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Abstract
This paper presented the implementation of UQ methods towards the quantitative characterization of ion chemistry reactions during the oxidation of methane, and thus gain insight into the evolution of charged species. Attention was specifically focused on the ignition of dilute lean and stoichiometric methane-oxygen mixtures under isochoric and adiabatic conditions.
To describe the oxidation and ionization processes adequately, the present analysis relied on the GRI-Mech 3.0 mechanism [49], which was augmented with the ion chemistry assembled by Prager et al. [11]. We employed the TChem library [48] to integrate the stiff system of ODEs describing the evolution of the system.
The UQ analysis focused on the impact of uncertain rate parameters on the prediction of the concentrations of the charged species. In order to render the uncertainty quantification analysis manageable, a first screening was conducted to determine a reduced set of elementary reactions that affect ion formation and recombination significantly. To this end, a heuristic reaction analysis approach was used, leading to the selection of 15 ion chemistry reactions and 7 reactions involving neutrals. We adopted the chemi-ionization rate recommended by Warnatz [56], and whenever possible relied on the UMIST database [22] to determine suitable ranges for the uncertain rate parameters. A sparse adaptive pseudo-spectral sampling technique was then applied in order to efficiently sample the resulting 22-dimensional probability space used to parametrize the uncertain rates of reactions.
The UQ study considered four cases comprising different initial temperatures and mixtures of CH4 and O2 in Ar diluent. These match the initial conditions in shock-tube experiments [70] available in the literature and feature three cases with lean mixtures ( ) of various strengths and a stoichiometric case (case 4). The analysis of the computations revealed that:
@article{KIM20152904, title = {Uncertainty quantification of ion chemistry in lean and stoichiometric homogenous mixtures of methane, oxygen, and argon}, journal = {Combustion and Flame}, volume = {162}, number = {7}, pages = {2904-2915}, year = {2015}, issn = {0010-2180}, doi = {https://doi.org/10.1016/j.combustflame.2015.03.013}, url = {https://www.sciencedirect.com/science/article/pii/S001021801500098X}, author = {Daesang Kim and Francesco Rizzi and Kwok Wah Cheng and Jie Han and Fabrizio Bisetti and Omar Mohamad Knio}, keywords = {Chemi-ionization, Ion chemistry, Electrons, Uncertainty quantification, Polynomial chaos, Sparse-adaptive sampling}, abstract = {Uncertainty quantification (UQ) methods are implemented to obtain a quantitative characterization of the evolution of electrons and ions during the ignition of methane–oxygen mixtures under lean and stoichiometric conditions. The GRI-Mech 3.0 mechanism is combined with an extensive set of ion chemistry pathways and the forward propagation of uncertainty from model parameters to observables is performed using response surfaces. The UQ analysis considers 22 uncertain rate parameters, which include both chemi-ionization, proton transfer, and electron attachment reactions as well as neutral reactions pertaining to the chemistry of the CH radical. The uncertainty ranges for each rate parameter are discussed. Our results indicate that the uncertainty in the time evolution of the electron number density is due mostly to the chemi-ionization reaction CH+O⇌HCO++E− and to the main CH consumption reaction CH+O2⇌O+HCO. Similar conclusions hold for the hydronium ion H3O+, since electrons and H3O+ account for more than 99% of the total negative and positive charge density, respectively. Surprisingly, the statistics of the number density of charged species show very little sensitivity to the uncertainty in the rate of the recombination reaction H3O++E−→products, until very late in the decay process, when the electron number density has fallen below 20% of its peak value. Finally, uncertainties in the secondary reactions within networks leading to the formation of minor ions (e.g., C2H3O+, HCO+, OH−, and O−) do not play any role in controlling the mean and variance of electrons and H3O+, but do affect the statistics of the minor ions significantly. The observed trends point to the role of key neutral reactions in controlling the mean and variance of the charged species number density in an indirect fashion. Furthermore, total sensitivity indices provide quantitative metrics to focus future efforts aiming at improving the rates of key reactions responsible for the formation of charges during hydrocarbon combustion.} }