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## Brazilian Journal of Chemical Engineering

##
*Print version* ISSN 0104-6632*On-line version* ISSN 1678-4383

### Braz. J. Chem. Eng. vol.17 n.4-7 São Paulo Dec. 2000

#### http://dx.doi.org/10.1590/S0104-66322000000400010

**PERFORMANCE ANALYSIS AND DESIGN OF SMALL DIAMETER CYCLONES**

**M.R.T. Halasz ^{1} and G. Massarani ^{2* }**

^{1}PEQ/COPPE/UFRJ,

^{2}PEQ/COPPE/UFRJ

C.P.68502, CEP 21945-970, Rio de Janeiro - RJ, Brazil

Phone: +55 21 590-2241, Fax: +55 21 590-7135

E-mail: gmassa@peq.coppe.ufrj.br

*(Received: September 20, 1999 ; Accepted: April 6, 2000)*

Abstract -In this work, the effect of the configuration on the collection efficiency and pressure drop in small diameter cyclones is evaluated based on neural networks (Functional Link Networks). The experiences were conducted at LSP/COPPE Laboratory in a Stairmand high efficiency prototype (D_{c}= 5 cm) with variable overflow diameter. Three different configurations were tested, and it is possible to observe a significant increase in the collection efficiency with the reduction of the overflow diameter.

Keywords: small diameter cyclone, neural networks, radioactive wastes.

**INTRODUCTION**

This work stands for one of the development steps of an efficient gas treatment system, involving high performance small diameter cyclones with a high separation efficiency, for treatment of gases from radioactive waste incineration.

Annually a great amount of radioactive waste is generated, originated in nuclear power plants, radioisotope applications in industry, teaching and research institutions, hospitals, etc. [Raduan, 1993]. A traditional way of treating those wastes is using incineration, which is able to reduce the amount of waste for the safe disposal in fillings or storage facilities. The incineration process generates gases, ashes and vapors that must be treated before disposing. In general, the first step of such treatment is accomplished using cyclones, responsible for the removal of part of the particle solids.

The cyclones are solid-gas separators that use the same principle as the centrifuges, i.e., sedimentation by centrifugal field, and have been used in industry since the beginning of this century [Dirgo, 1985]. The cyclones present as main features the extreme versatility, low operational and maintenance costs, easy construction and installation [Leith and Licht, 1972].

The cyclone collection efficiency is directly affected by the cylindrical section diameter. The decrease in this parameter causes an immediate increase in the centrifugal field intensity formed inside the cyclone, increasing the separation efficiency. Small diameter cyclones are defined as the cyclones with diameter smaller than 5.0 cm, that can be used in the separation of small particles (smaller than 10mm) with high separation efficiency.

Small diameter cyclones can be used for treating radioactive wastes, due to their better ability to separate smaller particles than the traditional cyclones [Büttner, 1986 and Kim and Lee, 1990].

In this work a FLN (Functional Link Network) neural network was used for obtaining a model capable of describing the particle collection efficiency. The ortogonal estimator procedue of Billings *et al*. (1988) was used as implemented by Henrique and Lima (1996). The Matlab^{â} package was used for carrying out the computations.

In the literature it is possible to find a multitude of experimental data for cyclones with body diameter in the range of 20 to 100 cm. The experimental data used in this work, however, are related to small diameter cyclones with body diameter in the range of 1 to 5 cm. These data were obtained from Büttner (1986), Kim and Lee (1990) and Griffiths and Boysan (1992).

It is possible to build a model, using neural networks, that is able to predict the separation efficiency of small diameter cyclones with a good degree of confidence. In this work a neural network (Functional Link Network) was used, trained with literature data and validated using experimental results obtained for small diameter cyclones with the high efficiency Stairmand configuration. The equation obtained is presented below. In a detailed analysis (Figure 1) it can be noted that the separation efficiency tends to increase with a decrease in the overflow diameter (keeping the other parameters constant).

