Channel curvature

Booy, M.L., Influence of Channel Curvature on Flow, Pressure Distribution, and Power Requirements of Screw Pumps and Melt Extruders, SPE Trans., 3, 176 (1963)... 

Modihcations of this model, including a nonlinear temperature prohle in the melt him, channel curvature effects, and an approximate method to account for the flight clearance effect, are presented by Tadmor and Klein (1), together with expressions for power calculations. Numerous other improvements of the melting model have been suggested in the literature (33,41 -6). A detailed discussion of these, however, is beyond the scope of this text. 

Lor the flow inside the manifold of a circular cross-section9 channel, we assume that, locally, we have fully developed tube (capillary) flow. That is, we disregard the channel curvature, the channel tapering off, and the effects of the leak flow into the slit region. The following relationship was derived previously (see Table 12.3) ... 

Seim, H.E., and Gregg, M.C. (1997) The importance of aspiration and channel curvature in producing strong mixing over a sill. J. Geophys. Res. 102, 3451-3471. 

LIQUID FILM BETWEEN GAS BUBBLE AND CHANNEL WALL EFFECTS OF CHANNEL CURVATURE... 

Figure 12. Effects of the channel curvature on the axial dispersion, (a) The variation of solute concentration within hquid slug as a function of time for various Peclet numbers in straight and serpentine channels, (b) Computational results and theoretical predictions in the absence of molecular diffusion for Ca = 0.01 and 0.005.

M. Muradoglu, Axial Dispersion in Segmented Gas-Liquid Flow Effects of Channel Curvature, preprint to be submitted (2009). 

A category of models has developed for use in two-dimensional cases employing a curvilinear (natural) coordinate system. The curvilinear coordinate system recognizes the natural channel curvature which almost always exists in natural streams of any length. In addition, even in rather straight channels, irregularities in the channel bottom due to structures, sediment deposition, and the like may... 

Due to channel curvature and changes in width, metric coefficients and rriy are introduced to correct for differences between the distances measured along any given surface and those measured along the corresponding axes. These are illustrated in Fig. 1. The values of nix and niy may vary from point to point, being functions of both x and y. Note that = 1 on the x axis and = 1 on the y axis. Due to the parallel nature of all horizontal coordinate surfaces, the value of niz is 1 everywhere. As Yotsukura 105) notes, this natural coordinate system is therefore based on the premise that the total velocity vector everywhere... 

Considering that in most extruder screws the screw diameter is much larger than the channel depth (D/H 1, usually about 5), the change in channel width and helix angle over the depth of the channel will be rather small. If it is assumed that the channel curvature can be neglected, the screw channel can be unrolled onto a flat plane. The error that is made in this process may be acceptable considering the limited accuracy and reproducibility of most data on the coefficient of friction, as discussed in Section 6.1.2. Two simplifications resuit from this assumption. The first one is that now the channel width and helix angie are constant over the depth of the channei. The second simplification is that the extra force F can be determined directiy from a force balance in the cross-channei direction ... 

The channel curvature is negligible (flat plate model)... 

It was discussed in Section 7.2.2 that there appears to be an optimum channel depth for which the solids conveying rate reaches a maximum. At low values of the pressure increase over the solids conveying section, this optimum channel depth is indeed apparent because this optimum channel depth does not occur when the channel curvature is taken into account. At higher values of the pressure increase, however, there is an actual optimum channel depth even when the channel curvature is taken into account. This is shown in Fig. 8.20 for a 114-mm (4.5-in) extruder running at 60 rpm the coefficient of friction is 0.5 on the barrel and 0.3 on the screw. When the pressure gradient increases, the optimum channel depth decreases. 

Channel curvature in the down-channel direction is negligible... 

Booy ML (1963) Influence of Channel Curvature on Flow, Pressure Distribution and Power Requirements of Screw Pumps and Melt Extmders, Soc Plastics Engrs Trans., 3 pp 176. Cameiro OS, Covas JA et al (2000) Experimental and theoretical study of twin-screw extrasion of polypropylene. J Appl Polym Sci 78(7) 1419-1430 Che D, KotipaUi U et al (2010) Atorvastatin calcium propylene glycol solvates, USPTO Crowley MM, Zhang F et al (2007) Pharmaceutical applications of hot-melt extrusion part I. Drug Dev Ind Pharm 33(9) 909-926... 

Booy M L (1963), Influence of channel curvature on flow, pressure distribution and power reqnirement of screw pumps and melt extruders , SPE Transactions, 3, 176-185. 

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