A level set method to study foam processing: a validation study

SUMMARY We have developed a production-level foam processing computational model suitable for predicting the self-expansion of foam in complex geometries. The model is based on a finite element representation of the equations of motion, with the movement of the free surface represented using the level set method. An empirically based time-dependent and temperature-dependent density model is used to encapsulate the complex physics of foam nucleation and growth in a numerically tractable manner. The evolving density drives the dynamics of foam self-expansion. This continuum-level model uses a homogenized description of foam, which does not include the gas explicitly, but allows varying local fields, such as temperature and gas volume fraction, and material models. In addition, material models vary with the location of the level set interface, taking properties of the displaced air phase in the negative level set region and the foam in the positive region. The level set zero describes the location of the interface, where surface forces are applied using the continuous surface force treatment. The variation from foam to gas properties is handled with a diffuse interface method using a smooth Heaviside function and equation averaging. Material model development was guided and populated by careful experiments. Results from the model are compared with temperature-instrumented flow visualization experiments giving the location of the foam front as a function of time for a physically blown, epoxy foam. Good qualitative agreement is seen between simulations and experiments, although some of the subtleties of the filling process are lost to the model. Published 2011. This article is a US Government work and is in the public domain in the USA.