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Vortical interactions in turbulent thermoacoustic systems

Published online by Cambridge University Press:  01 September 2025

Ankit Sahay*
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai 600 036, India Centre of Excellence for studying Critical Transitions in Complex Systems, Indian Institute of Technology Madras, Chennai 600 036, India
Muralikrishnan Gopalakrishnan Meena
Affiliation:
National Center for Computational Sciences, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
R.I. Sujith
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai 600 036, India Centre of Excellence for studying Critical Transitions in Complex Systems, Indian Institute of Technology Madras, Chennai 600 036, India
*
Corresponding author: Ankit Sahay, ankitsahay02@gmail.com

Abstract

This study examines the dynamics of vortical interactions and their implications for mitigating thermoacoustic instability in a turbulent combustor. The regions of intense vortical interactions are identified as vortical communities in the network space of weighted directed vortical networks constructed from two-dimensional experimental velocity data. One can expect vortical interactions in the combustor to be strongest near the moment of vortex shedding, as the shed vortices gradually weaken due to dissipation while convecting downstream. However, we show that, during the state of thermoacoustic instability, there is a non-trivial consistent phase lag of approximately $52^\circ$ between the shedding of the coherent structures from the backward-facing step and the time instant when the vortical interactions attain their local maximum value. We explain this phase lag by investigating the correlation between acoustic pressure fluctuations, spatio-temporal dynamics of coherent structures and vortical interactions in the reaction field of the combustor. We also show the aperiodic variation of vortical interactions during the states of combustion noise and aperiodic epochs of intermittency. Furthermore, the spatio-temporal evolution of pairs of vortical communities with the maximum inter-community interactions provides insight into explaining the critical regions detected in the reaction field during the states of intermittency and thermoacoustic instability, also identified in previous studies. We further show that the most efficient suppression of thermoacoustic instability via air microjet injection is achieved when steady air jets are introduced to disrupt the maximum inter-community interactions present during the state of thermoacoustic instability.

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Type
JFM Papers
Copyright
© UT-Battelle, LLC and the Author(s), 2025. Published by Cambridge University Press

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References

Altay, H.M., Hudgins, D.E., Speth, R.L., Annaswamy, A.M. & Ghoniem, A.F. 2010 Mitigation of thermoacoustic instability utilizing steady air injection near the flame anchoring zone. Combust. Flame 157 (4), 686700.10.1016/j.combustflame.2010.01.012CrossRefGoogle Scholar
Altay, M., Speth, R., Snarheim, D., Hudgins, D., Ghoniem, A.F. & Annaswamy, A.M. 2007 Impact on microjet actuation on stability of a backward-facing step combustor. In 45th AIAA Aerospace Sciences Meeting and Exhibit, pp. AIAA–2007-0563. American Institute of Aeronautics and Astronautics.10.2514/6.2007-563CrossRefGoogle Scholar
Barabási, A. 2012 The network takeover. Nat. Phys. 8 (1), 1416.10.1038/nphys2188CrossRefGoogle Scholar
Blondel, V.D., Guillaume, J.-L., Lambiotte, R. & Lefebvre, E. 2008 Fast unfolding of communities in large networks. J. Stat. Mech.: Theory Exp. 2008 (10), P10008.10.1088/1742-5468/2008/10/P10008CrossRefGoogle Scholar
