Uncertainty and complexity in pyrolysis modelling
The use of numerical tools in fire safety engineering became usual nowadays and this tendency is expected to increase with the evolution of performance based design. Despite the constant development of fire modelling tools, the current state of the art is still not capable of predicting accurately solid ignition, flame spread or fire growth rate from first principles. The condensed phase, which plays an important role in these phenomena, has been a large research area since few decades, resulting in an improvement of its global understanding and in the development of numerical pyrolysis models including a large number of physical and chemical mechanisms. This growth of complexity in the models has been justified by the implicit assumption that models with a higher number of mechanisms should be more accurate. However, as direct consequence, the number of parameters required to perform a simulation increased significantly. The problem is when the uncertainty in the input parameters accumulates in the model output beyond a certain level. The global error induced by the parameters uncertainty balances the improvements obtained with the incorporation of new mechanisms, leading to the existence of an optimum of model complexity.While one of the first modelling tasks is to select the appropriate model to represent a physical phenomenon, this step is often subjective, and detailed justifications of the inclusion or exclusion of the different mechanisms are infrequent. The issue of how determining the most beneficial level of model complexity is becoming a major concern and this work presents a methodology to estimate the affordable level of complexity for polymer pyrolysis modelling prior ignition. The study is performed using PolyMethylMethAcrylate (PMMA) which is a reference material in fire dynamics due to the large number of studies available on its pyrolysis behaviour. The methodology employed is based on a combination of sensitivity and uncertainty analyses.In the first chapter, the minimum level of complexity required to explain the delay times to ignition of black PMMA samples at high heat flux levels is obtained by exploring one by one the effect on the condensed phase of several mechanisms. It is found that the experimental results cannot be explained without considering the in-depth radiation absorption mechanism. In the second chapter, a large literature review of the variability associated with the main parameters encountered in pyrolysis models is performed in order to establish the current level of confidence associated with the predictions using simple uncertainty analyses. In the third chapter, a detailed analysis of the governing parameters (parametric sensitivity) is performed on the model obtained in chapter 1 to predict the delay time to ignition. Using the ranges obtained in chapter 2 for the input parameters, a detailed uncertainty analysis is performed revealing a large spread of the numerical predictions outside the experimental uncertainty. While several parameters, including the attenuation coefficient (from the in-depth radiation absorption mechanism), present large sensitivity, only a few are responsible for the large spread observed. The parameter uncertainty is shown as the limiting step in the prediction of solid ignition. In the fourth chapter, a new methodology is developed in order to investigate the predominant mechanisms for the prediction of the transient pyrolysis behaviour of clear PMMA (no ignition). This approach, which corresponds to a mechanism sensitivity, consists of applying step-by-step assumptions to the most complex model used in the literature to model non-charring polymer pyrolysis behaviour. This study reveals the relatively high importance of the heat transfer mechanisms, including the process of in-depth radiation. In the fifth chapter, an investigation of the uncertainty related to the calibration of pyrolysis models by inverse modelling is performed using several levels of model complexity. Inverse modelling couples the experimental data to the model equations and this dependency is often ignored. Varying the model complexity, this study reveals the presence of compensation effects between the different mechanisms. The phenomenon grows in importance with model complexity leading to unrealistic values for the calibrated parameters.From the performed sensitivity and uncertainty analyses, the mechanism of in-depth absorption appeared critical for some applications. In the sixth chapter, an experimental investigation on specific conditions impacting the sensitivity of this mechanism shows its large dependency on the heat source emission wavelength when comparing the two heat sources of the most used pyrolysis test apparatuses in fire safety engineering. More fundamental investigations presented in the seventh chapter enabled to quantify this dependency that needs to be considered for modelling or experimental analyses. The impact of the heat source on the radiation absorption (depth and magnitude) is shown to be predictable thanks to the detailed measurements of the attenuation coefficient of PMMA and the emissive power of the heat sources. The global uncertainty associated with the input parameters, extracted either from independent studies or by inverse modelling, appears as a limiting step in the improvement of pyrolysis modelling when a high level of complexity is implemented. A combination of numerical (sensitivity and uncertainty) analyses and experimental studies is required before increasing the level of complexity of a pyrolysis model.
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