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2 - Decomposition and Evolution of Disturbances

Published online by Cambridge University Press:  27 October 2021

Tim C. Lieuwen
Tim C. Lieuwen
Affiliation:
Georgia Institute of Technology
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Summary

A key focus of this text is to relate the manner in which fluctuations in flow or thermodynamic variables propagate and interact in combustion systems. In this chapter, we demonstrate that combustor disturbances can be decomposed into three canonical types of fluctuations – acoustic, entropy, and vorticity disturbances. This decomposition is highly illustrative in understanding the spatial/temporal dynamics of combustor disturbances [1]. For example, the velocity field can be decomposed into acoustic fluctuations, which propagate at the speed of sound with respect to the flow, and vorticity fluctuations, which are advected by the flow. This decomposition is important because, as shown in Chapters 11 and 12, two velocity disturbances of the same magnitude can lead to very different influences on the flame, depending on their phase speeds and space–time correlation. Section 2.9 further emphasizes how this decomposition provides insight into behavior measured in a harmonically oscillating flow field.

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Unsteady Combustor Physics , pp. 27 - 80
Publisher: Cambridge University Press
Print publication year: 2021

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References

Muthukrishnan, M., Strahle, W.C. and Neale, D.H., Separation of hydrodynamic, entropy, and combustion noise in a gas turbine combustor. AIAA Journal, 1978, 16(4): pp. 320–327.CrossRefGoogle Scholar
Chu, B.T. and Kovásznay, L.S.G., Non-linear interactions in a viscous heat-conducting compressible gas. Journal of Fluid Mechanics, 1957, 3(5): pp. 494–514.Google Scholar
Jou, W. and Menon, S., Modes of oscillation in a nonreacting ramjet combustor flow. Journal of Propulsion and Power, 1990, 6(5): pp. 535–543.CrossRefGoogle Scholar
Goldstein, M., Characteristics of the unsteady motion on transversely sheared mean flows. Journal of Fluid Mechanics, 1978, 84(2): pp. 305–329.Google Scholar
Laverdant, A. and Thévenin, D., Interaction of a Gaussian acoustic wave with a turbulent premixed flame. Combustion and Flame, 2003, 134(1–2): pp. 11–19.CrossRefGoogle Scholar
Pierce, A.D., Acoustics: An Introduction to its Physical Principles and Applications. 1989, Melville: Acoustical Society of America. 678.Google Scholar
Goldstein, M.E., Aeroacoustics. 1976, New York: McGraw-Hill.Google Scholar
Lighthill, M.J., On the energy scattered from the interaction of turbulence with sound or shock waves. Mathematical Proceedings of the Cambridge Philosophical Society, 1952, 49: pp. 531–551.Google Scholar
Lieuwen, T., Theoretical investigation of unsteady flow interactions with a premixed planar flame. Journal of Fluid Mechanics, 2001, 435: pp. 289–303.CrossRefGoogle Scholar
Marble, F.E. and Candel, S.M., Acoustic disturbance from gas non-uniformities. Journal of Sound and Vibration, 1977, 55(2): pp. 225–243.Google Scholar
Cuadra, E., Acoustic wave generation by entropy discontinuities flowing past an area change. The Journal of the Acoustical Society of America, 1966, 42(4): pp. 725–732.CrossRefGoogle Scholar
Cumpsty, N.A. and Marble, F.E., Core noise from gas turbine engines. Journal of Sound and Vibration, 1977, 54(2): pp. 297–309.Google Scholar
Komarek, T. and Polifke, W., Impact of swirl fluctuations on the flame response of a perfectly premixed swirl burner. Journal of Engineering for Gas Turbines and Power, 2010, 132(6): pp. 061503(1)–061503(7).Google Scholar
Palies, P., Durox, D., Schuller, T., and Candel, S., Modeling of premixed swirling flames transfer functions. Proceedings of the Combustion Institute, 2011, 33(2): pp. 2967–2974.Google Scholar
