The rate-controlled constrained equilibrium (RCCE) method for reducing chemical kinetics in systems with time-scale separation

Turbulent combustion is the ultimate multiscale problem, with chemical reactions exhibiting time scales spanning more than ten orders of magnitude and turbulent motion, introducing further. space and time scales. The integration of the chemical kinetics equations is severely hampered by their excessive stiffness, resulting from the range of time scales present. The mathematical modeling of combustion can be significantly simplified by taking advantage of the time-scale separation to assume that fast reactions, typically associated with intermediate species, are in a local equilibrium. In the rate-controlled constrained equilibrium method (RCCE), the dynamical evolution of the system is governed by the kinetics of the species associated with the slower time scales (kinetically controlled), while the remaining species are calculated via a constrained minimization of the Gibbs free energy of the mixture. This permits the derivation of a general set of differential-algebraic equations (DAEs), which apply to any reduced system given a particular selection of kinetically controlled species. In this paper, it is shown how the differential-algebraic formulation of RCCE can be derived from first principles, in the form of an extension of the computation of chemical equilibrium via miminisation of the free energy. Subsequently, RCCE is employed to reduce a comprehensive combustion mechanism and to calculate the burning velocity of premixed H-2-O-2 and CH4-air flames under a range of pressures and equivalence ratios.