Autoignition in nonhomogeneous mixtures: Conditional statistics and implications for modeling

Conditional statistics associated with the problem of nonhomogeneous autoignition are investigated using direct numerical simulations (DNS). The chemical model is based on a single-step, second-order, and irreversible reaction mechanism with reaction rate expressed by the Arrhenius law. The mixture is initialized as a random distribution with variable mixture strength in decaying isotropic turbulence. Both low- and high-turbulence conditions are studied and three Lewis number cases are examined for the high-turbulence conditions. Simulation results show that under conditions of nonhomogeneous mixture and preheated air, autoignition is initiated in a fuel-lean mixture and evolves by propagation to richer mixtures. The propagation elements of the autoignition process are found in statistics of mean quantities for reactive scalars as well as covariances and variances of these scalars with the rate of dissipation. The addition of a second conditioning variable based on a reduced temperature is investigated. Results show that the addition of a second conditioning variable that measures the extent of completion of combustion may be a reasonable choice for nonhomogeneous autoignition modeling. However, additional nontrivial closure models are required for both reactive scalars' phase space equations and the transport equations for the second conditioning variable.