Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-26T07:25:37.280Z Has data issue: false hasContentIssue false
  • English
  • Français

Feedback control of cavity flow oscillations using simple linear models

Published online by Cambridge University Press:  29 August 2012

Simon J. Illingworth ,
Aimee S. Morgans  and
Clarence W. Rowley
Simon J. Illingworth*
Affiliation:
Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, UK
Aimee S. Morgans
Affiliation:
Department of Aeronautics, Imperial College London, South Kensington SW7 2AZ, UK
Clarence W. Rowley
Affiliation:
Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Using data from direct numerical simulations, linear models of the compressible flow past a rectangular cavity are found. The emphasis is on forming simple models which capture the input–output behaviour of the system, and which are useful for feedback controller design. Two different approaches for finding a linear model are investigated. The first involves using input–output data of the linearized cavity flow to form a balanced, reduced-order model directly. The second approach is conceptual, and involves modelling each element of the flow physics separately using simple analytical expressions, the parameters of which are chosen based on simulation data at salient points in the cavity’s computational domain. Both models are validated: first in the time domain by comparing their impulse responses to that of the full system in direct numerical simulations; and second in the frequency domain by comparing their frequency responses. Finally, the validity of both linear models is shown most clearly by using them for feedback controller design, and then applying each controller in direct numerical simulations. Both controllers completely eliminate oscillations, and demonstrate the advantages of model-based feedback controllers, even when the models upon which they are based are very simple.

