The flow rate
corresponds to the flow rate passing through the side surface formed by
the range from the mid-point of the two constituent sides of the
quadrilateral element, including node α.
Degree of fill
calculation
The finite element formulation composed by superimposing Eq. (17) on the
entire problem domain requires the boundary condition of either the
pressure or the flow rate. In general, in the operation of a TSE, the
extrusion amount is often intentionally controlled using a
weight-controlled-feeder, and it is smaller than the full capacity of
the extruder; thus, it is called the “starved state.”
Setting the boundary conditions of pressure and flow together on the
same boundary results in excessive constraint, making it impossible to
obtain a solution. This difficulty is solved by adding an unknown
quantity called the degree of fill. However, even when the degree of
fill is added, the finite element equation does not allow the setting of
both the pressure and the flow rate boundary condition on the same
boundary surface.
The basic idea of a one-dimensional calculation algorithm of the FAN
method is expanded to two dimensions as a quantification method of the
unfilled element. The pressure boundary condition at the inflow surface
(feeding port) is set to atmospheric pressure, and the flow rate is set.
A prescribed (backpressure) value obtains the pressure boundary
condition at the outflow surface (head). A finite element calculation is
performed, and the pressure of each element is determined. At this time,
there is no guarantee that the calculated pressure value of the outflow
surface will agree with the prescribed value.
As incompressible conditions are assumed, the pressure dependence of the
material properties are ignored, and the equations of continuity and
motion are invariant to the addition and subtraction of constant
pressure. The flow behavior does not change if the pressure gradient is
unchanged. The pressure distribution is recalculated using the down-wind
pressure update scheme in