Modèles de flammelette en combustion turbulente avec extinction et réallumage : étude asymptotique et numérique, estimation d’erreur a posteriori et modélisation adaptative
We are interested here in the modeling errors of subgrid flamelet models in nonpremixed turbulent combustion. The goal of this thesis is to develop an a posteriori error estimation strategy to determine the best model within a hierarchy, with a numerical cost at most that of using the models in the first place. Firstly, we develop and test a dual-weighted residual estimator strategy on a system of advection-diffusion-reaction equations. Secondly, we test that methodology on another system of equations, where quenching and ignition effects are added. In the absence of advection, a rigorous asymptotic analysis shows the existence of many combustion regimes already observed in numerical simulations. We obtain approximations of the quenching and ignition parameters, alongside the S-shaped curve, a plot of the maximal flame temperature as a function of the Damköhler number, consisting of three branches and two bends. When advection effects are added, we still obtain a S-shaped curve corresponding to the known combustion regimes. We compare the modeling errors of the asymptotic approximations in the two stable regimes and establish new model hierarchies for each combustion regime. These errors are compared with the estimations obtained by using the error estimation strategy. When only one stable combustion regime exists, the error estimator correctly identifies that regime; when two or more regimes are possible, it gives a systematic way of choosing one regime. For regimes where more than one model is appropriate, the error estimator’s predicted hierarchy is correct.
Adaptive modeling Flamelet Modeling errors A posteriori error estimation Turbulent combustion Nonpremixed combustion Quenching Ignition Asymptotic analysis