Screw pumps modeling

Figure 8.16. Planar model of part of a screw pump...

Hence, the physical model of the screw pump served as a tool to understand the underlying physics of extrusion, as well as a means to validate mathematical models of polymer processes. 

In this section we derive a simple mathematical model for the single screw pump. In such a model, we seek relationships between performance and operating variables with the geometrical variables as parameters. 

The basic function of the screw pump or extruder is to shear the fluid in the channel between the screw and the wall of the barrel, as shown schematically in Figure 3.36. The mechanism that generates the pressure cau be visualised in terms of a model consisting of an open channel covered by a moving plane surface (Figure 3.37). 

The high-pressure water supply is employed for the operation of the ordinary filter pump , which finds so many applications in the laboratory. Several types of water-jet pumps of glass, plastic or metal construction are available from most laboratory suppliers. These are often fitted with a suitable non-return valve to prevent the apparatus being flooded as a result of fluctuating water pressure. Connection to the water tap in the case of the metal pump is by a direct screw-threaded joint with the glass or plastic models high-pressure tubing of suitable bore is wired to the tap and to the pump. 

Pure pressure flow was first formulated and solved by Joseph Boussinesq in 1868, and combined pressure and drag flow in 1922 by Rowell and Finlayson (19) in the first mathematical model of screw-type viscous pumps. The detailed solution by the method of separation of variables is given elsewhere (17c), and the resulting velocity profile is given by... 

Note that the shape factors plotted in Fig. 6.13 are a function of only the II/W ratio. The effect of the flight on the pressure flow is stronger than that on drag flow. When the ratio Il/W diminishes, both approach unity. In this case, Eq. 6.3-19 reduces to the simplest possible model for pumping in screw extruders, that is, isothermal flow of a Newtonian fluid between two parallel plates. 

We have seen how the screw extruder pump is synthesized from a simple building block of two parallel plates in relative motion. We have also seen how the analysis of the screw extruder leads in first approximation back to the shallow channel parallel plate model. We carried out the analysis for isothermal flow of a Newtonian fluid, reaching a model (Eq. 6.3-27) that is satisfactory for gaining a deeper insight into the pressurization and flow mechanisms in the screw extruder, and also for first-order approximations of the pumping performance of screw extruders. 

The equations given in Fig. 6.5a and/or 6.5b can also be applied to an extruder section. In general, however, we do not know the power input to the shafts for an extruder section or, therefore, the specific energy input for this section. The pumping efficiency can be of use here it is determined in advance for the screw geometry in question (measurements taken with a model fluid are adequate, see Section 6.7) or determined by 3-dimensional calculations (as shown in Fig. 6.7). 

Twin-screw extruder Pressure flow model for Newtonian liquid in the pumping section. Vergnes et al., 1983, 1986... 

Fig. 4. Diagram of Perkin-Elmer Model 601 pumping system, a = pump, b = screws, c = motor, d pressure gauge, e = filter, f = drain valve, g = shut-off valve, h = small column, i = to column.

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