PARTICLE REMOVAL Cyclones in Industrial Ventilation

13.2.1.1 Working Principles of the Cyclone

Cyclone collectors are popularly used both for particle removal and for particle sampling (Fig. 13.1). The separation process of a cyclone rtlits on the centrifugal accelerations that are produced when particle-laden flmJ txperi-

Ences a rapidly swirling motion in the cyclone. The larger the particle, the stronger the centripetal acceleration it acquires and, therefore, the easier it is for the particle to be collected. Figure 13.2 is a schematic diagram of the tra­jectories for a small and a large particles in a typical cyclone. A particle of small diameter penetrates the cyclone, whereas a particle of large diameter finds its way to the side wall of the cylindrical portion of the cyclone and is then collected at the apex of the cyclone via the boundary layer flow.

The collection efficiency curve is usually employed to demonstrate the performance of a cyclone. Figure 13.3 shows a typical collection efficiency curve for a cyclone at a particular airflow rate. The size of particles that have a collection efficiency of 50% is usually employed as a simple indication of the separation efficiency of the cyclone, and is known as the cut-off particle size ds0. Particles larger than the cut-off size D50 are more likely to be separated by the cyclone, and particles smaller than the cut-off size are more likely to pene­trate the cyclone.

Particle

{a) Particle of small diameter

Pressure loss through the cyclone is also a key performance parameter, and this depends mainly on the design of the cyclone. In general, the pressure drop across the cyclone collector is small compared with most other dust col­lectors, but the higher the collection efficiency required, the larger the pressure drop and hence the energy consumption required.

Particle

(b) Particle of large diameter

FIGURE 13.2 A schematic diagram of the trajectories for two different sizes of particles in a typical cyclone.

Particle diameter (|Xm) FIGURE 13.3 Typical collection efficiency curve of a cyclone.

13.2.1.2 Theoretical Analysis

A series of theoretical analyses of the fluid and particle collection effi­ciency of cyclones were performed in the 1970s by Bloor and Ingham1-3 And they have been found to be in good agreement with the experimental data.

Fluid Flow Model

The steady, laminar, incompressible fluid flow in cyclone collectors is gov­erned by the Navier-Stokes equations:

P. Vz P 2	Vxf I = ^Vxfl P
(13.1)

V-V = 0, (13.2)

Where V is the fluid velocity; V x V is the vorticity; and P, p, and /x are the pressure, density, and viscosity of the fluid, respectively.

It is convenient to employ two sets of coordinate systems. Spherical polar coordinates (r, 9, A) are defined with the origin at the vertex of the cone; the axis is 0=0, the surface of the conical portion of the cyclone is the cone 8 = a*, and the azimuthal coordinate is A. Using the same origin, cylindrical polar coordinates (R, A, Z) are defined, where R = R sin 0 and the Z-axis co­incides with the axis 0=0.

Flow in the (r, 9) Plane The experimental data of Kelsall4 gave strong evidence that fluid flow in the cyclone may be assumed to be axisymmetrical.

Therefore, a stream function Ґ may be introduced in the meridian plane of the cyclone, i. e., the (r, 9) plane in the spherical coordinate system: Ay

Ay Dr

= — V9r sin

= Vrr- sin 0 ,

(13.3

D9

I yy 3 Sin 6 dr2 d0

I ay

Ode

R2sin

R2Sin0

Where the subscripts denote the particular components of the fluid velocity V. For fluid flow in the (r, 6) plane, it is reasonable to assume that the fluid is inviscid, as the Reynolds number of the fluid flow usually exceeds 0(105). Thus Eq. (13.1), with Fx = 0, may be integrated along the streamlines to give the Bernoulli equation as follows: P + V1 = H(‘Ґ). f 1.3.4) P 2 Similarly, integrating the A component of Eq. (13.1) along a streamline shows that the angular momentum of the fluid remains constant throughout everv streamline as follows:

R sin 0 VA = C(VK).