Acharya, V. and Lieuwen, T., Effect of azimuthal flow fluctuations on flow and flame dynamics of axisymmetric swirling flames. Physics of Fluids, 2015, 27(10).CrossRefGoogle Scholar
Mohring, W., On energy, group velocity and small damping of sound waves in ducts with shear flow. Journal of Sound and Vibration, 1973, 29(1): pp. 93–101.CrossRefGoogle Scholar
Howe, M.S., Acoustics of Fluid-Structure Interactions. 1st ed. Cambridge Monographs on Mechanics. 1998, Cambridge: Cambridge University Press, p. 572.CrossRefGoogle Scholar
O’Shea, S., Sound scattering by a potential vortex. Journal of Sound and Vibration, 1975, 43(1): pp. 109–116.CrossRefGoogle Scholar
Chih-Ming, H. and Kovasznay, L.S.G., Propagation of a coherent acoustic wave through a turbulent shear flow. Journal of the Acoustical Society of America, 1975, 60(1): pp. 40–45.Google Scholar
George, J. and Sujith, R.I., Emergence of acoustic waves from vorticity fluctuations: Impact of non-normality. Physical Review E, 2009, 80(4): pp. 046321:1–6.Google Scholar
Myers, M.K., Transport of energy by disturbances in arbitrary steady flows. Journal of Fluid Mechanics, 1991, 226: pp. 383–400.CrossRefGoogle Scholar
Morfey, C.L., Acoustic energy in non-uniform flows. Journal of Sound and Vibration, 1971, 14(2): pp. 159–170.CrossRefGoogle Scholar
Nicoud, F. and Poinsot, T., Thermoacoustic instabilities: Should the Rayleigh criterion be extended to include entropy changes? Combustion and Flame, 2005, 142: pp. 153–159.Google Scholar
Jenvey, P.L., The sound power from turbulence: A theory of the exchange of energy between the acoustic and non-acoustic fields. Journal of Sound and Vibration, 1989, 121(1): pp. 37–66.CrossRefGoogle Scholar
Myers, M.K., An exact energy corollary for homentropic flow. Journal of Sound and Vibration, 1986, 109(2): pp. 277–284.Google Scholar
Doak, P.E., Momentum potential theory of energy flux carried by momentum fluctuations. Journal of Sound and Vibration, 1989, 131(1): pp. 67–90.CrossRefGoogle Scholar
Chu, B.T., On the energy transfer to small disturbances in fluid flow (Part I). Acta Mechanica, 1965, 1(3): pp. 215–234.CrossRefGoogle Scholar
Chu, B.T. and Apfel, R.E., Are acoustic intensity and potential energy density first or second order quantities? American Journal of Physics, 1983, 51(10): pp. 916–918.CrossRefGoogle Scholar
George, J. and Sujith, R.I., On Chu’s disturbance energy. Journal of Sound and Vibration, 2011, 330: pp. 5280–5291.Google Scholar
Rayleigh, J.W.S., The Theory of Sound, Vol. 2. 1896, New York: Macmillan and Co.Google Scholar
Kim, K.T., Lee, J.G., Quay, B., and Santavicca, D., The dynamic response of turbulent dihedral V flames: An amplification mechanism of swirling flames. Combustion Science and Technology, 2011, 183(2): pp. 163–179.Google Scholar
Cantrell, R.H. and Hart, R.W., Interactions between sound and flow in acoustic cavities: Mass, momentum, and energy considerations. The Journal of the Acoustical Society of America, 1964, 36(4): pp. 697–706.CrossRefGoogle Scholar
Karimi, N., Brear, M.J., and Moase, W.H., Acoustic and disturbance energy analysis of a flow with heat communication. Journal of Fluid Mechanics, 2008, 597: pp. 67–98.Google Scholar
Lieuwen, T.C., Experimental investigation of limit-cycle oscillations in an unstable gas turbine combustor. Journal of Propulsion and Power, 2002, 18(1): pp. 61–67.Google Scholar
Oefelein, J.C. and Yang, V., Comprehensive review of liquid-propellant combustion instabilities in F-1 engines. Journal of Propulsion and Power, 1993, 9(5): pp. 657–677.Google Scholar
Cohen, J.M., Proscia, W., and Delaat, J., Characterization and control of aeroengine combustion instability: Pratt & Whitney and NASA experience, in Combustion Instabilities in Gas Turbine Engines. Operational Experience, Fundamental Mechanisms, and Modeling, Lieuwen, T.C. and Yang, V., eds. 2005, AIAA, pp. 113–144.Google Scholar
