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Nonlinear response of swirling premixed flames to helical flow disturbances

Published online by Cambridge University Press:  27 May 2020

Vishal Acharya Open the ORCID record for Vishal Acharya [Opens in a new window]  and
Timothy Lieuwen
Vishal Acharya*
Affiliation:
School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA30332, USA
Timothy Lieuwen
Affiliation:
School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA30332, USA
*
†Email address for correspondence: [email protected]
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Abstract

This paper considers the relationship between nonlinearly interacting helical flow disturbances and flame area response in a swirling premixed flame. The present study was performed to determine whether there are nonlinear mechanisms through which helical modes ($m_{u}\neq 0$) can lead to non-zero unsteady heat release rate oscillations. The results show that for single frequency content (at $\unicode[STIX]{x1D714}_{0}$), helical modes excite unsteady heat release rate response of $O(\unicode[STIX]{x1D716}^{3})$ and that two-frequency excitation (e.g. at $\unicode[STIX]{x1D714}_{0}$ and $2\unicode[STIX]{x1D714}_{0}$), leads to a response of $O(\unicode[STIX]{x1D716}^{2})$ at $\unicode[STIX]{x1D714}_{0}$. There are two mechanisms through which this can occur: First, helical flow disturbances can distort the time-averaged flame shape to have an azimuthal component that matches that of the incident disturbance, $\exp (im_{u}\unicode[STIX]{x1D703})$. Second, multiple helical modes can nonlinearly interact to cause axisymmetric unsteady flame wrinkling. The paper derives the various modal contributions in the incident velocity disturbance that satisfy these criteria. These results suggest that it is only the $m_{u}=0$ mode which controls the linear dynamics (e.g. instability inception conditions) of these flames (where $\unicode[STIX]{x1D716}\ll 1$), but that their nonlinear dynamics is also controlled by the $m_{u}\neq 0$ helical modes.

JFM classification

Reacting Flows: Flames
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 896 , 10 August 2020 , A6
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