(13.5)

Where H(‘F) and C(*P) are arbitrary functions of the stream function. There­fore, the following differential equation for ‘F may be obtained from Eq. (13.1)

(13.6)

Subject to the boundary conditions that must be imposed at the axis, at the inlet, and on the wall boundaries of the cyclone, Bloor and Ingham3 found that the solution for may be approximated by the expression

(13.7)

Z

Y = B(r6)i/2(a* — 9) or = BR3/2

Where A* is the semi-angle of the cone of the cyclone and B is a constant that may be determined by the volume flux of air through the cyclone as follows:

2vBc3/2(a’ — C/t) = Q, (13.8)

Where C is the outer radius of the vortex finder and I is the distance be­tween the entrance plane of the vortex finder and the vertex of the cone.

Thus, the velocity components of the fluid may be determined, in cylindri­cal polar coordinates, as follows:

B TjR

V Vz~ RdR

(13.10)

V — I3V_ BRi/2 Vr RdZ z2

The Spin Velocity Under the inviscid flow assumption, where all fluid that enters the cyclone does so with approximately the same amount of mo­mentum, a free vortex may be predicted for the spin velocity distribution as

VA = A/K

(13.1:

Where A is a constant and N = 1. Due to the effects of viscosity, this expression actually overestimates the spin velocity. Therefore, Svarovsky ■ suggests that N Takes a value in the region 0.2-0,9 and has to be determined experimentally.

However, more accurate predictions for the spin velocity may be ob­tained with allowance made for the effect of viscosity in the governing equj — tion for the spin velocity. According to the experimental data of Kelsali,4 Which indicates that the spin velocity in a cyclone is a function of R only, the A component of Eq. (13.1) in the cylindrical polar coordinate system may re­duce to

DR R

Vr d f T 7 D _ P R dR{V*R)

(13.12)

DR R

A proper representation of the effective viscosity is often problematic. Based on the Prandtl mixing length model for turbulence, Bloor and Ingham2 Suggest that the variation in (x should be of the form

Й^-^ + K | DR R

= M z2

(13.13)

Where M is a constant related to the turbulence viscosity at the inlet of the cyclone and K is another constant that reflects the shear near the axis of the cyclone.

Since Vx is independent of Z in Eq. (13.1), the boundary condition at the level of the inlet may be employed as follows:

V* = 0

At R = 0

(13.14)

(13.15)

VA = v, at R = Rc,

Where Vi is the speed of the fluid at the inlet and Rc is the radius of the cy­clone. If VR can be regarded as known from Eq. (13.10), then Eq. (13.12) may be solved numerically to obtain VA.

Particle Collection Model

In most cyclone applications in industrial ventilation, the particle concen­tration in the cyclone is very low and it may be assumed that the particles have very little chance of colliding with each other in the main body of the cyclone. Hence, the fate of the particles, whether they are collected or they penetrate the cyclone, may be determined by tracking the motions of individual, isolated particles suspended in the fluid flow.

The motion of an isolated particle in a highly rotating cyclone airflow is normally determined based on the balance on the resulting centrifugal force acting on the particle and the drag exerted by the airflow. In industrial ventila­tion, cyclone collectors are often employed as precleaners and the particle to be separated is normally larger than about 10 mm. Therefore, the drag exerted on the particles may be considered the dominate force on the particle by the
air flow, and the effects of the turbulent diffusions may be ignored. For a spherical Particle of diameter D placed in a fluid stream of speed V, the drag F is given By Stokes’s law as follows:

F = 377-jLl(V — Wp)d , (13.16)

Provided that the particle Reynolds number Rcf,, which is defined by

Re?; = p|V-pd/ix , (13.17)

Is less than 0(1). Fortunately, in most cases of interest, Rep is very small and the use of Eq. (13.16) is adequate. In the case where the particle Reynolds num­ber is not small, empirical formulas may be obtained for the drag as follows:

F = 3CDirix(V~Vl,)d , (1.3,18)

Where CD is the drag coefficient, often expressed as an empirical function of the particle Reynolds number

CD = 1, 0 < Re;, I (13.19)

Cr

1 < Re,, <4 (13.20)

