Optimized single-step (OSS) chemistry models for the simulation of turbulent premixed flame propagation

A simple and efficient triple-optimization procedure (TOP) is introduced to determine single-step chemistry model parameters. The cornerstone of the proposed approach lies in the introduction of a fictive (or virtual) chemical species, the physical characteristics of which are set to recover some essential properties of combustion and flames. Special emphasis is presently placed on the capability of such a global kinetic scheme to recover three parameters that are recognized as the most influential in terms of turbulence-chemistry interactions and turbulent premixed combustion regimes. These parameters are (i) the burnt gases temperature Tb, which settles the value of the thermal expansion factor τ=(Tb−Tu)/Tu, (ii) the propagation velocity SL0, which is mandatory to reproduce the flame dynamics, and (iii) the laminar premixed flame thickness δL0. In practice, the thermochemical properties of the fictive species (hereafter denoted by AΦ) are set to account for the impact of dissociation effects and partial oxidation of the fuel, i.e., presence of species other than H2O and CO2 in the burnt gases, which allows to recover a satisfactory estimate of Tb. The value of the pre-exponential factor associated to the single-step Arrhenius law is also optimized to reproduce the laminar flame propagation velocity. Finally, the transport characteristics are determined to recover a satisfactory estimate of the thermal flame thickness. The method is general in its principles and quite easy to implement. It is applicable to any couple of fuel and oxidizer. Attention is focused on the application of the method to any stoichiometry but it is also shown that the influence of both pressure and fresh reactants temperature can be recovered. The performance of the resulting optimized single step (OSS) chemistry models are assessed through a direct comparison with detailed chemistry results. Computations of one-dimensional laminar flames are performed with the OSS model using the Cantera software for a wide range of pressure levels, fresh reactant temperatures, and equivalence ratios. Obtained results do show that the flame propagation velocity is correctly reproduced for the whole range of parameters, with a maximum value recovered in the vicinity of stoichiometry, a decrease towards rich conditions, and a satisfactory pressure dependence. Burnt gases temperature as well as thermal flame thickness values are also in excellent agreement with those issued from the reference detailed kinetics models. The OSS model is then used to perform direct numerical simulation (DNS) computations of flame kernel growths in both laminar and turbulent conditions. The comparison of obtained OSS results with detailed chemistry computations further confirms the relevance and performance of the proposed methodology.