Influence of injection gate definition on the flow-front approximation in numerical simulations of mold-filling processes

Flow through porous media has been used to model resin impregnation in composites manufacturing processes such as resin transfer molding. Many numerical schemes have been used to explore the efficiency and accuracy in description of the movement of the liquid front when it is introduced through injection gates into a mold containing stationary and compacted fibrous porous media. In all numerical schemes, injection gates are modelled with a single node. Mathematically, a single node definition for a finite radius injection gate imparts a singularity. In this paper, an approach to avoid this singularity by modelling the injection gate with more than one node is presented. An analytical solution relating the fill time to the injection gate radius is developed for a constant pressure injection from a spherical injection gate into an isotropic media. A new parameter ‘mesh density level’, defined as the ratio of the injection radius to the element size, is used to investigate the accuracy and the convergence of the numerical results. It is shown that the numerical results converge when the mesh density level is increased. The accuracy of the results depends on the ratio of the flow-front radius to the injection gate radius as well as on the mesh density level. In many situations, a spherical injection gate may not represent the correct physics and model simplification may be necessary. The impact of such simplifications is also quantified. The systematic analysis presented in this paper should prove useful to the modeller in taking the decision whether to select the proper, geometric definition for the injection gate to obtain accurate results or to define the injection gate using a single node and be aware of the errors introduced due to the singularity.