Cn = (0.324 + 21.9416/Re<F18)Re?/24 4 < Kep < 2000 (13.21)

CD = 0.4Rep/24 Rep > 2000 (13.22)

Theoretically, for a particle of a given size that moves in the highly rotat­ing fluid flow in a cyclone, a particular radial orbit position may be found in every horizontal plane of the cyclone where the outward centrifugal force is just balanced by the drag exerted on the particle by the radial inward fluid flow. If Stokes’s law (13.16) is assumed, then the position of the equilibrium orbit on each horizontal plane of the cyclone may be obtained and is Given by

BR3/2 _ , A Dlyl Z2 (Pp P)8ixR‘ (13.23)

See Bloor and Ingham2 for more details.

In the vertical plane of the cyclone, two important lines may be obtained that determine the fate of the particle in the cyclone. One is the equilibrium line (Fig. 13.4), which may be obtained from Eq. (13.23), and the other is the line of zero vertical fluid velocity, which is obtained from Eq. (13.9) as follows:

R = 3aZ/S. (13.24)

Particles inside the equilibrium line penetrate the cyclone with the inward fluid flow, while the particles outside the equilibrium line, and cannot reach the equilib­rium line, are collected by the downward fluid flow. When the particles do reach the equilibrium line, their fate is determined by the direction of the vertical fluid velocity at this point (i. e., whether it is upward or downward at the equilibrium line). If a particle is in equilibrium in an upward-moving stream, it will penetrate the cyclone; otherwise it will be collected. It is evident that small particles find their equilibrium orbit at small radii and therefore are more likely to join the upward

Fluid flow and penetrate the cyclone, while the large particles find their equilibrium line m the region of the downward fluid flow and are collected.

Ror a given particle of size D, from the point M where tne equilibrium line meets the line of zero vertical velocity (see Fig. 13.4), the critical path of the par­ticle may be defined. All particles of this size between points D and G are en­trained in the downward stream and are collected. The remaining particles of this size join in the upward-moving stream of fluid and penetrate the cyclone. The point D may be obtained by tracking back the particle trajectory from the point M using the equation of the particle trajectory, which is given by

(13.25)

V» +

(,Pp-P)d2vп

ОSfjuR

Therefore, Bloor and Ingham2 found that the collection efficiency of a cyclone for the particle size D may be estimated by the following formula:

3/2

El Rr

Al/c3’2-

*J2 Rc

1

(13.26)

Where RD is the value of R at point D, and Rcis the radius of the cyclone.

Estimation of the Pressure Losses through Cyclones

Conventionally, the pressure drop of a cyclone is expressed in terms of the fluid velocity head in the cyclone. If the head of the fluid velocity at the inlet of

The cyclone is employed, then the pressure loss of a cyclone may be expressed As Follows:

A Pc = Cf%Vl, (1.3.27)

And we know from dimensional analysis that the total loss factor C, is a func­tion of the fluid Reynolds number, Re. However, under the normal operating conditions of cyclones, Re is usually larger than ~105, indicating that the iner­tial force dominates over the viscous force and thus Cf becomes practically a constant for the particular cyclone type.

A number of attempts to relate the geometric design parameters of a cy­clone to the pressure drop have led to various empirical formulas for the Loss

Factor Cf. One of the simplest formulas is an expression proposed by Sheperd and Lapple:6

Cf=-M^=Uab/D}, (13.28)

‘ pVi/2

Where A is the width of the cyclone inlet orifice, B is the height of the cyclone inlet orifice, and De is the diameter of the outlet pipe of the cyclone.

A more sophisticated theory was given by Barth,7 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:

A Pc=cЈvie, (13.29)

Ia V7

Where Cf is the total loss factor of the cyclone. The swirling component of the fluid velocity at the outlet pipe may be estimated using the balance between the angular momentum at the inlet and at the outlet of the cyclone, taking into consideration the wall friction of the cyclone:

—— (13.30)

A, a+CKTrHR,

Where A, is the cross-sectional area of the inlet pipe, R, is the radial dis­tance from the axis of the cyclone to the axis of the inlet pipe, Re is the ra­dius of the outlet pipe, CA is a surface friction factor, and H is the length of the cyclone chamber below the outlet pipe at the diameter of the outlet of the pipe (see Fig. 13.4). The constant a takes values ranging from 0.5 to 1.0 depending on the design of the inlet pipe of the cyclone (see, for exam­ple, Klinzing et al,8).

