Fractal Based, Scale-adaptive Closure Model for Darrieus–Landau Instability Effects on Large-scale Hydrogen-air Flames

References

• Altantzis, C., C. Frouzakis, A. Tomboulides, and K. Boulouchos. 2013. ‘Numerical simulation of propagating circular and cylindrical lean premixed hydrogen/air flames. Proc. Combust. Inst, 34(1): 1109–15. doi:10.1016/j.proci.2012.07.072.
   Google Scholar
• Altantzis, C., C. E. Frouzakis, A. G. Tomboulides, and K. Boulouchos. 2015. Direct numerical simulation of circular expanding premixed flames in a lean quiescent hydrogen-air mixture: Phenomenology and detailed flame front analysis. Combust. Flame 162 (2):331–44. doi:10.1016/j.combustflame.2014.08.005.
   Web of Science ®Google Scholar
• Altantzis, C., C. Frouzakis, A. Tomboulides, S. Kerkemeier, and K. Boulouchos. 2011. ‘Detailed numerical simulations of intrinsically unstable two-dimensional planar lean premixed hydrogen/air flames. Proc. Combust. Inst, 33(1): 1261–68. doi:10.1016/j.proci.2010.06.082.
   Google Scholar
• Aung, K., M. Hassan, and G. Faeth. 1997. Flame stretch interactions of laminar premixed hydrogen/air flames at normal temperature and pressure. Combust. Flame 109 (1–2):1–24. doi:10.1016/S0010-2180(96)00151-4.
   Web of Science ®Google Scholar
• Bauwens, C. R., J. M. Bergthorson, and S. B. Dorofeev. 2015. ‘Experimental study of spherical-flame acceleration mechanisms in large-scale propaneair flames Proc. Combust. Inst, 35(2): 2059–66. doi:10.1016/j.proci.2014.06.118.
   Web of Science ®Google Scholar
• Bauwens, C. R. L., J. M. Bergthorson, and S. B. Dorofeev. 2017. Experimental investigation of spherical-flame acceleration in lean hydrogen-air mixtures. Int. J. Hydrogen Energy 42 (11):7691–97. doi:10.1016/j.ijhydene.2016.05.028.
   Web of Science ®Google Scholar
• Bechtold, J. K., and M. Matalon. 2001. The dependence of the Markstein length on stoichiometry. Combust. Flame 127 (1–2):1906–13. doi:10.1016/S0010-2180(01)00297-8.
   Web of Science ®Google Scholar
• Becker, T., and F. Ebert. 1985. Vergleich zwischen Experiment und Theorie der Explosion grosser, freier Gaswolken. Chemie Ingenieur Technik 57 (1):42–45. doi:10.1002/cite.330570110.
   Google Scholar
• Bentaïb, A., N. Meynet, and A. Bleyer. 2015. Overview on hydrogen risk research and development activities: Methodology and open issues. Nucl. Eng. Technol 47 (1):26–32. doi:10.1016/j.net.2014.12.001.
   Web of Science ®Google Scholar
• Berger, L., A. Attili, and H. Pitsch. 2022a. Intrinsic instabilities in premixed hydrogen flames: Parametric variation of pressure, equivalence ratio, and temperature. part 1 - dispersion relations in the linear regime. Combust. Flame 240:111935. doi:10.1016/j.combustflame.2021.111935.
   Web of Science ®Google Scholar
• Berger, L., A. Attili, and H. Pitsch. 2022b. Intrinsic instabilities in premixed hydrogen flames: Parametric variation of pressure, equivalence ratio, and temperature. part 2 nonlinear regime and flame speed enhancement. Combust. Flame 240:111936. doi:10.1016/j.combustflame.2021.111936.
   Web of Science ®Google Scholar
• Berger, L., M. Grinberg, B. Jürgens, P. E. Lapenna, F. Creta, A. Attili, and H. Pitsch (2022), ‘Flame fingers and interactions of hydrodynamic and thermodiffusive instabilities in laminar lean hydrogen flames’, Proceedings of the Combustion Institute. URL: https://www.sciencedirect.com/science/article/pii/S1540748922000372
   Google Scholar
• Berger, L., K. Kleinheinz, A. Attili, and H. Pitsch. 2019. ‘Characteristic patterns of thermodiffusively unstable premixed lean hydrogen flames Proc. Combust. Inst, 37(2): 1879–86. doi:10.1016/j.proci.2018.06.072.
   Web of Science ®Google Scholar
• Blinnikov, S. I., and P. V. Sasorov. 1996. Landau-Darrieus instability and the fractal dimension of flame fronts. Phys. Rev. E 53 (5):4827–41. doi:10.1103/PhysRevE.53.4827.
