Efficient numerical methods for the optimization of large kinetic reaction mechanisms
Simret Kidane Goitom, Máté Papp, Márton Kovács, Tibor Nagy, István Gy. Zsély, Tamás Turányi, László Pál
Combustion Theory Modelling, 26, 1071-1097 (2022)

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.
Identification of homogeneous chemical kinetic regimes of methane-air ignitionÉva Valkó, Máté Papp, Peng Zhang, Tamás Turányi
Proc. Combust. Inst., 39, available online (2023)

Sensitivity
analysis results for ignition delay time (IDT) may be very different
depending on the initial temperature, pressure and equivalence ratio φ,
but similar in some regions of these variables. This phenomenon was
investigated systematically by carrying out ignition simulations and
local sensitivity calculations of methane−air mixtures using the
Aramco-II-2016 mechanism at 14,417 combinations of initial temperature
(changed between 500 and 3000 K), initial pressure (0.05−500 atm) and φ
(0.05−8.0) values. The cluster analysis of the sensitivity vectors
identified five large kinetically homogeneous regions. Each region has
well defined borders in the (T, p φ) space and can be characterized by
different sets of important reactions. The related kinetic scheme is
very different in each region. Regions 1 and 2 are dominated by
catalytic cycles based on species CH3O2/CH3O2H and HO2/H2O2/CH3O,
respectively. In regions 3, 4, and 5 the H atoms are converted to CH3 in
an identical chain branching sequence, but the back conversion is via
three different routes. Literature experimental data on the IDTs of
methane−air mixtures were sorted according to these five regions.
Regions 1 to 5 contain 214, 328, 3, 0, and 237 experimental data points,
respectively. In regions 1, 2 and 5 the data points are well reproduced
by the Aramco-II-2016 mechanism, but little or no experimental
information is available about kinetic regions 3 and 4. Further
experimental exploration of the ignition of methane−air mixtures may aim
the study of these regions. A similar approach can be used for the
characterization of other combustion systems and sorting the related
experimental data.
A novel active parameter selection strategy for the efficient optimization of combustion mechanismsMárton Kovács, Máté Papp, Tamás Turányi, Tibor Nagy
Proc. Combust. Inst., 39, available online (2023)

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.
Comparison and analysis of butanol combustion mechanisms
Martin Bolla, Máté Papp, Carsten Olm, Hannes Böttler, Tibor Nagy, István Gy. Zsély, Tamás Turányi
Energy&Fuels, 36, 11154–11176 (2022)

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.
The importance of chemical mechanisms in sonochemical modelling
Cs. Kalmár, T. Turányi, I. Gy. Zsély, M. Papp, F. Hegedűs
Ultrasonics Sonochemistry, 83, 105925 (2022)

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.
Comparison of methane combustion mechanisms using laminar burning velocity measurements
Peng Zhang, István Gy. Zsély, Máté Papp, Tibor Nagy,
Tamás Turányi
Combust Flame, 238, 111867 (2022)
Publication Date: December 22, 2021
Large
amount of experimental data for laminar burning velocity (LBV)
measurements of methane (+H2/CO) − oxygen − diluent mixtures (5500 data
points in 646 datasets) covering wide ranges of equivalence ratio,
diluent ratio, cold side temperature and pressure were collected from
111 publications. The diluents included N2 , H2O, CO2 , Ar and He. The
data files are available on the ReSpecTh site (http://respecth.hu).
Performances of 12 methane combustion mechanisms on reproducing these
LBV
measurements were analyzed according to experiment types and
conditions. Most mechanisms could predict well the LBVs for
stoichiometric and fuel-lean mixtures and for diluent ratios higher than
60%. The performances of several mechanisms were relatively poor at
other conditions. Focusing on the operating conditions of natural gas
engines, we recommend the application of mechanisms FFCM-I-2016,
SanDiego-2014, and NUIG1.1-2021 for engine simulations. Mechanisms
Aramco-II-2016, Konnov-2009, Caltech-2015 and Glarborg-2018 have the
lowest average errors for the reproduction of all available methane LBV
data.
Using local sensitivity analysis on the most accurate
mechanisms, we identified 29 important elementary reactions, which,
however, were not present in all the 12 mechanisms. We also collected
large amount of directly measured and theoretically calculated rate
coefficients for these reactions and compared them with the rate
coefficients used in the 12 mechanisms. Reactions found important in any
of the Aramco-II-2016, Konnov-2009 and Glarborg-2018 mechanisms, but
missing from the Aramco-II-2016, Konnov-2009, Glarborg-2018,
Caltech-2015, FFCM-I-2016 and NUIG1.1-2021 mechanisms were added to
these six mech-
anisms to investigate if the extended mechanism
performs better than the original one. Some of the extended mechanisms
became the best performing mechanisms.
Comparison of Methane Combustion Mechanisms Using Shock Tube and Rapid Compression Machine Ignition Delay Time MeasurementsP. Zhang, I. Gy. Zsély, V. Samu, T. Nagy, T. Turányi
Energy Fuels,
35, 12329–12351 (2021)
Publication Date: July 9, 2021
https://doi.org/10.1021/acs.energyfuels.0c04277-
We intended to collect all published experimental data on the ignition methane - oxygen mixtures, with possible added fuel: H2 and CO; possible diluents: N2, Ar, He). These included shock tube and RCM data (5521 data points in 643 datasets from 76 publications), covering wide ranges of temperature T, pressure p, equivalence ratio φ, and diluent concentration. Thirteen recent methane combustion mechanisms were tested against these experimental data.
Design of combustion experiments using differential entropyÉva Valkó, Máté Papp, Márton Kovács, Tamás Varga,
István Gy. Zsély, Tibor Nagy, Tamás Turányi
Combustion Theory and Modelling,
26, 67-90 (2022)
Publication Date: November 9, 2021
https://doi.org/10.1080/13647830.2021.1992506-

The
aim of several combustion experiments is the determination of the rate
coefficients of important elementary reactions. Sheen and Manion (J.
Phys. Chem. A, 118 (2014) 4929–4941) suggested a method for the design
of shock tube experiments based on differential entropy. Their method
was modified and extended in this work. In the extended method, both the
experimental and residual errors of the measurements are considered at
the calculation of the posterior uncertainty of the determined rate
parameters, the differential entropy matrix is calculated in an
analytical way and the net information flux value is calculated for each
suggested experimental point. In an iterative procedure, all
investigated experimental points with negative net information flux
values are discarded and the remaining experimental conditions are
recommended for the measurements. The most valuable candidate
experimental points can be determined based on the net information flux
values.