Generalized Newtonian method

The combined mass flow for rotation-driven and pressure-driven flow is given by Eq. 1.28 and is the expected rate of the process. The average shear viscosity is calculated using the average shear rate in the channel for screw rotation and the bulk temperature. This method is also known as the generalized Newtonian method. 

Two different calculation methods were used for the simulations (1) the generalized Newtonian method as developed above, and (2) the three-dimensional numerical method presented in Section 7.5.1. The generalized Newtonian method used a shear viscosity value that was based on the average barrel rotation shear rate and temperature in the channel. The average shear rate based on barrel rotation (7ft) is provided by Eq. 7.52. Barrel rotation shear rate and the generalized Newtonian method are used by many commercial codes, and that is why it was used for this study. 

Figure 7.18 Ratio of the rotational flow rate calculated using the generalized Newtonian method to the rotational flow calculated using the numerical method as a function of screw diameter...

The ratio of the rotational flows indicated that the diameter of the extruder is not a factor for the deviation shown in Fig. 7.16. That is, for this channel with a small H/Wthe simplified analysis produces less than a 10% error when compared to the exact numerical solution. Thus, the rotational flow rate can be calculated quite reliably using the simple generalized Newtonian method at these conditions. 

The previous calculations were performed using a range of commercial resins with different levels of shear thinning behavior. In order to show the deviation for the generalized Newtonian method, the data presented in Figs. 7.20 and 7.21 were plotted as a function of n for several ///IF values, as shown in Figs. 7.22 and 7.23. As the n value was reduced from 1.0 towards 0, and as the/ /PFratio increases, the... 

To obtain the correction factors, the rotational flow rate must be calculated using the generalized Newtonian method and the three-dimensional numerical method... 

Since the generalized Newtonian method was based on a constant viscosity for the entire channel, any factor that would cause the viscosity to vary in the channel may cause F to be different from 1. The factors known to cause the viscosity to... 

The 500 mm diameter extrusion problem presented in Section 7.5.1 was simulated using the generalized Newtonian method with and without the iy correction factor. The simulations and the experimentally determined pressure at a position 5.6 diameters downstream are shown in Fig. 7.29. Recall that the generalized Newtonian method over-predicts the pressure by a factor of 1.7 (a 70% over-prediction) at 10.8 MPa. The method with the F, correction factor predicts a pressure of 5.9 MPa, a pressure that is slightly lower than the experimentally determined pressure of... 

Figure 7.29 Simulated axial pressure profile for a 500 mm diameter extruder running 11,800 kg/h at 46 rpm for the 0.8 Ml LORE resin using the generalized Newtonian method with and without the A correction...

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