*(José Salvador Ochoa, March 2010)*

In this work, a strategy based on the Linear Eddy Model (LEM) as subgrid model (called hereafter S-LEM) is developed for modeling turbulent reactive flows. In S-LEM, all physical processes that occur below the grid-scale (molecular diffusion, stirring and, where appropriate, chemical reactions) are modeled in a one-dimensional domain immersed in each cell of the computational mesh. The subgrid domain is discretized to solve the whole range of scales between the cell-characteristic size (LES filter size) and the smaller flow-scale (Kolmogorov scale) so that diffusion and chemical reactions can be determined accurately, avoiding turbulence-chemistry assumptions. Therefore, subgrid processes are represented by a transient diffusion-reaction one-dimensional equation. The stirring (convection by subgrid turbulent eddies) are modeled by stochastic (triplet maps) events according to the Kerstein's LEM procedure. The effects of large-scale convection (transport between subgrid domains) is modeled using a technique called “splicing” that exchanges portions of sub-domains according to the mass-flow rate between adjacent cells and the local intensity of turbulent fluctuations. A reduced numerical diffusion approach has been proposed to improve the accuracy of splicing algorithm by means of an analogy with the high-order finite-volume convection schemes.

The flames analyzed are the turbulent partially-premixed piloted Sandia flames C, D and E. The eulerian-governing equations are filtered and discretized by a finite-volume approach. The combustion and the turbulence-chemistry interactions are modeled using two strategies: a steady-state flamelet model (with assumed-shape filtered probability density functions) and the Linear Eddy Model for the first time for these flames.

The document reviews briefly the state-of-art of LES and the combustion modeling. The most important numerical algorithms are evaluated prior to the main simulations. The predictions can be classified into: (a) LES with flamelets, (b) LES with a non-reacting S-LEM and © LES with a combustion-like S-LEM. In case (a), LES-flamelets modeling (with a 35-step, 16-specy chemical kinetics) shows an adequate prediction of the flow, major chemical species and temperature. This asses the validity of the steady-state flamelet model for these flames, including the E, which has a higher probability of local extinction. In case (b), S-LEM is coupled to the LES-flamelet predictions for solving the evolution of a passive scalar (the mixture fraction) and its subgrid variance and scalar dissipation rate. This quantities show an adequate agreement with the correspondent variables coming from the eulerian equations and with experimental observations. In case (c ), the combustion reaction is incorporated into the subgrid processes of S-LEM in order to determine the complete thermochemical state of the flames. In this case, a one-step chemical kinetics is used. The chemical mechanism considers the effect of partial oxidation in rich- or very lean- fuel zones adjusting the heat release and the activation temperature as a function of local equivalence ratio. The results improve significantly the agreement with experimental data shown by flamelet modeling.

Information extracted from the sub-domains of S-LEM is used to analyze the subgrid structure of the scalars, mainly the scalar dissipation rate (for which there are experimental measurements at different positions of the flames). The results show that the S-LEM predicts reasonably well this structure. The dispersion of chemical species is similar to the experimental one. By analogy with the flamelet theory, it has been shown that the developed model captures adequately the complex interactions between chemical kinetics and turbulence in the three turbulent flames.