  One of the most important and difficult parts of constructing a
multidimensional numerical simulation of flame acceleration and
deflagration-to-detonation transition (DDT) in a reacting flow is finding a
reliable and affordable model of the chemical and diffusive properties. For
simulations of realistic scenarios, full detailed chemical models are
computationally prohibitive. In addition, they are usually inaccurate for
high-temperature and high-pressure shock-laden flows. This paper presents a
general approach for developing an automated procedure to determine the
reaction parameters for a simplified chemical-diffusive model to simulate flame
acceleration and DDT in stoichiometric methane-air and ethylene-oxygen
mixtures. The procedure uses a combination of a genetic algorithm and
Nelder-Mead optimization scheme to find the optimal reaction parameters for a
reaction rate based on an Arrhenius form for conversion of reactants to
products. The model finds six optimal reaction parameters that reproduce six
target flame and detonation properties. Results from the optimization procedure
show that the optimal reaction parameters, when used in 1-D reactive
Navier-Stokes simulations, closely reproduce the target flame and detonation
properties for the stoichiometric methane-air and ethylene-oxygen mixtures.
When the reaction parameters are used as input in a 2-D simulation of flame
acceleration and DDT in an obstacle-laden channel containing stoichiometric
methane-air, the simulation results closely follow the transition to detonation
observed in experiments. This automated procedure for finding parameters for a
proposed reaction model makes it possible to simulate the behavior of flames
and detonations in large, complex scenarios, which would otherwise be an
incalculable problem.
