Transformed Frame Flow Analysis

Traditionally the fluid mechanics of the extrusion process are summarized by the simple plate model illustrated in Fig. A7.1 and as described in Section 7.4. The motion of the screw is unchanged, but the reference frame has been moved to transform the problem to a fixed boundary problem for the observer. The flow in the rectangular channel is reduced into the x-direction flow across the channel and the z-direction flow down the channel. 

Additional assumptions were made in order to derive a two-dimensional analytical model to calculate the flow rate and viscous dissipation  

The flow is steady state and fully developed in the down-channel direction. 

The polymer is so viscous that the inertial force can be neglected. 

The simplified governing equations of continuity and motion are as follows  

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Figure 7.10 Transformed (Lagrangian) frame for the analysis of extruder fluid flow. Here the reference frame is positioned on the bottom of the screw channel. The observer on the frame would see the barrel move with the component velocities of and V, ...

In this case the forcing is absent from (53) and the initial conditions drive the instability. We will proceed using transform methods rather than the standard normal mode analysis. It is useful to analyze the stability in a frame which moves with the jet velocity F, thus making the base flow zero. The initial conditions for equations (53), (54) are taken to be of the form... 

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