Mold Filling Simulations Using the Control Volume Approach

4 MOLD FILLING SIMULATIONS USING THE CONTROL VOLUME APPROACH 

1 Two-Dimensional Mold Filling Simulation of Non-Planar Parts (2.5D Model) 

Based on the flow analysis network, Wang etal., [18] and Osswald [11] developed the finite element/control volume appproach (FEM-CVA) for injection and compression molding, respectively. Similar to FAN, FEM-CVA assigns a fill factor to every nodal point or nodal control volume. The nodal control volumes are constructed by connecting element centroids to element midsides, as shown in Fig. 9.28. 

The boundary conditions are defined in the same way as with the flow analysis network. The nodes whose control volumes are empty or partially filled are assigned a zero pressure, and the gate nodes are either assigned an injection pressure or an injection volume flow rate. Just as is the case with flow analysis network, a mass balance about each nodal control volume will lead to a linear set of algebraic equations, identical to the set finite element formulation of Poisson s or Laplace s equation. The mass balance (volume balance for incompressible fluids) is given by 

Once the boundary conditions are applied, the pressure field can be solved using the appropriate matrix solving routines. Note that for mold filling problems, there is a natural boundary condition that satisfies no flow across mold boundaries or shear edges, dp/dn = 0. Once the pressure field has been solved, it is used to perform a mass balance using eqn. (9.144) or (9.145). Once the flowrates across nodal control volume boundaries are known, a simulation program updates the nodal control volume fill factors using 

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Based on the control volume approach and using the three-dimensional finite element formulations for heat conduction with convection and momentum balance for non-Newtonian fluids presented earlier, Turng and Kim [10] and [17] developed a three-dimensional mold filling simulation using 4-noded tetrahedral elements. The nodal control volumes are defined by surfaces that connect element centroids and sides as schematically depicted in Fig. 9.33. 

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