Barth assumed that the pressure loss of a cyclone consists mainly of the pressure loss required to overcome the wall friction of the cyclone and the pres­sure drop to drive the fluid out of the cyclone outlet pipe. This leads to the fol­lowing expression for the total loss factor CR:

Pipes and 3.4 for rounded-edged pipes. An experimental value of Q ■= 0.018 was found to suit a wide range of applications, but a modified value may be obtained in situations where the mass load ratio of the solid particles is to be taken into account—for example, in a pneumatic conveying system. In this case, the following expression may be employed to determine the value of CA (see, for example, Klinzing et al.8):

(13.32)

Where Ms and Trij are the mass flow rate of the solid and of the fluid, respectively.

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.

13.2.1.3Numerical Simulations of the Fluid and Particulate Flows in the Cyclone

The rapid development of high-speed digital computers has made it prac­tically possible to fully simulate three-dimensional turbulent fluid flow and particle movement in cyclones by numerically solving the governing fluid and particulate flow equations. As a result of the numerical solution, a group of discrete values for the fluid velocity, pressure drop, particle trajectories, etc. can be obtained, and this may give a clear picture of what is going on in the cyclone being investigated.

Simulation of the Fluid Flow

Due to the very low volumetric concentration of the dispersed particles in­volved in the fluid flow for most cyclones, the presence of the particles does not have a significant effect on the fluid flow itself. In these circumstances, the fluid and the particle flows may be considered separately in the numerical sim­ulation. A common approach is to first solve the fluid flow equations without considering the presence of particles, and then simulate the particle flow based on the solution of the fluid flow to compute the drag and other interactive forces that act on the particles.

For steady, incompressible fluid flow in a cyclone separator, the governing Navier-Stokes equations of motion are given, in a Cartesian coordinate system, by:

(13.33)

Where U‘ is the fluid velocity, with the superscripts I, j = 1, 2, 3 indicating the com­ponents in the Cartesian coordinate system, and t" is known as the Reynolds stress tensor, which represents the effects of the turbulent fluctuations of the fluid flow.

An appropriate model of the Reynolds stress tensor is vital for an accurate prediction of the fluid flow in cyclones, and this also affects the particle flow simulations. This is because the highly rotating fluid flow produces a strong nonisotropy in the turbulent structure that causes some of the most popular tur­bulence models, such as the standard K-e turbulence model, to produce inaccu­rate predictions of the fluid flow. The Reynolds stress models (RSMs) perform much better, but one of the major drawbacks of these methods is their very com­plex formulation, which often makes it difficult to both implement the method and obtain convergence. The renormalization group (RNG) turbulence model has been employed by some researchers for the fluid flow in cyclones, and some reasonably good predictions have been obtained for the fluid flow.

Simulation of the Particle Motion

In practice, particle tracking is usually performed in a Lagrangian frame of reference, and the motion of a particle is governed by

P^vd’du!,

-V-7f = f’’ <13-35>

Wiiere P is given by Eq. (13.18).

By integrating Eq. (13.35) step by step in time, the particle trajectory of the particle may be obtained. In the integration, the interaction between the particle and the wall may be approximated as being fully elastic; however, when the par­ticle hits the sidewall of the cyclone, the particle may be treated as being col­lected and the computation for the particle may terminated in order to save the computational time that may be required to track the particle to the bottom of the cyclone. If the particle trajectories for a range of particle diameters at differ­ent rates of fluid flow through the cyclone are determined, then the particle effi­ciency curve and the cut-off particle diameter of the cyclone may be obtained.

