Evolutionary equations for the disturbed flame stabilised at the flat burner

References

• A.M. Grishin, V.N. Bertsun and V.M. Agranat, Investigation of the diffusion-thermal instability of laminar flames. Sov. Phys. Dokl. 22(3) (1977), pp. 373–375.
   Google Scholar
• Y.B. Zeldovich, G.I. Barenblatt, V.B. Librovich and G.M. Makhviladze, Mathematical theory of combustion and explosions, United States, NY, 1985.
   Google Scholar
• G. Joulin, Flame oscillations induced by conductive losses to a flat burner. Combust. Flame 46 (1982), pp. 271–281.
   Web of Science ®Google Scholar
• G. Joulin and P. Clavin, Linear stability analysis of nonadiabatic flames: diffusional thermal model. Combust. Flame 35 (1979), pp. 139–153.
   Web of Science ®Google Scholar
• D.B. Spalding and V.S. Yumlu, Experimental demonstration of the existence of two flame speeds. Combust. Flame 3 (1959), pp. 553–556.
   Web of Science ®Google Scholar
• S.B. Margolis, Bifurcation phenomena in burner-stabilized premixed flames. Combust. Sci. Technol. 22(3–4) (1980), pp. 143–169.
   Web of Science ®Google Scholar
• J. Buckmaster, Stability of the porous plug burner flame. SIAM J. Appl. Math. 43(6) (1983), pp. 1335–1349.
   Web of Science ®Google Scholar
• B.J. Matkowsky and D.O. Olagunju, Pulsations in a burner-stabilized premixed plane flame. SIAM J. Appl. Math. 40(3) (1981), pp. 551–562.
   Web of Science ®Google Scholar
• B.H. Chao and C.K. Law, Duality, pulsating instability, and product dissociation in burner-stabilized flames. Combust. Sci. Technol. 62(4–6) (1988), pp. 211–237.
   Web of Science ®Google Scholar
• V.N. Kurdyumov and M. Matalon, The porous-plug burner: flame stabilization, onset of oscillation, and restabilization. Combust. Flame 153(1) (2008), pp. 105–118.
   Web of Science ®Google Scholar
• B.H. Chao, Instability of burner-stabilized flames with volumetric heat loss. Combust. Flame 126(1) (2001), pp. 1476–1488.
   Web of Science ®Google Scholar
• V.V. Gubernov, V. Bykov and U. Maas, Hydrogen/air burner-stabilized flames at elevated pressures. Combust. Flame 185 (2017), pp. 44–52.
   Web of Science ®Google Scholar
• V. Bykov, V.V. Gubernov and U. Maas, Mechanisms performance and pressure dependence of hydrogen/air burner-stabilized flames. Math. Model Nat. Phenom 13(6) (2018), pp. 51.
   Web of Science ®Google Scholar
• A.C. McIntosh, On the cellular instability of flames near porous-plug burners. J. Fluid Mech. 161 (1985), pp. 43–75.
   Web of Science ®Google Scholar
• V. Mislavskii, N. Pestovskii, S. Tskhai, B. Kichatov, V. Gubernov, V. Bykov and U. Maas, Diffusive-thermal pulsations of burner stabilized methane-air flames. Combust. Flame 234 (2021), pp. 111638.
   Web of Science ®Google Scholar
• S. Nechipurenko, T. Miroshnichenko, N. Pestovskii, S. Tskhai, B. Kichatov, V. Gubernov, V. Bykov and U. Maas, Experimental observation of diffusive-thermal oscillations of burner stabilized methane-air flames. Combust. Flame 213 (2020), pp. 202–210.
   Web of Science ®Google Scholar
• U. Maas and J. Warnatz, Ignition processes in hydrogen–oxygen mixtures. Combust. Flame 74(1) (1988), pp. 53–69.
   Web of Science ®Google Scholar
• K. Robbins, M. Gorman, J. Bowers and R. Brockman, Spiral dynamics of pulsating methane–oxygen flames on a circular burner. Chaos Interdis. J. Nonlin. Sci. 14(2) (2004), pp. 467–476.
   PubMed Web of Science ®Google Scholar
• M. Gorman and S. Perrollier, Unusual pulsating states in hydrocarbon–oxygen premixed flames. Chaos Interdis. J. Nonlin. Sci. 16(4) (2006), pp. 043124.
   PubMed Web of Science ®Google Scholar
• H. Pearlman, Target and spiral wave patterns in premixed gas combustion. J. Chem. Soc., Faraday Trans. 93(15) (1997), pp. 2487–2490.
   Google Scholar
• G.I. Sivashinsky, Diffusional-thermal theory of cellular flames. Combust. Sci. Technol. 15(3–4) (1977), pp. 137–145.
   Web of Science ®Google Scholar
• F.A. Williams, Combustion theory, 2nd ed., CRC Press, Taylor & Francis Group, New York, 1985.
   Google Scholar
• A.D. Moroshkina, A.A. Ponomareva, V.V. Mislavskii, E.V. Sereshchenko, V.V. Gubernov and V.V. Bykov, Determining the global activation energy of methane–air premixed flames. Combust. Theor. Model. (2023). doi:10.1080/13647830.2023.2245380.
   Web of Science ®Google Scholar
• J.D. Buckmaster and G.S.S. Ludford, Theory of laminar flames, Cambridge University Press, 1982.
   Google Scholar
• G.I. Sivashinsky, Instabilities, pattern formation, and turbulence in flames. Ann. Rev. Fluid Mech. 15 (1983), pp. 179.
   Web of Science ®Google Scholar
• R. Reissig, G. Sansone and R. Conti, Qualitative theorie nichtlinearer differentialgleichungen, Edizioni Cremonese, Roma, 1963.
   Google Scholar