Tapered channel flow

Norway built a wave energy station on the coast near Bergen in 1985. It combined an OWC with a Norwegian device called aTapchan (TAPered CHANnel). The waves move up a concrete slope where they fill a reservoir. As the water flows back to the ocean, it drives a turbine generator. 

In another report, an on-chip chamber containing a capture matrix was used for sample cleanup. A 2- dL unpurified sample is concentrated into a smaller volume ( 10 nL), and this yields a volumetric concentration factor of 200. Longer residence time can be achieved by using a doubly tapered chamber. Here, the electric field is 10-fold lower within the chamber than within the tapered channel. So, a high-field (fast) sample introduction is followed by a low-field (slow) sample flow past the capture matrix, increasing the residence time so that the binding kinetics are dominant over electromigration [971]. 

The lubrication approximation facilitates solutions to flow problems in complex geometries, where analytical solutions either cannot be obtained or are lengthy and difficult. The utility of this approximation can well be appreciated by comparing the almost exact solution of pressure flow in slightly tapered channels to that obtained by the lubrication approximation. 

Without too much difficulty, we can extend the model to any screw design consisting of constant depth channels, and moderate tapers by using the taper correction factors of Eq. 6.4-4 separately for each section, and adding up the pressure drops (rises) according to Eq. 9.2.2. Thus, for a tapered channel, the drag and pressure flow terms are multiplied by the expressions 2/(1 + 0) and 2/ 0(l + CoX respectively, where 0 = Hq/H, with Hq... 

Debbaut, B., Dooley, J., Flow of a Low Density Polyethylene In Straight and Tapered Channels Experiments and 3-D Finite Element Simulation, Xlll-th International Conference on Rheology, Cambridge, UK, 2, 170 (2000)... 

The flow field channels may have different shapes, often resulting from the manufacturing process rather than from functionality. For example, slightly tapered channels would be very difficult to obtain by machining, but they are essential if the bipolar plate is manufactured by molding. Channel geometry may have effect on water accumulation. In the round-bottomed chaimel, condensed water forms a film of water at the bottom, whereas in the channel with tapered walls, condensed water forms small droplets... 

We consider a co-extrusion die consisting of an outer circular distribution channel of rectangular cross-section, connected to an extrusion slot, which is a slowly tapering narrow passage between two flat, non-parallel plates. The polymer melt is fed through an inlet into the distribution channel and flows into... 

Screw presses have been used extensively in North America, but are not popular in Europe. The mash is added at the top of a vertical rotating screw. As the mash moves down it is compressed in the taper and juice flows out through slatted conical walls. Compression of the pomace blocks channels for juice flow and iuhibits juice extraction. Extensive use of press aids is necessary for efficient operation. 

Most processing methods involve flow in capillary or rectangular sections, which may be uniform or tapered. Therefore the approach taken here will be to develop first the theory for Newtonian flow in these channels and then when the Non-Newtonian case is considered it may be seen that the steps in the analysis are identical although the mathematics is a little more complex. At the end of the chapter a selection of processing situations are analysed quantitatively to illustrate the use of the theory. It must be stressed however, that even the more complex analysis introduced in this chapter will not give precisely accurate... 

In many practical situations involving the flow of polymer melts through dies and along channels, the cross-sections are tapered. In these circumstances, tensile stresses will be set up in the fluid and their effects superimposed on the effects due to shear stresses as analysed above. Cogswell has analysed this problem for the flow of a power law fluid along coni-cylindrical and wedge channels. The flow in these sections is influenced by three factors ... 

By using a tapered inlet instead of an abrupt constriction, different variations of convergent flow could be envisioned axisymmetric flow in a conical channel... 

The flow configuration of building block 3, of two non-parallel plates in relative motion, shown in Fig. 6.19, was analyzed in detail in Example 2.8 using the lubrication approximation and the Reynolds equation. This flow configuration is not only relevant to knife coating and calendering, but to SSEs as well, because the screw channel normally has constant-tapered sections. As shown in Fig. 6.19, the gap between the plates of length L is Ho and II at the entrance and exit, respectively, and the upper plate moves at constant velocity Vo-... 

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) ... 

The die design equation proposed by Pearson (60) utilizes a constant die lip opening, but an approach-channel-taper that varies with the die width. Thus, in the region between the manifold and the die lip opening both the pressure and flow fields are two-dimensional. This may affect the flow in the die lip region, since the fluid is viscoelastic with memory of this recent upstream flow experience. 

We know that the tubular die flow channel is composed of a series of more or less annular flow regions, which are straight, tapering, of almost uniform cross section, or interrupted... 

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