Candel, S., Durox, D. & Schuller, T. 2004 Flame interactions as a source of noise and combustion instabilities. AIAA.10.2514/6.2004-2928CrossRefGoogle Scholar
Castagliola, P., Achouri, A., Taleb, H., Celano, G. & Psarakis, S. 2013 Monitoring the coefficient of variation using a variable sampling interval control chart. Qual. Reliab. Engng Intl 29 (8), 11351149.10.1002/qre.1465CrossRefGoogle Scholar
Coats, C.M. 1996 Coherent structures in combustion. Prog. Energy Combust. Sci. 22 (5), 427509.10.1016/S0360-1285(96)00011-1CrossRefGoogle Scholar
Cordeiro, M., Sarmento, R.P. & Gama, J. 2016 Dynamic community detection in evolving networks using locality modularity optimization. Soc. Netw. Anal. Min. 6 (1), 120.10.1007/s13278-016-0325-1CrossRefGoogle Scholar
Desai, R., Chakravarthy, S. & Ramgopal, S. 2010 Effect of fuel injection location on combustion instability in a dump combustor. In 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, pp. 216. American Institute of Aeronautics and Astronautics.10.2514/6.2010-216CrossRefGoogle Scholar
Fiedler, H.E. 1988 Coherent structures in turbulent flows. Prog. Aerosp. Sci. 25 (3), 231269.10.1016/0376-0421(88)90001-2CrossRefGoogle Scholar
Fortunato, S. 2010 Community detection in graphs. Phys. Rep. 486 (3–5), 75174.10.1016/j.physrep.2009.11.002CrossRefGoogle Scholar
Fortunato, S. & Barthelemy, M. 2007 Resolution limit in community detection. Proc. Natl Acad. Sci. 104 (1), 3641.10.1073/pnas.0605965104CrossRefGoogle ScholarPubMed
Fruchterman, T.M.J. & Reingold, E.M. 1991 Graph drawing by force-directed placement. Softw. Pract. Exp. 21 (11), 11291164.10.1002/spe.4380211102CrossRefGoogle Scholar
Geikie, M.K. & Ahmed, K.A. 2018 Pressure-gradient tailoring effects on the turbulent flame-vortex dynamics of bluff-body premixed flames. Combust. Flame 197, 227242.10.1016/j.combustflame.2018.08.001CrossRefGoogle Scholar
Geikie, M.K., Rising, C.J., Morales, A.J. & Ahmed, K.A. 2021 Turbulent flame-vortex dynamics of bluff-body premixed flames. Combust. Flame 223, 2841.10.1016/j.combustflame.2020.09.023CrossRefGoogle Scholar
George, N.B., Unni, V.R., Raghunathan, M. & Sujith, R.I. 2018 Pattern formation during transition from combustion noise to thermoacoustic instability via intermittency. J. Fluid Mech. 849, 615644.10.1017/jfm.2018.427CrossRefGoogle Scholar
Ghoniem, A.F., Annaswamy, A.M., Park, S. & Sobhani, Z.C. 2005 Stability and emissions control using air injection and H2 addition in premixed combustion. Proc. Combust. Inst. 30 (2), 17651773.10.1016/j.proci.2004.08.175CrossRefGoogle Scholar
Gopalakrishnan Meena, M., Nair, A.G. & Taira, K. 2018 Network community-based model reduction for vortical flows. Phys. Rev. E 97 (6), 063103.10.1103/PhysRevE.97.063103CrossRefGoogle ScholarPubMed
Gopalakrishnan Meena, M. & Taira, K. 2021 Identifying vortical network connectors for turbulent flow modification. J. Fluid Mech. 915, A10.10.1017/jfm.2021.35CrossRefGoogle Scholar
Guimerà, R. & Amaral, L.A.N. 2005 Functional cartography of complex metabolic networks. Nature 433 (7028), 895900.10.1038/nature03288CrossRefGoogle ScholarPubMed
Gürcan, Ö.D. 2017 Nested polyhedra model of turbulence. Phys. Rev. E 95 (6), 063102.10.1103/PhysRevE.95.063102CrossRefGoogle ScholarPubMed
Gürcan, Ö.D. 2018 Nested polyhedra model of isotropic magnetohydrodynamic turbulence. Phys. Rev. E 97 (6), 063111.10.1103/PhysRevE.97.063111CrossRefGoogle ScholarPubMed
Hadjighasem, A., Karrasch, D., Teramoto, H. & Haller, G. 2016 Spectral-clustering approach to Lagrangian vortex detection. Phys. Rev. E 93 (6), 063107.10.1103/PhysRevE.93.063107CrossRefGoogle ScholarPubMed