Acharya, V. & Lieuwen, T. 2016 Premixed flame response to helical disturbances: mean flame non-axisymmetry effects. Combust. Flame 165, 188–197.CrossRefGoogle Scholar
Acharya, V., Shin, D.-H. & Lieuwen, T. 2013 Premixed flames excited by helical disturbances: flame wrinkling and heat release oscillations. J. Propul. Power 29 (6), 1282–1291.CrossRefGoogle Scholar
Armitage, C. A., Balachandran, R., Mastorakos, E. & Cant, R. S. 2006 Investigation of the nonlinear response of turbulent premixed flames to imposed inlet velocity oscillations. Combust. Flame 146 (3), 419–436.CrossRefGoogle Scholar
Balachandran, R., Ayoola, B. O., Kaminski, C. F., Dowling, A. P. & Mastorakos, E. 2005 Experimental investigation of the nonlinear response of turbulent premixed flames to imposed inlet velocity oscillations. Combust. Flame 143 (1–2), 37–55.CrossRefGoogle Scholar
Balachandran, R., Dowling, A. P. & Mastorakos, E. 2008 Non-linear response of turbulent premixed flames to imposed inlet velocity oscillations of two frequencies. Flow Turbul. Combust. 80 (4), 455–487.CrossRefGoogle Scholar
Bellows, B. D.2006 Characterization of nonlinear heat release-acoustic interactions in gas turbine combustors. PhD thesis, Georgia Institute of Technology.Google Scholar
Bellows, B. D., Bobba, M. K., Forte, A., Seitzman, J. M. & Lieuwen, T. 2007 Flame transfer function saturation mechanisms in a swirl-stabilized combustor. Proc. Combust. Inst. 31 (2), 3181–3188.CrossRefGoogle Scholar
Boyer, L. & Quinard, J. 1990 On the dynamics of anchored flames. Combust. Flame 82 (1), 51–65.CrossRefGoogle Scholar
Cala, C. E., Fernandes, E. C., Heitor, M. V. & Shtork, S. I. 2006 Coherent structures in unsteady swirling jet flow. Exp. Fluids 40 (2), 267–276.CrossRefGoogle Scholar
Candel, S., Durox, D., Ducruix, S., Birbaud, A.-L., Noiray, N. & Schuller, T. 2009 Flame dynamics and combustion noise: progress and challenges. Intl J. Aeroacoust. 8 (1), 1–56.CrossRefGoogle Scholar
Cohen, J. & Wygnanski, I. 1987a The evolution of instabilities in the axisymmetric jet. Part 1. The linear growth of disturbances near the nozzle. J. Fluid Mech. 176, 191–219.CrossRefGoogle Scholar
Cohen, J. & Wygnanski, I. 1987b The evolution of instabilities in the axisymmetric jet. Part 2. The flow resulting from the interaction between two waves. J. Fluid Mech. 176, 221–235.CrossRefGoogle Scholar
Creta, F., Fogla, N. & Matalon, M. 2011 Turbulent propagation of premixed flames in the presence of Darrieus–Landau instability. Combust. Theor. Model. 15 (2), 267–298.CrossRefGoogle Scholar
Dowling, A. P. & Stow, S. R. 2005 Acoustic analysis of gas-turbine combustors. In Combustion Instabilities in Gas-Turbine Engines: Operational Experience, Fundamental Mechanisms and Modeling (ed. Lieuwen, T. & Yang, V.), vol. 210, pp. 369–414.Google Scholar
Durox, D., Schuller, T., Noiray, N. & Candel, S. 2009 Experimental analysis of nonlinear flame transfer functions for different flame geometries. Proc. Combust. Inst. 32 (1), 1391–1398.CrossRefGoogle Scholar
Fick, W., Griffiths, A. J. & O’Doherty, T. 1997 Visualisation of the precessing vortex core in an unconfined swirling flow. Opt. Diagnost. Engng 2 (1), 19–31.Google Scholar
Fleifil, M., Annaswamy, A. M., Ghoneim, Z. A. & Ghoniem, A. F. 1996 Response of a laminar premixed flame to flow oscillations: a kinematic model and thermoacoustic instability results. Combust. Flame 106 (4), 487–510.CrossRefGoogle Scholar
Hirsch, C., Wäsle, J., Winkler, A. & Sattelmayer, T. 2007 A spectral model for the sound pressure from turbulent premixed combustion. Proc. Combust. Inst. 31 (1), 1435–1441.CrossRefGoogle Scholar
Huang, Y. & Yang, V. 2009 Dynamics and stability of lean-premixed swirl-stabilized combustion. Prog. Energy Combust. Sci. 35 (4), 293–364.CrossRefGoogle Scholar
Jochmann, P., Sinigersky, A., Hehle, M., Schäfer, O., Koch, R. & Bauer, H.-J. 2006 Numerical simulation of a precessing vortex breakdown. Intl J. Heat Fluid Flow 27 (2), 192–203.CrossRefGoogle Scholar
Karimi, N., Brear, M. J., Jin, S.-H. & Monty, J. P. 2009 Linear and non-linear forced response of a conical, ducted, laminar premixed flame. Combust. Flame 156 (11), 2201–2212.CrossRefGoogle Scholar
Kim, K. T. & Hochgreb, S. 2011 The nonlinear heat release response of stratified lean-premixed flames to acoustic velocity oscillations. Combust. Flame 158 (12), 2482–2499.CrossRefGoogle Scholar
Külsheimer, C. & Büchner, H. 2002 Combustion dynamics of turbulent swirling flames. Combust. Flame 131 (1-2), 70–84.CrossRefGoogle Scholar
Kuramoto, Y. & Tsuzuki, T. 1976 Persistent propagation of concentration waves in dissipative media far from thermal equilibrium. Progr. Theor. Phys. 55 (2), 356–369.CrossRefGoogle Scholar
Lacarelle, A., Faustmann, T., Greenblatt, D., Paschereit, C. O., Lehmann, O., Luchtenburg, D. M. & Noack, B. R. 2009 Spatiotemporal characterization of a conical swirler flow field under strong forcing. Trans. ASME J. Engng Gas Turbines Power 131 (3), 031504.CrossRefGoogle Scholar
Lee, D.-H. & Lieuwen, T. C. 2003 Acoustic near-field characteristics of a conical, premixed flame. J. Acoust. Soc. Am. 113 (1), 167–177.CrossRefGoogle ScholarPubMed
Lee, J. G. & Santavicca, D. A. 2003 Experimental diagnostics for the study of combustion instabilities in lean premixed combustors. J. Propul. Power 19 (5), 735–750.CrossRefGoogle Scholar
