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Onset of global instability in a premixed annular V-flame

Published online by Cambridge University Press:  28 October 2024

Chuhan Wang Open the ORCID record for Chuhan Wang [Opens in a new window] ,
Christopher M. Douglas Open the ORCID record for Christopher M. Douglas [Opens in a new window] ,
Yu Guan Open the ORCID record for Yu Guan [Opens in a new window] ,
Chunxiao Xu Open the ORCID record for Chunxiao Xu [Opens in a new window]  and
Lutz Lesshafft Open the ORCID record for Lutz Lesshafft [Opens in a new window]
Chuhan Wang*
Affiliation:
AML, Department of Engineering Mechanics, Tsinghua University, 100084 Beijing, PR China LadHyX, CNRS, École Polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France
Christopher M. Douglas
Affiliation:
LadHyX, CNRS, École Polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC, USA
Yu Guan
Affiliation:
Department of Aeronautical and Aviation Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong
Chunxiao Xu
Affiliation:
AML, Department of Engineering Mechanics, Tsinghua University, 100084 Beijing, PR China
Lutz Lesshafft
Affiliation:
LadHyX, CNRS, École Polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France
*
†Email address for correspondence: cwang@ladhyx.polytechnique.fr
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Abstract

We investigate self-excited axisymmetric oscillations of a lean premixed methane–air V-flame in a laminar annular jet. The flame is anchored near the rim of the centrebody, forming an inverted cone, while the strongest vorticity is concentrated along the outer shear layer of the annular jet. Consequently, the reaction and vorticity dynamics are largely separated, except where they coalesce near the flame tip. The global eigenmodes corresponding to the linearised reacting flow equations around the steady base state are computed in an axisymmetric setting. We identify an arc branch of eigenmodes exhibiting strong oscillations at the flame tip. The associated eigenvalues are robust with respect to domain truncation and numerical discretisation, and they become destabilised as the Reynolds number increases. The frequency of the leading eigenmode is found to correspond to the Lagrangian disturbance advection time from the nozzle outlet to the flame tip. The essential role of this convective mechanism is also supported by resolvent analysis, which finds that the same flame-tip disturbance structure and frequency are optimally amplified when the flame is subjected to external white noise forcing. Strong non-modal effects in the form of pseudo-resonance are not found. Nonlinear time-resolved simulation further reveals notable hysteresis phenomena in the subcritical regime prior to instability. Hence, even when the flame is linearly stable, perturbations of sufficient amplitude can trigger limit-cycle oscillations and higher-dimensional dynamics sustained by nonlinear feedback. A Monte Carlo simulation of passive tracers in the unsteady flame suggests a nonlinear non-local instability mechanism. Notably, linear analysis of the subcritical time-averaged limit-cycle state yields eigenvalues that do not match the nonlinear periodic oscillation frequencies. This mismatch is attributed to the fundamentally nonlinear dynamics of the subcritical V-flame instability, where the dichromatic, non-local interaction between the heat release rate along the flame surface and the vortex dynamics in the jet shear layer cannot be approximated as a simple distortion of the mean flow.

JFM classification

Instability: Shear-flow instability Reacting Flows: Flames Wakes/Jets: Jets

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 998 , 10 November 2024 , A23
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© The Author(s), 2024. Published by Cambridge University Press

