Source Terms for Heavy Species Transport Equations
The rate expression for species k, Rk, is determined by the stoichiometry of the system through the formula
(5-7)
where νkj are the stoichiometric coefficients, defined as negative for reactants and positive for products, and rj is the reaction rate corresponding to reaction j. The reaction rates depend on the order of the reaction and the molar concentration of each species. In compact form, the equation for the jth reaction rate is
where:
•
ck is the molar concentration of species k (SI unit: mol/m3)
•
kfj and krj are the forward and reverse rate constants, respectively, for the jth forward reaction (SI unit: 1/s for first-order reactions, m3/(mol·s) for second-order reactions or m6/(mol2·s) for third-order reactions)
The molar concentration of the kth species is computed via
.
The rate constants can depend exponentially on the gas temperature through Arrhenius law
where Aj is the frequency factor for reaction j, β is the temperature exponent and Ej is the activation energy for reaction j.