   Web of Science ®Google Scholar
• Bradley, D., T. Cresswell, and J. Puttock. 2001. Flame acceleration due to flame- induced instabilities in large-scale explosions. Combust. Flame 124 (4):551–59. doi:10.1016/S0010-2180(00)00208-X.
   Web of Science ®Google Scholar
• Bychkov, V., and M. A. Liberman. 2000. Dynamics and stability of premixed flames. Phys. Rep. 325 (4–5):115–237. doi:10.1016/S0370-1573(99)00081-2.
   Web of Science ®Google Scholar
• Cai, X., J. Wang, Z. Bian, H. Zhao, H. Dai, and Z. Huang. 2020. On transition to self-similar acceleration of spherically expanding flames with cellular instabilities. Combust. Flame 215:364–75. doi:10.1016/j.combustflame.2020.02.001.
   Web of Science ®Google Scholar
• Chakraborty, N., and R. S. Cant. 2011. Effects of Lewis number on flame surface density transport in turbulent premixed combustion. Combust. Flame 158 (9):1768–87. doi:10.1016/j.combustflame.2011.01.011.
   Web of Science ®Google Scholar
• Chaudhuri, S., V. Akkerman, and C. K. Law. 2011. Spectral formulation of turbulent flame speed with consideration of hydrodynamic instability. Phys. Rev. E 84 (2):026322. doi:10.1103/PhysRevE.84.026322.
   Web of Science ®Google Scholar
• Creta, F., N. Fogla, and M. Matalon. 2011. Turbulent propagation of premixed flames in the presence of Darrieus-Landau instability. Combust. Theory Modelling 15 (2):267–98. doi:10.1080/13647830.2010.538722.
   Web of Science ®Google Scholar
• Creta, F., P. E. Lapenna, R. Lamioni, N. Fogla, and M. Matalon. 2020. Propagation of premixed flames in the presence of Darrieus-Landau and thermal diffusive instabilities. Combust. Flame 216:256–70. doi:10.1016/j.combustflame.2020.02.030.
   Web of Science ®Google Scholar
• Creta, F., and M. Matalon. 2011. Propagation of wrinkled turbulent flames in the context of hydrodynamic theory. J. Fluid. Mech. 680:225264. doi:10.1017/jfm.2011.157.
   Web of Science ®Google Scholar
• Darwish, M., L. Mangani, and F. Moukalled. 2016. The finite volume method in computational fluid dynamics: An advanced introduction with OpenFOAM and Matlab. Switzerland: Springer. doi:10.1007/978-3-319-16874-6.
   Google Scholar
• Dinkelacker, F., B. Manickam, and S. Muppala. 2011. Modelling and simulation of lean premixed turbulent methane/hydrogen/air flames with an effective Lewis number approach. Combust. Flame 158 (9):1742–49. doi:10.1016/j.combustflame.2010.12.003.
   Web of Science ®Google Scholar
• Dowdy, D. R., D. B. Smith, S. C. Taylor, and A. Williams. 1991. The use of expanding spherical flames to determine burning velocities and stretch effects in hydrogen/air mixtures, 23rd Symposium (International) on Combustion, Orléans, France.
   Google Scholar
• Fernández-Galisteo, D., V. N. Kurdyumov, and P. D. Ronney. 2018. Analysis of premixed flame propagation between two closely-spaced parallel plates. Combust. Flame 190:133–45. doi:10.1016/j.combustflame.2017.11.022.
   Web of Science ®Google Scholar
• Fiorina, C., I. Clifford, S. Kelm, and S. Lorenzi. 2022. On the development of multi- physics tools for nuclear reactor analysis based on OpenFOAM: State of the art, lessons learned and perspectives. Nucl. Eng. Des. 387:111604. doi:10.1016/j.nucengdes.2021.111604.
   Web of Science ®Google Scholar
• Frankel, M., and G. Sivashinsky. 1982. The effect of viscosity on hydrodynamic stability of a plane flame front. Combust. Sci. Technol 29 (3–6):207–24. doi:10.1080/00102208208923598.
   Web of Science ®Google Scholar
• Gostintsev, Y. A., A. Istratov, and Y. V. Shulenin. 1988. Self-similar propagation of a free turbulent flame in mixed gas mixtures. Combust. Explos. Shock Waves 24 (5):563–69. doi:10.1007/BF00755496.
   Web of Science ®Google Scholar
• Gouldin, F. C. 1987. An application of fractals to modeling premixed turbulent flames. Combust. Flame 68 (3):249–66. doi:10.1016/0010-2180(87)90003-4.
