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

Abstract

In this work, an enthalpy-temperature hybrid method is proposed for the numerical solution of generalized phase change problems, and applied to the prediction of polymer pyrolysis and ignition. The basic idea of this method is to treat both enthalpy and temperature as independent variables, and to solve the conservation equations and the constitutive equations (enthalpy-temperature relations) simultaneously. The formula of the enthalpy-temperature relations are not necessary the same for different phases, but can be chosen independently according to the characteristics of physical problems and the convenience of numerical analysis for each respective phase. Therefore this method applies to the problems regardless of the form of the constitutive equations. It overcomes the difficulty or even impossibility encountered in the traditional enthalpy-temperature method, of which either enthalpy or temperature must be consistently and explicitly expressed as a function of the other over all the phases. The method is first applied to a one-dimensional classical freezing problem for method demonstration and verification. It is found that the numerical results of temperature history and the position of 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 fiberglass 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 distribution of oxygen in the molten layer has a strong effect on pyrolysate rate, and therefore on ignition and combustion of 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 s urface describes best the ignition process for a homogeneously blended polypropylene/fiberglass composite.1

Generalized pyrolysis model for combustible solids

“…A model that includes melting has been developed and used to successfully predict the time to ignition of a polypropylene/glass composite [192]. More recently, polymer melt flow behavior in laboratory-scale experiments has been modeled with encouraging results [190].…”

Kinetic modeling of polypropylene thermal oxidation during its processing by rotational molding

“…45 This method does not need to use a solid/liquid interface and thus, to calculate specific boundary conditions at this interface. Moreover, it takes directly into account the local changes in melting temperature in a particles based material.…”

Thermal transfer simulation regarding the rotational moulding of polyamide 11

“…This method makes it possible to use only one equation to describe thermal phenomenon in both two phases (liquid polymer and solid powder), and makes it possible, thus, to free from the calculation of boundary conditions on liquid/solid interface. It is named enthalpy method [15,16]. If we leave the assumption that melting or crystallization does not occur at a constant temperature, which is more realistic for a particulate solid, enthalpy evolution according to temperature can be schematized as on …”

“…This study is divided into two main parts, the first one is focused on the rotational moulding of polyamide 11, and the second one is devoted to simulation of thermal transfer phenomenon in rotational moulding and modelling of phase changes by enthalpy method [14][15][16] coupled to Ozawa model [17]. The results obtained allow us to validate the theoretical approach adopted by the experimentation and to observe that the two shutters (theoretical and experimental) are closely dependant.…”