Ho, C.M. & Huerre, P. 1984 Perturbed free shear layers. Annu. Rev. Fluid Mech. 16 (1), 365424.10.1146/annurev.fl.16.010184.002053CrossRefGoogle Scholar
Hong, S., Speth, R.L., Shanbhogue, S.J. & Ghoniem, A.F. 2013 Examining flow-flame interaction and the characteristic stretch rate in vortex-driven combustion dynamics using PIV and numerical simulation. Combust. Flame 160 (8), 13811397.10.1016/j.combustflame.2013.02.016CrossRefGoogle Scholar
Hussain, A.K.M.F. 1983 Coherent structures–reality and myth. Phys. Fluids 26 (10), 28162850.10.1063/1.864048CrossRefGoogle Scholar
Hussain, A.K.M.F. 1986 Coherent structures and turbulence. J. Fluid Mech. 173, 303356.10.1017/S0022112086001192CrossRefGoogle Scholar
Hussain, M., Jamshed, S. & Ozair, M. 2022 Simulations and analysis of vortex driven combustion instability. In 2022 19th International Bhurban Conference on Applied Sciences and Technology (IBCAST), pp. 765770. IEEE.10.1109/IBCAST54850.2022.9990249CrossRefGoogle Scholar
Iacobello, G., Ridolfi, L. & Scarsoglio, S. 2021 A review on turbulent and vortical flow analyses via complex networks. Phys. A: Stat. Mech. Appl. 563, 125476.10.1016/j.physa.2020.125476CrossRefGoogle Scholar
Iacobello, G., Scarsoglio, S., Kuerten, J.G.M. & Ridolfi, L. 2019 Lagrangian network analysis of turbulent mixing. J. Fluid Mech. 865, 546562.10.1017/jfm.2019.79CrossRefGoogle Scholar
Iacobello, G., Scarsoglio, S. & Ridolfi, L. 2018 Visibility graph analysis of wall turbulence time-series. Phys. Lett. A 382 (1), 111.10.1016/j.physleta.2017.10.027CrossRefGoogle Scholar
Jadhav, V., Guttal, V. & Masila, D.R. 2022 Randomness in the choice of neighbours promotes cohesion in mobile animal groups. R. Soc. Open Sci. 9 (3), 220124.10.1098/rsos.220124CrossRefGoogle ScholarPubMed
Karrer, B., Levina, E. & Newman, M.E. 2008 Robustness of community structure in networks. Phys. Rev. E 77 (4), 046119.10.1103/PhysRevE.77.046119CrossRefGoogle ScholarPubMed
Kawano, K., Gotoda, H., Nabae, Y., Ohmichi, Y. & Matsuyama, S. 2023 Complex-network analysis of high-frequency combustion instability in a model single-element rocket engine combustor. J. Fluid Mech. 959, A1.10.1017/jfm.2023.52CrossRefGoogle Scholar
Krishnan, A., Manikandan, R., Midhun, P.R., Reeja, K.V., Unni, V.R., Sujith, R.I., Marwan, N. & Kurths, J. 2019 a Mitigation of oscillatory instability in turbulent reactive flows: A novel approach using complex networks. EPL (Europhys. Lett.) 128 (1), 14003.10.1209/0295-5075/128/14003CrossRefGoogle Scholar
Krishnan, A., Sujith, R., Marwan, N. & Kurths, J. 2021 Suppression of thermoacoustic instability by targeting the hubs of the turbulent networks in a bluff body stabilized combustor. J. Fluid Mech. 916, A20.10.1017/jfm.2021.166CrossRefGoogle Scholar
Krishnan, A., Sujith, R.I., Marwan, N.K. & J 2019 b On the emergence of large clusters of acoustic power sources at the onset of thermoacoustic instability in a turbulent combustor. J. Fluid Mech. 874, 455482.10.1017/jfm.2019.429CrossRefGoogle Scholar
Lancichinetti, A. & Fortunato, S. 2011 Limits of modularity maximization in community detection. Phys. Rev. E 84 (6), 066122.10.1103/PhysRevE.84.066122CrossRefGoogle ScholarPubMed
Lancichinetti, A., Fortunato, S. & Radicchi, F. 2008 Benchmark graphs for testing community detection algorithms. Phys. Rev. E 78 (4), 046110.10.1103/PhysRevE.78.046110CrossRefGoogle ScholarPubMed
Leicht, E.A. & Newman, M.E.J. 2008 Community structure in directed networks. Phys. Rev. Lett. 100 (11), 118703.10.1103/PhysRevLett.100.118703CrossRefGoogle ScholarPubMed
Malmendier, A. & Reid, J.T. 2020 Application of the Biot–Savart law to parabolic vortex segments using elliptic integrals. Zeitschrift für Angewandte Mathematik Und Physik 71 (4), 120.10.1007/s00033-020-01319-3CrossRefGoogle Scholar
