Screw rotation analysis

The screw rotation analysis leads to the model equation for the extruder discharge rate. There are now two screw-rotation-driven velocities, and and a pressure-driven velocity, Pp that affect the rate. and transport the polymer fluid at right angles to one another. In order to calculate the net flow from screw rotation It Is necessary to resolve the two screw-rotation-driven velocities into one velocity, Vpi, that can be used to calculate the screw rotation-driven flow down the screw parallel to the screw axis (or centerline) as discussed in Chapter 1 and as depicted in Fig. 7.14. The resolved velocity will then be integrated over the screw channel area normal to the axis of the screw. 

Experimental and simulation results presented below will demonstrate that barrel rotation, the physics used in most texts and the classical extrusion literature, is not equivalent to screw rotation, the physics involved in actual extruders and used as the basis for modeling and simulation in this book. By changing the physics of the problem the dissipation and thus adiabatic temperature increase can be 50% in error for Newtonian fluids. For example, the temperature increase for screw and barrel rotation experiments for a polypropylene glycol fluid is shown in Fig. 7.30. As shown in this figure, the barrel rotation experiments caused the temperature to increase to a higher level as compared to the screw rotation experiments. The analysis presented here focuses on screw rotation analysis, in contrast to the historical analysis using barrel rotation [15-17]. It was pointed out recently by Campbell et al. [59] that the theory for barrel and screw rotation predicts different adiabatic melt temperature increases. 

This appendix contains the detailed development for the equations that are presented in Chapter 3. Full understanding of these developments is not required for detailed analysis and troubleshooting of the extrusion process. They are presented here for those who desire a deep understanding of the mathematics involved with the screw rotation analysis. Some of the equations and figures are duplicated in this appendix for clarity. The nomenclature used here is consistent with that used earlier. The reader is directed to Chapter 3 for nomenclature. 

Screw rotation analysis is used here so the barrel velocity Is 0. For Film C, as diagrammed In Fig. A6.3(a), two velocities are relevant the velocity of the solid... 

The analysis developed here is based on screw rotation physics [13], and thus several other definitions are developed here. The velocities at the screw core, indicated by the subscript c, in the x and z directions are as follows ... 

The coefficients of dynamic friction need to be determined first for this analysis. The average pressure and temperatures are specified, but the velocities at the sliding interfaces need to be determined. The sliding velocities need to be calculated based on screw rotation physics. The sliding velocity at the barrel interface is as follows ... 

Model Parameter New Analysis (Screw Rotation) Historical Analysis [8] (Barrel Rotation)... 

Campbell, G.A. and Spalding, M.A., Numerical Analysis of the Melting Process for Barrier-Flighted Single-Screw Extruders Using Screw Rotation Physics, SPE ANTEC Tech. Papers, 56, 418 (2010)... 

Since historically the dissipation is evaluated using the local velocity at the boundary and the shear stress is evaluated as the product of the viscosity and the shear rate at the boundary, it follows that if the velocity is not frame indifferent then the dissipation will not be frame indifferent. As discussed previously in this chapter, rotation of the barrel at the same angular velocity as the screw are the conditions that produce the same theoretical flow rate as the rotating screw. Because the flow rate is the same and the dissipation is different, it follows that the temperature increase for barrel and screw rotation is different. This section will demonstrate this difference from both experimental data and a theoretical analysis. 

The double integral represents the nonzero terms of the dissipation rate tensor as adapted by Middleman [61] and Bernhardt and McKelvey for adiabatic extrusion [62]. The nontensorial approach was adopted by Tadmor and Klein in their classical text on extrusion [9]. In essence these are the nonzero terms of the dissipation rate tensor when it is applied to the boundary of the fluid at the solid-fluid interface. In the following development this historic analysis was adopted for energy dissipation for a rotating screw. In this case the velocities Ui are evaluated at the screw surface s and calculated in relation to screw rotation theory. The work in the flight clearance was previously described in the literature [9]. The shear... 

The theory developed up to this point is based on a model where the screw is stationary and the barrel rotates around the screw. It is assumed that the flow that results is the same as when the barrel is stationary and the screw rotates in the opposite direction. This assumption was considered valid for over fifty years until several workers challenged this assumption, first in the early 1990s [272-276], and then more recently [323]. Because of the importance of this issue we will critically analyze this assumption to determine to what extent the assumption is correct. Flow will be analyzed using the parallel plate assumption with either the barrel or the screw considered moving. Flow will also be analyzed without the parallel plate assumption, using a cyhndrical coordinate system, again considering both cases. This analysis is based on a study by Osswald et al. [281]. 

The theoretical scheme we applied here are totally as same as our previous papers [3, 7]. The non-Newtonian and non-isothermal 3-D flow analysis is conducted and the dynamic motion of the screw rotation is solved under the hypothesis of quasi steady state flow field. 

Residual pendimethalin in various crops was determined as follows." A 10-20-g amount of fruits or vegetables was extracted by blending twice with 200 mL of methanol. Grasses and mint were extracted with 200 mL of methanol-water (1 1, v/v). Nuts were extracted with 200 mL of n-hexane-2-propanol (3 1, v/v). For the residue analysis of the dinitroaniline herbicides butralin, dinitramine, ethalfluralin, pendimethalin, and trifluralin, a tomato sample (5 g) was extracted twice with 20 mL of methanol in a Sorvall homogenizer and filtered through filter paper. Benfluralin and trifluralin residues in the sample (10 g) were extracted with 100 mL of acetonitrile-water (99 1, v/v) in 250-mL screw-cap jars with Teflon liners rotated for 1 h on an end-over-end shaker (40 rpm). ... 

Knowledge of the geometry and mathematical description of a screw Is required to understand the analysis of the functional sections of the screw and the troubleshooting of case studies. In Chapter 1 the geometry and mathematical descriptions are presented. Also In this chapter, the calculation of the rotational flow (also known as drag flow) and pressure flow rates for a metering channel Is Introduced. Simple calculation problems are presented and solved so that the reader can understand the value of the calculations. 

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