PUFoam : A novel open-source CFD solver for the simulation of polyurethane foams

Abstract

In this work a transient three-dimensional mathematical model is formulated and validated for the simulation of polyurethane (PU) foams. The model is based on computational fluid dynamics (CFD) and is coupled with a population balance equation (PBE) to describe the evolution of the gas bubbles/cells within the PU foam. The front face of the expanding foam is monitored on the basis of the volume-of-fluid (VOF) method using a compressible solver available in OpenFOAM version 3.0.1. The solver is additionally supplemented to include the PBE, solved with the quadrature method of moments (QMOM), the polymerization kinetics, an adequate rheological model and a simple model for the foam thermal conductivity. The new solver is labelled as PUFoam and is, for the first time in this work, validated for 12 different mixing-cup experiments. Comparison of the time evolution of the predicted and experimentally measured density and temperature of the PU foam shows the potentials and limitations of the approach.Program summaryProgram Title: PUFoamProgram Files doi:http://dx.doi.org/10.17632/62ggzx623g.1Licensing provisions: GNU General Public License 3 (GPL)Programming language: C++.Supplementary material: In order to test the main solver all the required input files have been provided within the testCase directory. This could be either directly used or modified according to user’s needs.Nature of problem: The CFD solver developed through this research work provides a numerical mean for the simulation of polyurethane foam. The problem includes a reacting multi-phase system in which the liquid mixture expands due to the polymerization phenomenon and the presence of different additives. In that, the gas bubbles nuclei within the reacting liquid mixture start to grow owing to the diffusion of gases produced due to the chemical reactions. Further, industrial applications such as mould-filling seek for capturing the foam front face and the evolution of its physical and thermal properties during the foaming process. Thus, the solver shall facilitate the evolution of gas bubbles via a population balance equation, capturing the foam interface using a volume-of-fluid method, and eventually predicts the foam characteristics.Solution method: Conservation equations for mass and momentum as well as phase fraction equations are solved using the standard finite volume method. The indicator function (i.e., the phase fraction equation in this case) is solved for the primary phase taking into account the density variation of the foam which is implemented as the compressibility effect. Additional transport equations are also solved to yield the progress of the polymerization process through the conversions of water, isocyanate, and the amount of gases produced. Finally, the evolution of the cell size distribution inside the foam phase is evaluated by using a population balance equation. The solution of PBE inside the CFD code is performed by transforming the problem into a set of transport equations for the moments of bubble/cell size distribution. The quadrature method of moments (QMOM) is applied to approximate the right hand side of moments equations which represent the growth and coalescence of bubbles.External routines/libraries: OpenFOAM® (version 3.0.1) (http://www.openfoam.org)Restrictions: Due to lack of available experimentally-based or analytical models, the current version of the solver supports two different blowing agents including n-pentane and R-11. Further, the growth rate of the bubbles is assumed to be diffusion-controlled and its rate associated with the concentration gradient around the bubbles. This restriction will be relaxed in near future by adopting a detailed model for the bubble growth rate. It must be also reminded that the solver is compiled with OpenFOAM version 3.0.1 and compiling it with other versions might require additional efforts.