Uncertainty quantification of ion chemistry in lean and stoichiometric homogenous mixtures of methane, oxygen, and argon

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@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.} }

[syoukera]

Abstract

• 希薄と両論条件におけるメタン空気混合気の点火中における電子とイオンの変化の定量的な特定のために不確かさの定量化(UQ)法を行った
• 電子の数密度の時間変化における不確実性はchemi-ionization反応CH + O <=> HCO + E-と主要なCHの消費反応CH + O2 <=> O + HCOによるものだった．
• 電子とH3O+が合計の正負電荷の99%以上を占めており，荷電粒子の数密度は，電子数密度がピークの値から20%以下まで減少する崩壊過程の遅い時刻まで，H3O+ + E- の反応に対してごく小さな感度を持っていた．

[syoukera]

4. Conclusions

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:

1. The most important contribution to the number density of CH originates from the main consumption channel CH + O2 ⇌ O + HCO, followed by the production channel H + CH2 ⇌ CH + H2. The relative importance of these two reaction does not change significantly during ignition, and is only slighted affected by the mixture stoichiometry and initial conditions. From a practical perspective, the predictions suggest that conducting experiments at stoichiometric conditions is most desirable because higher CH number densities are beneficial from the perspective of maximizing signal to noise ratio.
2. Electrons E− and hydronium ions H3O+ are the most abundant charged species and account for close to 99% of the charge. In zero-dimensional reactors, the mixture is characterized by charge neutrality, so that the concentrations of E− and H3O+ are nearly identical throughout ignition. Due to the abundance of CH radicals, the stoichiometric case displays the largest peak value of electrons. The standard deviation σ is maximum shortly after ignition in correspondence with peak electron concentration, when the coefficient of variation ranges between 0.2 and 0.3. From the time of ignition onwards, the ratio decreases monotonically and reaches an asymptotic value ≈0.1 late during the electron decay phase.
3. The chemi-ionization reaction and the main consumption reaction for CH account for most of the variance in the time evolution of the electron number density. This trend persists until late into the decay process. For the case of the stochiometric mixture, the total sensitivity index due to CH + O ⇌ HCO+ + E− is highest (≈0.8) and it is lowest for case 1 (≈0.6). Conversely, the total sensitivity index for CH + O2 ⇌ O + HCO is lowest for case 4 and highest for case 1. From a practical perspective, the observed trends point to the role of key neutral reactions involving CH in controlling the mean and variance of the electron number density in an indirect fashion, and that stoichiometric mixtures are preferred over lean ones, as they mitigate the role of neutral chemistry in controlling electron concentrations.
4. The sensitivity index of the electron number density due to the recombination reactions does not increase above all others until late into the decay process, when the electron number density has dropped more than fourfold with respect to its peak value. Thus, the contribution of the uncertainty in the recombination reactions is overshadowed by that of the chemi-ionization reaction until late into the electron decay phase. The sensitivity index due to recombination is highest and grows sooner for the stoichiometric case.
5. The contribution of the recombination rates to the variance of the peak concentration of all charged species is negligibly small. The total sensitivities of the decay timescale due to recombination reactions are also small. These observations have important implications from an experimental perspective. If one aims at improving the rate parameters of the recombination reactions, measuring the electron decay rate from peak to 50% of the peak value may not be quite helpful due to the small sensitivity indices of this quantity of interest to the recombination reactions. Furthermore, these trends indicate that one needs to wait late into the decay process before the recombination reactions become the dominant contributors to the statistics of the number density of E−. By then, the number density of electrons may have decreased to less that 20% of the peak value and accurate measurements may be difficult to accomplish.