Finite element simulation of fountain flow in injection molding

Abstract

Fountain flow is the phenomenon of deceleration and outward motion of fluid particles as they approach a slower moving interface. The use of a general purpose finite element program for the appropriate boundary conditions made possible the detailed flow description behind an advancing liquid front moving at constant speed inside two-dimensional channels and tubes. The results were qualitatively the same for both Newtonian and shear-thinning fluids.he term "fountain effect" was apparently FLOW GEOMETRY AND MATHEMATICAL MODELING Injection mold filling involves unsteady flow of polymer melts and solidification of the melt POLYMER ENGlNEERlNG AND SCENCE, MIPAPRIL, 7986, Vot. 26, No. 7

An Approximate Analytical Solution of Flow Fields at the Front of Poiseuille Flows

“…2. This prediction is qualitatively in agreement with the results of FEM calculations 7) and more elaborate calculations by using conformal mapping. 12,13) In principle, the constant F (or equivalently, the constant r 0 , see eq.…”

“…Indeed, FEM calculations and experiments suggest that the velocity fields at the flow front are not very sensitive to the constitutive equation. 7,8) Our rather simple theory may therefore capture a universal feature of the fluid dynamics of soft matters at the flow front. …”

“…The velocity fields ensure the mass conservation and force balance, except for the local force balance at the free surface. Previously, the velocity fields at the flow front and the shape of the free surface have been predicted by using elaborate calculations, such as FEM 7) and conformal mapping by an analytical function of infinite power series. With the velocity fields that are predicted by our theory, the local forces at the free surface do not balance for any choices of the length r 0 because of the approximate nature of our treatment.…”

“…The velocity fields at the flow front have been analyzed by using finite element methods (FEM) [7][8][9][10][11] and conformal mapping by using a complex function of an infinite power series. 12,13) These calculations predict that the velocity fields in the flowing direction decrease, while the velocity in the perpendicular direction increases, as one moves from the bulk to the free surface, in qualitative agreement with experiments.…”

The kinematics of fountain flow in mold‐filling

“…Huang (1978) attempted a detailed numerical solution using the marker-and-cell method, but his formulation violates symmetry near the interface. Silliman (1979), Lowndes (1980), andMavridis et al (1986a) have used the finite-element method to accurately calculate the flow field, but none of these has focused on the details of the deformation of material as it moves through the flow. Very recently Mavridis et al (1986b) did focus on this problem, but as will be shown later captured only part of the deformation.…”