(568d) Obtaining Accurate Solutions Using Reduced Chemical Kinetic Models

In simulations of combustion and other reacting flows, reduced chemical kinetic models are often used in place of the detailed mechanism, since it is too difficult and expensive to solve the full system of coupled transport + chemistry equations. This approximation introduces uncontrolled errors: after solving the model using the approximate chemistry one usually has no idea whether the result is close to the solution that would have been obtained if the detailed mechanism had been used. Here we present the first method that rigorously bounds the error introduced by using reduced chemistry models in combustion simulations.

Mathematical methods for model reduction are usually associated with a nominal set of reaction conditions for which the model is reduced, and often it is known that the reduced model is faithful to the detailed model at this nominal point. However, the important effects of variability in these nominal conditions are often ignored because there is no convenient way to deal with them. In this work, we introduce a simple method to identify rigorous valid ranges for reduced models, i.e. the reduced models are guaranteed to replicate the full model to within an error tolerance at all conditions in the identified valid range. Previous methods have estimated valid ranges using a limited set of variables (usually temperature and a few species compositions) and cannot guarantee that the reduced model is accurate at all points in the estimated range. Using well-established techniques from Interval Arithmetic, our method rigorously bounds the errors due to model reduction in any given range of reaction conditions, allowing identification of rigorous valid ranges. Tighter bounds are achieved by using Taylor expansions (including a remainder term) of the model error functions. Unlike previous approaches, our method does not rely on sampling and remains efficient in high dimensions (large number of species). The method is demonstrated by identifying valid ranges for models reduced from the GRI-mech 3.0 mechanism (with 53 species and 325 reactions), and models reduced from a propane mechanism with 94 species and 505 reactions (derived from the mechanism of Marinov et al [1]). Valid ranges for the reduced models are identified in temperature and concentrations of all species. A library of reduced models is also generated for several prespecified ranges comprising a desired state space. The use of these reduced models with error control in reacting flow simulations is demonstrated through Adaptive Chemistry examples in 1-D and 2-D spatial domains. By using the reduced models in the simulation only when they are valid the Adaptive Chemistry solution is guaranteed to lie within a tight tolerance of the solution that would have been obtained using the detailed mechanism, i.e. one can achieve guaranteed accuracy without ever having to solve the full combustion chemistry model.

[1]Marinov, N.M., Pitz, W.J., Westbrook, C.K., Vincitore, A.M., Castaldi, M.J., Senkan, S.M. ?Aromatic and Polycyclic Aromatic Hydrocarbon Formation in a Laminar Premixed n-Butane Flame? Combustion and Flame 114 192-213 (1998).