The cyclone is a commonly used piece of equipment that makes use of the centrifugal and gravitational fields to separate particles in gaseous streams (Ogawa, 1997). One of the reasons for the wide variety of applications of cyclones is due to the fact that they are easy to inspect and maintain. They are easy to build, relatively economical to operate and can be adapted to a wide range of operational conditions (Leith, 1984). Therefore, they are preferred to other gas-solid separators for a number of applications (Koch and Licht, 1980).

The main parameter for evaluating the performance of a cyclone is its collection efficiency, i.e., its capacity to remove the solid particles dispersed in the gas stream that enters the equipment.

Collection efficiency is influenced by the operational conditions, physical properties of the solid material fed and the geometry of the cyclone. It is known that an increase in the inlet gas velocity and in the diameter and density of the particles results in an increase in efficiency (Leith, 1984). For the same powder, cyclones with different geometrical proportions show different efficiencies, and these influences have received relatively little attention from researchers. Optimization of a cyclone by the careful establishment of its operational conditions and/or its geometrical characteristics improves its performance and reduces the need for more sophisticated and expensive secondary gas cleaning devices (Koch and Licht, 1980).

The objective of this study was to evaluate the influence of the geometrical characteristics of the equipment and the inlet gas velocity on the overall collection efficiency of a cylindrical-conical cyclone. Considering its wide practical acceptance, the project criteria proposed by Leith and Licht (1972) were used as the basis for construction of a series of cyclones, departing from the classical tangential entrance Stairmand cyclone. Starting with this basic configuration, the heights of the gas exit duct (vortex finder) and the cylinder were varied. The influence of these parameters on the efficiency of collection of particulate material was then studied.

MATERIALS AND METHODS

The dimensions of a cylindrical-conical cyclone are schematized in Figure 1.

According to Leith and Licht (1972), collection efficiency for a cyclone can be expressed by

where Q is the gas volumetric flow rate and t_i is called relaxation time, given by

where d_pi and r_p are the particle diameter and density, respectively, and m the gas viscosity.

The exponent, n, normally called the vortex index, can be estimated as a function of cyclone diameter (in ft) and of gas temperature (in ⁰F) by the following expression:

The effects of cyclone configuration on separation efficiency are considered using factor G, given by

where

The annular volume above the exit duct up to the middle of the gas entrance duct, V_s, is given by

The natural length of the vortex, l, can be estimated by

For l <(H-S), volume V_nl,, which is the volume of the region that includes the natural length of the vortex excluding the central core, can be estimated by

where the diameter of the central core, d_n, is defined by

For l>(H-S), volume V_H, which is the volume of gas below the gas exit duct excluding the core, can be calculated by

These design criteria, proposed Leith and Licht (1972), will be used for comparison throughout this work. A more detailed description of each one of these terms can be found in the above reference.

Experimental Rig

Figure 2 shows a schematic view of the experimental system used in this work.

The rig includes a powder-feeding port (1), linked by a hose to a powder dispenser of the rotating-plate type (2). The powder was isokinetically sampled before entering the cyclone using a probe (3) linked to a filtering membrane (4). Suction was achieved by a vacuum pump (5) regulated for constant flow rate by a flow controller (6). An identical sampling system was placed after the cyclone exit (9).

The air was supplied to the system by a blower and the entrance velocity was measured with a Pitot tube, positioned in the same manner as the sampling probe. The entrance temperature was measured by a copper-constantan thermocouple (7). The dust accumulated in the reservoir (8).

The particulate material used in the tests was a phosphatic concentrate with a density of 3.03 g/cm³, median diameter of 30.5 mm and concentration of approximately 3 g/m³.

Statistical Analysis

For the experimental tests performed, a 3³ experimental design was utilized and the results were analyzed using response surfaces. The parameters of the statistical model were estimated by linear regression, utilizing the least squares method. The variables referring to the cyclone dimensions (h and L) were used in dimensionless form, in relation to the diameter, Dc.

