Chemistry:Zel'dovich number
From HandWiki
The Zel'dovich number is a dimensionless number which provides a quantitative measure for the activation energy of a chemical reaction which appears in the Arrhenius exponent, named after the Russian scientist Yakov Borisovich Zel'dovich, who along with David A. Frank-Kamenetskii, first introduced in their paper in 1938.[1][2][3] In 1983 ICDERS meeting at Poitiers, it was decided to name after Zel'dovich.[4] It is defined as
- [math]\displaystyle{ \beta = \frac {E_a} {RT_b} \cdot \frac{T_b-T_u}{T_b} }[/math]
where
- [math]\displaystyle{ E_a }[/math] is the activation energy of the reaction
- [math]\displaystyle{ R }[/math] is the universal gas constant
- [math]\displaystyle{ T_b }[/math] is the burnt gas temperature
- [math]\displaystyle{ T_u }[/math] is the unburnt mixture temperature.
In terms of heat release parameter [math]\displaystyle{ \alpha }[/math], it is given by
- [math]\displaystyle{ \beta = \frac{E_a}{RT_b} \alpha }[/math]
For typical combustion phenomena, the value for Zel'dovich number lies in the range [math]\displaystyle{ \beta\approx 8-20 }[/math]. Activation energy asymptotics uses this number as the large parameter of expansion.
References
- ↑ Williams, Forman A. "Combustion theory." (1985).
- ↑ Linan, Amable, and Forman Arthur Williams. "Fundamental aspects of combustion." (1993).
- ↑ Y.B. Zel’dovich and D.A. Frank-Kamenetskii,Theory of thermal propagation of flame,Zh. Fiz. Khim+. 12 (1938), pp. 100–105.
- ↑ Clavin, P. (1985). Dynamic behavior of premixed flame fronts in laminar and turbulent flows. Progress in energy and combustion science, 11(1), 1-59.
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