@article{cao_echekki_2008, title={A low-dimensional stochastic closure model for combustion large-eddy simulation}, volume={9}, ISSN={["1468-5248"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-50849101348&partnerID=MN8TOARS}, DOI={10.1080/14685240701790714}, abstractNote={A novel formulation for the large-eddy simulation (LES) of turbulent combustion flows is presented. The formulation is based on coupling LES equations for mass and momentum, with the corresponding 1D stochastic governing equations using the One-Dimensional Turbulence (ODT) model. ODT domains, or elements, on which fine-grained ODT simulations are implemented, are embedded in the flow to represent unresolved scalar and momentum statistics. The formulation is designed to address important coupling between turbulent transport and molecular processes (reaction and diffusion) over a wide range of length and time scales. This coupling poses difficult challenges for the LES modeling of turbulent mixing and combustion flows. The LES-ODT approach is implemented for the problem of autoignition in non-homogeneous mixtures. The LES-ODT model yields excellent agreement with direct numerical simulations (DNS) of reactive scalars' statistics at different turbulence and Lewis number conditions. Comparisons of the LES-ODT results with DNS show that the model represents adequately turbulent transport through its filtered advection and stochastic stirring. Molecular transport exhibits important roles in determining the rate of heat and mass dissipation from the autoignition kernels and their propagation.}, number={2}, journal={JOURNAL OF TURBULENCE}, author={Cao, Shufen and Echekki, Tarek}, year={2008}, pages={1–35} }
 @article{cao_echekki_2007, title={Autoignition in nonhomogeneous mixtures: Conditional statistics and implications for modeling}, volume={151}, ISSN={["1556-2921"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-34548516342&partnerID=MN8TOARS}, DOI={10.1016/j.combustflame.2007.03.008}, abstractNote={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.}, number={1-2}, journal={COMBUSTION AND FLAME}, author={Cao, Shufen and Echekki, Tarek}, year={2007}, month={Oct}, pages={120–141} }