   Web of Science ®Google Scholar
• Goulier, J., A. Comandini, F. Halter, and N. Chaumeix. 2017. ‘Experimental study on turbulent expanding flames of lean hydrogen/air mixtures. Proc. Combust. Inst, 36(2): 2823–32. doi:10.1016/j.proci.2016.06.074.
   Web of Science ®Google Scholar
• Gu, G., J. Huang, W. Han, and C. Wang. 2021. Propagation of hydrogen oxygen flames in heleshaw cells. Int. J. Hydrogen Energy 46 (21):12009–15. doi:10.1016/j.ijhydene.2021.01.071.
   Web of Science ®Google Scholar
• Gupta, S., and G. Langer. 2019. Experimental research on hydrogen deflagration in multi-compartment geometry and application to nuclear reactor conditions. Nucl. Eng. Des. 343:103–37. doi:10.1016/j.nucengdes.2018.12.012.
   Web of Science ®Google Scholar
• Hasslberger, J., H. K. Kim, B. J. Kim, I. C. Ryu, and T. Sattelmayer. 2017. Three- dimensional CFD analysis of hydrogen-air-steam explosions in APR1400 containment. Nucl. Eng. Des. 320:386–99. doi:10.1016/j.nucengdes.2017.06.014.
   Web of Science ®Google Scholar
• Jiang, Y., G. Li, H. Li, G. Zhang, and J. Lv. 2020. Experimental study on the influence of hydrogen fraction on self-acceleration of H2/CO/air laminar premixed flame. Int. J. Hydrogen Energy 45 (3):2351–59. doi:10.1016/j.ijhydene.2019.11.044.
   Web of Science ®Google Scholar
• Katzy, P. (2021), Combustion Model for the Computation of Flame Propagation in Lean Hydrogen-Air Mixtures at Low Turbulence, Doctoral Dissertation, Technical University Munich, Germany.
   Google Scholar
• Katzy, P., J. Hasslberger, L. R. Boeck, and T. Sattelmayer. 2017. The effect of intrinsic instabilities on effective flame speeds in under-resolved simulations of lean hydrogenair flames. J. Nucl. Eng. Radiat. Sci 3 (4). doi:10.1115/1.4036984.
   Google Scholar
• Katzy, P., J. Hasslberger, and T. Sattelmayer. 2017. On the effect of pressure on intrinsic flame instabilities in lean hydrogen-air mixtures - Part II: Experimental investigation based on OH-PLIF technique, 26th International Colloquium on the Dynamics of Explosions and Reactive Systems (ICDERS), Boston, USA.
   Google Scholar
• Keppeler, R., and M. Pfitzner. 2015. Modelling of Landau-Darrieus and thermo-diffusive instability effects for CFD simulations of laminar and turbulent premixed combustion. Combust. Theory Modelling 19 (1):1–28. doi:10.1080/13647830.2014.975747.
   Web of Science ®Google Scholar
• Ketcheson, D. I. 2010. RungeKutta methods with minimum storage implementations. J. Comput. Phys. 229 (5):1763–73. doi:10.1016/j.jcp.2009.11.006.
   Web of Science ®Google Scholar
• Kim, W. K., T. Mogi, and R. Dobashi. 2013. Flame acceleration in unconfined hydrogen/air deflagrations using infrared photography. J. Loss Prev. Process Ind 26 (6):1501–05. doi:10.1016/j.jlp.2013.09.009.
   Web of Science ®Google Scholar
• Kim, W. K., T. Mogi, K. Kuwana, and R. Dobashi. 2015a. Prediction model for self- similar propagation and blast wave generation of premixed flames. Int. J. Hydrogen Energy 40 (34):11087–92. doi:10.1016/j.ijhydene.2015.06.123.
   Web of Science ®Google Scholar
• Kim, W. K., T. Mogi, K. Kuwana, and R. Dobashi. 2015b. ‘Self-similar propagation of expanding spherical flames in large scale gas explosions Proc. Combust. Inst, 35(2): 2051–58. doi:10.1016/j.proci.2014.08.023.
   Google Scholar
• Kim, W., T. Namba, T. Johzaki, and T. Endo. 2020. Self-similar propagation of spherically expanding flames in lean hydrogenair mixtures. Int. J. Hydrogen Energy 45 (46):25608–14. doi:10.1016/j.ijhydene.2020.06.261.
   Web of Science ®Google Scholar
• Kim, W., Y. Sato, T. Johzaki, T. Endo, D. Shimokuri, and A. Miyoshi. 2018. Experimental study on self-acceleration in expanding spherical hydrogen-air flames. Int. J. Hydrogen Energy 43 (27):12556–64. doi:10.1016/j.ijhydene.2018.04.153.
