The reaction kinetics of hydrogen combustion was intensively studied already in the first half of the 20th century. The first, second and third explosion limits were discovered, and mechanistic explanations were given. However, fine details of the reaction mechanism and the exact rate parameters are still not known. New reaction steps were proposed even in the last few years. The explosive—non-explosive regions are separated by an inverted S-shape curve in the T − p plane. The backbone of the curve is approximately equal to the line where the rates of reactions H + O2 → OH + O and H + O2 + M → HO2 + M are equal. The regions of strong and weak explosions are below and above the backbone line, and these regions are dominated by H/O/OH and HO2/H2O2 catalytic cycles, respectively. In a small vessel, the adsorption of radicals HO2 and H form the upper and lower branches of the curve, respectively. All qualitative features of the hydrogen combustion system can be explained by a 10-step mechanism. Several web sites are recommended here which contain comprehensive collections of recent hydrogen combustion mechanisms, direct and indirect experimental data, and theoretical determinations.

Optimization of detailed combustion mechanisms means that the corresponding kinetic model is fitted to experimental data via optimizing their important rate and thermodynamic parameters within their domain of uncertainty. Typically, several dozen parameters are fitted to several hundred to several thousand data points. Many numerical optimization methods have been used, but the efficiency of these methods has not been compared systematically. In this work, parameters of a H2/O2/NOx mechanism (214 reaction steps of 35 species) were fitted to 1552 indirect (ignition delay times measured in shock tubes and concentrations measured in flow reactors) and 755 direct measurements. Three test cases were investigated: (1) fitting the Arrhenius parameters of 2 reaction steps to 732 data points; (2) fitting the Arrhenius parameters of 4 reaction steps to 1077 data points; (3) fitting the Arrhenius parameters of 10 reaction steps to 2307 data points. All three cases were investigated in two ways: fitting the A-parameters only and fitting all Arrhenius parameters (5, 11 and 29 parameters, respectively). A series of global (FOCTOPUS, genetic algorithm, simulated annealing, particle swarm optimization, covariance matrix adaptation evolutionary strategy (CMA-ES)) and local (simplex, pattern search, interior-point, quasi-Newton, BOBYQA, NEWUOA) optimization methods were tested on these cases, some of them in two variants. The methods were compared in terms of the final error function value and number of error function evaluations. The main conclusions are that the FOCTOPUS resulted in the lowest final error value in all cases, but this method required relatively many error function evaluations. As the task became more difficult, more and more methods failed. A variant of the BOBYQA method looked stable and efficient in all cases.

 

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Identification of homogeneous chemical kinetic regimes of methane-air ignition

Optimization of large combustion mechanisms means that a few dozen parameters (called active parameters) are optimized within their uncertainty limits to achieve a better reproduction of the experimental data, which is usually measured by a mean square error function. In previous studies, the active parameters were selected based either on their local sensitivity coefficients (strategy S) or on the products of local sensitivity coefficient and a corresponding uncertainty parameter (strategy SU). This latter measure is known by various names: optimization potential, sensitivity-uncertainty index or uncertainty-weighted sensitivity coefficient. In this work, we proposed three novel active parameter selection strategies of increasing complexity (PCA-SU, PCA-SUE, PCALIN) and demonstrated their superior performance in the optimization of pre-exponential factors (A) in a methanol/NOx combustion mechanism (562 reaction steps of 70 species) against 2360 data measured in shock tube, JSR and flow reactor experiments. The novel methods are based on the principal component analysis (PCA) of sensitivity matrices scaled by the uncertainties of parameters (U) and the uncertainty of the experimental data (E). These PCA-based methods take into account parameter correlations and designate parameter groups and corresponding relevant subsets of experimental data, thereby a factor of 4–7 savings in optimization time was achieved over the S and SU methods. PCA-SUE method performed better than the PCA-SU as it also considered the uncertainty of the experimental data. The PCALIN strategy is similar to PCA-SUE, but it also considers the linear change (LIN) of the error function, which depends on the simulation error of experimental data, and thereby it could provide the most accurate models as a function of the number of active parameters. Based on the PCALIN strategy, fitting all three Arrhenius parameters resulted in further improvements, however, it provided moderate improvements over simple A-factor tuning and required significantly more computer time.

A detailed review of the performances of 24 butanol combustion mechanisms, published between 2008 and 2020, is given using a comprehensive experimental data collection (89,388 data points in 266 datasets from 32 publications). The data cover wide ranges of equivalence ratio (φ = 0.38–2.67), diluent ratio (0.15–0.98), initial temperature (672–1886 K), and pressure (0.9–90 atm). The collection includes ignition delay time measurements in shock tubes and rapid compression machines, concentration determinations in shock tubes, jet-stirred reactors, flow reactors, and laminar burning velocity measurements. The experimental data were recorded in ReSpecTh Kinetics Data Format (RKD format) v.2.3 XML data files, which are available in the ReSpecTh site (http://respecth.hu). The standard deviations of the measurements were estimated using both the published experimental uncertainty and the scatter error of the datasets determined by code Minimal Spline Fit. Mechanism CRECK 2020 was found to be the best mechanism for n-butanol (biobutanol) combustion, while the mechanisms Sarathy 2014, Vasu 2013, and Yasunaga 2012 (in this order) were the best considering the experimental data for all isomers. A part of the simulations failed, and to improve the ratio of successful simulations, the code ThermCheck was created, which detects discontinuities and nonsmoothness of thermodynamic functions defined by NASA polynomials provided with the published mechanisms and corrects them by tuning their coefficients. Local sensitivity analysis applied to the experimental conditions was used to identify the most important reaction steps of the mechanism Sarathy 2014. The sensitivity analysis was extended to the adiabatic ignition of n-butanol–air mixtures by systematically changing the initial temperature and pressure. All butanol combustion mechanisms were also tested on a hydrogen combustion data collection, which indicated that some of them were inaccurate due to their inadequate hydrogen combustion reaction block. Suggestions were given for the improvement of the Sarathy 2014 mechanism.

A state-of-the-art chemical mechanism is introduced to properly describe chemical processes inside a harmonically excited spherical bubble placed in water and saturated with oxygen. The model uses up-to-date Arrhenius-constants, collision efficiency factors and takes into account the pressure-dependency of the reactions. Duplicated reactions are also applied, and the backward reactions rates are calculated via suitable thermodynamic equilibrium conditions. Our proposed reaction mechanism is compared to three other chemical models that are widely applied in sonochemistry and lack most of the aforementioned modelling issues. In the governing equations, only the reaction mechanisms are compared, all other parts of the models are identical. The chemical yields obtained by the different modelling techniques are taken at the maximum expansion of the bubble. A brief parameter study is made with different pressure amplitudes and driving frequencies at two equilibrium bubble sizes. The results show that due to the deficiencies of the former reaction mechanisms employed in the sonochemical literature, several orders of magnitude differences of the chemical yields can be observed. In addition, the trends along a control parameter can also have dissimilar characteristics that might lead to false optimal operating conditions. Consequently, an up-to-date and accurate chemical model is crucial to make qualitatively and quantitatively correct conclusions in sonochemistry.

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