An enthalpy-temperature hybrid method for solving phase-change problems and its application to polymer pyrolysis and ignition

A numerical approach based on the enthalpy method is proposed for solving generalized phase-change problems. The method is applied to predict pyrolysis and ignition of polymeric combustible materials. In contrast to the traditional approach, here both enthalpy and temperature are treated as independent variables, and the conservation equations are solved simultaneously in conjunction with the constitutive equations. Also, the formulation of the constitutive equations for the phase change is not necessarily the same for all of the possible phases, but can be chosen independently according to the characteristics of the physical problem and the requirements of the numerical analysis of each respective phase. Thus with this new approach, which we refer to as the enthalpy-temperature hybrid method the enthalpy method is applicable to the generalized phase-change problems regardless of the form of the constitutive equations. The proposed method is first applied to a one-dimensional classical freezing problem for verification. It is found that the numerical results for the temperature history and the position of the phase-change interface agree well with the analytic solution existing in the literature. The method is then applied to the numerical simulation of the pyrolysis and ignition of a composite material with a polymer as the matrix and fibreglass as the filling material. Three models of oxygen distribution in the molten layer are considered to explore the melting and oxygen effects on the polymer pyrolysis. Numerical calculation shows that high oxygen concentrations in the molten layer enhance the pyrolysis reaction, resulting in a larger amount of pyrolysate, but in lower surface temperatures of the sample. It also shows that the distribution of oxygen in the molten layer has a strong effect on the pyrolysate rate, and therefore on ignition and combustion of the polymers. Comparison with available experimental data indicates that a model of oxygen distribution in the molten layer that is limited to a thin layer near the surface best describes the ignition process for a homogeneously blended polypropylene/fibreglass composite.