JFM classification

Acoustics: Aeroacoustics Flow Control: Control theory Flow Control: Instability control
Type
Papers
Information
Journal of Fluid Mechanics , Volume 709 , 25 October 2012 , pp. 223 - 248
Copyright
Copyright © Cambridge University Press 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Ahuja, S. & Rowley, C. W. 2010 Feedback control of unstable steady states of flow past a flat plate using reduced-order estimators. J. Fluid Mech. 645, 447–478.CrossRefGoogle Scholar
2. Barbagallo, A., Sipp, D. & Schmid, P. J. 2009 Closed-loop control of an open cavity flow using reduced-order models. J. Fluid Mech. 641, 1–50.CrossRefGoogle Scholar
3. Cabell, R. H., Kegerise, M. A., Cox, D. E. & Gibbs, G. P. 2006 Experimental feedback control of flow-induced cavity tones. AIAA J. 44 (8), 1807–1815.CrossRefGoogle Scholar
4. Cattafesta, L. N. III, Garg, S., Choudhari, M. & Li, F. 1997 Active control of flow-induced cavity resonance. AIAA Paper 97–1804.CrossRefGoogle Scholar
5. Cattafesta, L. N. III, Song, Q., Williams, D. R., Rowley, C. W. & Alvi, F. S. 2008 Active control of flow-induced cavity oscillations. Prog. Aerosp. Sci. 44, 479–502.CrossRefGoogle Scholar
6. Doyle, J. 1978 Guaranteed margins for LQG regulators. IEEE Trans. Autom. Control 23 (4), 756–757.CrossRefGoogle Scholar
7. Freund, J. B. 1997 Proposed inflow/outflow boundary condition for direct computation of aerodynamic sound. AIAA J. 35 (4), 740–742.CrossRefGoogle Scholar
8. Gharib, M. 1987 Response of the cavity shear layer oscillations to external forcing. AIAA J. 25 (1), 43–47.CrossRefGoogle Scholar
9. Heller, H. H. & Bliss, D. B. 1975 The physical mechanism of flow-induced pressure fluctuations in cavities and concepts for their suppression. AIAA Paper 75–491, pp. 281–296.Google Scholar
10. Illingworth, S. J., Morgans, A. S. & Rowley, C. W. 2011 Feedback control of flow resonances using balanced reduced-order models. J. Sound Vib. 330, 1567–1581.CrossRefGoogle Scholar
11. Juang, J. N. & Pappa, R. S. 1985 Eigensystem realization algorithm for modal parameter identification and model reduction. J. Guid. Control Dyn. 8 (5), 620–627.CrossRefGoogle Scholar
12. Kegerise, M. A., Cabell, R. H. & Cattafesta, L. N. III 2007 Real-time feedback control of flow-induced cavity tones—Part 1: Fixed-gain control. J. Sound Vib. 307, 906–923.CrossRefGoogle Scholar
13. Kook, H., Mongeau, L. & Franchek, M. A. 2002 Active control of pressure fluctuations due to flow over Helmholtz resonators. J. Sound Vib. 255 (1), 61–76.CrossRefGoogle Scholar
14. Langhorne, P. J., Dowling, A. P. & Hooper, N. 1990 A practical active control system for combustion oscillations. J. Propul. Power 6 (3), 324–333.CrossRefGoogle Scholar
15. Lele, S. K. 1992 Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103 (1), 16–42.CrossRefGoogle Scholar
16. Ljung, L. 1999 System Identification: Theory for the User, 2nd edn. Prentice-Hall.Google Scholar
17. Ma, Z., Ahuja, S. & Rowley, C. W. 2011 Reduced order models for control of fluids using the Eigensystem Realization Algorithm. Theor. Comput. Fluid Mech. 25, 233–247.Google Scholar
18. Mezić, I. & Banaszuk, A. 2004 Comparison of systems with complex behaviour. Physica D: Nonlinear Phenom. 197, 101–133.CrossRefGoogle Scholar
19. Morgans, A. S. & Dowling, A. P. 2007 Model-based control of combustion instabilities. J. Sound Vib. 299, 261–282.CrossRefGoogle Scholar
20. Poinsot, T. J. & Lele, S. K. 1992 Boundary conditions for direct simulations of compressible viscous flows. J. Comput. Phys. 101 (1), 104–129.CrossRefGoogle Scholar
21. Powell, A. 1953 On edge tones and associated phenomena. Acustica 3, 233–243.Google Scholar
22. Rossiter, J. E. 1964 Wind–tunnel experiments on the flow over rectangular cavities at subsonic and transonic speeds. In Aeronaut. Res. Counc. R& M 3438.Google Scholar
23. Rowley, C. W., Colonius, T. & Basu, A. J. 2002a On self-sustained oscillations in two-dimensional compressible flow over rectangular cavities. J. Fluid Mech. 455, 315–346.CrossRefGoogle Scholar
24. Rowley, C. W. & Juttijudata, V. 2005 Model-based control and estimation of cavity flow oscillations. 44th IEEE Conference on Decision and Control, vol. 15, pp. 512–517.Google Scholar
25. Rowley, C. W., Williams, D. R., Colonius, T., Murray, R. M., MacMartin, D. G. & Fabris, D. 2002 b Model-based control of cavity oscillations part II: system identification and analysis. AIAA Paper 2002–0972.CrossRefGoogle Scholar
26. Rowley, C. W., Williams, D. R., Colonius, T., Murray, R. M. & Macmynowski, D. G. 2006 Linear models for control of cavity flow oscillations. J. Fluid Mech. 547, 317–330.CrossRefGoogle Scholar
27. Samimy, M., Debiasi, M., Caraballo, E., Serrani, A., Yuan, X., Little, J. & Myatt, J. H. 2007 Feedback control of subsonic cavity flows using reduced-order models. J. Fluid Mech. 579, 315–346.CrossRefGoogle Scholar
28. Sarohia, V. & Massier, P. F. 1977 Control of cavity noise. J. Aircraft 14 (9), 833–837.CrossRefGoogle Scholar
29. Shaw, L. & Northcraft, S. 1999 Closed loop active control for cavity acoustics. AIAA Paper 99–1902. pp. 683–689.CrossRefGoogle Scholar
30. Tierno, J. E. & Doyle, J. C. 1992 Multi mode active stabilization of a Rijke tube. In Active Control of Noise and Vibration, 1992: presented at the ASME Winter Annual Meeting, vol. DSC-Vol. 38, pp. 65–68.Google Scholar
31. Vinnicombe, G. 2000 Uncertainty and Feedback: Loop-Shaping and the -gap Metric . Imperial College Press.Google Scholar
32. Williams, D. R., Fabris, D. & Morrow, J. 2000 Experiments on controlling multiple acoustic modes in cavities. AIAA Paper 2000–1903.CrossRefGoogle Scholar
33. Yan, P., Debiasi, M., Yuan, X., Little, J., Özbay, H. & Samimy, M. 2006 Experimental study of linear closed-loop control of subsonic cavity flow. AIAA J. 44 (5), 929–938.CrossRefGoogle Scholar