Velocities hydrocyclones

Theoretical representation of the behaviour of a hydrocyclone requires adequate analysis of three distinct physical phenomenon taking place in these devices, viz. the understanding of fluid flow, its interactions with the dispersed solid phase and the quantification of shear induced attrition of crystals. Simplified analytical solutions to conservation of mass and momentum equations derived from the Navier-Stokes equation can be used to quantify fluid flow in the hydrocyclone. For dilute slurries, once bulk flow has been quantified in terms of spatial components of velocity, crystal motion can then be traced by balancing forces on the crystals themselves to map out their trajectories. The trajectories for different sizes can then be used to develop a separation efficiency curve, which quantifies performance of the vessel (Bloor and Ingham, 1987). In principle, population balances can be included for crystal attrition in the above description for developing a thorough mathematical model. 

In each of these groups, the characteristic length is the cyclone diameter, D, and the characteristic velocity is V = AQ/tzD1. Various empirical hydrocyclone models indicate that the relationship between these groups is... 

Radially split multistage pumps, 21 67-68 Radial patternators, 23 194 Radial thrust, 21 83-84 Radial velocity, in hydrocyclones, 22 285... 

In the hydrocyclone, or hydraulic cyclone, which is discussed extensively in the literature(29 35), separation is effected in the centrifugal field generated as a result of introducing the feed at a high tangential velocity into the separator. The hydrocyclone may be used for ... 

Most studies of hydrocyclone performance for particle classification have been carried out at particle concentrations of about 1 per cent by volume. The simplest theory for the classification of particles is based on the concept that particles will tend to orbit at the radius at which the centrifugal force is exactly balanced by the fluid friction force on the particles. Thus, the orbits will be of increasing radius as the particle size increases. Unfortunately, there is scant information on how the radial velocity component varies with location. In general, a particle will be conveyed in the secondary vortex to the overflow, if its orbital radius is less than the radius of that vortex. Alternatively, if the orbital radius would have been greater than the diameter of the shell at a particular height, the particle will be deposited on the walls and will be drawn downwards to the bottom outlet. 

Figure 1.39. Typical velocity distributions in a hydrocyclone. (a) axial (h) radial (c) tangential (broken line LZVV is the locus of zero axial velocity)...

There have been very few studies of the effects of non-Newtonian properties on flow patterns in hydrocyclones, although Dyakowski et al.,AU have carried out numerical simulations for power-law fluids, and these have been validated by experimental measurements in which velocity profiles were obtained by laser-doppler anemometry. 

Figure 15 Axial velocity contours in hydrocyclone (Cullivan et al, 2004) (see Plate 14 in Color Plate Section at the end of this book).

FIGURE 4M (a) Left Measured and predicted tangential velocities in a 75-nun hydro-( lone right measured and predicted axial velocities in a 75-nun hydrocydone. (b) Predicted fluid streamlines and particle tirgectories in a 75-nim hydrocyclone. 

During the last few years, interest has increased in reactors in which high mass transfer is realized by means of liquid jet or injection devices providing gas or liquid entrainment jet reactors (N3, B30), hydrocyclones (Bll), venturis (S16, J2), and other high-velocity gas-liquid contactors. 

Hydrocyclones (see Figure 22.55) are closely related to centrifuges in that centrifugal forces effect the separation of particles. Rotational motion is effected by bringing the slurry radially into the upper periphery of the cyclone at high velocity. Solids are thrown out to the wall, flow down the inclined walls, and exit at the bottom. In general, hydrocyclones operate as classifiers with large particles in the underflow and small particles in the overflow. 

A different situation arises for hydrocyclones, in which the density of the disperse phase is only moderately greater than the density of the continuous phase. Therefore, for hydrocyclones, < 1, and their CE (Eig. 19.4, b) is small and essentially depends on the profile of the tangential flow velocity. From the three laws of swirling considered above, the greatest efficiency is provided by the law of quasi-solid rotation. 

In large-scale industrial crystallization processes, the most commonly used classification device is a hydrocyclone. The advantages of the hydrocyclone are its high capacity within a small equipment volume and an easily adjustable cutting size by the control of the feed-flow rate and the ratio of the up-flow to the down-flow. The fluid bed or elutriation leg is another method often used for classification in crystallization processes. With the elutriation leg, the feed or clear solution is fed from the bottom of the elutriation leg. The up-flow velocity is set based on the settling velocity of the cutting size... 

The tangential velocity inside the hydrocyclone is very inqrortant, it is the means by which a suspended particle following the liquid flow path because of drag will experience a centrifugal force. The tangential velocity of the solid will be similar to the liquid on entry into the hydrocyclone and it is assumed that this is also the case at any instant at radii less than that of the entry. 

Equation (8.28) provides a value for the tangential velocity at the outer radius of the hydrocyClone. Tang tial velocities at radii less than that of the hydrocyclone can be estimated by means of the princ le of conservation of angular momentum under flictionless conditions ... 

The net solid and liqtud flows are in the same direction, unlike radial flow, but there axe two distinct regions inside the hydrocyclone with net velocities in different directions. The secondary vortex spins into the vortex finder and, therefore, takes material into the overflow. Thus net flow in the secondary vortex is upwards. In the primary vortex net flow is dovmwards towards the underflow. 

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