Fountain flow of pseudoplastic and viscoplastic fluids

Numerical simulations have been undertaken for the benchmark problem of fountain flow present in injection-mold filling. The Finite Element Method (FEM) is used to provide numerical results for both cases of planar and axisymmetric domains under steady-state conditions. The Herschel-Bulkley model of viscoplasticity is used, which reduces with appropriate modifications to the Bingham, power-law and Newtonian models. The present results extend previous ones regarding the shape of the front, which is essential in correctly capturing the flow field. In particular the centreline front position is found as a function of the dimensionless power-law index (in the case of pseudoplasticity) and the dimensionless yield stress (in the case of viscoplasticity). The pressures from the simulations have been used to compute the excess pressure losses in the system (front pressure correction or exit correction). Both shear-thinning and shear-thickening lead to more extended front positions relative to the Newtonian values, which are 0.895 for the planar case and 0.835 for the axisymmetric one. Viscoplasticity leads also to more extended front positions as the dimensionless yield stress goes from zero (Newtonian behaviour) to higher values of the yield stress. In both cases of non-Newtonian behaviour, the front tends to follow the development of the fully developed Poiseuille velocity profile, which tends towards a plug-like profile at the extreme cases of non-Newtonianness. The front pressure (exit) correction increases monotonically with the decrease in the power-law index and the increase in the dimensionless yield stress.