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On the relevance of optimization methods for the systematic improvement of combustionreaction mechanisms
This work concerns the use of optimization methods to systematically improve the agreement of chemical kinetic combustion models with available experimental pro les. Under many circumstances, chemical kinetic parameters can neither be evaluated analytically from experiments nor accurately calculated through quantum chemistry methods. Thus, optimization methods relying on the numerical solution of the underlying di erential equations (accounting for the experiments) are needed [14]. The program package Kine t has been developed in C++. Based on the software Homrea, for the simulation of gas phase homogeneous systems, it allows the optimization/estimation of parameters against experimental data. It uses four optimization methods, namely an adaptive Random Search (RS), a Genetic Algorithm (GA) and CONDOR and BOBYQA, two optimization programs based on trust regions. Since in many cases several sub-optimal local minima exist, the three local optimization methods (RS, BOBYQA and CONDOR) were globalized through the introduction of random restarts in the parameter space. The classical analysis methods for reaction mechanisms (sensitivity analyses and reaction flow analysis) have proven to be insufficient for identifying the influential parameters suitable for the optimization. Thus, a new method, called "reaction signi cance analysis" has been developed. It shows the in uence of all parameters on the global distance between model prediction and experimental values. Only the parameters having a signi cant influence are candidates for the optimization. Box constraints on each parameter are often not sufficient if several parameters of the same reaction are optimized simultaneously. Consequently, penalty terms were implemented to put constraints on the whole reaction rate coefficient. Numerical tests were created to validate the optimization methods. They use the H2-O2 sub-mechanism of the GRI-mechanism [54]. Arti cial experimental pro les were generared using all initial values of the parameters. The most influential parameters were then identi ed and modi ed in such a way to introduce great discrepancies with the "experimental" pro les. One cause of the oscillations of the distance as a function of separately varied parameters was identi ed: it is related to the exponential decrease of concentrations due to self-ignition. Optimization problems based on six experiments with respectively three pro les were constructed. The optimization methods were rst validated for problems without self ignition. It was shown that they can reliably identify optimal parameter sets for problems involving respectively 6 pre-exponential factors, six pre-exponential factors located on bounds while using the penalty terms and 6 pre-exponential factors, temperature coeffi- cients and activation energies. The optimization methods were then validated for problems where a signi cant amount of oscillations occur. All methods were able to solve a problem involving seven parameters, all methods except one could solve a problem with 7 temperature coefficients and activation energies. All optimization methods failed for a complex problem involving seven pre-exponential factors, temperature coefficients and activation energies. The program package Kine t was then used to evaluate whether or not the GRI-mechanism is refuted by real experiments involving the pyrolysis of CH3 and C2H6 [47]. With the initial parameter values, considerable discrepancies exist whereas after the optimization good agreements were achieved. Mechanism reduction methods are often utilized for chemical kinetic optimization and can be relevant for problems pertaining to soot formation, always characterized by very large reaction mechanisms. As a consequence a C++ reduction program was developed during this work. The reliability of reduction approaches in the contex of parameter optimization was evaluated on an example involving the experiments of CH3 and C2H6 pyrolysis to which the GRI-mechanism was optimized [47]. The results indicate that reduction methods are only reliable for optimization problems where parameters are varied within narrow ranges. Finally, the program package Kine t was employed for an optimization problem involving a semi-detailed reaction mechanism accounting for the pyrolyses of the propargyl radical and 1,5-hexadyine [59]. Propargyl is a vital species for accurate simulations of PAH (PolyAromatic Hydrocarbons) and soot formation since it plays a crucial role for the formation of the fi rst aromatic ring.
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540 Chemie
540 Chemistry and allied sciences