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
![{\displaystyle \beta ={\frac {E_{a}}{RT_{b}}}\cdot {\frac {T_{b}-T_{u}}{T_{b}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5470598ce98e7dc44e23ab132a98e7db598d5f68)
where
is the activation energy of the reaction
is the universal gas constant
is the burnt gas temperature
is the unburnt mixture temperature.
In terms of heat release parameter
, it is given by
![{\displaystyle \beta ={\frac {E_{a}}{RT_{b}}}\alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/d3c547cdc0d6751982899c63e677616e1a4a9123)
For typical combustion phenomena, the value for Zel'dovich number lies in the range
. Activation energy asymptotics uses this number as the large parameter of expansion.
- ^ 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.