Abstract
The influence of hydrodynamic instability on the propagation velocity and distortion of an inward-propagating cylindrical flame is investigated theoretically and numerically. Theoretical investigations are conducted within the framework of a nonlinear model based on an evolution equation for the perturbed flame front, which may be derived from the general model, similar to the Sivashinsky equation. The phenomenon of surface distortion of an inward-propagating flame, leading to a decrease in the burning time, is studied both by analyzing the exact solutions of the nonlinear evolution equation and by numerical simulations of the general hydrodynamic model. Physical processes determining the inward-propagating flame dynamics are revealed.
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References
M. Wu and J. M. Driscoll, “A numerical simulation of a vortex convected through a laminar premixed flame,” Combust. Flame, 91, 310–332 (1991).
W. T. Ashrust, “Flame propagation through swirling eddies, a recursive pattern,” Combust. Sci. Technol., 92, 87–103 (1993).
J. Zhu and P. D. Ronney, “Simulation of front propagation at large non-dimensional flow disturbance intensities,” Combust. Sci. Technol., 100, 183–201 (1994).
T. Poinsot, D. Veynante, and S. Candel, “Diagrams of premixed turbulent combustion based on direct simulation,” in: Proc. Combustion Inst., 23, 613–619 (1990).
W. L. Roberts, J. F. Driscoll, M. C. Drake, and J. W. Ratcliffe, “OH fluorescence images of the quenching of a premixed flame during an interaction with a vortex,” in: Proc. Combustion Inst., 24, 169–176 (1992).
C. J. Mueller, J. F. Driscoll, D. L. Reuss, M. C. Drake, and M. E. Rosalik, “Vorticity generation and attenuation as vortices convect through a premixed flame,” Combust. Flame, 112, 342–358 (1998).
G. G. Lee, K. Y. Huh, and H. Kobayashi, “Measurement and analysis of flame surface density for turbulent premixed combustion on a nozzle-type burner,” Combust. Flame, 122, 43–57 (2000).
V. S. Babkin, I. L. Kuznetsov, and L. S. Kozachenko, “Effect of curvature on the laminar flame propagation velocity in a lean propane-air mixture,” Dokl. Akad. Nauk SSSR, 146, No. 3, 625–627 (1962).
G. Sivashinsky, “Some developments in premixed combustion modeling,” in: Proc. Combustion Inst., 29, 1737–1761 (2002).
S. J. Sun and C. K. Law, “On the consumption of fuel pockets via inwardly propagating flames,” in: Proc. Combustion Inst., 27, 963–970 (1998).
L. Kagan and G. Sivashinsky, “Incomplete combustion in nonadiabatic premixed gas flames,” Phys. Rev. E, 53, 6021–6027 (1996).
C. J. Sun, C. J. Sung, L. He, and C. K. Law, “Stretch effects in counterflow and propagating spherical flames,” AIAA Paper No. 97-0901 (1997).
M. L. Frankel and G. I. Sivashinsky, “On quenching of curved flames,” Combust. Sci. Technol., 40, 257–268 (1984).
G. Sivashinsky, “Nonlinear analysis of hydrodynamic instability in laminar flames. I. Derivation of basic equations,” Acta Astronaut., 4, 1177–1206 (1977).
L. Filyand, G. I. Sivahshinsky, and M. L. Frankel, “On self-acceleration of outward propagating wrinkled flames,” Physica D, 72, 110–118 (1994).
O. Thual, U. Frisch, and M. Henon, “Application of pole decomposition to an equation governing the dynamics of wrinkled flame fronts,” J. Phys., 46, 1485–1494 (1985).
S. S. Minaev, “Set of steady solutions describing a cellular flame in the case of hydrodynamic instability,” Combust., Expl., Shock Waves, 28, No. 1, 30–33 (1992).
P. Cambray, K. Joulain, and G. Joulin, “Mean evolution of wrinkle wavelengths in a model of weakly-turbulent premixed flame,” Combust. Sci. Technol., 103, 265–282 (1994).
K. A. Kazakov and M. A. Liberman, “Nonlinear theory of flame front instability,” Combust. Sci. Technol., 174, No. 7, 129–151 (2002).
M. L. Frankel, “An equation of surface dynamics modeling flame fronts as density discontinuities in potential flows,” Phys. Fluids A, 2, No. 10, 1879–1883 (1990).
S. S. Minaev, E. A. Pirogov, and O. V. Sharypov, “A nonlinear model for hydrodynamic instability of an expanding flame,” Combust., Expl., Shock Waves, 32, No. 5, 481–488 (1996).
G. Searby and J. Quinard, “Direct and indirect measurements of markstein numbers of premixed flames,” Combust. Flame, 82, No. 3, 298–311 (1990).
Ya. B. Zel’dovich, G. I. Barenblatt, V. B. Librovich, and G. M. Makhviladze, The Mathematical Theory of Combustion and Explosions, Plenum, New York (1985).
V. V. Bychkov and M. A. Liberman, “Dynamics and stability of premixed flames,” Phys. Reports, 325, 115–237 (2000).
D. Breadley and C. M. Harper, “The development of instabilities in laminar explosion flames,” Combust. Flames, 99, 562–572 (1994).
S. O. Unverdi and G. A. Tryggvason, “A front-tracking method for viscous incompressible multi-phase flows,” J. Comput. Phys., 100, 25–37 (1992).
J. Qian, G. Tryggavason, and C. K. Law, “A front tracking method for the motion of premixed flames,” J. Comput. Phys., 144, 52–69 (1998).
K. L. Pan, W. Shyy, and C. K. Law, “An immersed-boundary method for the dynamics of premixed flames,” Int. J. Heat Mass Transfer, 45, 3503–3516 (2002).
K. L. Pan, “Front-tracking simulation for outward propagation of spherical flames,” in: 45th AIAA Aerospace Sciences Meeting and Exhibit, January 8–11, 2007, Reno, Nevada (2007).
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Translated from Fizika Goreniya i Vzryva, Vol. 45, No. 5, pp. 8–15, September–October, 2009.
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Fursenko, R.V., Minaev, S.S. & Pan, K.L. Hydrodynamic instability of inward-propagating flames. Combust Explos Shock Waves 45, 511–517 (2009). https://doi.org/10.1007/s10573-009-0062-0
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DOI: https://doi.org/10.1007/s10573-009-0062-0