Chemical kinetic uncertainty quantification for Large Eddy Simulation of turbulent nonpremixed combustion

While the accuracy of chemical kinetic mechanisms continues to improve, these mechanisms are still models with, sometimes considerable, uncertainty. In order to rigorously validate turbulent combustion simulations against experimental data, this uncertainty must be separated from deficiencies in the turbulent combustion model itself. In this work, a method is developed for quantifying the uncertainty in turbulent flame simulations due to input uncertainty in the chemical mechanism. Here the method is developed for Large Eddy Simulation (LES) combined with a steady flamelet model. Rather than a brute force probabilistic approach in which hundreds or thousands of LES runs are required to compute statistics of outputs of interest, the method takes advantage of the actual algorithm employed with the steady flamelet model. First, the high-dimensional uncertainty in the chemical kinetics is propagated through the flamelet equations, and the resulting lower-dimensional joint distribution of the temperature, species mass fractions, and other derived quantities is used as a stochastic equation of state in the LES. Since only a few 'active' quantities are needed to evolve the LES governing equations, efficient non-intrusive stochastic collocation is used to propagate the uncertainty in the density, requiring only a few LES runs. This process captures the uncertainty in the flow field induced by the uncertainty in the chemical kinetic rates. The remaining uncertainty in 'passive' quantities, that is, quantities needed only for post-processing such as the temperature and species mass fractions, is computed with random sampling during the LES runs. The uncertainty quantification algorithm is demonstrated with Sandia flame D, and it is shown that the uncertainty in the simulation results caused by uncertainties in the kinetic rates is sufficiently large to account for the discrepancies with the experimental measurements. The implication is that the turbulent combustion model cannot be fairly assessed with such a large uncertainty.