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
β = E a R T b ⋅ T b − T u T b {\displaystyle \beta ={\frac {E_{a}}{RT_{b}}}\cdot {\frac {T_{b}-T_{u}}{T_{b}}}}
where
E a {\displaystyle E_{a}} is the activation energy of the reaction
R {\displaystyle R} is the universal gas constant
T b {\displaystyle T_{b}} is the burnt gas temperature
T u {\displaystyle T_{u}} is the unburnt mixture temperature. In terms of heat release parameter q {\displaystyle q} , it is given by
β = E a R T b q 1 + q {\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 β ≈ 8 − 20 {\displaystyle \beta \approx 8-20} . Activation energy asymptotics uses this number as the large parameter of expansion.
References