Cyclones theory

Important parameters in cyclone operation can be established by considering simple cyclone theory. Figure 8.1 shows a sketch of a typical cyclone. Air at a flow of Q cm3/s enters tangentially, revolving NT times in the cyclone before it is discharged. Dust that is removed from the air spirals down into the dust discharge port. 

Trefz M, Muschelknautz E. Extended cyclone theory for gas flows with high solids concentration. Chem Eng Technol 16 153-160, 1993. 

For smaller particles, the theory indicates that efficiency decreases according to the dotted line of Figure 7. Experimental data (134) (sofld line of Eig. 7) for a cyclone of Eig. 9 dimensions show that equation 15 tends to overstate collection efficiency for moderately coarse particles and understate efficiency for the finer fraction. The concept of particle cut-size, defined as the size of particle collected with 50% mass efficiency, determined by equation 16 has been proposed (134). 

A more sophisticated theory was given by Barth, in which the pressure drop of a cyclone is defined as a function of the swirling velocity head of the fluid in the outlet pipe as follows ... 

It should be noted that most of these theories for the prediction of the pressure losses in cyclones ultimately require the assignment of certain experimentally determined quantities in order to produce reasonable agreement between theory and experiment. The involvement of these empirical constants almost certainly restrains the use of the theories to the limited group of cyclones that the experiment has covered in order to produce good predictions of pressure drops through the cyclone. Therefore, these empirical theories may be used only as a preliminary estimate of the energy consumption in cyclones. Prototype cyclone experiments may well be required in order to obtain an accurate value of the pressure loss for a newly designed cyclone. 

Hugi and Reh [Chem. Eng. Technol. 21(9) 716-719 (1998)] have reported that (at high solids loadings) enhanced cyclone efficiency occurs when the solids form a coherent, stable strand at the entrance to a cyclone. The formation of such a strand is dependent upon several factors. They reported a higher cyclone efficiency for smaller = 40 rm) solids than for larger solids (dp,50 = 125 xm). This is not what theory would predict. However, they also found that the smaller particles formed coherent, stable strands more readily than the larger particles, which explained the reason for the apparent discrepancy. 

This equation is a result of the residence time theory of particle collection. In this theory, the time that it takes for a particle to reach the wall is balanced by the time that a particle spends in the cyclone. The particle size that makes it to the wall by the time that it exits the cyclone is the particle size collected at 50 percent collection efficiency, Dpth. 

The separators in Figure 2.3 may be either a cyclone type, as typified by the Bradley microsizer or a mechanical air separator. Cyclone separators, the theory of operation and application of which are fully discussed in Chapter 1, may be used. Alternatively, a whizzer type of air separator such as the NEI air separator shown in Figures 1.29 and 1.30 is often included as an integral part of the mill, as shown in the examples of the NEI pendulum mill in Figure 2.21. Oversize particles drop down the inner case and are returned directly to the mill, whilst the fine material is removed as a separate product stream. 

The papers in this section represent the theory and current industry practices in the separation process and in separator design. Because separation is such a basic requirement for the oil and gas industry, a wealth of information has been published concerning the process and the various design techniques used in the manufacture of separation equipment. Some of these techniques are proprietary, however, and the details of the design are not readily available. For instance. British Petroleum has done considerable design and testing of cyclone-type separation equipment in recent years with the objective of miniaturizing the equipment for use on offshore platforms. For further details on this and other proprietary equipment, one must contact the manufacturer or licensee of the equipment. 

In a separate investigation on the fragility of agglomerates, we have determined that the agglomerates up to modest sizes are sufficiently robust to withstand the rigors of the flow through cyclones and electrostatic precipitators (27). The research is based on experimental results with inertial separation devices (impactors) and comparing the experienced shear stresses in impactors as determined from theory, with the shear stresses experienced in cyclones. 

In elutriation methods, particles are classified in a column by a rising fluid stream. A series of cyclones are used to separate particles into different size ranges. Gas adsorption of a gas on a powder is another method for determining surface area. Measurements are usually interpreted by using the Braunauer, Emmett, and Teller (BET) theory. 

Many theories have been proposed to predict the performance of a cyclone, although no fundamental relationship has been accepted. Attempts have been made to predict the critical particle diameter, (Dp) j,. 

Apart from the northern winds blowing from May to October, frequently recurring are also southern winds which also increase the recurrence of cyclonic circulation of waters. But this does not change, in principle, Simonov s theory about the factors that induce anticyclonic circulation of water in the sea. 

