A novel methodology for chemical time scale evaluation with detailed chemical reaction kinetics

Interaction between turbulent mixing and chemical kinetics is the key parameter which determines the combustion regime: only understanding such interaction may provide insight into the physics of the flame and support the choice and/or development of modeling tools. Turbulence-chemistry interaction may be evaluated through the analysis of the Damköhler number distribution, which represents the flow to chemical time-scale ratio. Large Damköhler values indicate mixing controlled flames. On the other hand, low Damköhler values corresponds to slow chemical reactions: reactants and products are quickly mixed by turbulence, so the system behaves like a perfect stirred reactor. The calculation of the Damköhler number requires the definition of proper flow and chemical time-scales. For turbulent conditions, various flow time-scales can be used, such as the integral and Kolmogorov time-scales. Chemical time-scale calculation poses some issues. In the literature, several examples of Damköhler calculation are reported, but in most cases a global chemical reaction rate is used to estimate the chemical time scale. A method for considering more complex kinetic schemes is proposed by Fox [Computational Models for Turbulent Reacting Flows; Cambridge University Press: Cambridge, U. K., 2003], who defines the chemical time-scale in terms of the inverse of the eigenvalues from the decomposition of the chemical source term Jacobian matrix. The present work aims at developing a procedure for the calculation of the chemical time-scale (and thus of the Damköhler number) with complex kinetics starting from the analysis of the Jacobian matrix of the chemical species source terms. Emphasis is given on the dimension of the Jacobian matrix, as it is not fully understood how the species for the time-scale calculation should be chosen. In other words, one can refer to the full set of species (thus all species will have the same "weight") but also to a subset of them. The main concept is to perform a preliminary analysis, based on Principal Variables (PV), to determine the relative importance of the chemical species, in order to select an optimal subset for the chemical time-scale calculation. The procedure is illustrated and applied for the Moderate and Intense Low-oxygen Dilution (MILD) combustion, as this kind of regime shows a strong coupling between turbulence and chemistry, mainly because of slower reaction rates (due to the dilution of reactants) in comparison with conventional combustion. The methodology is further validated on a DNS data set modeling a CO/H2 jet flame