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References

Albayrak, A., Bezgin, D. & Polifke, W. 2018 Response of a swirl flame to inertial waves. Intl J. Spray Combust. Dyn. 10 (4), 277–286.CrossRefGoogle Scholar
Avdonin, A., Meindl, M. & Polifke, W. 2019 Thermoacoustic analysis of a laminar premixed flame using a linearized reactive flow solver. Proc. Combust. Inst. 37 (4), 5307–5314.CrossRefGoogle Scholar
Barkley, D. 2006 Linear analysis of the cylinder wake mean flow. Europhys. Lett. 75 (5), 750.CrossRefGoogle Scholar
Beneddine, S., Sipp, D., Arnault, A., Dandois, J. & Lesshafft, L. 2016 Conditions for validity of mean flow stability analysis. J. Fluid Mech. 798, 485–504.CrossRefGoogle Scholar
Birbaud, A.L., Ducruix, S., Durox, D. & Candel, S. 2008 The nonlinear response of inverted ‘V’ flames to equivalence ratio nonuniformities. Combust. Flame 154 (3), 356–367.CrossRefGoogle Scholar
Birbaud, A.L., Durox, D., Ducruix, S. & Candel, S. 2007 Dynamics of confined premixed flames submitted to upstream acoustic modulations. Proc. Combust. Inst. 31 (1), 1257–1265.CrossRefGoogle Scholar
Blanchard, M. 2015 Linear and nonlinear dynamics of laminar premixed flames submitted to flow oscillations. PhD thesis, Ecole Polytechnique.Google Scholar
Blanchard, M., Schuller, T., Sipp, D. & Schmid, P. 2015 Response analysis of a laminar premixed M-flame to flow perturbations using a linearized compressible Navier–Stokes solver. Phys. Fluids 27 (4), 043602.CrossRefGoogle Scholar
Brokof, P., Douglas, C.M. & Polifke, W. 2024 The role of hydrodynamic shear in the thermoacoustic response of slit flames. Proc. Combust. Inst. 40 (1), 105362.CrossRefGoogle Scholar
Candel, S., Durox, D., Schuller, T., Bourgouin, J.-F. & Moeck, J.P. 2014 Dynamics of swirling flames. Annu. Rev. Fluid Mech. 46, 147–173.CrossRefGoogle Scholar
Casel, M., Oberleithner, K., Zhang, F., Zirwes, T., Bockhorn, H., Trimis, D. & Kaiser, T. 2022 Resolvent-based modelling of coherent structures in a turbulent jet flame using a passive flame approach. Combust. Flame 236, 111695.CrossRefGoogle Scholar
CERFACS 2017 CANTERA User's Guide. Available at: https://www.cerfacs.fr/cantera/mechanisms/meth.php.Google Scholar
Cerqueira, S. & Sipp, D. 2014 Eigenvalue sensitivity, singular values and discrete frequency selection mechanism in noise amplifiers: the case of flow induced by radial wall injection. J. Fluid Mech. 757, 770–799.CrossRefGoogle Scholar
Chakravarthy, R.V.K., Lesshafft, L. & Huerre, P. 2018 Global stability of buoyant jets and plumes. J. Fluid Mech. 835, 654–673.CrossRefGoogle Scholar
Coenen, W., Lesshafft, L., Garnaud, X. & Sevilla, A. 2017 Global instability of low-density jets. J. Fluid Mech. 820, 187–207.CrossRefGoogle Scholar
Demange, S., Qadri, U.A., Juniper, M.P. & Pinna, F. 2022 Global modes of viscous heated jets with real gas effects. J. Fluid Mech. 936, A7.CrossRefGoogle Scholar
Di Renzo, M. & Urzay, J. 2021 Direct numerical simulation of a hypersonic transitional boundary layer at suborbital enthalpies. J. Fluid Mech. 912, A29.CrossRefGoogle Scholar
Douglas, C.M., Emerson, B.L., Hemchandra, S. & Lieuwen, T.C. 2021 a Forced flow response analysis of a turbulent swirling annular jet flame. Phys. Fluids 33 (8), 085124.CrossRefGoogle Scholar
Douglas, C.M., Emerson, B.L. & Lieuwen, T.C. 2021 b Nonlinear dynamics of fully developed swirling jets. J. Fluid Mech. 924, A14.CrossRefGoogle Scholar
Douglas, C.M., Emerson, B.L. & Lieuwen, T.C. 2022 Dynamics and bifurcations of laminar annular swirling and non-swirling jets. J. Fluid Mech. 943, A35.CrossRefGoogle Scholar
