Flow Simulation with Back Pressure Consideration

ABSTRACT

In the Die Cast process, the flow is a two phase, gas-liquid, flow in which molten metal coexists with air.  A program for a non-steady state 3-D gas-liquid flow analysis has been developed to take into account the variation of the back pressure of a gas in a cavity during the casting process.  In case of a two phase flow, there is a free surface between the two phases that deforms and moves as time passes.  Therefore, it is required to solve it as a non-linear simultaneous differential equation of time. 

The accuracy of a boundary condition for the free surface greatly affects the calculation accuracy.  Compared to a single phase flow, the numerical simulation model is getting too complicated to describe the movement and the deformation on the 3-D free surface when the gas and liquid are mixed.  Furthermore, the calculation time for a two phase flow analysis is extremely longer than a single flow.  Therefore, a practical simulation program is ambitious to analyze the gas-liquid flow phenomenon.

With this software, the back pressure in the cavity is calculated and set as a boundary condition for the free surface in order to be taken into account during the flow analysis.  Furthermore, this program has been applied to some other problems of a gas-liquid flow in order to validate the accuracy and method for this analysis.

VALIDATION OF ACCURACY

In order to validate the accuracy of this software, it was applied to a water model and compared with the experimental results.  The cavity is a rectangular shape having the dimensions of 100mmx200mmx5mm and a gate width of 40mm.  The water is injected from the gate at a constant flow rate of 120cm/s.  Figure 1 shows the cavity shape for this model.

For this model, the cavity is at atmospheric pressure before the injection.  When the water is injected, the cavity pressure gradually increases since there is no air outlet.  In order to simulate the water model experiment, the rectangular cavity was divided into 15,000 cubic elements of 50x100x3.  The flow rate at the gate was set to 120cm/s and the flow process was analyzed.  The experimental and calculated results of the filling process are shown in Figure 1 and Figure 2.

Figure 1  Experimental result of the water model

Figure 2 Analysis result considering back pressure

Comparing the experimental and calculated results, the shape of the free surface, the position of the eddy current and the shape of the gas phase, which was caught by the back pressure, can be predicted.  Even though the analytical model has been simplified by neglecting the fluid phenomenon and assuming the conservation of mass in the gas phase, it is achievable to take into account the back pressure with a sufficient degree of accuracy. 

In the case of the 2-D model, the computational time is about 15min. using a Pentium II 800MHz and 5MB RAM.  Minimizing the computational time and memory occupation, was successfully achieved compared to the conventional 2-D fluid model.  In the case of the 3-D model, the flow simulation results with the back pressure consideration is shown in Figure 3.  It was assumed that there was no air outlet in the die and the air can flow into the overflow.

     Figure 3 Flow simulation result considering back pressure

The filling pattern of the liquid is varied by the increasing air pressure, which is difficult to express by the conventional module, and is observed in the area which is surrounded by the liquid.  According to the analytical results by the software it shows agreement with the experimental results and it is therefore confirmed that this software can precisely predict the behavior of a gas.  Furthermore, it can be applied to a complex 3-D model with a sufficient accuracy and with a practical amount of time. Therefore, this software can be used as a design aid for the casting process optimization.