# Theory of Ignition of Gas Suspensions

• Nickolai M. Rubtsov
• Boris S. Seplyarskii
• Michail I. Alymov
Chapter
Part of the Heat and Mass Transfer book series (HMT)

## Abstract

The analytical method of calculation of the critical size of the hot spot is created for greater values of a coefficient of heat exchange of particles and gas. By means of numerical calculations the functional dependence of the critical size of the hot spot on parameters following from the theory is validated; the range of applicability of approximate formulas is determined. Two mechanisms of the ignition of gas suspension by the hot spot are revealed for the first time

1. (a)

ignition of gas suspension as ignition in quasi-homogeneous single-temperature medium;

2. (b)

ignition of particles in the center of the hot spot due to violation of thermal balance between the rate of heat allocation from a particle and heat dissipation into the gas.

It is shown that the value of the minimum energy of ignition does not practically depend on the mass concentration of particles in gas suspension at a constant value of initial temperature $$\theta_{\text{in}}$$. The method of calculation of the critical size of the hot spot $$R_{\text{cr}}$$ can be used for determination of $$R_{\text{cr}}$$ for the complex mechanism of interaction of particles with oxidizer (parallel, consecutive, independent reactions). Various mechanisms of critical phenomena for the kinetic and diffusion modes of ignition at pulse energy supply are established. At greater values of a heat exchange coefficient Z (a kinetic ignition mode) the critical duration of an impulse is equal to the time of establishment of a zero gradient on a border: a heater—gas suspension. At small values of a heat exchange coefficient Z (a diffusion mode of an ignition) the critical duration of an impulse is less than $$\tau_{0}$$ and is found from the equality $$\tau_{1} = \tau_{2}$$. Here $$\tau_{1}$$—the time of complete burning out of particles at the dimensionless coordinate $$\xi = 0$$, and $$\tau_{2}$$—the ignition time (transition to the diffusion mode of a reaction) of particles at $$\xi \to \xi_{\text{g}} + 0$$. The expressions allowing to determine necessary and sufficient conditions of the ignition of gas suspension by a heated body at pulse energy supply are obtained. Numerical calculations showed a possibility of application of approximate formulas for determining of minimum duration of an impulse necessary for the ignition of gas suspension. By means of numerical calculations, it is established that the minimum time required to attain the high-temperature combustion mode is reached at $$\tau_{\text{pul}} = \tau_{0}$$. The investigation described allows calculating the minimum energy of ignition of hybrid gas suspension (oxidizer + combustible gas + combustible particles) with a hot spot using the data on the kinetics and thermal effects of gas-phase and heterogeneous reactions as well as on the amount of condensed phase in a unit of volume. The results of such calculation are necessary for the creation of safe conditions for carrying out technological processes, in which suspensions of combustible particles in gas containing oxidizer and small additives of combustible gas are formed. It was experimentally shown that at 650–750 °C coal gas suspension containing stoichiometric mixture of natural gas and the air does not burn over surface coated with coal powder due to inhibiting effect of gases evolving during thermal treatment of coal powder. The ignition of that gas suspension can be promoted with small amounts of chemically active additive (e.g., dichlorosilane). Thus, we can conclude that the improved model of ignition of gas suspension of solid particles in a mix oxidizer—combustible gas must take into account both inhibiting effect of gases evolving during thermal treatment of coal powder and the branched chain mechanism of gas combustion. However, in the presence of small quantities of methane (lean mixtures) the ignition of volatiles evolved from coal, can provide the subsequent methane ignition, because the volatiles are hydrocarbons, probably, polycyclic aromatic hydrocarbons (PAH).

### Keywords

Coal gas suspension Critical condition Active additive Oxidizer Minimum energy Ignition Chain Kinetic Diffusion Pulse energy Approximate Numerical Calculation

