OptiSMOKE++: A toolbox for optimization of chemical kinetic mechanisms☆,☆☆
Introduction
The steady increase in computational power enables us to describe the behavior of complex combustion processes with more detail in Computational Fluid Dynamics (CFD) simulations, thus allowing us to more accurately predict how changes to the system would affect critical parameters, such as emissions, maximum temperature, efficiency, etc. This is crucial in the development of novel technologies, as a more traditional trial-and-error approach for many cases quickly becomes unfeasible, due to both time consumption and costs. The complexity of a combustion simulation can be expressed in many ways, i.e. geometric, flow modeling, chemical mechanism complexity, etc. Only in recent years it became feasible to account for more detailed chemical mechanisms in large scale simulations. This allows to improve the prediction of intermediates and final products of the combustion process significantly, as well as to enhance our fundamental understanding of the complex chemical process occurring in combustion.
A chemical kinetic mechanism is built up from species, thermodynamic and transport data and elementary reactions [1]. Each chemical reaction consists of rate constants (), which in turn can be expressed as a function of temperature with some parameters (the pre-exponential factor , the temperature exponent , and the activation energy ) according to the modified Arrhenius’ equation (, where is the temperature and is the ideal gas constant). The definition of these parameters for each reaction in a kinetic mechanism is not straightforward, as they can be based on experimental data and theoretical calculations carried out at different levels of theory [2]. Thus, there is an inherent uncertainty for each of these parameters, and as the size of the mechanism grows, also the number of uncertain parameters increases.
In order to cope with the large amount of uncertain parameters, Uncertainty Quantification (UQ) and Optimization have been increasingly adopted in the process of chemical mechanism development [3]. The widely used GRI mechanisms [4], [5], [6] are based on the Bound-To-Bound Data-Collaboration (B2B-DC) [7], [8], [9], [10] optimization methodology, where the optimal combination of the kinetic parameters was determined minimizing the distance between measurements and predictions, using surrogate modeling for the selected quantities of interest (ignition delay times, species profiles, and flame speed measurements). Their performance for conventional combustion of natural gas, together with the relatively small size, proved to be an effective combination. In the development of the GRI mechanisms [4], [5], [6], especially the pre-exponential factors for the most impactful reactions were optimized.
Wang and co-workers later developed the Method of Uncertainty Minimization using Polynomial Chaos Expansion (MUM-PCE) [11], which again utilizes surrogate modeling for representing the model responses. Then by finding the least-squares point within the parameter space, they determined the optimal mechanism. They used this approach for several different fuels [12], [13], [14], and also to develop the Foundational Fuel Chemistry Model (FFCM) [15] for small hydrocarbon fuels. However, in these works [12], [13], [14], [15], [16] they only considered the pre-exponential factors and some third body efficiencies as active parameters. A species is considered as a third body if it stays inert though the reaction process, and only transfers/removes energy from the process. Only in a recent study [17], they applied the MUM-PCE approach considering the joint probability distribution of the pre-exponential factors and the activation energies of some reactions.
Cai and Pitsch [18], [19] also used the MUM-PCE [11] methodology, but for the optimization of rate rules instead of specific reactions. Later, they also applied a Bayesian approach for the optimization of rate rules for alkanes [20]. Rate rules are used to derive kinetic parameters for reactions that behave in a similar way. As the determination of one rate rule directly inflicts changes to many reactions, it is a very efficient approach for developing kinetic mechanisms for fuels with larger molecules. Recently, they combined this with the optimization of thermochemical properties in the works of Vom Lehn et al. [21], [22], [23], showing a large impact of the thermochemical parameters at especially intermediate temperatures. However, in all these works [18], [19], [20], [21], [22], [23], only the pre-exponential factors for the rate rules were considered for the optimization.
The works of Turànyi and co-workers [24], [25], [26] have also been focused on the optimization of kinetic mechanisms, but, differently from [4], [5], [6], [7], [8], [9], [10], [12], [13], [14], [15], [16], [17], [18], [19], [20], they included all three Arrhenius parameters in the optimization, i.e. , and , as well as third body collision efficiencies. The approach used in [24], [25], [26] is based on using both direct and indirect experimental data, where direct experimental values refer to experimental data of the rate constant , while the indirect targets consist of concentration profiles, ignition delay times, and laminar burning velocities [24], [25], [26]. For some of these targets, they also used response surfaces to predict the effect of changing the kinetic parameters.
The approach based on the use of response surfaces can be highly efficient for mechanism optimization, but, as mentioned by Sikalo et al. [27], the nature of the objective function in mechanism optimization can be highly complex, since it consists of many local minima and maxima. Therefore, Sikalo et al. [27] suggest to use the Genetic Algorithm (GA) global optimization approach, which has been proven to perform very well in these conditions [27], [28], [29]. Indeed, Elliott and co-workers have applied GAs for optimizing kinetic mechanism for many different fuels [29], [30], [31], [32].
The use of heuristic optimization strategies for solving the problem at hand, i.e. kinetic mechanism optimization, presents an ideal application, and the present work focuses on the development of a flexible toolbox for the optimization of chemical mechanisms. This toolbox, named OptiSMOKE++, enables the user to optimize mechanisms performances handling numerous kinetic parameters, under uncertainty. The optimization targets can be experiments from many ideal reactors, considering species concentrations, Ignition Delay Times (IDT) or Laminar Flame Speeds (LFS). The toolbox relies on the OpenSMOKE++ [33] framework for the numerical simulations of combustion processes, while the DAKOTA toolkit [34] is used for the optimization. DAKOTA contains many different optimization algorithms, and the user is free to choose any of them. These and more features of OptiSMOKE++ are demonstrated in this work.
Section snippets
Code description
The following section describes the specific functionalities of the OptiSMOKE++ toolbox, together with some details about the two different codes OpenSMOKE++ and DAKOTA. An overall view of the OptiSMOKE++ workflow is depicted in Fig. 1. The code starts by reading the specified input file, then changes the parameters in the kinetic scheme. The code then double-checks if the rate parameters are within the uncertainty bounds (see Section 2.5), using a non-linear constraint, i.e.
Test cases
In this section, some test cases will be presented, which illustrates the functionality of the OptiSMOKE++ toolbox. The different procedures, and the cases, were not necessarily chosen based on efficiency or any specific interests, instead they were chosen in order to show the different features available in the OptiSMOKE++ toolbox.
Conclusions
This paper describes the different features of OptiSMOKE++, a toolbox that couples the optimization toolkit DAKOTA and OpenSMOKE++, a framework for solving reacting systems with detailed kinetics. OptiSMOKE++ can be used to optimize kinetic mechanisms with respect to specified experimental targets, to improve the performance of the kinetic mechanism. The toolbox consists of different features, which can be summarized as:
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possibility to use experimental targets from different facilities,
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This work has been carried out with the aid of the Short Term Scientific Mission Program of SMARTCATs COST Action (CM1404, www.smartcats.eu), supported by COST, Belgium (European Cooperation in Science and Technology, www.cost.eu) as well as it has received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie grant agreement No 643134, and from the European Research Council (ERC) under the European Union’s Horizon 2020 research and
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The review of this paper was arranged by Prof. Stephan Fritzsche.
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This paper and its associated computer program are available via the Computer Physics Communication homepage on ScienceDirect (http://www.sciencedirect.com/science/journal/00104655)