Journal of Computational & Applied Research in Mechanical Engineering (JCARME)

Document Type : Research Paper

Authors

¹ Research Center for Modeling and Simulation, National University of Sciences and Technology, H–12 Campus, Islamabad 44000, Pakistan

² Department of Mechanical & Construction Engineering, Northumbria University, Newcastle, United Kingdom

https://doi.org/10.22061/jcarme.2020.5182.1639

Abstract

The paper discusses the effect of compressor characteristic on surge phenomena in axial flow compressors. Specifically, the effect of nonlinearities on the compressor dynamics is analyzed. For this purpose, generalized multiple time scales method is used to parameterize equations in amplitude and frequency explicitly. The pure surge case of the famous Moore-Greitzer model is used as the basis of the study. The compressor characteristic used in the Moore-Greitzer model is generalized to evaluate the effect of the parameters involved. Subsequently, bifurcation theory is used to study the effect of nonlinear dynamics on surge behavior. It has been found that the system exhibits supercritical Hopf bifurcation under specific conditions in which surge manifests as limit cycle oscillations. Key parameters have been identified in the analytical solution which govern the nonlinear dynamic behavior and are responsible for the existence of limit cycle oscillations. Numerical simulations of the Moore-Greitzer model are carried out and found to be in good agreement with the analytical solution

Graphical Abstract

Keywords

dor

20.1001.1.22287922.2021.10.2.5.6

Main Subjects

Nonlinear Solution

References

[1] Day, I.J., Stall, surge, and 75 years of research. Journal of Turbomachinery,Vol. 138, No. 1, pp. 1-16, (2015).

[2] Bullock, R.O. and I.A. Johnsen, Compressor Surge, in Aerodynamic Design of Axial-Flow Compressors National Aeronautics and Space Administration: Washington, D.C. pp. 331–340, (1965).

[3] Bitikofer, C., M.P. Schoen, J.-C. Li, and F. Lin, Characteristic Moore-Greitzer model parameter identification for a one stage axial compressor system. 2017 American Control Conference. (2017).

[4] Greitzer, E.M., Surge and Rotating Stall in Axial Flow Compressors Part I: Theoretical Compression System Model. Journal of Engineering for Gas Turbines and Power,Vol. 98, No. 2, (1976).

[5] Moore, F.K. and E.M. Greitzer, A Theory of Post-Stall Transients in Multistage Axial Compression Systems, National Aeronautics and Space Administration, (1985).

[6] Moore, F.K. and E.M. Greitzer, A Theory of Post-Stall Transients in Axial Compression Systems: Part I–Development of Equations. Journal of Engineering for Gas Turbines and Power,Vol. 108, No. 1, pp. 68-76, (1986).

[7] Greitzer, E.M., Review–Axial Compressor Stall Phenomena. Journal of Fluids Engineering,Vol. 102, No. 2, pp. 134-151, (1980).

[8] Greitzer, E.M., The Stability of Pumping Systems—The 1980 Freeman Scholar Lecture. Journal of Fluids Engineering,Vol. 103, No. 2, pp. 193-242, (1981).

[9] Longley, J.P., A Review of Nonsteady Flow Models for Compressor Stability. Journal of Turbomachinery,Vol. 116, No. 2, pp. 202-215, (1994).

[10] Gu, G., A. Sparks, and S.S. Banda, An Overview of Rotating Stall and Surge Control for Axial Flow Compressors. IEEE Transactions on Control Systems Technology,Vol. 7, No. 6, pp. 639-647, (1999).

[11] Paduano, J.D., E.M. Greitzer, and A.H. Epstein, Compression System Stability and Active Control. Annual Review of Fluid Mechanics,Vol. 33, No. 1, pp. 491–517, (2001).

[12] McCaughan, F.E., Application of Bifurcation Theory to Axial Flow Compressor Instability. Journal of Turbomachinery,Vol. 111, No. 4, pp. 426-433, (1989).

[13] Abed, E.H., P.K. Houpt, and W.M. Hosny, Bifurcation Analysis of Surge and Rotating Stall in Axial Flow Compressors. Journal of Turbomachinery,Vol. 115, No. 4, pp. 817-824, (1993).

