Rotational flow rate

The correction factors (or shape factors) and /pare related to the reduced flow in the z direction due to the influence of the flights, as stated in Chapter 1. For channels with small aspect ratios, these terms are both essentially 1. As the aspect ratio of the channel increases, the channel gets boxy, and these corrections become quite important, and they can be much smaller than 1. The correction factors as a function of Fl/W are shown in Fig 7.15. As will be shown in Section 7.5.3, /d and Fp do not fully correct the flow calculation. A second empirical correction function will be presented to correct the rotational flow rate. 

The rotational flow rate is calculated using the data in Table 7.2 and Eq. 1.13 as follows ... 

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 generalized Newtonian model over-predicted the rotational flow rates and pressure gradients for the channel for most conditions. This over-prediction was caused in part by the utilization of drag flow shape factors (FJ that were too large. Then in order for the sum of the rotational and pressure flows to match the actual flow In the channel, the pressure gradient was forced to be higher than actually required by the process. It has been known for a long time [9] that the power law... 

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

Once A is determined using Eq. 7.56, the corrected rotational flow rate is calculated using Eq. 7.57. This corrected rotational flow rate should be very close to the actual rotational flow for the channel geometry. The calculation of the pressure gradient using Eq. 7.58 is now much more accurate since the pressure-induced flow rate is now more accurate that is, 0 p = Q d Qm-... 

Equations 7.57 and 7.58 that are developed above use the as the velocity component as shown for screw rotation physics. As previously discussed, the classic drag flow model [8] assumed that the equivalent flow rate will be obtained if the barrel is rotated in the direction opposite to that of the screw as long as the linear velocity of the unwound barrel Is numerically equal to the linear velocity of the screw core. For this classic barrel rotation model, is used as the velocity component instead of V(,z-Since is less than the drag flow rate would be reduced. It Is Interesting to note here that the classical model using reduced the drag flow rate such that It provided a better estimate of the actual rotational flow rate, but for the wrong reason. 

Figure 7.32 Screw rotation and barrel rotation flow rate comparison for a deep channel screw [5] running a polypropylene glycol fluid...

As indicated by Eig. 7.37 and Table 7.7 and as expected, the increase in melt temperature for a PC resin was always higher for the barrel rotation case as compared to screw rotation. If a very high die pressure was needed and the rate is reduced to 10 % of the rotational rate (T) = 0.9), the difference between discharge temperatures for the rotation cases was predicted at about 18 °C. In other terms, the temperature increase (47°C) for screw rotation was about 72% of the temperature increase (65 °C) for barrel rotation. The discharge temperature difference for the two rotation cases decreases to about 4 °C fora low die pressure case where the rate is 90% of the rotational flow rate (T) = 0.1). For this case, the melt temperature increase (6 °C) for screw rotation was about 60% of the temperature increase (10 °C) for barrel rotation. 

At the startup of the line, the extruder was operated at 91 rpm to produce the required rate of 148 kg/h for a specific rate of 1.63 kg/(h-rpm). The temperature of the extrudate was measured through the transfer line wall at 232 °C. Due to process safety constraints the extrudate temperature could not be measured using a handheld temperature sensor. The extrusion rate was required in order to maintain the downstream take-away equipment at its maximum rate. At first the extruder appeared to be operating well except that the specific rate was lower than predicted. That is, the screw was rotated at an rpm that was higher than expected to produce the 148 kg/h. At 91 rpm, the rotational flow rate was calculated at 228 kg/h the specific rotational flow rate was calculated at 2.51 kg/(h-rpm). Thus, the line was operating at only 65% of the rotational flow rate. A barrier design... 

After the screw modification, the 148 kg/h rate was obtained at a screw speed of about 69 rpm with an extrudate temperature of 223 °C. Thus, the specific rate increased from 1.63 kg/(h rpm) before the modification to 2.14 kg/(h-rpm) after the modification, a specific rate increase of about 30%. At a screw speed of 69 rpm, the rotationai flow rate was calculated at 173 kg/h now the extruder was operating at about 86% of the rotational flow rate. The calculated axial pressure gradient required to maintain the flow of the extruder at the reported flow rate showed that pressures in the screw never decreased to zero, indicating that the channels were full as shown in Fig. 11.21. No adverse effects were experienced with the reduced discharge temperature (8 °C lower), no unmelted material was observed in the extrudate, and no gel showers occurred after the modification. A summary of the extrusion performance before and after the modification is shown in Table 11.5. 

The lead length was 172 mm for the main flight of the barrier section and 114.3 mm for all other sections of the screw. The main flight width and clearance were 11 and 0.11 mm, respectively, in all sections of the screw. The first 2.7 diameters of the screw were inside a water-cooled feed casing. The compression ratio was 2.5 and the compression rate of the barrier section was 0.0030. The depth of the solids channel at the end of the barrier section was 3.2 mm. The specific rotational flow rate was calculated at 5.9 kg/(h-rpm). ... 

The injection-molding press was producing a part and runner system that had a mass of 2.15 kg. The mass was plasticated using a 120 mm diameter, 8L/D screw. The screw used for the process had a barrier melting section that extended to the end of the screw, as shown by the specifications in Table 11.9. That is, the screw did not have a metering channel. Instead, the last sections of the barrier section were required to produce the pressure that was needed to flow the resin through the nonreturn valve and into the front of the screw. The specific rotational flow rate for the screw for the IRPS resin was calculated at 9.3 kg/(h-rpm) based on the depth of the channel at the end of the transition section. The screw was built with an extremely low compression ratio and compression rate of 1.5 and 0.0013, respectively. For IRPS resins and other PS resins, screws with low compression ratios and compression rates tend to operate partially filled. The compression ratio and compression rate for the screw are preferred to be around 3.0 and 0.0035, respectively. The flight radii on the screw were extremely small at about 0.2 times the channel depth. For IRPS resin, the ratio of the radii to the channel depth should be about 1. 

Several mechanisms could cause the specific rate of the screw to be considerably less than the calculated specific rotational flow rate for the screw. These mechanisms include (1) normal operation for a screw with a very short metering section and a low-viscosity resin, (2) the screw is rate-limited by solids conveying, causing the downstream sections of the screw to operate partially filled, and (3) the entry to the barrier section is restricting flow (see Section 11.10.1) to the downstream sections of the screw and causing the downstream sections to operate partially filled. The goal was to determine which of the above mechanisms was responsible for the low specific rates for the plasticator. 

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