Fountain flow revisited: The effect of various fluid mechanics parameters

Abstract

AbstractNumerical 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 laminar, isothermal, steady‐state conditions for Newtonian fluids. The effects of inertia, gravity, surface tension, compressibility, slip at the wall, and pressure dependence of the viscosity are all considered individually in parametric studies covering a wide range of the relevant parameters. These results extend previous ones regarding the shape of the front, and in particular the centerline front position, as a function of the dimensionless parameters. The pressures from the simulations have been used to compute the excess pressure losses in the system (front pressure correction or exit correction). Inertia leads to highly extended front positions relative to the inertialess Newtonian values, which are 0.895 for the planar case and 0.835 for the axisymmetric one. Gravity acting in the direction of flow shows the same effect, while gravity opposing the flow gives a reduced bulge of the fountain. Surface tension, slip at the wall, and compressibility, all decrease the shape of the front. Pressure‐dependence of the viscosity leads to increased front position as a corresponding dimensionless parameter goes from zero (no effect) to higher values of the pressure‐shift factor. The exit correction increases monotonically with inertia, compressibility, and gravity, while it decreases monotonically with slip and pressure‐dependence of the viscosity. Contour plots of the primary variables (velocity‐pressure) show interesting trends compared with the base case (zero values of the dimensionless parameters and of surface tension). © 2009 American Institute of Chemical Engineers AIChE J, 2010