Zeldovich number

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


 * $$\beta = \frac {E_a} {RT_b} \cdot \frac{T_b-T_u}{T_b}$$

where
 * $$E_a$$ is the activation energy of the reaction
 * $$R$$ is the universal gas constant
 * $$T_b$$ is the burnt gas temperature
 * $$T_u$$ is the unburnt mixture temperature.

In terms of heat release parameter $$q$$, it is given by


 * $$\beta = \frac{E_a}{RT_b} \frac{q}{1+q}$$

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