13.2.1.4 General Recommendations

As a simple and efficient particle separation device, cyclone collectors can be used for anything from dust removal in a fluid stream to material collection in the fluid conveying system. However, the cyclone is not suitable or econom­ical for the separation of extremely small particles (say, less than 1 pun), which frequently occur in industrial processes. It is recommended that the size of particles to be separated in an industrial ventilation cyclone be in the region of around 10 to 100 |im. However, for the purpose of aerosol sampling, the size of particles to be separated may be much less than 10 |xm.

For a specific size of particle to be separated by the cyclone, a first rough es­timate of the cyclone size may be obtained by estimating the particle drift veloc­ity in the cyclone. A large cyclone may be used if the particle drift velocity is large. If N is the number of the revolutions that the particle travels with the fluid in the cylindrical part of the cyclone, then the smallest particle of diameter D That can be separated by the cyclone may be approximated by (see Baturin 9)
Where R,,iV is the radius of the inner wall of the inlet pipe of the cyclone., ftaturin9 Suggested that three full revolutions of the fluid stream in the cylindrical portion of the cyclone are adequate, as an increase in the number of revolutions improves the efficiency slightly but makes the construction unduly long and complex.

For conventional cyclones, it is recommended that the inlet thud veiociiy be around 10-20 m/s and the conical angle of the cyclone be usually made smaller than 25°. If a single cyclone cannot meet the large fluid throughput re­quired, then the use of multiple cyclones in parallel should be considered.

In general, a cyclone with a smaller diameter, longer length, and small ver­tex angle usually possesses a higher collection efficiency. While small cyclones are usually more efficient than the larger cyclones, it should be stressed that As The size of the cyclone decreases the pressure drop increases.

For a fixed value of pressure drop, the fluid flow rate is approximately proportional to the size of the overflow diameter. A reduction in the overflow diameter leads to an increase in the pressure drop over the cyclone in order to keep the fluid flow rate unchanged. When the fluid flow rate is fixed, then, in general, the reduction in the size of the overflow diameter results in an in­crease in efficiency. This is simply because a small outlet opening makes it dif­ficult for the particles to penetrate the cyclone.

Normally the vortex finder should extend down into the conical portion of the cyclone. It is thought that the vortex finder plays an important role in the maintenance of a stable spiraling fluid flow in the cyclone, and this makes it more difficult for the particles to leak through the boundary layer on the roof of the lid of the cyclone to the overflow tube.2 Without a vortex finder, the efficiency may be reduced by 4-5%.9 However, an excessive long vortex finder may hinder the high spin velocity in the fluid flow and thus reduce the efficiency of the cyclone.

/ 1 1/2 W Across the 1 1/4 >

‘50 ‘

*50 ’

For a cyclone of fixed dimensions, the collection efficiency may be im­proved by increasing the fluid flow rate through the cyclone. As a consequence of this, the pressure drop over the cyclone increases. It can be shown that the relationship between the cut-off diameter Dso and the fluid flow rate Q may be approximated as follows:5

(13.3′

In terms of the pressure drop &p across the cyclone, we have

{13.38)

And this implies the general rule that the higher the efficiency, the larger the pressure drop across the cyclone.

Once these first estimates for the geometric dimensions of the cyclone have been obtained, a full theoretical analysis of the fluid and particle mo­tions in the cyclone may be performed using the theoretical models given in Section 13.2.1.2. A substantial use of the expression (13.26) for the collec­tion efficiency should be employed so that an updated design of the geome­try of the cyclone can be obtained.

Based on the theoretical estimates of the design and operating condi­tions of the cyclone, the computational fluid dynamics approaches described

In Section 13.2.1.3 should then be employed for a more detailed analysis of the fluid and particle flows and the performance characteristics of the cy­clone.

Once a design of the cyclone has been estimated, a prototype of the cy­clone should be made with sufficient flexibility left in its design so that as many quantities as possible can be easily adjusted. Experimental investiga­tions should then be performed under realistic operating conditions. Using the observations made above on the adjustment of various operating conditions and geometric parameters, the cyclone should be modified in order to meet the needs of the particular application for which it is to be employed. Once this has been done, the bulk manufacture of the cyclone may be initiated.

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