On the Derivation of Polyurethane Kinetic Parameters Using Genetic Algorithms
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There is a lack of quantification for the kinetics mechanism of polyurethane thermal decomposition. The objective of this work is to derive a set of parameters for the kinetics of polyurethane valid for numerical models, with an emphasis on the conditions that pertain to smolder combustion (low-temperature, flameless form of combustion of a porous solid). Thermogravimetric analysis (TGA) is a testing procedure in which changes in the weight of a specimen are recorded as it is heated in air or in a controlled atmosphere such as nitrogen. TGA curves provide information regarding the different reactions of the solid material. The TGA experiments [Chao and Wang, J. Fire Sci. 19 (2001)] of polyurethane in inert atmosphere (100% N2) are used to study the pyrolysis paths of the foam and, in air atmosphere, to study the oxidation paths. TGA experiments for the inert atmosphere show two consecutive reaction-paths (Fig. 1a); pyrolysis of the foam and pyrolysis of the char. For air (Fig. 1b); results show three consecutive reaction-paths; the degradation (the output of the competitive reactions of oxidation and pyrolysis) of the foam, degradation of the char, and the last reaction is the secondary oxidation of char to ash. The temperature range for each reaction depends on the heating rate. The kinetics of polyurethane can be approximated by a few heterogeneous-reaction paths: pyrolysis and oxidations. A three-step chemical-reaction scheme for polyurethane foam was proposed by Ohlemiller [Progress Energy Combust. Sci. 11 (1985)]; foam pyrolysis, foam oxidation and char oxidation. The method consists of the integration of the solid weight time-change, assuming Arrhenius-type reactions rates, and comparison of experiments to extract the preexponential factors and the activation energies of each of the three reactions plus the yield coefficients for the solid products. For the three-step mechanism, the number of parameters to be optimized is on the order of 20 and, therefore, a multidimensional optimization technique, such as Genetic Algorithms (GA), is needed. GA is a robust and efficient optimization technique that imitates the principles of biological adaptation and evolution based upon the mechanics of the Darwinian survival-of-the-fittest theory. The procedure is as following; a population of parameter sets undergoes a process of selection such that only those giving the best results of every generation survive. Children of next generation are reproduced from the parameter-set pool of the parents, plus mutation. The fitness function used to measure the goodness of each parameter set is defined as the mean square error between the mathematical solution and the TGA data. The effect of different heating rates on the kinetic parameters is being studied.
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