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

$\beta =\frac{E_a}{R{T}_b}\cdot \frac{T_b-T_u}{T_b}$

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

$\beta =\frac{E_a}{R{T}_b}\frac{q}{1+q}$

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.