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We have developed a numerical method for unsteady three-dimensional (3D) simulation of rigid polyurethane (PU) foaming flow in a refrigerator cabinet in this study. The governing equation for the compressible foaming flow is approximated with the Navier-Stokes equation, which means the foaming flow is assumed to be Newtonian. Numerical methods of simulation for unsteady compressible PU foaming flow with a free surface have been designed using a finite volume method (FVM) and the semi-implicit method for pressure-linked equations (SIMPLE) scheme as a pressure correction method. The formulation of numerical methods is developed on the basis of hexahedral meshes. Air in a refrigerator cabinet is neglected in the numerical method, and the free surface is traced with the volume of fluid (VOF) method. Viscosity and density of foam are assumed to be uniform in space and time-dependent, which are obtained with experimental methods. Results of numerical simulation for filling pattern and a finally filled position have been compared with the experimental results in a plate mold and a simple refrigerator cabinet. Simulation results of foaming fronts and finally filled position show good agreement with the experimental results. Numerical simulation of PU foaming flow is a useful tool to design a new refrigerator model and predict foam quality related to distance of foaming flow, air trapping, and location of finally filled position.

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