Radial velocity, hydrocyclones

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

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. 

The flow pattern in a hydrocyclone has circular symmetry, with the exception of the region in and just around the tangential inlet duct. The velocity of flow at any point within the cyclone can be resolved into three components the tangential velocity Vt, the radial velocity Vr and the vertical or axial velocity Va, and these can be investigated separately. 

In developing the equilibrium orbit theory, a key assumption made by Bradley and Pulling (1959) is the existence of a mantel in the hydrocyclone, which precludes inward radial velocity in the region immediately below the vortex finder. Furthermore, the LZW is assumed to be in the form of an imaginary cone whose apex coincides with the apex of the hydrocyclone and whose base is at the bottom of the mantle. Based on these assumptions, the equilibrium orbit theory has led to the development of empirical correlations for determining the cut size and pressure drop in hydrocyclone operation. 

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)...

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. 

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. 

Due to the vortex flow in the hydrocyclone, the static pressure in the flow increases radially outward. This centrifugal static head is primarily determined by the distribution of both, the tangential fluid velocities and the suspension densities, within the flow and it constitutes the major contribution to the total pressure loss across an operating hydrocyclone. 

The velocity of the fluid flow in a hydrocyclone can be resolved into three components tangential, axial, and radial. The most useful and significant of these three components is the tangential velocity. 

Equilibrium Orbit Theory. The general concept that particles of a given size reach an equilibrium radial orbit position in the hydrocyclone forms the basis of equilibrium orbit theory. The fine particles reach equilibrium at small radii where the flow is moving upwards and transports fines to the overflow, while the coarse particles find equilibrium position at large radii where the flow is moving downwards and carries these particles to the underflow outlet (apex). The dividing surface is the locus of zero vertical velocity (LZW). The size of the particles that find equilibrium radius on LZW will be the cut size that has an equal chance to finish in either overflow or underflow. 

A few streamhnes of the secondary flow in a meridian plane of the hydrocyclone 0 = constant) are sketched in Figure 17.7. The secondary flow is determined by the radial and vertical components of the velocity. Under the hypothesis that the rotational component is dominant, the flow has a two-dimensional structirre (equations [17.4]). Only the axial component of the velocity varies with z. The variation with z is linear, resulting from the conditions of incompressibihty. 

In a hydrocyclone, the flow is of the vortex type. The rotational velocity (equation [17.18]) and pressure (equation [17.20]) in the irrotational zone enable the calculation of the rotational energy of a partiole sitnated at radial distance r from the rotation axis ... 

The separation takes place in the centrifugal field of soheavy particles are forced to the outer wall (HW cleaners) whereas the fight ones are driven to the center (LW cleaners). The flow streams where the heavy or fight particles are accumulated are separated from the cleaned stock stream. The flow in a hydrocyclone is a three-dimensional two-phase flow. The circumferential component generates the centrifugal force, the axial component moves the solid particles towards the cleaner outlet and the radial component of the suspension flow proceeds from the outside towards the center and vice versa. 

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