This study presents computational analysis of the complex dynamics observed in chemically blown polyurethane foams during reaction injection molding process. The mathematical formulation introduces an experimentally motivated non-divergence free setup for the continuity equations which reflects the self expanding behaviour observed in the physical system. The foam growth phenomena which is normally initiated by adequate pre-mixing of necessary reactant polymers, leading to an exothermic polymerization reaction, bubble nucleation, and gas formation, is captured numerically. We assume the dependence of material viscosity on the degree of cure/polymerization, gas volume fraction, and temperature as well as nondependence of mixture density on pressure. The set of unsteady nonlinear coupled partial differential equations describing the dynamics of the system are solved numerically for state variables using finite volume techniques such that the front of the flow is tracked w ith high resolution interface capturing schemes. Graphical representation of the foam volume fraction, evolution of foam heights, and temperature distributions is presented. Results from our simulations are validated with experimental data. These results show good quantitative agreement with observations from experiments

This paper computationally investigates heterogeneity in the distribution of foam fraction in chemically expanding blown polyurethane foam. The experimentally observed disparity in the volumes of expanded foam when an equal mass of the foaming mixture was injected into tubes of different dimensions motivated this study. To understand this phenomenon, attributed to local variations in the thermal and rheological properties of the expanding system, we explore available data from free-rise foam-expansion experiments in different geometries. Inspired by the mathematical framework for the microstructure modelling of bubble growth in viscous liquids, we study the reacting mixture as a continuum and formulate appropriate mathematical models that account for spatial inhomogeneity in the foam-expansion process. The nonlinear coupled system of partial differential equations governing flow was numerically solved using finite-volume techniques, and the associated results are presented and discussed with graphical illustrations. The proximity of the foaming-mixture core to the external environment and the thickness of a thermal-diffusion layer formed near the bounding geometry was seen to influence the distribution of the foam fraction. Our simulations showed an average spatial variation of about 1.1% in the distribution of solid foam fraction from the walls to the core, as verified with data from μ CT scan analysis of the expanded foam. This also reflects the distribution of void fraction in the foam matrix. The models were validated with experimental data, and our results favourably compared with the experiment observations.

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