Magnussen model

Magnussen model is a popular method for computing reaction rates as a function of both mean concentrations and turbulence levels . Originally developed for combustion, it can also be used for liquid reactions by tuning some of its parameters. The model consists of rates calculated by two primary means. An Arrhenius, or kinetic rate, $R_{K\_i',k}$, for species $i'$ in reaction $k$, is governed by the local mean species concentrations and temperature in the following way:

$R_{K\_i',k}=-\nu _{i',k}M_{i}A_{k}T^{\beta _{k}}\exp {\left(-{\frac {E_{k}}{RT}}\right)}\prod _{j'=1}^{N}\left[C_{j'}\right]^{\eta _{j',k}}=K_{i',k}M_{i'}\prod _{j'=1}^{N}\left[C_{j'}\right]^{\eta _{j',k}}$

This expression describes the rate at which species $i'$ is consumed in reaction $k$. The constants $A_{k}$ and $E_{k}$, the Arrhenius pre-exponential factor and activation energy, respectively, are adjusted for specific reactions, often as the result of experimental measurements. The stoichiometry for species $i'$ in reaction $k$ is represented by the factor \nu_{i',k}, and is positive or negative, depending upon whether the species serves as a product or reactant.

References

Magnussen, B. F., and B. H. Hjertager, “On Mathematical Mod- els of Turbulent Combustion with Special Emphasis on Soot For- mation and Combustion,” Proc. 16th Int. Symp. on Combustion, The Combustion Institute, Pittsburgh, PA (1976).