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.