[14] Liaw, D.C. and E.H. Abed, Active Control of Compressor Stall Inception: A Bifurcation-theoretic Approach. Automatica,Vol. 32, No. 1, pp. 109-115, (1996).

[15] Willems, F., W.P.M.H. Heemels, B.d. Jager, and A.A. Stoorvogel, Positive feedback stabilization of centrifugal compressor surge. Automatica,Vol. 38, No. 2, pp. 311-318, (2002).

[16] Shehata, R.S., H.A. Abdullah, and F.F.G. Areed, Variable structure surge control for constant speed centrifugal compressors. Control Engineering Practice,Vol. 17, No. 7, pp. 815-833, (2009).

[17] Fontaine, D., S. Liao, J.D. Paduano, and P.V. Kokotovic, Nonlinear control experiments on an axial flow compressor. IEEE Transactions on Control Systems Technology,Vol. 12, No. 5, pp. 683-693, (2004).

[18] Sheng, H., W. Huang, T. Zhang, and X. Huang, Robust adaptive fuzzy control of compressor surge using backstepping. Arabian Journal for Science and Engineering,Vol. 39, No. 12, pp. 9301-9308, (2014).

[19] Ziabari, M.T., M.R.J. Motlagh, K. Salahshoor, and A. Ramazani, Surge control in constant speed centrifugal compressors using nonlinear model predictive control. Modares Journal of Electrical Engineering,Vol. 12, No. 1, pp. 49-53, (2015).

[20] Hos, C., A. Champneys, and L. Kullmann, Bifurcation analysis of surge and rotating stall in the Moore–Greitzer compression system. IMA Journal of Applied Mathematics,Vol. 68, No. 2, pp. 205–228, (2003).

[21] Malathi, A.S. and A. Kushari, A Parametric Investigation of Geometric Variation on Fluid Dynamic Instabilities in Axial Compression Systems. International Journal of Rotating Machinery,Vol. 2012, No. 1, (2012).

[22] Ramnath, R.V., Multiple Scales Theory and Aerospace Applications. 2010: AIAA.

[23] Ramnath, R.V. and G. Sandri, A Generalized Multiple Scales Approach to a Class of Linear Differential Equations. Journal of Mathematical Analysis and Applications,Vol. 28, No. 2, pp. 339-364, (1969).

[24] Greitzer, E.M. and F.K. Moore, A Theory of Post-Stall Transients in Axial Compression Systems: Part II–Application. Journal of Engineering for Gas Turbines and Power,Vol. 108, No. 2, pp. 231-239, (1986).

[25] Go, T.H., Lateral-Directional Aircraft Dynamics Under Static Moment Nonlinearity. Journal of Guidance, Control and Dynamics,Vol. 32, No. 1, pp. 305-309, (2009).

[26] Go, T.H. and F.A.P. Lie, Analysis of Wing Rock Due to Rolling-Moment Hysteresis. Journal of Guidance, Control and Dynamics,Vol. 31, No. 4, pp. 849-857, (2008).

[27] Go, T.H. and R.V. Ramnath, Analysis of the Two-Degree-of-Freedom Wing Rock in Advanced Aircraft. Journal of Guidance, Control and Dynamics,Vol. 25, No. 2, (2002).

[28] Tiauw Hiong, G. and R.V. Ramnath, Analytical Theory of Three-Degree-of-Freedom Aircraft Wing Rock. Journal of Guidance, Control and Dynamics,Vol. 27, No. 4, pp. 657-664, (2004).

[29] Maqsood, A. and G. Tiauw Hiong, Multiple time scale analysis of aircraft longitudinal dynamics with aerodynamic vectoring. Nonlinear Dynamics,Vol. 69, No. 3, pp. 731-742, (2012).

[30] Ahmed, W., A. Maqsood, and R. Riaz, Multiple Time Scale Analysis of Pressure Oscillations in Solid Rocket Motors. Results in Physics,Vol. 8, No. 1, pp. 1068-1075, (2018).

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