## Numerical and asymptotic studies of flames - Grupo de modelización de procesos de combustión

#### Numerical and asymptotic studies of laminar and turbulent flames

Theoretical studies of laminar and turbulent flames usually make use of global one-step kinetics in oder to symplify the chemical terms in the reactive Navier-Stokes equations. In general, the fuel "F" is oxidated by the oxydizer "O" to give products "P", following the an Arrhenius type eaction F + O → P. A step forward in the global kinetics description it is the use of a two-step chain-branching model, where a intermediate specie "Z" is included. Since the 60s researchers as Zel'dovich, Liñán and more recently Dold, showed the usefulness of the two-step kinetics. For exmaple, the hydrogen oxidation can be described properly with this kind of kinetics for an ample range of equivalence ratios. The two-step kinetics involves a chain-branching reaction F + Z → 2Z, which produces another intermediate specie and a recombination reaction Z + M → P + M, which gives the products and releases heat. The specie "M" is any molecule.

In particular, the two-step model allows the definition of a kinetically controlled flammability limit, as found in planar hydrogen-air deflagrations. The Group investigates the planar flame structure with two-step kinetics (Fernández-Galisteo et al. 2012). The figure below shows the theoretical structure of a planar premixed flame for different values of the heat of reaction *q *(which represents a reduced measure of the equivalence ration at lean conditions). For very lean mixtures (*q<0.92*) we found fuel leakage and ultimately flame extinction. When the adiabatic flame temperature is below a critical value, known as crossover temperature, the rate of the recombination reactions exceeds the rate of branching and the flame extinguishes.

The flammability conditions can be obtained analytically with help of asymptotic methods which simplify the governing equations.