Zeldovich number

{{Short description|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.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. In 1983 ICDERS meeting at Poitiers, it was decided that the non-dimensional number will be named after Zeldovich.Clavin, P. (1985). Dynamic behavior of premixed flame fronts in laminar and turbulent flows. Progress in energy and combustion science, 11(1), 1-59.

It is defined as

:$\backslash beta\; =\; \backslash frac\; \{E\_a\}\; \{RT\_b\}\; \backslash cdot\; \backslash frac\{T\_b-T\_u\}\{T\_b\}$

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

:$\backslash beta\; =\; \backslash frac\{E\_a\}\{RT\_b\}\; \backslash frac\{q\}\{1+q\}$

For typical combustion phenomena, the value for Zel'dovich number lies in the range $\backslash beta\backslash approx\; 8-20$. Activation energy asymptotics uses this number as the large parameter of expansion.