   Web of Science ®Google Scholar
• Klein, M., N. Chakraborty, and M. Pfitzner. 2016. Analysis of the combined modelling of sub-grid transport and filtered flame propagation for premixed turbulent combustion. Flow Turbul. Combust. 96 (4):921–38. doi:10.1007/s10494-016-9714-9.
   Web of Science ®Google Scholar
• Konnov, A. A. 2008. Remaining uncertainties in the kinetic mechanism of hydrogen combustion. Combust. Flame 152 (4):507–28. doi:10.1016/j.combustflame.2007.10.024.
   Web of Science ®Google Scholar
• Kotchourko, A., A. Bentaïb, K. Fischer, N. Chaumeix, J. Yanez, S. Benz, and S. Kudryakov (2012), ISP-49 on hydrogen combustion, Technical report, Nuclear Energy Agency Committee on the Safety of Nuclear Installations.
   Google Scholar
• Lamoureux, N., N. Djebali-Chaumeix, and C. E. Paillard. 2003. Laminar flame velocity determination for H2airHeCO2 mixtures using the spherical bomb method. Exp. Therm Fluid Sci 27 (4):385–93. doi:10.1016/S0894-1777(02)00243-1.
   Web of Science ®Google Scholar
• Lapenna, P. E., R. Lamioni, and F. Creta. 2021. ‘Subgrid modeling of intrinsic instabilities in premixed flame propagation‘. Proc. Combust. Inst., 38(2), 2001–11. doi:10.1016/j.proci.2020.06.192.
   Web of Science ®Google Scholar
• Lapenna, P. E., R. Lamioni, G. Troiani, and F. Creta. 2019. ‘Large scale effects in weakly turbulent premixed flames‘. Proc. Combust. Inst. 37(2), 1945–52. doi:10.1016/j.proci.2018.06.154.
   Web of Science ®Google Scholar
• Liberman, M. A. 2021. Combustion physics: Flames, detonations, explosions, astro- physical combustion and inertial confinement fusion. Switzerland: Springer Nature doi:10.1007/978-3-030-85139-2.
   Google Scholar
• Liberman, M. A., M. F. Ivanov, O. E. Peil, D. M. Valiev, and L. E. Eriksson. 2004. Self- acceleration and fractal structure of outward freely propagating flames. Phys. Fluids 16 (7):2476–82. doi:10.1063/1.1729852.
   Web of Science ®Google Scholar
• Lind, C. (1974), Explosion hazards associated with spills of large quantities of hazardous materials. phase I, Technical report, Naval Weapons Center China Lake CA.
   Google Scholar
• Lipatnikov, A. N., V. A. Sabelnikov, S. Nishiki, and T. Hasegawa. 2018. Letter: Does flame-generated vorticity increase turbulent burning velocity? Phys. Fluids 30 (8):081702. doi:10.1063/1.5046137.
   Web of Science ®Google Scholar
• Lipatnikov, A. N., V. A. Sabelnikov, S. Nishiki, and T. Hasegawa. 2019. A direct numerical simulation study of the influence of flame-generated vorticity on reaction- zone-surface area in weakly turbulent premixed combustion. Phys. Fluids 31 (5):055101. doi:10.1063/1.5094976.
   Web of Science ®Google Scholar
• Liu, F., X. Bao, J. Gu, and R. Chen. 2012. Onset of cellular instabilities in spherically propagating hydrogen-air premixed laminar flames. Int. J. Hydrogen Energy 37 (15):11458–65. doi:10.1016/j.ijhydene.2012.05.013.
   Web of Science ®Google Scholar
• Liu, Z., V. R. Unni, S. Chaudhuri, R. Sui, C. K. Law, and A. Saha. 2021. “Self- turbulization in cellularly unstable laminar flames.” J. Fluid. Mech. 917. doi:10.1017/jfm.2021.330.
   PubMed Web of Science ®Google Scholar
• Matalon, M. 2018. The Darrieus–Landau instability of premixed flames. Fluid Dyn. Res. 50 (5):051412. doi:10.1088/1873-7005/aab510.
   Web of Science ®Google Scholar
• Matalon, M., and B. J. Matkowsky. 1982. Flames as gasdynamic discontinuities. J. Fluid. Mech. 124 (–1):239259. doi:10.1017/S0022112082002481.