According to the statistical method, the variables were coded and their original values with the respective coded values are shown in Table 3.

RESULTS AND DISCUSSION

The effect of G, defined by Equation 4, on the cyclone’s overall efficiency, obtained both experimentally and by theoretical calculation using Equation 1, is shown in Figures 4 to 6 for the three gas velocities tested.

For the whole range of velocities studied, a decrease in efficiency is verified with the increase in G for the experimental points and an inverse tendency is predicted by the theoretical curves. Observing Figures 4 to 6, it can be seen that there is a convergence of the predicted and experimental values as G decreases. For smaller values of G, the curves tend towards similar values of overall efficiency for all the velocities studied. The deviations of the experiment from theory for G smaller than 1000 lie below 5%, except for Vi = 6.2 m/s with G=864.09 and 798.06, where the deviations were of 11.2 and 14.3%, respectively.

The values of G for the classic high-efficiency Stairmand and Swift cyclones are 551.3 and 699.2, respectively. These values fall within the range where there is a closer agreement between the theoretical curves and experimental points. Therefore, Equation 1 gives a good estimate of overall efficiency for classic geometries, which have lower values for parameter G.

It can also be observed in Figures 4, 5 and 6 that, with the increase in gas velocity, the agreement between the theoretical and experimental curves tends to improve, but the dependency between G and efficiency remains inverse. These results indicate that the equation proposed by Leith and Licht (1972) seems to be restricted to a narrow range of G and fails in the prediction of cyclone efficiency for large variations in cyclone configuration.

Results from the Statistical Model

Equation 12 results from the statistical treatment of the data. The parameters were estimated within a significance level of 5% and the correlation coefficient, R², for the model was 0.9401.

where h is the overall efficiency of the cyclone and the constants A to E, valid for coded variables, are listed in Table 4.

The results of the influence of the variables studied on the overall efficiency of the cyclone, obtained by statistical analysis, are presented in Figures 7 to 9.

The strong influence of variable Vi on overall collection efficiency can be seen on the response surfaces in Figures 7 and 8. Efficiency increases significantly with the increase in inlet gas velocity. According to Hoffman et al. (1995), vortex length increases with the increase in gas velocity, for a fixed cyclone geometry. Therefore, besides increasing the centrifugal force, an increase in gas velocity also increases the effective collection area in the cyclone, and both effects result in an appreciable improvement in collection efficiency.

Figure 7 shows that initially efficiency tends to increase with the length of the internal tube, L*, until a maximum value is reached when L*=0. Conversely, Figure 9 shows a decrease in efficiency with increasing L* for the whole range studied. In Figure 9 the general tendency for efficiency to decrease as the length of the internal tube is increased can be verified. This influence is in accordance with the analysis of Dullien (1989), which suggests that an optimum value for the length of the gas exit duct is the cyclone diameter.

Efficiency decreases with increasing h*, as can be seen in Figure 9, for the whole range of L* tested. Yoshida et al. (1991) report an experimental and theoretical study of the collection efficiency of a reverse-flow cyclone, and they verified that large particles are collected in the upper part of the cyclone and small particles in the conical section. This conclusion can be an indication that the increase in ratio h* decreases the collection area for fine particles (conical section), thereby affecting overall efficiency.

The influence of gas velocity is stronger than that of any of the other variables when analyzed separately. It can be observed that the regions where velocity is higher correspond to higher efficiencies than those where velocity is lower, independently of the other variables.

CONCLUSIONS

1. The methodology used in this work allowed the study of the influence of gas velocity, Vi, and the geometrical parameters, h* and L*, on the overall efficiency of cyclones.

3. The inlet gas velocity of the cyclone was the variable with the greatest stronger influence on its efficiency: the higher the velocity, the higher the overall collection efficiency within the studied range.

4. Variables h* and L* also influenced efficiency: the higher the values for these variables, the smaller the overall collection efficiency.

NOMENCLATURE

The authors would like to thank PRONEX-FINEP and CNPq for the financial aid given for this work.

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