Flow in a hydrocyclone

Hydrocyclones are centrifugal separators which enable the separation of solid partieles that are denser than the fluid, or of less dense partieles (those are often non-tniscible droplets in another liquid). Such apparatus present the advantage of not including any moving parts. The rotation results from the winding of the flow in a circular cyhndrical cavity. 

In the inlet section of the apparatus, it is sirrrpler to express the velocity components in the Cartesian coordinate system Assuming the flow to be 

The velocity components are denoted by ux,Uy,u ) in the Cartesian coordinate system (0,XjV,z) and (ur, ug, u,) in the citcirlar cyUndtical coordinate system (0,r,d ). V designates the mean streamwise velocity in the inlet section where the flow is irrotational (a = curl( ) = 6). 

At high Reynolds numbers, if transit through the apparatus is fast, vorticity does not have enough time to diffuse. Kelvin s theorem resirlts in the flow being irrotational in the part of the apparatus through which the flow passes. It is therefore also irrotational in the outlet sectiorts (spigot and overflow). This resirlt has two consequences  

The rotating flow is of vortex type in the hydrocyclone. This is modeled by a Rankine vortex of radius a and circrrlation T, using equation [17.18]. The radius a depends directly on the geometrical corrtraction ratios Ri/R and R /R between the radius of the upper cavity and those of the extraction apertures. 

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The flow patterns in the hydrocyclone are complex, and much development work has been necessary to determine the most effective geometry, as theoretical considerations alone will not allow the accurate prediction of the size cut which will be obtained. A mathematical model has been proposed by Rhodes et alP6), and predictions of streamlines from their work are shown in Figure 1.38. Salcudean and Gartshore137 have also carried out numerical simulations of the three-dimensional flow in a hydrocyclone and have used the results to predict cut sizes. Good agreement has been obtained with experimental measurements. 

Figure 14.20. Schematic representation of spiral flow in a hydrocyclone [77].

Numerical calculations of the complete flowfield, using axially symmetric flow models and solving the full viscous equations of motion, have been carried out by Boyson, Ayers and Swithenbank and by Rhodes, Pericleous and Drake. These simulations are suitable for assessing parameters in design optimization provided they are based on realistic boundary conditions and a comprehensive flow model. Bloor, Ingham and Ferguson have also produced a numerical simulation for viscous flow in a hydrocyclone but at unrealistically low Reynolds numbers. Unlike the others they did not, however, ignore the three-dimensional character of the flow around the entry point and used three different models to simulate the entry flow. 

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. 

The fluid flow in a hydrocyclone has been described in section 17.2.3. Hydrocyclones are used for separating particles that are denser than the fluid or for separating lighter elements (oil droplets, for example). In the first case, the particles are thrown onto the conical sidewall of the apparatus and then extracted through the spigot. In the second, the droplets migrate toward the Oz axis of the apparatus and are extracted via the overflow. 

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. 

The vessel design features a Chinese hat-like conical core stopper above the underflow sump, which is there to prevent the vortex from reaching the latter and reentraining the settled soHds. The core stopper is also beheved to stabilize and locate the vortex flow in the vessel. Overflow from the vessel is through a wide cylindrical insert through the Hd, similar to a vortex finder in a hydrocyclone (16), and an optional provision can be made for collecting any floatables in a float trap. 

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. 

Brayshaw, M.D., 1990. Numerical model for the inviscid flow of a fluid in a hydrocyclone to demonstrate the effects of changes in the vorticity function of the flow field on particle classification. International Journal of Mineral Processing, 29, 51. 

The rheological properties of the drilling fluid have a marked influence on the performance of solids control equipment. Froment et al. (163) have pointed out that an increase in the viscosity of the drilling fluid will decrease the flow rate capacity of the shale shaker and will increase the minimum particle size of the solids in the separated stream from a hydrocyclone that is returned to the circulating drilling fluid. For example, Figure 59 shows the particle size distribution of the solids in the under flow from a hydrocyclone. The density and viscosity of the drilling fluid are observed to have a marked effect on the separation characteristics of the hydrocyclone. 

Estimate the cut point when treating 1 L/s of suspension in a hydrocyclone of 2 in diameter. The concentration of the suspension is 15% by volume, its density is 1250 kg/m , and behaves as non-Newtonian with determined values of the flow behavior index of 1.28 and the fluid consistency index of 2.03 x 10 . The density of the suspended solids is 2800 kg/m . 

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. 

It should be pointed out here that this short account of velocity profiles in a hydrocyclone is only qualitative the flow patterns are highly complex even for water with a low specific gravity and viscosity, and it may be incorrect to assume that precisely similar profiles occur in cyclones with a considerably different geometry or with liquids of high viscosity. 

A vast amount of work has been published concerned with modelling the flow and the separation process in a hydrocyclone. The different approaches to the problem can be classified into seven categories Figure 6.8) as follows. 

Another theoretical approach to cut size prediction that can be classified as another version of the residence-time theory is that of Trawinski. In direct analogy with gravity settling Trawinski used Stokes law, an effective clarification area and an average acceleration in a hydrocyclone to derive an expression for the cut size. The same author also proposed a rather simplistic correlation for the pressure drop-flow rate relationship. 

Bloor, M. I. G., Ingham, D. B. and Ferguson, J. W. J., A viscous model for flow in the hydrocyclone . Session I, Solid-Liquid Separation Practice III, 397th Event of the European Federation of Chemical Engineering (Bradford, 1989)... 

The modification of hydrodynamic aspects is exploited in the falling-film cell [12], where the electrolyte flows as a thin fllm in the channel between an inclined plane plate and a sheet of expanded metal which work as electrodes. Other proposal is to include turbulence promoters in the interelectrode gap in conventional parallel plate electrochemical reactors [13-16], or the use of expanded metal electrodes immersed in a fluidized bed of small glass beads, called Qiemelec cell [17]. Likewise, the Metelec cell [18] incorporates a cylindrical foil cathode concentric arranged around an inner anode, with a helical turbulent electrolyte flow between the electrodes. The electrochemical hydrocyclone cell [19] makes use of the good mass-transfer conditions due to the helical downward accelerated flow in a modified conventional hydrocyclone. 

The pattern of fluid flow within the hydrocyclone body is best described as a spiral within a spiral with circular symmetry. A schematic view of the spiral flow inside a hydrocyclone is shown in Fig. 23b. The entering fluid flows down the outer regions of the hydrocyclone body. This combined with the rotational motion creates the outer spiral. At the same time, because of the wall effect, some of the downward moving fluid begins to feed across toward the center. The amount of inward motion of fluid increases as the fluid approaches the cone apex, and fluid that flows in this inward stream ultimately reverses its direction and flows upward to the cyclone overflow outlet via the vortex finder. This reversal applies only to the vertical component of velocity, and the spirals still rotate in the same circular direction. In the meantime, the downward flow near the wall carries solid particles to the apex opening (bottom outlet). 

The centrifugal force may be imposed by virtue of the flow of the slurry, as in a hydrocyclone, or by means of mechanically driven rotation, as in the sedimenting centrifuge. 

Separation criteria are fundamentally different depending on whether the flnid flow is of sohd-body rotation type or vortex type. By way of example, the qnality of separation is affected when the flow rate through a centrifugal separator is increased, while the inverse property is obtained in a hydrocyclone. 

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 ... 

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