Douglas, C.M., Polifke, W. & Lesshafft, L. 2023 Flash-back, blow-off, and symmetry breaking of premixed conical flames. Combust. Flame 258, 113060.CrossRefGoogle Scholar
Duan, L. & Martín, M.P. 2011 Assessment of turbulence-chemistry interaction in hypersonic turbulent boundary layers. AIAA J. 49 (1), 172–184.CrossRefGoogle Scholar
Durox, D., Schuller, T. & Candel, S. 2005 Combustion dynamics of inverted conical flames. Proc. Combust. Inst. 30 (2), 1717–1724.CrossRefGoogle 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
Emerson, B., Lieuwen, T. & Juniper, M. 2016 Local stability analysis and eigenvalue sensitivity of reacting bluff-body wakes. J. Fluid Mech. 788, 549–575.CrossRefGoogle Scholar
Emerson, B., O'Connor, J., Juniper, M. & Lieuwen, T. 2012 Density ratio effects on reacting bluff-body flow field characteristics. J. Fluid Mech. 706, 219–250.CrossRefGoogle Scholar
Garnaud, X., Lesshafft, L., Schmid, P. & Huerre, P. 2013 a Modal and transient dynamics of jet flows. Phys. Fluids 25 (4), 044103.CrossRefGoogle Scholar
Garnaud, X., Lesshafft, L., Schmid, P.J. & Huerre, P. 2013 b The preferred mode of incompressible jets: linear frequency response analysis. J. Fluid Mech. 716, 189–202.CrossRefGoogle Scholar
Guan, Y., Gupta, V., Kashinath, K. & Li, L.K.B. 2019 Open-loop control of periodic thermoacoustic oscillations: experiments and low-order modelling in a synchronization framework. Proc. Combust. Inst. 37 (4), 5315–5323.CrossRefGoogle Scholar
Hallberg, M.P. & Strykowski, P.J. 2006 On the universality of global modes in low-density axisymmetric jets. J. Fluid Mech. 569, 493–507.CrossRefGoogle Scholar
Joos, F. & Vortmeyer, D. 1986 Self-excited oscillations in combustion chambers with premixed flames and several frequencies. Combust. Flame 65 (3), 253–262.CrossRefGoogle Scholar
Kaiser, T.L., Varillon, G., Polifke, W., Zhang, F., Zirwes, T., Bockhorn, H. & Oberleithner, K. 2023 Modelling the response of a turbulent jet flame to acoustic forcing in a linearized framework using an active flame approach. Combust. Flame 253, 112778.CrossRefGoogle Scholar
Karban, U., Bugeat, B., Martini, E., Towne, A., Cavalieri, A.V.G., Lesshafft, L., Agarwal, A., Jordan, P. & Colonius, T. 2020 Ambiguity in mean-flow-based linear analysis. J. Fluid Mech. 900, R5.CrossRefGoogle Scholar
Kyle, D.M. & Sreenivasan, K.R. 1993 The instability and breakdown of a round variable-density jet. J. Fluid Mech. 249, 619–664.CrossRefGoogle Scholar
Lang, W. 1991 Harmonic frequency generation by oscillating flames. Combust. Flame 83 (3), 253–262.CrossRefGoogle Scholar
Lesshafft, L. 2018 Artificial eigenmodes in truncated flow domains. Theor. Comput. Fluid Dyn. 32 (3), 245–262.CrossRefGoogle Scholar
Lesshafft, L., Huerre, P., Sagaut, P. & Terracol, M. 2006 Nonlinear global modes in hot jets. J. Fluid Mech. 554, 393–409.CrossRefGoogle Scholar
Lieuwen, T. 2003 Modeling premixed combustion–acoustic wave interactions: a review. J. Propul. Power 19 (5), 765–781.CrossRefGoogle Scholar
Lieuwen, T. 2005 Nonlinear kinematic response of premixed flames to harmonic velocity disturbances. Proc. Combust. Inst. 30 (2), 1725–1732.CrossRefGoogle Scholar
Manoharan, K. & Hemchandra, S. 2015 Absolute/convective instability transition in a backward facing step combustor: fundamental mechanism and influence of density gradient. Trans. ASME J. Engng Gas Turbines Power 137 (2), 021501.CrossRefGoogle Scholar
Marquet, O. & Lesshafft, L. 2015 Identifying the active flow regions that drive linear and nonlinear instabilities. arXiv:1508.07620.Google Scholar
McMurtry, P., Jou, W., Riley, J. & Metcalfe, R. 1986 Direct numerical simulations of a reacting mixing layer with chemical heat release. AIAA J. 24 (6), 962–970.CrossRefGoogle Scholar
