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.^[1][2][3] In 1983 ICDERS meeting at Poitiers, it was decided that the non-dimensional number will be named after Zeldovich.^[4]

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.