Nayfeh, A.H. and Mook, D.T., Nonlinear Oscillations. 1995, Wiley.CrossRefGoogle Scholar
Gardiner, C.W., Handbook of Stochastic Methods. 1997, Springer: New York.Google Scholar
Lieuwen, T.C., Statistical characteristics of pressure oscillations in a premixed combustor. Journal of Sound and Vibration, 2003, 260(1): pp. 3–17.CrossRefGoogle Scholar
Lieuwen, T.C., Online combustor stability margin assessment using dynamic pressure measurements. Journal of Engineering for Gas Turbines and Power, 2005, 127(3): pp. 478–482.CrossRefGoogle Scholar
Roberts, J.B. and Spanos, P.D., Stochastic averaging: An approximate method of solving random vibration problems. International Journal of Non-Linear Mechanics, 1986, 21(2): pp. 111–134.CrossRefGoogle Scholar
Hilborn, R.C., Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers. 1994, New York: Oxford University Press.Google Scholar
Nair, V., Thampi, G., and Sujith, R.I., Intermittency route to thermoacoustic instability in turbulent combustors. Journal of Fluid Mechanics, 2014, 756: pp. 470–487.Google Scholar
Mallat, S.G. and Mallat, C., A Wavelet Tour of Signal Processing. 2nd ed. Wavelet Analysis and Its Applications. 1999, Elsevier Science & Technology.Google Scholar
Courant, R. and Hilbert, D., Methods of Mathematical Physics. 1989, John Wiley & Sons.Google Scholar
Petropulu, A.P., Higher-Order Spectral Analysis. 2000, CRC Press LLC.Google Scholar
Holmes, P., Lumley, J.L., Berkooz, G., and Rowley, C.W., Turbulence, Coherent Structures, Dynamical Systems and Symmetry. 1996, New York: Cambridge University Press.Google Scholar
Emerson, B., Dynamical Characteristics of Reacting Bluff Body Wakes. 2013, Georgia Institute of Technology.Google Scholar
Oberleithner, K., Sieber, M., Nayeri, C.N., Paschereit, C.O., Petz, C., Hege, H.-C., Noack, B.R., and Wygnanski, I., Three-dimensional coherent structures in a swirling jet undergoing vortex breakdown: Stability analysis and empirical mode construction. Journal of Fluid Mechanics, 2011, 679: pp. 383–414.Google Scholar
Towne, A., Schmidt, O.T., and Colonius, T., Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis. Journal of Fluid Mechanics, 2018, 847: pp. 821–867.Google Scholar
Lumley, J.L., The structure of inhomogeneous turbulent flows, in Atmospheric Turbulence and Radio Wave Propagation, Yaglom, A.M. and Tatarsky, V.I., eds. 1967, Nauka, pp. 166–176.Google Scholar
Sieber, M., Paschereit, C., and Oberleithner, K., Spectral proper orthogonal decomposition. Journal of Fluid Mechanics, 2016, 792: pp. 798–828.Google Scholar
Sieber, M., Paschereit, C., and Oberleithner, K., On the nature of spectral proper orthogonal decomposition and related modal decompositions. 2017, arXiv:1712.08054.Google Scholar
Kutz, J.N., Brunton, S.L., Brunton, B.W., and Proctor, J.L, Dynamic Mode Decomposition: Data-Driven Modeling of Complex Systems. 2016, Society for Industrial and Applied Mathematics.Google Scholar
Schmid, P.J., Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics, 2010, 656(1): pp. 5–28.Google Scholar
Hussain, A.K.M.F. and Reynolds, W.C., The mechanics of an organized wave in turbulent shear flow. Journal of Fluid Mechanics, 1970, 41(2): pp. 241–258.Google Scholar
Smith, T.E., Chterev, I.P., Emerson, B.L., Noble, D.R., and Lieuwen, T.C., Comparison of single- and multinozzle reacting swirl flow dynamics. Journal of Propulsion and Power, 2017, 34(2).Google Scholar
Pope, S.B., Turbulent Flows. 2000, Cambridge University Press.CrossRefGoogle Scholar
Shanbhogue, S.J., Seelhorst, M., and Lieuwen, T., Vortex phase-jitter in acoustically excited bluff body flames. International Journal of Spray and Combustion Dynamics, 2009, 1(3): pp. 365–387.CrossRefGoogle Scholar

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