Flight flank

However, in reality the flights are S-shaped, as seen in Fig. 7.1. If a cross-section is made perpendicular to the flights, it can be seen that the screw channel is not a true rectangle. The bottom and top surface of the screw channel are curved and the flight flanks diverge. Thus, the channel width is larger at the screw O.D. than at the root of the screw. 

Fna is the normai force on the solid bed on the active flight flank ... 

F, is the frictional force between the solid bed and the passive flight flank ... 

It should be noted, that the effect of the channel depth on the solids conveying rate as determined from a flat plate analysis is different when the curvature of the channel is taken into account. In reality, when the channel depth increases, the area of the flight flanks will increase but the area of the root of the screw will decrease this decrease is not taken into account in the flat plate model. The contact area between the differential element of the solid bed and the barrel is ... 

Equations 7.57(a) and (b) assume a zero radius of curvature between the flight flank and the screw root. If the radius is taken into account, the screw contact area is reduced by Rc(4 -ti). From this point of view one would like to use a large radius i.e., R. = H. The resulting flight geometry is shown in Fig. 7.13 and also in... 

Spalding et al. recommend using a flight flank radius in the feed section of about 1/4 of the channel depth. However, the basis for this recommendation is not entirely clear because the radii tested were all larger (0.54 H and 1.71 H) than 1/4 of the channel depth (0.25 H). This recommendation may be appropriate for smooth bore extruders where the pressure development in solids conveying is modest. This recommendation most likely is not appropriate for grooved feed extruders because the pressure development in these extruders is usually substantial. 

Another method to reduce the screw contact area is to use flat slanted flight flanks, i.e., a trapezoidal flight geometry see also Fig. 8.4(b). If the flight flank angle is 45°, the screw contact area in the flat plate model becomes ... 

The melt flows from the melt film towards the active flight flank. Only a small fraction of the material can flow through the clearance. As a result, the majority of the melt will flow into the melt pool. A circulating flow will be set up in the melt pool as a result of the barrel velocity. Since most of the viscous heat generation occurs in the upper melt film, it is generally assumed that all melting takes place at the upper solid bed-melt film interface. As melting proceeds, the cross-sectional area of the solid bed will reduce and the cross-sectional area of the melt pool will tend to increase. The melt pool, therefore, will exert considerable pressure on the solid bed. This reduces the width of the solid bed, while the melt film between the solid bed... 

The infinite channel width assumption applies to shallow channels, channels with a width-to-depth ratio higher than 10 (W/H > 10). If the depth of the channel is large relative to the width of the channel, the effect of the flight flanks on the down-channel velocity profile has to be taken into account. Several reviews of the work on melt conveying in extruders have been written [101-106]. 

The next section wiii start with an analysis of melt conveying of isothermal fluids. This wiii be foiiowed by a non-isothermal analysis of melt conveying of cases that allow exact analytical solutions. More general analyses of the effect of temperature on flow will be discussed in more detail in Chapter 12 on modeling and computer simulation. In the next section, melt conveying of Newtonian fluids and non-Newtonian fluids will be analyzed. The non-Newtonian fluids will be described with the power law equation (Eq. 6.23). The effect of the flight flank will be discussed and the difference between one- and two-dimensional analysis will be demonstrated with particular emphasis on the implications for actual extruder performance. 

It can be seen that the cross channel velocity at y = 2H/3 is zero. Thus, the material in the top one-third of the channel moves towards the active flight flank and the material in the bottom two-thirds of the channel moves towards the passive flight flank. It is clear that in reality the situation becomes more complex at the flight flanks because normal velocity components must exist to achieve the circulatory flow patterns in the cross-channel direction. However, these normal velocity components will be neglected in this analysis. Normal velocity components were analyzed by Perwadtshuk and Jankow [129] and several other workers. The actual motion of the fluid is the combined effect of the cross- and down-channel velocity profiles. This is shown in Fig. 7.57. 

This equation does not take into account the leakage flow or the effect of the flight flanks. The diehead pressure P is related to the total volumetric flow rate V by the die constant K ... 

In order to properly determine the RTD of an extruder we have to consider not only down- and cross-channel velocity components but also normal velocity components that occur at the flight flanks. This will require a numerical analysis either FDA, FEA, or BEA. Even though the depth of the channel is usually quite small compared to the channel width, the residence time at the flight flanks is substantial because... 

The flight in this mixer is offset so that the material in the center region is cut by the offset flight and then pushed to the screw and barrel surfaces by the normal pressure gradients that occur at the flight flank. Results of particle tracking using BEM are shown in Fig. 7.162. 

The volumetric melt conveying rate for a Newtonian fluid, neglecting the effect of the flight flanks, is given by Eq. 7.198. Considering that the channel width W = (rt D sincp/p) -w, down-channel barrel velocity Vb = 7t D N coscp, and down-channel pres-... 

Tangential pushing barrier flight flank tangential with inlet channel radius R... 

From this expression the criticai parameters for the flight flank geometry can be determined. Unfortunateiy, the expressions above are vaiid only for small values of the wedge angle a. As a result, these expressions have limited usefulness. If we... 

To help determine the flight flank geometry and clearance, a two-dimensional BEM analysis was initiaiiy performed. To evaluate the strength of the elongational flow versus the shear flow, the flow number [76] was analyzed. The flow number is the ratio of the magnitude of the rate of deformation tensor y to the sum of y + co, where CO is the magnitude of the vorticity tensor. 

Not self-wiping barrel is wiped but screw root and flight flanks are not... 

The material close to the passive flight flank cannot flow into the channel of the adjacent screw because it is obstructed by the flight of the adjacent screw. The material, therefore, will undergo a circulatory flow as shown in Fig. 10.7. 

The channel depth reduces along the flight flank. If circumferential angle 0 starts at the beginning of the flight flank the channel depth as a function of angle 0 can be written as ... 

Interscrew leakage through the gap between the flight flanks (the tetrahedron gap), Vt, in the radial direction... 

For screws with straight flight flanks, the flight width is ... 

Leakage through the tetrahedron gap causes interscrew material transfer. In fact, it is the only leakage flow that causes interscrew transfer. The tetrahedron gap increases when the flight flank angle is increased. Janssen, Mulders, and Smith [16] developed an empirical formula for the leakage flow through the tetrahedron gap ... 

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