On the most general assumptions (taking account of the Lewis-Semenov number, thermal expansion, variability of thermophysical parameters, etc.), analytical estimates are obtained for the normal velocities of combustion of laminar and turbulent flames. In the case of an Arrhenius dependence of the reaction velocity on the temperature, the combustion velocity is represented by an asymptotic series with respect to the Frank-Kamenetskii dimensionless temperature; for turbulent flames, with respect to a parameter of the relative scale of turbulence. The final results over a wide range of change of parameters are compared with a numerical calculation on a computer of the exact equations and with the relations obtained by the method of combined asymptotic expansions.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
S. S. Novikov and Yu. S. Ryazantsev, “The existence and uniqueness of a solution of the system of equations for the thermal theory of combustion,” Zh. Prikl. Mekh. Tekh. Fiz., No. 4 (1964).
E. Kamke, Ordinary Differential Equations, Akad. Verl.-Ges. Geest und Partig, Leipzig, (1959).
W. E. Johnson and W. Nachbar, in: Eighth International Symposium on Combustion, Baltimore, USA (1962).
Ya. B. Zel'dovich, “Theory of flame propagation,” Zh. Fiz. Khim.,22, No. 1 (1948).
D. A. Vaganov and S. I. Khudyaev, “One steady-state problem of the theory of combustion,” Fiz. Goreniya Vzryva,5, No. 2 (1969).
V. S. Bermanand Yu. S. Ryazantsev, “Analysis of the problem of thermal propagation of flame by the method of combined asymptotic expansions,” Prikl. Mat. Mekh.,36, No.4 (1972).
V. S. Berman and Yu. S. Ryazantsev, “Application of the method of combined asymptotic expansions to the problem of steady-state thermal propagation of the front of an exothermal reaction in a condensed medium,” Zh. Prikl. Mekh. Tekh. Fiz., No. 5 (1972).
V. S. Baushev and V. N. Vilyunov, “Velocity of propagation and limits of existence of turbulent flame,” Zh. Prikl. Mekh. Tekh. Fiz., No. 3 (1972).
V. S. Baushev and V. N. Vilyunov, “The mathematical theory of steady-state velocity of propagation of very small-scale turbulent flame,” Zh. Prikl. Mekh. Tekh. Fiz., No. 4 (1973).
S. A. Chaplygin, Selected Works on Mechanics and Mathematics [in Russian], Moscow (1954), p. 490.
V. S. Baushev and V. N. Vilyunov, “A method of estimates of the normal velocity of flame propagation,” in: Abstracts of the Third Scientific Conference on Mathematics and Mechanics [in Russian], Izd. Tomsk. Univ., Tomsk (1973).
Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 28–37, May–June, 1976.
About this article
Cite this article
Baushev, V.S., Vilyunov, V.N. Estimates of the normal velocities of propagation of laminar and very small-scaled turbulent flames. J Appl Mech Tech Phys 17, 321–328 (1976). https://doi.org/10.1007/BF00853563
- Mathematical Modeling
- Mechanical Engineer
- Thermal Expansion
- Numerical Calculation