Zeldovich number

Dimensionless parameter in fluid mechanics

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

\beta ={\frac {E_{a}}{RT_{b}}}\cdot {\frac {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

\beta ={\frac {E_{a}}{RT_{b}}}{\frac {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 $\beta \approx 8-20$ {\displaystyle \beta \approx 8-20}. Activation energy asymptotics uses this number as the large parameter of expansion.

References

[edit ]

^ Williams, Forman A. "Combustion theory." (1985).
^ Linan, Amable, and Forman Arthur Williams. "Fundamental aspects of combustion." (1993).
^ Y.B. Zel’dovich and D.A. Frank-Kamenetskii, Theory of thermal propagation of flame, Zh. Fiz. Khim+. 12 (1938), pp. 100–105.
^ Clavin, P. (1985). Dynamic behavior of premixed flame fronts in laminar and turbulent flows. Progress in energy and combustion science, 11(1), 1-59.