Entrance Flows

Entrance flow is also accompanied by the growth of a boundary layer (Fig. 5b). As the boundary layer grows to fill the duct, the initially flat velocity profile is altered to yield the profile characteristic of steady-state flow in the downstream duct. For laminar flow in a tube, the distance required for the velocity at the center line to reach 99% of its asymptotic values is given by... 

Fig. 5. Entrance flows in a tube or duct (a) separation at sharp edge (b) growth of a boundary layer (illustrated for laminar flow).

Entrance flow Flow within the inlet region of a conduit that has not devel-... 

For most general-service noncorrosive applications, the wheels use medium- to heavy-gauge carbon or alloy steel. For the centrifugal types, a die-formed entrance shroud provides smooth entrance flow of the air into the wheel. A solid steel plate serves as a back plate of the single entrance wheel, but of course, cannot be used on a double-entry wheel. Flere, both sides of the wheel have entrance shrouds. Figure 12-120C. 

For triangular micro-channels of d = 130 pm results based on experimental measurements at the same entrance flow rate m = 0.046 g/s are presented in Figs. 2.62 and 2.63. 

In practice, the process regime will often be less transparent than suggested by Table 1.4. As an example, a process may neither be diffusion nor reaction-rate limited, rather some intermediate regime may prevail. In addition, solid heat transfer, entrance flow or axial dispersion effects, which were neglected in the present study, may be superposed. In the analysis presented here only the leading-order effects were taken into account. As a result, the dependence of the characteristic quantities listed in Table 1.5 on the channel diameter will be more complex. For a detailed study of such more complex scenarios, computational fluid dynamics, to be discussed in Section 2.3, offers powerful tools and methods. However, the present analysis serves the purpose to differentiate the potential inherent in decreasing the characteristic dimensions of process equipment and to identify some cornerstones to be considered when attempting process intensification via size reduction. 

As the cross-sectional area expands beyond the entrance, flow separation occurs and results in turbulence and eddies, which continue as the air goes through the passages around the turbinates. The linear velocity... 

Figure 7.69 Entrance flow patterns in molten polymers. From Z. Tadmor and C. G. Gogos, Principles of Polymer Processing. Copyright 1979 by John Wiley Sons, Inc. This material is used by permission of John Wiley Sons, Inc.

Hence alternating flows can also be achieved by repetitive induction of entrance flow effects [152], This relies to a constant re-direction of flows from one curved channel into another. 

The sum of both effects, the flow-pattern switch and the entrance flow effects, is achieved when the sign of curvature is simply altered [152], The respective design is that of a meander channel. At large Dean numbers, chaotic flow can be induced in this way, as evidenced by cross-sectional views of different segments of the meander channel. 

Polymer melts and solutions, on the other hand, are Theologically more complex fluids and, even under simple radiating flows in the entrance region, would need more stress components to sustain them thus there are larger entrance pressure drops. Additionally, the entrance flow patterns with polymer melts and solutions are typically more complex.6... 

Fig. 12.16 Entrance flow patterns in molten polymers, (a) Schematic representation of the wine glass and entrance vortex regions with the entrance angle. [Reprinted by permission from J. L. White, Critique on Flow Patterns in Polymer Fluids at the Entrance of a Die and Instabilities Leading to Extrudate Distortion, App/. Polym. Symp., No. 20, 155 (1973).] (b) Birefringence entrance flow pattern for a PS melt. [Reprinted by permission from J. F. Agassant, et al., The Matching of Experimental Polymer Processing Flows to Viscoelastic Numerical Simulation, Int. Polym. Process., 17, 3 (2002).]...

The site of the sharkskin distortion is again the die exit, and so is the screw thread pattern. The site of, and the mechanism for the gross extrudate distortion are problems that have no clear answers. The work of White and Ballenger, Oyanagi, den Otter, and Bergem clearly demonstrates that some instability in the entrance flow patterns is involved in HDPE melt fracture. Clear evidence for this can be found in Fig. 12.18. Slip at the capillary wall, to quote den Otter, does not appear to be essential for the instability region, although it may occasionally accompany it. ... 

D. Sarkar and M. Gupta, Further investigation of the effect of elongational viscosity on entrance flow, J. Reinf. Plast. Comp., 20, 1473-1484 (2001). 

Estimation of Entrance Pressure-Pressure Losses from the Entrance Flow Field17 Consider the entrance flow pattern observed with polymer melts and solutions in Fig. 12.16(a). The flow can be modeled, for small values of a, as follows for 0 < a/2 the fluid is flowing in simple extensional flow and for a/2 < 0 < rc/2 the flow is that between two coaxial cylinders of which the inner is moving with axial velocity V. The flow in the outer region is a combined drag-pressure flow and, since it is circulatory, the net flow rate is equal to 0. The velocity V can be calculated at any upstream location knowing a and the capillary flow rate. Use this model for the entrance flow field to get an estimate for the entrance pressure drop. 

It is doubtful, however, if melt fracture can be predicted from shear rate criteria alone, without taking the geometry of the apparatus into account. Especially the form of the channel at the entrance of the die is very important. In using extrusion dies with a conical entrance, flow instabilities are suppressed by decreasing the cone angle. This effect has been found experimentally by Tordella (1956), Clegg (1958) and Ferrari (1964). 

One technique for measurement of extensional flow that has been used to study various doughs is that of Cogswell (1972, 1978) for entrance flows. The analysis is based on several assumptions (Padmanabhan and Bhattacharya, 1993) (1) The flow is isothermal and creeping (negligible inertial effects), (2) the fluid is incompressible and has a pressure-independent viscosity, (3) the shear viscosity follows the power law model, t]a = Ky" (4) there is no slip at the edge of the converging profile, and (5) that the entrance pressure drop (Ape) in converging flow from a circular barrel in to a circular die can be considered to be made up of that due to shear (Ape,s) and extensional flow (Ape,E) ... 

The difference operator "A" here signifies the difference between exit and entrance flows and the snbscript "fs" indicates that the term applies to all flowing streams. 

Problem (3.29) with the formulated boundary conditions possesses a unique solution over the length of the entrance flow region 0 < x < Lx, but the value Lx, the unknown length of the entrance region, is to be chosen at a distance, where no further transformation of the flow field takes place. Lx can be easily adjusted in the course of the numerical performance. 

It is best to use a HPLC column always in the same direction or to know why the direction of flow has been changed. Many columns have an arrow which indicates the direction in this case it is not clear if it is possible to reverse the column. If the frits at both ends are identical in porosity it is no technical problem to run the column in the other direction, however, frits may differ in pore width and the wide-pore frit would be at the entrance. Flow reversal could not be recommended under these circumstances. If a column has no arrow it is good advice to draw one oneself. The column is then always used in the same direction, therefore fines and non-eluted compounds are concentrated at the inlet. The column is only turned for the purpose of regeneration. 

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