Mankbadi, R. & Liu, J.T.C. 1984 Sound generated aerodynamically revisited: large-scale structures in a turbulent jet as a source of sound. Philos. Trans. R. Soc. A 311 (1516), 183217.Google Scholar
Meilă, M. 2007 Comparing clusterings–an information based distance. J. Multivar. Anal. 98 (5), 873895.10.1016/j.jmva.2006.11.013CrossRefGoogle Scholar
Mondal, S., Unni, V.R. & Sujith, R.I. 2017 Onset of thermoacoustic instability in turbulent combustors: an emergence of synchronized periodicity through formation of chimera-like states. J. Fluid Mech. 811, 659681.10.1017/jfm.2016.770CrossRefGoogle Scholar
Murayama, S., Kinugawa, H., Tokuda, I.T. & Gotoda, H. 2018 Characterization and detection of thermoacoustic combustion oscillations based on statistical complexity and complex-network theory. Phys. Rev. E 97 (2), 022223.10.1103/PhysRevE.97.022223CrossRefGoogle ScholarPubMed
Nair, A.G., Brunton, S.L. & Taira, K. 2018 Networked-oscillator-based modeling and control of unsteady wake flows. Phys. Rev. E 97 (6), 063107.10.1103/PhysRevE.97.063107CrossRefGoogle ScholarPubMed
Nair, A.G. & Taira, K. 2015 Network-theoretic approach to sparsified discrete vortex dynamics. J. Fluid Mech. 768, 549571.10.1017/jfm.2015.97CrossRefGoogle Scholar
Nair, S. & Lieuwen, T. 2007 Near-blowoff dynamics of a bluff-body stabilized flame. J. Propul. Power 23 (2), 421427.10.2514/1.24650CrossRefGoogle Scholar
Nair, V., Thampi, G. & Sujith, R.I. 2014 Intermittency route to thermoacoustic instability in turbulent combustors. J. Fluid Mech. 756, 470487.10.1017/jfm.2014.468CrossRefGoogle Scholar
Neamtu-Halic, M.M., Krug, D., Haller, G. & Holzner, M. 2019 Lagrangian coherent structures and entrainment near the turbulent/non-turbulent interface of a gravity current. J. Fluid Mech. 877, 824843.10.1017/jfm.2019.635CrossRefGoogle Scholar
Newman, M. 2018 Networks. Oxford University Press.10.1093/oso/9780198805090.001.0001CrossRefGoogle Scholar
Newman, M.E.J. 2004 Fast algorithm for detecting community structure in networks. Phys. Rev. E 69 (6), 066133.10.1103/PhysRevE.69.066133CrossRefGoogle ScholarPubMed
Newman, M.E.J. & Girvan, M. 2004 Finding and evaluating community structure in networks. Phys. Rev. E 69 (2), 026113.10.1103/PhysRevE.69.026113CrossRefGoogle ScholarPubMed
Poinsot, T.J., Trouve, A.C., Veynante, D.P., Candel, S.M. & Esposito, E.J. 1987 Vortex-driven acoustically coupled combustion instabilities. J. Fluid Mech. 177, 265292.10.1017/S0022112087000958CrossRefGoogle Scholar
Premchand, C., Krishnan, A., Raghunathan, M., Midhun, P., Reeja, K., Sujith, R. & Nair, V. 2024 Identifying optimal location for control of thermoacoustic instability through statistical analysis of saddle point trajectories. Chaos: Interdisciplinary J. Nonlinear Sci. 34 (8), 083113.10.1063/5.0175991CrossRefGoogle Scholar
Raffel, M. et al. 1998 Particle Image Velocimetry: A Practical Guide. Springer.10.1007/978-3-662-03637-2CrossRefGoogle Scholar
Reichardt, J. & Bornholdt, S. 2006 Statistical mechanics of community detection. Phys. Rev. E 74 (1), 016110.10.1103/PhysRevE.74.016110CrossRefGoogle ScholarPubMed
Renard, P.H., Thevenin, D., Rolon, J.C. & Candel, S. 2000 Dynamics of flame/vortex interactions. Prog. Energy Combust. Sci. 26 (3), 225282.10.1016/S0360-1285(00)00002-2CrossRefGoogle Scholar
Rising, C.J., Morales, A.J., Geikie, M.K. & Ahmed, K.A. 2021 The effects of turbulence and pressure gradients on vorticity transport in premixed bluff-body flames. Phys. Fluids 33 (1), 017106.10.1063/5.0031068CrossRefGoogle Scholar
Rogers, D.E. & Marble, F.E. 1956 A mechanism for high-frequency oscillation in ramjet combustors and afterburners. J. Jet Propuls. 26 (6), 456462.10.2514/8.7049CrossRefGoogle Scholar
