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The Zeldovich 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 Zeldovich, who along with David A. Frank-Kamenetskii, first introduced in their paper in 1938. In 1983 ICDERS meeting at Poitiers, it was decided that the non-dimensional number will be named after Zeldovich.

It is defined as

${\displaystyle \beta ={\frac {E_{a}}{RT_{b}}}\cdot {\frac {T_{b}-T_{u}}{T_{b}}}}$

where

• ${\displaystyle E_{a}}$ is the activation energy of the reaction
• ${\displaystyle R}$ is the universal gas constant
• ${\displaystyle T_{b}}$ is the burnt gas temperature
• ${\displaystyle T_{u}}$ is the unburnt mixture temperature.

In terms of heat release parameter ${\displaystyle q}$, it is given by

${\displaystyle \beta ={\frac {E_{a}}{RT_{b}}}{\frac {q}{1+q}}}$

For typical combustion phenomena, the value for Zel'dovich number lies in the range ${\displaystyle \beta \approx 8-20}$. Activation energy asymptotics uses this number as the large parameter of expansion.

References

1. Williams, Forman A. "Combustion theory." (1985).
2. Linan, Amable, and Forman Arthur Williams. "Fundamental aspects of combustion." (1993).
3. Y.B. Zel’dovich and D.A. Frank-Kamenetskii, Theory of thermal propagation of flame, Zh. Fiz. Khim+. 12 (1938), pp. 100–105.
4. 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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