Liepmann, D. & Gharib, M. 1992 The role of streamwise vorticity in the near-field entrainment of round jets. J. Fluid Mech. 245, 643–668.CrossRefGoogle Scholar
Lieuwen, T. C. 2012 Unsteady Combustor Physics. Cambridge University Press.CrossRefGoogle Scholar
Markstein, G. H. 1964 Non-steady Flame Propagation. Pergarmon.Google Scholar
Matalon, M. & Matkowsky, B. J. 1982 Flames as gasdynamic discontinuities. J. Fluid Mech. 124, 239–259.CrossRefGoogle Scholar
Meliga, P., Gallaire, F. & Chomaz, J.-M. 2012 A weakly nonlinear mechanism for mode selection in swirling jets. J. Fluid Mech. 699, 216–262.CrossRefGoogle Scholar
Michalke, A. 1984 Survey on jet instability theory. Prog. Aerosp. Sci. 21, 159–199.CrossRefGoogle Scholar
Moeck, J. P., Bourgouin, J.-F., Durox, D., Schuller, T. & Candel, S. 2012 Nonlinear interaction between a precessing vortex core and acoustic oscillations in a turbulent swirling flame. Combust. Flame 159 (8), 2650–2668.CrossRefGoogle Scholar
Noiray, N., Durox, D., Schuller, T. & Candel, S. 2008 A unified framework for nonlinear combustion instability analysis based on the flame describing function. J. Fluid Mech. 615, 139–167.CrossRefGoogle Scholar
Oberleithner, K., Schimek, S. & Paschereit, C. O. 2015 Shear flow instabilities in swirl-stabilized combustors and their impact on the amplitude dependent flame response: a linear stability analysis. Combust. Flame 162 (1), 86–99.CrossRefGoogle Scholar
Oberleithner, K., Sieber, M., Nayeri, C. N., Paschereit, C. O., Petz, C., Hege, H.-C., Noack, B. R. & Wygnanski, I. 2011 Three-dimensional coherent structures in a swirling jet undergoing vortex breakdown: stability analysis and empirical mode construction. J. Fluid Mech. 679, 383–414.CrossRefGoogle Scholar
O’Connor, J., Acharya, V. & Lieuwen, T. 2015 Transverse combustion instabilities: acoustic, fluid mechanic, and flame processes. Prog. Energy Combust. Sci. 49, 1–39.CrossRefGoogle Scholar
O’Connor, J. & Lieuwen, T. 2012 Recirculation zone dynamics of a transversely excited swirl flow and flame. Phys. Fluids 24 (7), 2893–2900.CrossRefGoogle Scholar
Paschereit, C. O., Gutmark, E. & Weisenstein, W. 2000 Excitation of thermoacoustic instabilities by interaction of acoustics and unstable swirling flow. AIAA J. 38 (6), 1025–1034.CrossRefGoogle Scholar
Pier, B. 2008 Local and global instabilities in the wake of a sphere. J. Fluid Mech. 603, 39–61.CrossRefGoogle Scholar
Preetham, T., Sai, K., Lieuwen, T. & Santosh, H. 2010 Linear response of laminar premixed flames to flow oscillations: unsteady stretch effects. J. Propul. Power 26 (3), 524–532.Google Scholar
Rajaram, R. & Lieuwen, T. 2009 Acoustic radiation from turbulent premixed flames. J. Fluid Mech. 637, 357–385.CrossRefGoogle Scholar
Reynolds, W. C., Parekh, D. E., Juvet, P. J. D. & Lee, M. J. D. 2003 Bifurcating and blooming jets. Annu. Rev. Fluid Mech. 35 (1), 295–315.CrossRefGoogle Scholar
Schimek, S., Ćosić, B., Moeck, J. P., Terhaar, S. & Paschereit, C. O. 2015 Amplitude-dependent flow field and flame response to axial and tangential velocity fluctuations. Trans. ASME J. Engng Gas Turbines Power 137 (8), 081501.CrossRefGoogle Scholar
Schimek, S., Moeck, J. P. & Paschereit, C. O. 2011 An experimental investigation of the nonlinear response of an atmospheric swirl-stabilized premixed flame. Trans. ASME J. Engng Gas Turbines Power 133 (10), 101502.CrossRefGoogle Scholar
Shtork, S. I., Vieira, N. F. & Fernandes, E. C. 2008 On the identification of helical instabilities in a reacting swirling flow. Fuel 87 (10–11), 2314–2321.CrossRefGoogle Scholar
Sivashinsky, G. I. 1977 Nonlinear analysis of hydrodynamic instability in laminar flames – I. Derivation of basic equations. Acta Astron. 4, 1177–1206.CrossRefGoogle Scholar
Smith, T., Emerson, B., Proscia, W. & Lieuwen, T. 2018 Role of induced axial acoustics in transverse acoustic flame response. Combust. Flame 195, 140–150.CrossRefGoogle Scholar
Stöhr, M., Boxx, I., Carter, C. D. & Meier, W. 2012 Experimental study of vortex-flame interaction in a gas turbine model combustor. Combust. Flame 159 (8), 2636–2649.CrossRefGoogle Scholar
Syred, N. 2006 A review of oscillation mechanisms and the role of the precessing vortex core (PVC) in swirl combustion systems. Prog. Energy Combust. Sci. 32 (2), 93–161.CrossRefGoogle Scholar
Tammisola, O. & Juniper, M. P. 2016 Coherent structures in a swirl injector at Re = 4800 by nonlinear simulations and linear global modes. J. Fluid Mech. 792, 620–657.CrossRefGoogle Scholar
Terhaar, S., Oberleithner, K. & Paschereit, C. O. 2014 Impact of steam-dilution on the flame shape and coherent structures in swirl-stabilized combustors. Combust. Sci. Technol. 186 (7), 889–911.CrossRefGoogle Scholar
Thumuluru, S. K. & Lieuwen, T. 2009 Characterization of acoustically forced swirl flame dynamics. Proc. Combust. Inst. 32 (2), 2893–2900.CrossRefGoogle Scholar
Wang, H. Y., Law, C. K. & Lieuwen, T. 2009 Linear response of stretch-affected premixed flames to flow oscillations. Combust. Flame 156 (4), 889–895.CrossRefGoogle Scholar
Williams, F. A. 1985 Turbulent combustion. In The Mathematics of Combustion, pp. 97–131. SIAM.CrossRefGoogle Scholar
Worth, N. A. & Dawson, J. R. 2013 Modal dynamics of self-excited azimuthal instabilities in an annular combustion chamber. Combust. Flame 160 (11), 2476–2489.CrossRefGoogle Scholar