Meindl, M., Silva, C. & Polifke, W. 2021 On the spurious entropy generation encountered in hybrid linear thermoacoustic models. Combust. Flame 223, 525–540.CrossRefGoogle Scholar
Meliga, P., Sipp, D. & Chomaz, J.-M. 2010 Effect of compressibility on the global stability of axisymmetric wake flows. J. Fluid Mech. 660, 499–526.CrossRefGoogle Scholar
Monkewitz, P.A., Bechert, D.W., Barsikow, B. & Lehmann, B. 1990 Self-excited oscillations and mixing in a heated round jet. J. Fluid Mech. 213, 611–639.CrossRefGoogle Scholar
Noack, B.R. & Eckelmann, H. 1994 A global stability analysis of the steady and periodic cylinder wake. J. Fluid Mech. 270, 297–330.CrossRefGoogle Scholar
Oberleithner, K., Stöhr, M., Im, S., Arndt, C. & Steinberg, A. 2015 Formation and flame-induced suppression of the precessing vortex core in a swirl combustor: experiments and linear stability analysis. Combust. Flame 162 (8), 3100–3114.CrossRefGoogle Scholar
Poinsot, T. & Veynante, D. 2005 Theoretical and Numerical Combustion. RT Edwards.Google Scholar
Qadri, U.A., Chandler, G.J. & Juniper, M.P. 2015 Self-sustained hydrodynamic oscillations in lifted jet diffusion flames: origin and control. J. Fluid Mech. 775, 201–222.CrossRefGoogle Scholar
Sayadi, T. & Schmid, P. 2021 Frequency response analysis of a (non-)reactive jet in crossflow. J. Fluid Mech. 922, A15.CrossRefGoogle Scholar
Schmid, P. & Henningson, D. 2001 Stability and Transition in Shear Flows. Springer.CrossRefGoogle Scholar
Schuller, T. 2003 Mécanismes de couplage dans les interactions acoustiques-combustion. PhD thesis, Ecole Centrale Paris.Google Scholar
Schuller, T., Durox, D. & Candel, S. 2003 A unified model for the prediction of laminar flame transfer functions: comparisons between conical and V-flame dynamics. Combust. Flame 134 (1–2), 21–34.CrossRefGoogle Scholar
Schuller, T., Poinsot, T. & Candel, S. 2020 Dynamics and control of premixed combustion systems based on flame transfer and describing functions. J. Fluid Mech. 894, P1.CrossRefGoogle Scholar
Silva, C.F. 2023 Intrinsic thermoacoustic instabilities. Prog. Energy Combust. Sci. 95, 101065.CrossRefGoogle Scholar
Sipp, D. & Lebedev, A. 2007 Global stability of base and mean flows: a general approach and its applications to cylinder and open cavity flows. J. Fluid Mech. 593, 333–358.CrossRefGoogle Scholar
Skene, C. & Schmid, P. 2019 Adjoint-based parametric sensitivity analysis for swirling M-flames. J. Fluid Mech. 859, 516–542.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
Trefethen, L.N. & Embree, M. 2005 Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators. Princeton University Press.CrossRefGoogle Scholar
Turton, S., Tuckerman, L. & Barkley, D. 2015 Prediction of frequencies in thermosolutal convection from mean flows. Phys. Rev. E 91 (4), 043009.CrossRefGoogle ScholarPubMed
Vishnu, R., Sujith, R.I. & Aghalayam, P. 2015 Role of flame dynamics on the bifurcation characteristics of a ducted V-flame. Combust. Sci. Technol. 187 (6), 894–905.CrossRefGoogle Scholar
Wang, C. 2022 Global linear analysis of flame instability. PhD thesis, Ecole Polytechnique.Google Scholar
Wang, C., Kaiser, T., Meindl, M., Oberleithner, K., Polifke, W. & Lesshafft, L. 2022 a Linear instability of a premixed slot flame: flame transfer function and resolvent analysis. Combust. Flame 240, 112016.CrossRefGoogle Scholar
Wang, C., Lesshafft, L. & Oberleithner, K. 2022 b Global linear stability analysis of a flame anchored to a cylinder. J. Fluid Mech. 951, A27.CrossRefGoogle Scholar
Zhu, Y., Gupta, V. & Li, L.K.B. 2017 Onset of global instability in low-density jets. J. Fluid Mech. 828, R1.CrossRefGoogle Scholar