics and aeroelasticity of Turbomachine, T.H. Fransson (ed.), Kluwer Academic Publishers, 1998, pp. 243-257. [6] He L., Computational study of Rotating-Stall inception in axial compressors, Journal of Propulsion and Power, Vol. 13, 1997, pp. 31-38. [7] Saxer-Flelici, H. M., Saxer, A. P., Inderbitzen, A., Gyarmathy, G., Prediction and Measurement of Rotating Stall Cell in an Axial Compressor, ASME Journal of Turbomachinery, Vol.121, 1999, pp. 365-375. [8] Nishizawa T., and Takata, H., Numerical Study on Stall Flutter of a Compressor Cascade, ISME Int. Journal, VoL 43, No.3, 2000, pp. 351-36l. [9] Farh~nieh, B., Amanifard N., and Ghorbanian, K., A 2-D Numerical Investigation on the Modal' Characteristics of Rotating-Stall with a Variable-Cascade-length Approach in an Axial Compressor International Journal of Engineering, V01.16.No.2, 2003, pp 97-105. [10]Farhanieh, B., Amanifard N., and Ghorbanian, K., A Numerical Investigation on the Unstable Flow in a single Stage of an an Axial Compressor International Journal of Engineering, Vol.16. No.2, June 2003, pp 171-182. [11] Nima Amanifard, Stall Vortex Shedding over a Compressor Cascade, International Journal of Engineering, Vol. 16,No.1, 2005, pp 9-16. [12] N. Gourdain, S. Burguburu, F. Leboeuf and H. Miton, Numerical simulation of rotating stall in a subsonic compressor, Article Aerospace Science and Technology, Volume 10, Issue 1, January 2006, PP. 9-18. [13] R. M. Murray, S. Yeung, and Y. Wang, Evaluation of Bleed valve Rate requirements in nonlinear control of rotating stall on axial compressors, CDS, 1998, Technical Report, port 98-100. [14] N. Amanifard, N. Nariman-zadeh, A. Jamali, M.H. Farahani, and R. Farzaneh-kari, Multi-Objective Pareto Optimization of Axial Compressors Using Genetic Algorithms, WSEAS Transactions on Computers, July 2006,ID.534-593. [15] Mahir A. Nayfeh and Eyad H. Abed, High-gain feedback control of rotating stall in axial flow compressors, Automatica, Volume 38, Issue 6, June 2002, pp. 995-1001. [16] Bohn D. and Emunds R., 1995, A Navier-Stokes computer code for theoretical investigations on the www.SID.ir application of various turbulence models for flow prediction along turbine blades, Proceeding of the International Gas Turbine and Aero-engine Congress and Exposition, Houston, Texas-June 5-8, 95-GT-90.