Channel velocity profile

Figure 6.3 Down-channel velocity profiles for different pumping situations with a single screw extruder.

The integration of constants C and C2 is evaluated from the boundary conditions Vj (0) = 0 and vx(H) = Vt,x. Substituting these boundary conditions into Eq. 6.3-12 yields the cross-channel velocity profile... 

Thus we observe that the cross-channel gradient is proportional to screw speed and barrel diameter, and inversely proportional to the square of the channel depth. By substituting Eq. 6.3-15 into Eq. 6.3-13, we obtain the cross-channel velocity profile... 

Fig. 6.10 Cross-channel velocity profile from Eq. 6.3-16. Note that melt circulates around a plane located at exactly two-thirds of the height.

Let us next consider the simple isothermal drag flow (dP/dz = 0) of a shear-thinning fluid in the screw channel. The cross-channel flow, induced by the cross-channel component of the barrel surface velocity, affects the down-channel velocity profile and vice versa. In other words, the two velocity profiles become coupled. This is evident by looking at the components of the equation of motion. Making the common simplifying assumptions, the equation of motion in this case reduces to... 

The cross- and down-channel velocity profiles are (see Section 6.3) ... 

Thus, the operating conditions affect the down-channel velocity profile, but not the crosschannel velocity profile. At closed discharge conditions (Qp/Qd = — 1), both the down-channel and cross-channel velocities vanish at / 2/3, implying that the whole plane at... 

The SSE is an important and practical LCFR. We discussed the flow fields in SSEs in Section 6.3 and showed that the helical shape of the screw channel induces a cross-channel velocity profile that leads to a rather narrow residence time distribution (RTD) with crosschannel mixing such that a small axial increment that moves down-channel can be viewed as a reasonably mixed differential batch reactor. In addition, this configuration provides self-wiping between barrel and screw flight surfaces, which reduces material holdback to an acceptable minimum, thus rendering it an almost ideal TFR. 

C.E. Camp, W.B. Kolb, K.L. Sublette, and R.L. Cerro, The Measurement of Square Channel Velocity Profiles Using a Microcomputer-Based Image Analysis System, Experiments in Fluids I0 S1 (1990). 

Observe the experimental performance of the mixer from Figure 10.35. The experimental cross channel temperature profiles are given however, to determine the CO Vs of the inlet and outlet stream we would also need the cross channel velocity profile. We would need the velocity profile because proper averaging must be done on a flowing enthalpy basis that is, the averaging would have to be done as follows ... 

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]. 

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. 

The shear stresses can be evaluated from Eqs. 7.223 and 7.224 and the equations for down-channel velocity profile, Eq. 7.197 or 7.216, and the-cross channel velocity profile, Eq. 7.211. The power consumption in the screw channel can be written as ... 

Velocity profiles and temperature profiles in extruder dies are intimately related because of the high polymer melt viscosity and because the melt viscosity is temperature dependent. It is important to understand and appreciate this interrelationship in order to understand the die forming process and the variables that influence this process. The relationship between velocity and temperature profiles can be illustrated by considering the down-channel velocity profile in a circular die. Typical velocity profiles are shown in Fig. 7.106 for several values of the power law index. 

If it is assumed that the down-channel velocity profile can be approximated with Eq. 10.28, then the volumetric throughput is approximately ... 

Rowell and Finlayson [1] solved the down channel velocity profile for a screw pump. 

The current response of the thin layer detector (TLD) reflects the constraining of the boundary layer by the wall opposite the electrode. When the width of the channel is less than the boundary layer thickness according to Eq. (111) a channel velocity profile not unlike the parabolic geometry in a narrow tube can be expected. 

Fig. 46. Down-channel velocity profiles for three pressure conditions.

FIGURE 12.14 Illustration of the Internal Channel Velocity Profile Change at the Propellant Tank Liquid/Vapor Interface. The model assumes that the velocity transitions from a skewed parabolic profile to a fully developed, parabolic profile at the tank LA/ interface. 

Referring to the mixing process mechanisms described in Sections 8.2 and 8.3, the variables of screw geometry and flow restriction effect down channel velocity profile but not those of the cross channel. 

Choo K P, Neelakantan N R and Pittman J F T (1980), Experimental deep-channel velocity profiles and operating characteristics for a single-screw extruder , Polymer Engineering Science, 20,349-356. 

Substituting the expression for dp/dx back into Eq. 8.95, we obtain the cross-channel velocity profile ... 

Thus, Q is directly proportional to the degree of All and the screw speeed, N. The cross-channel velocity profile, Vx, is... 

Fig. 11 (a) Channel velocity profile for the flow of air at 4001pm in a 80 channel PEMFC of different port dimensions (b) Channel velocity profile for the flow of air through 18/16 mm, 80 channel PEMFC of different flow rates (Ganesh Mohan et al., 2004),... 

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