### References

1. 1.
Taubkin, S.I., Taubkin, I.S.: Fire and Explosion Safety of Dusty Materials and its Technological Processing. Moscow, Chemistry (1976). (in Russian)Google Scholar
2. 2.
Korolchenko, A.Y.: Fire and Explosion Safety of Industrial Dust. Moscow, Chemistry (1986). (in Russian)Google Scholar
3. 3.
Gubin, E.I., Dik, I.G.: On ignition of a dusty cloud with a spark, Combustion, Explosion, and Shock Waves. 22(10) (1986). (in Russian)Google Scholar
4. 4.
Burkina, R.S.: Ignition of a dusty cloud with a hot spot, Russian Journal of Physical Chemistry B. 9(12):1626 (1990). (in Russian)Google Scholar
5. 5.
Krainov, A.Y.: Numerical investigation of ignition of hybrid gas suspension (a mixture of reacting gases and particles) with different sources, Chemical Physics of processes of combustion and explosion, XII Symposium on combustion and explosion, Chernogolovka, 2000. (in Russian)Google Scholar
6. 6.
Merzhanov A.G.: On critical conditions of thermal explosion of a hot spot. Comb. Flame. 10(64), 341 (1966)Google Scholar
7. 7.
Vilunov V.N.: Theory of ignition of condensed substances, Novosibirsk. Science (1984). (in Russian)Google Scholar
8. 8.
Seplyarskii B.S., Afanasiev S.Yu. On the theory of a local thermal explosion. Rus. J. Chem. Phys. B. 8(5), 646 (1989)Google Scholar
9. 9.
Seplyarskii, B.S., Afanasiev, S.Y.: On the theory of a local thermal explosion. Combust. Explosion Shock Waves. 22(6), 9 (1989). (in Russian)Google Scholar
10. 10.
Rumanov, E.N., Haykin B.I.: Critical conditions of self-ignition of the assembly of particles. Combust. Explosion Shock Waves. 5, 129 (1969). (in Russian) Google Scholar
11. 11.
Lisitsin V.I., Rumanov E.N., Haykin B.I.: On the induction period of self-ignition of the assembly of particles. Combust. Explosion Shock Waves. 7, 3 (1971). (in Russian)Google Scholar
12. 12.
Eckhoff, R.K.: Dust Explosions in the Process Industries, 2nd edn. Butterworth-Heinemann, Oxford (1997)Google Scholar
13. 13.
Seplyarskii, B.S.: Analytical method of calculation of temporal characteristics of ignition of gas suspension with a heated body. Dokl. Phys. Chem. RAS 377(5), 653 (2001)Google Scholar
14. 14.
Frank-Kamenetskii, D.A.: Diffusion and heat exchange in chemical kinetics. ISBN: 9780691626932, http://blogs.rediff.com/shynkedizuwh93/2016/11/28/diffusion-and-heat-exchange-in-chemical-kinetics-book/
15. 15.
Seplyarskii, B.S., Gordopovova, V.S.: Investigations into features of ignition of condensed systems interacting through the layer of the product. Rus. J. Chem. Phys. B. 13(6), 117 (1994)Google Scholar
16. 16.
Seplyarskii, B.S.: Nonstationary theory of ignition of condensed systems with a heated surface. Dokl. Phys. Chem. USSR 300(1), 96 (1988)Google Scholar
17. 17.
Seplyarskii B.S.: Ignition of condensed systems at gas filtration. Combust. Explosion Shock Waves. 27(1), 3 (1991). (in Russian)Google Scholar
18. 18.
Zel’dovich Y.B.: Theory of ignition with a heated surface. J. Exp. Theor. Phys. 9(1), 1530. (in Russian)Google Scholar
19. 19.
Franke, H.: Bestimmung der Minderstzudenergie von Kohlenstaub/Methan/Luft Gemisches (hybride Gemische), VDI-Berichte. N 304, P. 69 (1978)Google Scholar
20. 20.
Krainov, A.Y., Baimler, V.A.: Critical conditions of spark ignition of the mixture of gaseous oxidizer and fuel with reacting particles. Combust. Explosion Shock Waves. 38(3), 30 (2002). (in Russian)Google Scholar
21. 21.
Seplyarskii, B.S., Kostin, S.V., Ivleva, T.P.: Analytical method of calculation of temporary characteristics of ignition of hybrid gas suspensions with a heated body. Dokl. Phys. Chem. RAS 394(5), 643 (2004)Google Scholar
22. 22.
Seplyarskii B.S., Ivleva, T.P.: Analysis of critical conditions of ignition of gas suspension with a heated body at pulse energy supply. Combust. Explosion Shock Waves. 2, 3 (2004). (in Russian)Google Scholar
23. 23.
Seplyarskii, B.S., Kostin, S.V., Ivleva, T.P.: Analytical method for calculating time characteristics of ignition of hybrid gas suspensions by a hot body. Heat Transf. Res. 38, N2, 171 (2007)Google Scholar
24. 24.
Rubtsov, N.M., Seplyarskii, B.S., Tsvetkov, G.I., Chernysh, V.I.: Investigation into the ignition of coal powders in the presence of oxygen and natural gas by means of high-speed cinematography. Mendeleev Commun. 22, 47 (2012)Google Scholar
25. 25.
Lykov, A.V.: Theory of Heat Transfer. Moscow, High School (1967). (in Russian)Google Scholar
26. 26.
Rubtsov, N.M., Seplyarskii, B.S., Tsvetkov, G.I., Chernysh, V.I.: Thermal ignition of coal–gas suspensions containing natural gas and oxygen. Mendeleev Commun. 18, 340 (2008).Google Scholar
27. 27.
Herzberg, G.: Molecular Spectra and Molecular Structure, Vol. 1, Spectra of Diatomic Molecules, 2nd edn. Van Nostrand, New York (1950)Google Scholar
28. 28.
Wainner, R.T., Seitzman, J.M.: Soot diagnostics using laser-induced incandescence in flames an exhaust flows. Am. Inst. Aeronaut. Astronaut. (AIAA) J. 37, 738 (1999)Google Scholar
29. 29.
Rubtsov, N.M.: The Modes of Gaseous Combustion. Springer International Publishing, Switzerland (2016)
30. 30.
Rubtsov, N.M., Seplyarskii, B.S., Tarasov, A.G., Tsvetkov, G.I., Chernysh, V.I.: Suppression of the ignition of coal powders in the presence of oxygen and natural gas with small additives of octadecafluorodecahydronaphthalene vapour. Mendeleev Commun. 22(3), 154 (2012)Google Scholar
31. 31.
Rubtsov, N.M., Seplyarskii, B.S., Tsvetkov, G.I., Chernysh, V.I.: Thermal ignition of coal powders in the presence of natural gas, oxygen and chemically active additives. Mendeleev Commun. 20(2), 98 (2010)
32. 32.
Rubtsov, N.M., Tsvetkov, G.I., Chernysh, V.I.: Different effects of active minor admixtures on hydrogen and methane ignitions. Kinet. Catal. 49, 344 (2008)Google Scholar
33. 33.
Semenov, N.N.: On Some Problems of Chemical Kinetics and Reaction Ability. AS USSR, Moscow (1958). (in Russian)Google Scholar

© Springer International Publishing AG 2017

## Authors and Affiliations

• Nickolai M. Rubtsov
• 1
• Boris S. Seplyarskii
• 1
• Michail I. Alymov
• 1
1. 1.Institute of Structural Macrokinetics and Materials ScienceRussian Academy of SciencesMoscowRussia