ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)


For citation:

Yakupov E. О., Gubernov V., Polezhaev A. A. Modeling of wave patterns at the combustion front. Izvestiya VUZ. Applied Nonlinear Dynamics, 2021, vol. 29, iss. 4, pp. 538-548. DOI: 10.18500/0869-6632-2021-29-4-538-548

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
(downloads: 644)
Language: 
Russian
Article type: 
Article
UDC: 
530.182

Modeling of wave patterns at the combustion front

Autors: 
Yakupov Eduard Олегович, P.N. Lebedev Physical Institute of the Russian Academy of Sciences
Gubernov Vladimir, P.N. Lebedev Physical Institute of the Russian Academy of Sciences
Polezhaev Andrej Aleksandrovich, P.N. Lebedev Physical Institute of the Russian Academy of Sciences
Abstract: 

In experimental studies of the propagation of combustion waves in gaseous media, it was found that, under certain conditions, autowave – spiral or target – patterns appear at the wave front. The purpose of the present study is to propose a mathematical model that can explain this phenomenon based on the known chemical kinetics of hydrogen combustion. Model. The original detailed model was first reduced to four equations that adequately describe the propagation of the combustion wave. To explain the structures at the combustion front, the model was further reduced to two equations. Results. An analytical study of the resulting model was carried out, which demonstrated that it can describe the occurrence of spiral waves, and the corresponding conditions for the parameters of the model were determined. These analytical results have been confirmed in numerical experiments. Conclusion. Thus, it has been demonstrated that the model constructed on the basis of the reduction of the known kinetic scheme of hydrogen combustion is capable of explaining the experimentally observed autowave patterns at the propagating combustion front. 

