The results of a numerical evaluation of the equations in the proceeding section are presented in Figure , which exhibits the final pressure when 90% of the stroke has elapsed as a function of .

Parameters influencing the process are the area ratio, , and the friction parameter, . From other detailed calculations [#!poro:genickthesis!#] it was found that the influence of the parameter on the pressure development in the cylinder is quite small. The influence is small on the residual air mass in the cylinder, but larger on the Mach number, . The effects of the area ratio, , are studied here since it is the dominant parameter.

Note that in air venting is slightly different from that in vacuum venting [#!poro:genickvac!#] by a factor of . This factor has significance for small and small when the Mach number is large, as was shown in other detailed calculations [#!poro:genickthesis!#]. The definition chosen here is based on the fact that for a small Mach number the factor can be ignored. In the majority of the cases is small.

For values of the area ratio greater than 1.2, , the pressure increases the volume flow rate of the air until a quasi steady-state is reached. In air venting, this quasi steady-state is achieved when the volumetric air flow rate out is equal to the volume pushed by the piston. The pressure and the mass flow rate are maintained constant after this state is reached. The pressure in this quasi steady-state is a function of . For small values of there is no steady-state stage. When is greater than one the pressure is concave upwards, and when is less than one the pressure is concave downwards. These results are in direct contrast to previous molds by Sachs poro:sachs, Draper poro:draper, Veinik poro:veinik1 and Lindsey and Wallace poro:lindsey, where models assumed that the pressure and mass flow rate remain constant and are attained instantaneously for air venting.

To refer to the stroke completion (100% of the stroke) is meaningless since 1) no gas mass is left in the cylinder, thus no pressure can be measured, and 2) the vent can be blocked partially or totally at the end of the stroke. Thus, the ``completion'' (end of the process) of the filling process is described when 90% of the stroke is elapsed. Figure presents the final pressure ratio as a function for . The final pressure (really the pressure ratio) depends strongly on as described in Figure . The pressure in the die cavity increases by about 85% of its initial value when for air venting. The pressure remains almost constant after reaches the value of 1.2. This implies that the vent area is sufficiently large when for air venting and when for vacuum venting. Similar results can be observed when the residual mass fraction is plotted.

This discussion and these results are perfectly correct in a case where all the assumptions are satisfied. However, the real world is different and the assumptions have to examined and some of them are:

- Assumption is not a restriction to the model, but rather
guide in the design.
The engineer has to ensure that the resistance in the mold to air flow (and metal flow)
has to be as small as possible.
This guide dictates that engineer designs the path for air (and the liquid metal) as
as short as possible.
- Assumptions , , and
are very realistic assumptions. For example, the error in using
assumption is less than 0.5%.
- This model is an indication when assumption is good.
In the initial stages (of the filling process) the pressure is very small
and in this case the pressure (force) to open the plates is small, and
therefore the gap is almost zero.
As the filling process progresses, the pressure increases, and therefore
the gap is increased.
A significant gap requires very significant pressure which occurs only
at the final stages of the filling process and only when the area ratio
is small,
.
Thus, this assumption is very reasonable.
- Assumption is associated with assumption
, but is more sensitive.
The change in the resistance (a change in assumption in
creates consequently a change in the plunger velocity.
The plunger reaches the constant velocity very fast, however,
this velocity decrease during the duration of the filling process.
The change again depends on the resistance in the mold.
This can be used as a guide by the engineer and enhances the importance
of creating a path with a minimum resistance to the flow.
- Another guide for the venting system design (in vacuum venting) is assumption .
The engineer has to reduce the vent volume so that less gas has to be evacuated.
This restriction has to be design carefully keeping in mind that the resistance also
has to be minimized (some what opposite restriction).
In air venting, when this assumption is not valid,
a different model describes the situation.
However, not fulfilling the assumption can improve the casting because larger
portion of the liquid metal which undergoes mixing with the air is exhausted
to outside the mold.
- Assumption is one of the bad assumptions in this model.
In many cases there is more than one vent, and the entrance Mach number for
different vents could be a different value.
Thus, the suggested method of conversion is not valid, and therefore
the value of the critical area is not exact.
A better, more complicated model is required.
This assumption cannot be used as a guide for the design since as
better venting can be achieved (and thus enhancing the quality) without
ensuring the same Mach number.
- Assumption is a partially appropriate assumption.
The resistance in venting system is a function of and Mach numbers.
Yet, here the resistance,
, is calculated based on the assumption
that the Mach number is a constant and equal to .
The error due to this assumption is large in the initial stages where and
Mach numbers are small.
As the filling progress progresses, this error is reduced.
In vacuum venting the Mach number reaches the maximum instantly and therefore
this assumption is exact.
The entrance Mach number is very small (the flow is even not choke flow) in
air venting when the area ratio,
is very large and therefore the
assumption is poor.
However, regardless the accuracy of the model, the design achieves its aim
and the trends of this model are not affected by this error.
Moreover, this model can be improved by taking into consideration the change of
the resistance.
- The change of the vent area does affect the resistance.
However, a detailed calculation can show that as long as the vent area
is above half of the typical cross section, the error is minimal.
If the vent area turns out to be below half of the typical vent cross section
a improvement is needed.

copyright Dec , 2006

The pdf version is also available here