   Google Scholar
• Menter, F. R., and Y. Egorov. 2010. The scale-adaptive simulation method for unsteady turbulent flow predictions. part 1: Theory and model description. Flow Turbul. Combust. 85 (1):113–38. doi:10.1007/s10494-010-9264-5.
   Web of Science ®Google Scholar
• Molkov, V., D. Makarov, and H. Schneider. 2006. LES modelling of an unconfined large-scale hydrogenair deflagration. J. Phys. D: Appl. Phys. 39 (20):4366–76. doi:10.1088/0022-3727/39/20/012.
   Web of Science ®Google Scholar
• Mukaiyama, K., S. Shibayama, and K. Kuwana. 2013. Fractal structures of hydrodynamically unstable and diffusive-thermally unstable flames. Combust. Flame 160 (11):2471–75. doi:10.1016/j.combustflame.2013.05.017.
   Web of Science ®Google Scholar
• Muppala, S. R., N. K. Aluri, F. Dinkelacker, and A. Leipertz. 2005. Development of an algebraic reaction rate closure for the numerical calculation of turbulent premixed methane, ethylene, and propane/air flames for pressures up to 1.0 MPa. Combust. Flame 140 (4):257–66. doi:10.1016/j.combustflame.2004.11.005.
   Web of Science ®Google Scholar
• Ozel-Erol, G., M. Klein, and N. Chakraborty. 2021. Lewis number effects on flame speed statistics in spherical turbulent premixed flames. Flow Turbul. Combust. 106 (4):1043–63. doi:10.1007/s10494-020-00173-7.
   Web of Science ®Google Scholar
• Sathiah, P., T. Holler, I. Kljenak, and E. Komen. 2016. The role of CFD combustion modeling in hydrogen safety management V: Validation for slow deflagrations in homogeneous hydrogen-air experiments. Nucl. Eng. Des 310:520–31. doi:10.1016/j.nucengdes.2016.06.030.
   Web of Science ®Google Scholar
• Schneider, H., and H. Pförtner (1983), Prozebgasfreisetzung-Explosion in der gasfabrik und auswirkungen von Druckwellen auf das Containment, Technical report, Fraunhofer-ICT Internal Report: PNP-Sichcrheitssofortprogramm.
   Google Scholar
• Sivashinsky, G. I. 1977. Nonlinear analysis of hydrodynamic instability in laminar flames—i. derivation of basic equations. Acta Astronaut. 4 (11–12):1177–206. doi:10.1016/0094-5765(77)90096-0.
   Web of Science ®Google Scholar
• Sun, Z. Y., F. S. Liu, X. C. Bao, and X. H. Liu. 2012. Research on cellular instabilities in outwardly propagating spherical hydrogen-air flames. Int. J. Hydrogen Energy 37 (9):7889–99. doi:10.1016/j.ijhydene.2012.02.011.
   Web of Science ®Google Scholar
• Taylor, S. C. 1991. “Burning velocity and the influence of flame stretch“. Doctoral Dissertation, UK: University of Leeds.
   Google Scholar
• Veiga-López, F., M. Kuznetsov, J. Yanez, J. Grüne, and M. Sánchez-Sanz. 2019. Flame propagation near the limiting conditions in a thin layer geometry, in 8th International Conference on Hydrogen Safety (ICHS), Adelaide, Australia.
   Google Scholar
• Velikorodny, A., E. Studer, S. Kudriakov, and A. Beccantini. 2015. Combustion modeling in large scale volumes using EUROPLEXUS code. J. Loss Prev. Process Ind 35:104–16. doi:10.1016/j.jlp.2015.03.014.
   Web of Science ®Google Scholar
• Weller, H., G. Tabor, A. Gosman, and C. Fureby. 1998. Application of a flame- wrinkling les combustion model to a turbulent mixing layer. Symp. (Int.) Combust 27 (1):899–907. doi:10.1016/S0082-0784(98)80487-6.
   Google Scholar
• Weller, H. G., G. Tabor, H. Jasak, and C. Fureby. 1998. A tensorial approach to computational continuum mechanics using object-oriented techniques. Comput. Phys 12 (6):620–31. doi:10.1063/1.168744.
   Google Scholar
• Yu, R., X. S. Bai, and V. Bychkov. 2015. Fractal flame structure due to the hydrodynamic Darrieus-Landau instability. Phys. Rev. E 92 (6):063028. doi:10.1103/PhysRevE.92.063028.
   Web of Science ®Google Scholar
• Zivkovic, D., and T. Sattelmayer (2021), Towards efficient and time-accurate simulations of early stages of industrial scale explosions, in 9th International Conference on Hydrogen Safety (ICHS), Edinburgh, Scotland.
   Google Scholar