The theory of particle removal by cyclones is well developed and equipment dimension ratios are well established, making it possible to design cyclones to remove particles of a known size range with reasonable estimates of particle collection efficiency as a function of particle size. However, the efficiency of cyclones is greater for the larger particles. Smaller particles can only be removed with cyclones of small diameter. Pressure drops in cyclones can be substantial and often limit the smallest particle size that can be removed. Multiple cyclones are sometimes used in series or parallel. 

EquHibrium orbit theory is a useful means of correlating and eiq>kiiimg the relation between flow rate and hydrocyclone cut size. Its use as a predictive tool is limited, however, as tests must be conducted to determine several parameters required in the model notably the flow split and the eiqionent on the radius in the cyclone. It does not provide any information on the pressure drop required to perform the separation, or on the arpness of the cut. 

Theory for cyclone separators. It is assumed that particles on entering a cyclone quickly reach their terminal settling velocities. Particle sizes are usually so small that Stokes law is considered valid. For centrifugal motion, the terminal radial velocity v,n is given by Eq. (14.4-8), with v,] being used for v,. 

Several authors have attempted to calculate particle trajectories in the cyclone and to derive formulae at least for the equiprobable size X50 if not for the whole grade efficiency curve. Some of these theories are discussed in section 6.6 certain observations are given here and refer to the probable behaviour of solid particles in sufficiently dilute suspensions. 

Simple, fundamental theories which take no or little account of the effect of the flow ratio (or the size of the underflow orifice), of the feed concentration and of the feed size distribution. The influence of some cyclone dimensions on the cyclone performance is included. 

The crowding theory which explains the strong effect of the size of the underflow orifice on cyclone performance in some cases. 

The equilibrium orbit theory is based on the concept of the equilibrium radius, originally proposed by Dries sen" and Criner. According to this concept, particles of a given size attain an equilibrium radial orbit position in the cyclone where their terminal settling velocity is equal to the radial velocity of the liquid. Particles are therefore elutriated by the inward radial flow according to the balance of the centrifugal and drag forces, and Stokes law is usually assumed. 

The equilibrium orbit theory in all its various forms suggested by various authors, can be criticized on the grounds that it takes no account of the residence time of the particles in the cyclone. Not all particles may be able to attain equilibrium orbits within their residence time. The theory also takes no account of turbulence as it might affect particle separation. Despite the above disadvantages, many of the various forms of the equilibrium orbit theory (as reviewed more fully by Svarovsky ) give reasonable predictions of cyclone performance at low feed solids concentrations, particularly if used under similar conditions and with similar cyclone designs and sizes as in the original work of their respective proposers. 

The residence-time theory assumes non-equilibrium conditions and considers whether a particle will reach the cyclone wall in the residence time available. Rietema first proposed this theory and assumed homogeneous distribution of all particles across the inlet. The cut size will then be the size of the particle which, if entering precisely in the centre of the inlet pipe will just reach the wall in residence time T. In mathematical terms, this means that the particle radial settling velocity integrated with time should therefore be equal to half... 

Rietema s theory does not take into account the radial fluid flow, it neglects any effects of inertia, it takes no account of hindered settling at higher concentrations and it assumes any influence of turbulence to be negligible. A more recent version of the residence-time theory, the so-called bulk model due to HoUand-Batt °, does take into account the radial fluid flow. He simply used the hold-up time of the liquid in the cyclone (flow rate per cyclone volume) as the residence time, average radial fluid velocity (flow rate per wall area of the cyclone) and a general continuity equation for two-dimensional flow to derive an expression for the cut size. 

A more rigorous viscous turbulent model of single-phase flow, based on a Prandtl mixing length theory was published by Bloor and Ingham. Like Rietema, these authors obtained theoretical velocity profiles, but they used variable radial velocity profiles calculated from a simple mathematical theory. The turbulent viscosity was then related to the rate of strain in the main flow and the distribution of eddy viscosity with radial distance at various levels in the cyclone was derived. 

A much more scientific proof of the crowding theory has recently emerged from some mathematical modelling work by Bloor et This is a hydro-dynamic model of the flow both in the cyclone body and in the boundary layer (the cyclone design is that of Kelsall ), but it makes no predictions of conditions at underflow because it breaks down at the vertex. The model assumes inviscid flow in the main body and viscous flow in the boundary layer. It allows plots of particle trajectories, assuming their homogeneous distribution on entry to the cyclone cone. 

Unlike the theories reviewed in the previous sections, the model by Bloor et al. does not lead to any simple correlations for the cut size or the grade efficiency curve, but it is the first time that any direct proof of the crowding theory is given. On the basis of an actual set of conditions studied, the authors give a quantitative example if a cyclone operates satisfactorily at 5% solids concentration and this is increased to 15%, the underflow rate must be increased by a factor of 1.6 in order to prevent overcrowding and possible blocking of the underflow orifice. 

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