Smoldering combustion and transition to flaming has been studied both computationally and experimentally in the past, but no theoretical studies have examined smoldering combustion followed by a spontaneous transition to flaming in two-dimensions. In this dissertation, a numerical transport model for polyurethane foam to simulate smoldering combustion and transition to flaming is developed using Gpyro, a generalized pyrolysis model for decomposing solid materials, and an eight-step reduced reaction mechanism for polyurethane foam. Gpyro includes the effects of heat transfer, mass transfer, momentum transfer, and gas phase and condensed phase chemical reactions and is capable of modeling in zero, one and two-dimensions. The spontaneous transition from smoldering to flaming numerical transport model is capable of simulating complex physical processes that have been observed experimentally and offers additional insight into the spontaneous transition from smoldering to flaming process.;The reduced reaction mechanism contains eight reactions: seven heterogeneous reactions and one homogeneous gas phase reaction. In the development of the reaction mechanism, the heterogeneous portion is developed first before adding the gas phase reaction. The seven heterogeneous reactions were developed using optimization techniques and ThermoGravimetric Analysis data. The heats of reaction were fit using one-dimensional conservation equations assuming thermal equilibrium between the condensed phase and the gas phase to one-dimensional forward smolder microgravity combustion data. The resulting smolder model was then used to study the two-dimensionality of a forward propagating smolder wave assuming thermal equilibrium. Model results show a two-dimensional structure in the temperature, species, and reaction profiles that agree qualitatively with experimental observations.;Next, the numerical transport model was expanded to be a generalized smolder model, capable of simulating both forward and opposed smolder combustion. Modeling both forward and opposed smolder is crucial to predict real smoldering scenarios where both opposed and forward smolder occur at the same time. Furthermore in transition to flaming experiments, experimental observations suggest that a smolder wave propagates in both a forward and an opposed manner. Using the generalized smolder model, a comparison of model formulations with and without assuming thermal equilibrium was performed. Assuming thermal equilibrium is indeed a good approximation for modeling both forward and opposed smoldering combustion.;To simulate transition to flaming, a global gas phase reaction was added to the generalized smolder model and a two-temperature model formulation was applied. The spontaneous transition from smoldering to flaming numerical transport model is the first attempt to use a two-temperature model with a global gas phase reaction to simulate transition to flaming. Transition to flaming in normal gravity is examined for forced forward smolder combustion as a function of an externally applied heat flux, the oxygen mole fraction of a forced gas flow, and the duct flow velocity. Details for a base case of the temperature, species, reaction rates, and porosity profiles are reported. A comparison to previously obtained experimental data is discussed. It is shown that the spontaneous transition from smoldering to flaming numerical transport model is capable of predicting experimental results well and provides further insight on the mechanisms leading to the transition from smoldering to flaming. Further comparison to a range of experimental data varying the externally applied heat flux, the oxygen mole fraction of a forced gas flow, and the duct flow velocity is provided. The model is capable of predicting a range of experimental conditions. A discussion of a non-transition to flaming simulation is presented and compared to the base case results. The parametric study shows that model parameters are sensitive to changes, however significant changes to transition to flaming time was not observed.;The developed spontaneous transition from smoldering to flaming numerical transport model provides an important tool in the simulation and prediction of a problem that is of great importance in the onset of unwanted fires. Furthermore, the procedure followed for model development can be applied to additional materials to further study transition to flaming.
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