Acknowledgments: 
This work was supported by Russian Foundation for Basic Research, grant No. 19-02-00610
Reference: 
  1. Trubetskov DI. Introduction to Synergetics. Oscillations and Waves. Moscow: URSS; 2011. 224 p. (in Russian).
  2. Trubetskov DI. Inroduction To Synergetics: Chaos And Structures. Moscow: URSS; 2014. 240 p. (in Russian).
  3. Ilyin IV, Aleshkovski IA, Ivanov AV, Koronovskii AA, Strakhova LM, Trubetskov AD, Trubetskov DI, Hramov AE, Yashkov IA. Nonlinear Dynamics Of Global Processes In Nature And Society. M.: Moscow University Press; 2014. 453 p. (in Russian).
  4. Walgraef D. Spatio-Temporal Pattern Formation: With Examples from Physics, Chemistry, and Materials Science. Springer-Verlag New York; 1997. 306 p. DOI: 10.1007/978-1-4612-1850-0.
  5. Cross MC, Hohenberg PC. Pattern formation outside of equilibrium. Rev. Mod. Phys. 1993;65(3): 851. DOI: 10.1103/RevModPhys.65.851.
  6. Camazine S, Deneubourg JL, Franks NR, Sneyd J, Theraula G, Bonabeau E. Self-Organization in Biological Systems. Princeton University Press; 2003. 562 p.
  7. Sivashinsky GI. Instabilities, pattern formation, and turbulence in flames. Annu. Rev. Fluid Mech. 1983;15(1):179–199. DOI: 10.1146/annurev.fl.15.010183.001143.
  8. Ju Y, Maruta K. Microscale combustion: Technology development and fundamental research. Prog. Energy Combust. Sci.. 2011;37(6):669–715. DOI: 10.1016/j.pecs.2011.03.001.
  9. Liesegang R. Ueber einige Eigenschaften von Gallerten. Naturw. Wochenschr. 1896;11(30): 353–362 (in German).
  10. Merzhanov AG, Borovinskaya IP. Self-spreading high-temperature synthesis of refractory inorganic compounds. Proc. USSR Acad. Sci. 1972;204(2):366–369 (in Russian).
  11. Matkowsky BJ, Olagunju DO. Propagation of a pulsating flame front in a gaseous combustible mixture. SIAM J. Appl. Math. 1980;39(2):290–300. DOI: 10.1137/0139025.
  12. Zeldovich YB, Barenblatt GI, Librovich VB, Makhviladze GM. The Mathematical Theory of Combustion and Explosions. Consultants Bureau, New York; 1985. 597 p.
  13. Buckmaster J. Stability of the porous plug burner flame. SIAM J. Appl. Math. 1983;43(6): 1335–1349. DOI: 10.1137/0143089.
  14. Gorman M, Hamill CF, El-Hamdi M, Robbins KA. Rotating and modulated rotating states of cellular flames. Combust. Sci. Technol. 1994;98(1–3):25–35. DOI: 10.1080/00102209408935394.
  15. Gorman M, El-Hamdi M, Robbins KA. Chaotic dynamics near the extinction limit of a premixed flame on a porous plug burner. Combust. Sci. Technol. 1994;98(1–3):47–56. DOI: 10.1080/00102209408935396.
  16. Kurdyumov VN, Sanchez–Sanz M. Influence of radiation losses on the stability of premixed ´ flames on a porous-plug burner. Proc. Combust. Inst. 2013;34(1):989–996. DOI: 10.1016/j.proci.2012.06.039.
  17. Gubernov VV, Bykov V, Maas U. Hydrogen/air burner-stabilized flames at elevated pressures. Combust. Flame. 2017;185:44–52. DOI: 10.1016/j.combustflame.2017.07.001.
  18. Margolis SB. Bifurcation phenomena in burner-stabilized premixed flames. Combust. Sci. Technol. 1980;22(3–4):143–169. DOI: 10.1080/00102208008952379.
  19. Jomaas G, Bechtold JK, Law CK. Spiral waves in expanding hydrogen–air flames: Experiment and theory. Proc. Combust. Inst. 2007;31(1):1039–1046. DOI: 10.1016/j.proci.2006.08.100.
  20. Jomaas G, Law CK. Observation and regime classification of pulsation patterns in expanding spherical flames. Phys. Fluids. 2010;22(12):124102. DOI: 10.1063/1.3525358.
  21. Wang G, Li Y, Yuan W, Wang Y, Zhou Z, Liu Y, Cai J. Investigation on laminar flame propagation of n-butanol/air and n-butanol/o2/He mixtures at pressures up to 20 atm. Combust. Flame. 2018;191:368–380. DOI: 10.1016/j.combustflame.2018.01.025.
  22. Yakupov EO, Polezhaev AA, Gubernov VV, Miroshnichenko TP. Investigation of the mechanism of emergence of autowave structures at the reaction front. Phys. Rev. E. 2019;99(4):042215. DOI: 10.1103/PhysRevE.99.042215.
  23. Yakupov EO, Gubernov VV, Polezhaev AA. Mathematical modeling of spatiotemporal patterns formed at a traveling reaction front. Chaos. 2020;30(8):083147. DOI: 10.1063/5.0012435.
  24. Stahl G, Warnatz J. Numerical investigation of time-dependent properties and extinction of strained methane and propane-air flamelets. Combust. Flame. 1991;85(3–4):285–299. DOI: 10.1016/0010-2180(91)90134-W.
  25. Korsakova AI, Gubernov VV, Kolobov AV, Bykov V, Maas U. Stability of rich laminar hydrogen-air flames in a model with detailed transport and kinetic mechanisms. Combust. Flame. 2016;163:478–486. DOI: 10.1016/j.combustflame.2015.10.024.
  26. Sal’nikov IY. On the theory of periodic occurrence of homogeneous chemical reactions. II. Thermokinetic self-oscillatory model. Russ. J. Phys. Chem. 1949;23(3):258–272 (in Russian).
  27. Scott SK, Wang J, Showalter K. Modelling studies of spiral waves and target patterns in premixed flames. J. Chem. Soc. Faraday Trans. 1997;93(9):1733–1739. DOI: 10.1039/A608474E.
  28. Ge Y, Zhao F, Wei J. A high order compact ADI method for solving 3D unsteady convection diffusion problems. Applied and Computational Mathematics. 2018;7(1):1–10. DOI: 10.11648/j.acm.20180701.11. 
Received: 
31.03.2021
Accepted: 
19.04.2021
Published: 
30.07.2021