Chemical kinetic models comprise large numbers of parameters, such as rate coefficients and thermochemical parameters. These model parameters can exhibit large uncertainties, which are propagated into the model response and ultimately induce uncertainties in model predictions. The characterization of how the model prediction uncertainties depend upon uncertainties in model parameters is of high importance, as it can guide the model development towards the improvement of those parameters which most strongly affect the prediction uncertainties. Furthermore, the knowledge on the uncertainty relationship between model parameters and model predictions also allows to use experimental data for the inverse minimization of the joint uncertainties of model parameters.

At the Institute of Combustion Technology, uncertainty quantification (UQ) techniques based on polynomial chaos expansions and Bayesian inference are employed to characterize model uncertainties and optimize model parameters. A particular emphasis lies on the low-temperature ignition chemistry, where kinetic models often exhibit very high uncertainties due to various competing reaction channels. As kinetic models are often developed based on the concept of reaction classes, where rate rules are used for sets of multiple elementary reactions, the employed UQ techniques consider the rate rules as input parameters rather than the elementary reaction rate coefficients. This allows to inherently incorporate the correlation between rate coefficients which use the same rate rules, and additionally retains the consistency in a mechanism even if the same rate rules are applied for various fuels. This approach has been used to derive optimized mechanisms for n-pentane [1], a gasoline surrogate mixture [2], the class of higher n-alkanes up to n-dodecane [3], and the class of novel synthetic e-fuels oxymethylene ethers (OMEs) [4].

The prediction of fuel ignition at low-temperatures is not only affected by uncertainties in rate coefficients and rate rules, but also by the thermochemical properties of intermediate species due to their impacts on chemical equilibria and backward rate coefficients. Therefore, the UQ techniques have been extended to incorporate the uncertainties induced by uncertain thermochemical property data of enthalpies of formation, standard entropies, and heat capacities [5]. This allows to jointly optimize the kinetic and thermochemical parameters in a model based on experimental data [6]. Analogous to the estimation of rate coefficients based on rate rules, the thermochemical parameters of species are often estimated based on the group additivity method, due to which the thermochemical parameters are correlated as well. Hence, the UQ and optimization based on group values has been developed to assess the uncertainty propagation of group uncertainties into kinetic model predictions and inversely use experimental data to jointly optimize rate rules and group values [7]. Finally, the knowledge on uncertainty correlation between model predictions and model parameters can also be used to design new experiments which allow to most effectively discriminate between different models [8] or to minimize the model uncertainties [9].

Example: Surface of the D-optimal experimental design criterion at 25 atm in an experimental design process for ignition delay times of dimethyl ether [9]

[1] L. Cai, H. Pitsch, Mechanism optimization based on reaction rate rules, Combustion and Flame 161 (2014) 405-415.

[2] L. Cai, H. Pitsch, Optimized chemical mechanism for combustion of gasoline surrogate fuels, Combustion and Flame 162 (2015) 1623-1637.

[3] L. Cai, H. Pitsch. S.Y. Mohamed, V. Raman, J. Bugler, H. Curan, S.M. Sarathy, Optimized reaction mechanism rate rules for ignition of normal alkanes, Combustion and Flame 173 (2016) 468-482.

[4] L. Cai, S. Jacobs, R. Langer, F. vom Lehn, K.A. Heufer, H. Pitsch, Auto-ignition of oxymethylene ethers (OMEn, n = 2–4) as promising synthetic e-fuels from renewable electricity: shock tube experiments and automatic mechanism generation, Fuel 264 (2020) 116711.

[5] F. vom Lehn, L. Cai, H. Pitsch, Sensitivity analysis, uncertainty quantification, and optimization for thermochemical properties in chemical kinetic combustion models, Proceedings of the Combustion Institute 37 (2019) 771-779.

[6] F. vom Lehn, L. Cai, H. Pitsch, Impact of thermochemistry on optimized kinetic model predictions: Auto-ignition of diethyl ether, Combustion and Flame 210 (2019) 454–466.

[7] F. vom Lehn, L. Cai, H. Pitsch, Investigating the impacts of thermochemical group additivity values on kinetic model predictions through sensitivity and uncertainty analyses, Combustion and Flame 213 (2020) 394-408.

[8] L. Cai, S. Kruse, D. Felsmann, C. Thies, K.K. Yalamanchi, H. Pitsch, Experimental design for discrimination of chemical kinetic models for oxy-methane combustion, Energy & Fuels 31 (5) (2017) 5533-5542.

[9] F. vom Lehn, L. Cai, H. Pitsch, Iterative model-based experimental design for efficient uncertainty minimization of chemical mechanisms, Proceedings of The Combustion Institute (2021).