Cyclone geometry

For a properly designed and operated cyclone, the sharpness iadex is constant, typically 0.6. The cut size and apparent bypass are a function of the cyclone geometry, the volumetric feed rate, the material relative density, the feed soflds concentration, and the slurry rheology. The relationship for a standard cyclone geometry, where if is the cylinder diameter ia cm and inlet area = 0.05 vortex finder diameter = 0.35 ... 

As with dust cyclones, no reliable pressure-drop equations exist (see Sec. 17), although many have been published. A part of the problem is that there is no standard cyclone geometry. Calvert (R-12) experimentally obtained AP = 0.000513 J Q /hiWi) 2.8hiWi/dl), where AP is in cm of water Pg is the gas density, g/cm is the gas volumetric flow rate, cmVs hj and Wj are cyclone inlet height and width respectively, cm and is the gas outlet diameter, cm. This equation is in the same form as that proposed by Shepherd and Lapple [Ind. Eng. Chem, 31, 1246 (1940)] but gives only 37 percent as much pressure drop. 

In determining the proper size and number of cyclones required for a given application, two main objectives must be considered. The first is the classification or separation that is required, and the second is the volume of feed slurry to be handled. In the case of hydroclones, before determining whether these objectives can be achieved, it is necessary to establish a base condition as follows Feed liquid - water at 20 C. Feed solids - spherical particles of 2.65 specific gravity Feed concentration - less than 1 % solids by volume Pressure drop - 69 kPa (10 psi) Cyclone geometry - "standard cyclone" as described above. 

The Bradley hydrocyclone has a lower capacity than the Reitema geometry but is more efficient. For the Rietema cyclone geometry the cor-relatins are (Antunes and Medronho, 1992)... 

The computer program PROG44 calculates the pressure drop and the efficiency of the cyclone using the cyclone geometry, fluid and particle specifications. Table 4-8 gives the input data and computer results with an efficiency of 63.305%, and a pressure drop of 7.834 in HjO. The calculated ratio of the particle diameter relative to the critical diameter is 0.51. From Figure 4-8, the percentage removal of the particle is 23%. 

A simple and reliable set of equations to predict cyclone performance from a known size distribution, cyclone geometry and flow rate does not exist. Laboratory testing must be used to ensure that a desired separation can be accon li ed. It is usefiil, therefore, to have some notion of how the important variables are related, in order to minimise the required amount of test work to optimise performance. The inqtortant design and process variables are cut size, cyclone diameter, flow rate and pressure drop. 

The Euler number represents the ratio of pressure forces to the inertial forces acting on a fluid element. Its value is practically constant for a given cyclone geometry, independent of the cyclone body diameter (see Section 9.4). 

The values of the radial and tangential velocity components at the cyclone wall, Ur and U r, in Equation (9.20) may be found from a knowledge of the cyclone geometry and the gas flow rate. 

Letters refer to the cyclone geometry diagram shown in Figure 9.5.)... 

Ideally it should be possible to predict simply from the fresh feed catalyst size analysis and a specific reactor and cyclone geometry how the bed analysis and reactor losses will change with time and how these will converge to an equilibrium. If attrition were not a significant factor it is obvious that the addition of fresh make-up catalyst coarser than the losses would cause the bed size distribution to become continually coarser until theoretically losses would be reduced to zero. 

Over the decades that cyclones have been used, many different reverse-flow cyclone geometries have been tried to improve efficiency, prevent particle attrition, prevent erosion of the cyclone wall, or prevent particle buildup on the cyclone surfaces. However, there are a few basic types that have emerged as the most popular over the years. Some of these cyclone types are shown in Fig. 3. The cyclones shown in this figure are the tangential inlet cyclone, the volute Met cyclone, and the axial inlet cyclone. This last type of cyclone uses axial swirl vanes to impel the gas solids mixture into rotary centrifugal motion. 

Figure 7.3.15. (a) Geometry of a conventional reverse-flow cyclone (b) particle trajectory in a cyclone having an idealized flow pattern. (After Flagan and Seinfield (1988).) (c) Modified cyclone geometry for analysis. (After Dietz (1981).)... 

Equation (5.2.2) represents one functional form for representing the grade-efficiency curve (GEC). The writers own analysis on numerous commercial and laboratory cyclones reveals that the form of Eq. (5.2.2) describes some cyclone geometries quite well, especially smooth, well-designed laboratory cyclones. The exponent 6.4 is, however, a little larger than the values t3q>i-cally observed in some large-scale, refractory-lined, commercial cyclones and in some poorly designed small-scale cyclones. In these latter cases, the exponent typically lies between 2 and 4. 

The performance predictions in Fig. 5.2.2 are for a standard cyclone geometry with a typical inlet velocity used in laboratory testing. In Appendix 5. A we shall be looking at a case involving a much larger inlet velocity, namely the one for which we predicted the pressure drop in Chap. 4. 

Mothes and Loffler simplified the cyclone geometry by making the cyclone cylindrical as shown in Fig. 5.B.I. They chose the radius of their cylindrical cyclone R q so that the volume of the cylindrical cyclone, and therefore the gas residence time, equals that of the physical one ... 

Fig. 5.B.I. Simplified cyclone geometry for the Dietz and Mothes-Loffler models. Dietz does not have Region 3...

In this section we will present formulas required to design or evaluate a conventional cylinder-on-cone or a predominately cylindrical type of cyclone geometry. In doing so, we shall follow closely the methods of Muschelknautz (1970, for example) and, to some extent, those of Muschelknautz and Trefz (1990, 1991, 1992). Some departures from the MM will be worked into the development that follow the writers own experiences and preferences. 

We mentioned that one assumption in Derksen (2003) was one-way coupling between the gas and the solid phase. In Derksen et al. (2006), this assumption is relaxed, and the effect of the solids on the gas flow pattern, i.e. two-way coupling, is taken into account in simulations of the flow in the same cyclone geometry as in Derksen (2003). In order to do this without having to trace prohivitively many particles, each particle that is traced is considered to represent a whole assembly of like particles, the action of which on the gas flow Is fed back Into the gas equations to determine the effect of the particles on the gas flow field. 

As is standard in scaling, we assume that the model and the prototype are geometrically similar. This means that all dimensionless numbers describing the cyclone geometry, for example the ratio of the vortex finder diameter to the body diameter Dx/D, are the same between model and prototype. 

Both the models of Smolik and Zenz predict cyclone separation efficiency as a function of loading purely from knowledge of the efficiency at low loading and the loading itself. Physical and operational factors, such as cyclone geometry and size, solids size distribution and density, inlet velocity and other operating conditions, are not included in these models, and the effect of these parameters is thus not thought to be of primary importance. In the Muschelknautz model, on the other hand, the inlet velocity, the cyclone dimensions, and the mean size and density of the inlet solids all feature. 

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