At the same time, considering the pressure and speed in the filling process of lost foam castings, so far, the numerical solutions to the filling problem mainly include simple method, MAC method, SMAC method, SOLA-VOF method and lattice gas model method. The first three methods are the mainstream methods in the late 1980s, and SOLA-VOF method is the mainstream algorithm since the 1990s, The lattice gas model is expected to be the future filling process algorithm.
SOLA-VOF method, as the name suggests, is the coupling model of sola method and VOF method. Sola method is solution algorithm, which can calculate temperature field and pressure field; VOF method is volume of fluid, that is, the position of free surface is calculated by volume fraction F. About volume fraction f:
Where, VF refers to the volume of fluid in the cell grid, that is, the volume of metal liquid in the grid, and V refers to the total volume of the cell grid. This method adopts F as the marker particle to represent the position of free surface, which has the advantage of greatly improving the computational efficiency. However, the most commonly used method at present, when expanding from two-dimensional to three-dimensional, due to the existence of free surface orientation, the boundary conditions are difficult to determine, and the operation process is prone to errors.
Lattice gas model method, also known as discrete particle technology, is a new method of physical modeling and flow field equation processing. This method is based on the idea of micro representation of macro, and uses a large number of micro particles to carry out “regular Brownian motion” in the grid space to represent the macro flow phenomenon. The discrete particles are regularly distributed on the grid nodes. In each step change, the particles will undergo migration and collision. The algorithm has the advantages of high stability, simple boundary processing and easy parallel operation. However, the method can not solve the potential transfer process in the filling process, so it is still in the process of further development and popularization, It is the development trend of calculation methods for mold filling problems in the future.
In addition, there is also an unsteady heat transfer between metal liquid, foam pattern (filling), coating and casting mold in the process of mold filling and solidification, and its mathematical model will be mentioned in the next part of the theoretical model of solidification simulation.