Physics:Zeldovich mechanism
Zel'dovich mechanism is a chemical mechanism that describes the oxidation of nitrogen and NOx formation, first proposed by the Russian physicist Yakov Borisovich Zel'dovich in 1946.[1][2][3][4] The reaction mechanisms read as
- [math]\ce{ {N2} + O <->[k_1] {NO} + {N} }[/math]
- [math]\ce{ {N} + O2 <->[k_2] {NO} + {O} }[/math]
where [math]\displaystyle{ k_1 }[/math] and [math]\displaystyle{ k_2 }[/math] are the reaction rate constants in Arrhenius law. The overall global reaction is given by
- [math]\ce{ {N2} + {O2} <->[k] 2NO }[/math]
The overall reaction rate is mostly governed by the first reaction (i.e., rate-determining reaction), since the second reaction is much faster than the first reaction and occurs immediately following the first reaction. At fuel-rich conditions, due to lack of oxygen, reaction 2 becomes weak, hence, a third reaction is included in the mechanism, also known as extended Zel'dovich mechanism (with all three reactions),[5][6]
- [math]\ce{ {N} + {OH} <->[k_3] {NO} + {H} }[/math]
Assuming the initial concentration of NO is low and the reverse reactions can therefore be ignored, the forward rate constants of the reactions are given by[7]
- [math]\displaystyle{ \begin{align} k_{1f} &= 1.47\times 10^{13} \, T^{0.3} \mathrm e^{-75286.81/RT}\\ k_{2f} &= 6.40\times 10^9 \, T \mathrm e^{-6285.5/RT} \\ k_{3f} &= 3.80\times 10^{13} \end{align} }[/math]
where the pre-exponential factor is measured in units of cm, mol, s and K (these units are incorrect), temperature in kelvins, and the activation energy in cal/mol; R is the universal gas constant.
NO formation
The rate of NO concentration increase is given by
- [math]\displaystyle{ \frac{d[\mathrm{NO}]}{dt}= k_{1f} [\mathrm{N}_2] [\mathrm{O}] + k_{2f} [\mathrm{N}] [\mathrm{O}_2] + k_{3f} [\mathrm{N}] [\mathrm{OH}] - k_{1b} [\mathrm{NO}] [\mathrm{N}] - k_{2b} [\mathrm{NO}] [\mathrm{O}] - k_{3b} [\mathrm{NO}] [\mathrm{H}] }[/math]
N formation
Similarly, the rate of N concentration increase is
- [math]\displaystyle{ \frac{d[\mathrm{N}]}{dt}= k_{1f} [\mathrm{N}_2] [\mathrm{O}] - k_{2f} [\mathrm{N}] [\mathrm{O}_2] - k_{3f} [\mathrm{N}] [\mathrm{OH}] - k_{1b} [\mathrm{NO}] [\mathrm{N}] + k_{2b} [\mathrm{NO}] [\mathrm{O}] + k_{3b} [\mathrm{NO}] [\mathrm{H}] }[/math]
References
- ↑ Y.B. Zel'dovich (1946). "The Oxidation of Nitrogen in Combustion Explosions". Acta Physicochimica U.S.S.R. 21: 577–628
- ↑ Zeldovich, Y. A., D. Frank-Kamenetskii, and P. Sadovnikov. Oxidation of nitrogen in combustion. Publishing House of the Acad of Sciences of USSR, 1947.
- ↑ Williams, Forman A. "Combustion theory". (1985).
- ↑ Zeldovich, I. A., Barenblatt, G. I., Librovich, V. B., Makhviladze, G. M. (1985). Mathematical theory of combustion and explosions.
- ↑ Lavoie, G. A., Heywood, J. B., Keck, J. C. (1970). Experimental and theoretical study of nitric oxide formation in internal combustion engines. Combustion science and technology, 1(4), 313–326.
- ↑ Hanson, R. K., Salimian, S. (1984). Survey of rate constants in the N/H/O system. In Combustion chemistry (pp. 361–421). Springer, New York, NY.
- ↑ "San Diego Mechanism". http://web.eng.ucsd.edu/mae/groups/combustion/mechanism.html.
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