Roy, A., Premchand, C.P., Raghunathan, M., Krishnan, A., Nair, V. & Sujith, R.I. 2021 Critical region in the spatiotemporal dynamics of a turbulent thermoacoustic system and smart passive control. Combust. Flame 226, 274284.10.1016/j.combustflame.2020.12.018CrossRefGoogle Scholar
Schadow, K.C. & Gutmark, E. 1992 Combustion instability related to vortex shedding in dump combustors and their passive control. Prog. Energy Combust. Sci. 18 (2), 117132.10.1016/0360-1285(92)90020-2CrossRefGoogle Scholar
Ser-Giacomi, E., Rossi, V., López, C. & Hernández-Garcia, E. 2015 Flow networks: a characteri- zation of geophysical fluid transport. Chaos 25 (3), 036404.10.1063/1.4908231CrossRefGoogle Scholar
Shanbhogue, S.J., Seelhorst, M. & Lieuwen, T. 2009 Vortex phase-jitter in acoustically excited bluff body flames. Intl J. Spray Combust. Dyn. 1 (3), 365387.10.1260/175682709789141528CrossRefGoogle Scholar
Sivakumar, R. & Chakravarthy, S. 2008 Experimental investigation of the acoustic field in a bluff-body combustor. Intl J. Aeroacoust. 7 (3–4), 267299.10.1260/1475-472X.7.3.267CrossRefGoogle Scholar
Smith, D.A. & Zukoski, E.E. 1985 Combustion instability sustained by unsteady vortex combustion. In 21st Joint Propulsion Conference, AIAA.Google Scholar
Smith, K., Brighton, H. & Kirby, S. 2003 Complex systems in language evolution: the cultural emergence of compositional structure. Adv. Complex Syst. 6 (04), 537558.10.1142/S0219525903001055CrossRefGoogle Scholar
Sujith, R.I. & Pawar, S.A. 2021 Thermoacoustic Instability. Springer Series in Synergetics.10.1007/978-3-030-81135-8CrossRefGoogle Scholar
Tachibana, S., Zimmer, L., Kurosawa, Y. & Suzuki, K. 2007 Active control of combustion oscillations in a lean premixed combustor by secondary fuel injection coupling with chemiluminescence imaging technique. Proc. Combust. Inst. 31 (2), 32253233.10.1016/j.proci.2006.08.037CrossRefGoogle Scholar
Taira, K. & Nair, A.G. 2022 Network-based analysis of fluid flows: progress and outlook. Prog. Aerosp. Sci. 131, 100823.10.1016/j.paerosci.2022.100823CrossRefGoogle Scholar
Taira, K., Nair, A.G. & Brunton, S.L. 2016 Network structure of two-dimensional decaying isotropic turbulence. J. Fluid Mech. 795, R2.10.1017/jfm.2016.235CrossRefGoogle Scholar
Tandon, S. & Sujith, R.I. 2023 Multilayer network analysis to study complex inter-subsystem interactions in a turbulent thermoacoustic system. J. Fluid Mech. 966, A9.10.1017/jfm.2023.338CrossRefGoogle Scholar
Tietjens, O.K.G. & Prandtl, L. 1957 Applied hydro-and aeromechanics: based on lectures of L. Prandtl, vol. 2, Courier Corporation.Google Scholar
Uhm, J.H. & Acharya, S. 2005 Low-bandwidth open-loop control of combustion instability. Combust. Flame 142 (4), 348363.10.1016/j.combustflame.2005.03.015CrossRefGoogle Scholar
Yeh, C.A., Gopalakrishnan Meena, M. & Taira, K. 2021 Network broadcast analysis and control of turbulent flows. J. Fluid Mech. 910, A15.10.1017/jfm.2020.965CrossRefGoogle Scholar
Yu, K.H. & Schadow, K.C. 1997 Role of large coherent structures in turbulent compressible mixing. Exp. Therm. Fluid Sci. 14 (1), 7584.10.1016/S0894-1777(96)00103-3CrossRefGoogle Scholar
Yu, K.H., Trouvé, A. & Daily, J.W. 1991 Low-frequency pressure oscillations in a model ramjet combustor. J. Fluid Mech. 232, 4772.10.1017/S0022112091003622CrossRefGoogle Scholar
Zilitinkevich, S. 1970 Non-local turbulent transport: pollution dispersion aspects of coherent structure of connective flows. WIT Trans. Ecol. Environ. 9, 5360.Google Scholar
Zou, Y., Donner, R.V., Marwan, N., Donges, J.F. & Kurths, J. 2019 Complex network approaches to nonlinear time series analysis. Phys. Rep. 787, 197.10.1016/j.physrep.2018.10.005CrossRefGoogle Scholar