The Zeldovich number is a

dimensionless number Dimensionless quantities, or quantities of dimension one, are quantities implicitly defined in a manner that prevents their aggregation into unit of measurement, units of measurement. ISBN 978-92-822-2272-0. Typically expressed as ratios that a ...

which provides a quantitative measure for the

activation energy In the Arrhenius model of reaction rates, activation energy is the minimum amount of energy that must be available to reactants for a chemical reaction to occur. The activation energy (''E''a) of a reaction is measured in kilojoules per mole (k ...

of a

chemical reaction A chemical reaction is a process that leads to the chemistry, chemical transformation of one set of chemical substances to another. When chemical reactions occur, the atoms are rearranged and the reaction is accompanied by an Gibbs free energy, ...

which appears in the Arrhenius exponent, named after the

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scientist A scientist is a person who Scientific method, researches to advance knowledge in an Branches of science, area of the natural sciences. In classical antiquity, there was no real ancient analog of a modern scientist. Instead, philosophers engag ...

Yakov Borisovich Zeldovich, who along with David A. Frank-Kamenetskii, first introduced in their paper in 1938. In 1983 ICDERS meeting at

Poitiers Poitiers is a city on the river Clain in west-central France. It is a commune in France, commune, the capital of the Vienne (department), Vienne department and the historical center of Poitou, Poitou Province. In 2021, it had a population of 9 ...

, 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 :

\beta = \frac   \cdot \frac

where *

E_a

is the

of the reaction *

R

is the

universal gas constant The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol or . It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature, temperature ...

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 \frac

For typical

combustion Combustion, or burning, is a high-temperature exothermic redox chemical reaction between a fuel (the reductant) and an oxidant, usually atmospheric oxygen, that produces oxidized, often gaseous products, in a mixture termed as smoke. Combustion ...

phenomena, the value for Zel'dovich number lies in the range

\beta\approx 8-20

Activation energy asymptotics Activation energy asymptotics (AEA), also known as large activation energy asymptotics, is an asymptotic analysis used in the combustion field utilizing the fact that the reaction rate is extremely sensitive to temperature changes due to the large ...

uses this number as the large parameter of expansion.

References

Chemical kinetics Combustion Dimensionless numbers of fluid mechanics Fluid dynamics Dimensionless numbers of chemistry {{fluiddynamics-stub