(1) |

where

(2) |

It is worth to note that the equation is a function of operational conditions [flow (**Q**), diameter of the particle to be separated (**d _{p}**) and ratio between fluid viscosity and particle density (

**m**

**/r**)], the equipment characteristic relations [

_{s}**(a/D)**,

**(b/D)**,

**(De/D)**,

**(H/D)**,

**(h/D)**,

**(B/D)**,

**(S/D)**] and cylindrical section diameter,

**D**. The limit values for the parameters are reported in Table 1.

The pressure drop is an essential parameter in the design of cyclone systems that allows to evaluate the blower specifications. Equation 3 represents one expression that can be used to calculate this parameter.

(3) |

where N_{H} is a dimensionless parameter and depends on the cyclone proportions, that by Shephered and Lapple (1939) is equivalent to:

(4) |

According to Figure 2, that represents Equation 3, it can be observed that the decrease in the overflow diameter (keeping other parameters constant) leads to an increase in the pressure drop in the cyclone.

Usually the methodology to determine the equations and design parameters for cyclones is semi-empirical and well known for some configurations. The equations for the design of a high efficiency Stairmand cyclone can be written according to the methodology proposed by Massarani (1991).

where K = 0.041 |
(5) |

where |
(6) |

(7) |

(8) |

D* is the cut diameter of the equipment, i.e., the diameter of the particle that is separated with 50% efficiency, K is the dimensionless constant that considers the cyclone geometry, DP is the pressure drop between the feed and the overflow, v is the velocity at the cylindrical section of the cyclone, r is the fluid density b is a dimensionless constant, which depends on the cyclone configuration, is the global collection efficiency and h(d_{p}) is the grade collection efficiency.

In this work the collection efficiency is evaluated for three different cyclone configurations, resulting from the variation of the diameter of the high efficiency Stairmand cyclone.

**MATERIALS AND METHODS**

The experimental system presented in Figure 3 was assembled using a high efficiency Stairmand cyclone with 5 cm diameter. Three different outlet diameters were adapted to this cyclone (D_{e} = 2.50, 2.35 and 2.25 cm). The feed inlet diameter could not be altered, because this section was fixed to the cylindrical section. A dust bunker was adapted to equipment underflow outlet, in order to collect the particle material. One-inch diameter piping was connected to the cyclone overflow outlet and to the blower suction inlet. An expansion tank was connected to the piping, between the blower and the cyclone, in order to avoid the retention of small particles in the rotameter.

The feed system is composed of two parts: one feed bin of 30 cm height and 8 cm of cylindrical section diameter, and a rotating disk of 20 cm diameter. The feed bin outlet is attached to a vibrator, which facilitates the particle flow from the feed bin. The rotating disk is used to guide the particles to the cyclone inlet.

In this work a gas-solid system was investigated. The solid materials studies are described in Table 2. The material present physical properties similar to the ashes resulting from the radioactive waste incineration (r_{s} = 3.0g/cm^{3} and dp_{mean} = 20mm). It could be observed that 40 wt% of the sand and 30 wt% of the neodymium carbonate particles have diameter smaller than 10 mm. It was possible to adjust the particle distribution of every condition studied using the Rosin-Rammler-Bennet (RRB) model, described by the following equation.

(9) |

where X is the mass fraction of particles with diameter smaller than D; D and m are model parameters, which represent the diameter correspondent to X=0.632 and to the dispersion, respectively.

The particle distribution was determined using the Malvern Masterizer X equipment and the solid density presented in Table 2 was determined using classic picnometry.

**RESULTS AND DISCUSSION**

Experiments using three different configurations of the small diameter cyclone were carried out. The first configuration **(1)** was the high efficiency Stairmand cyclone with D_{e}/D_{c} = 0.50, the second **(2)** and the third **(3)** were variations of the high efficiency Stairmand cyclone with D_{e}/D_{c} = 0.47 and D_{e}/D_{c} = 0.45, respectively.

When the collection efficiency is high, it could not be observed almost any differences between the particle distribution curves of the feed and the underflow. This leads to imprecision in the cut diameter determination and consequently in the determination of the design parameters, following the methodology described by Massarani (1991) (Eq. 5, 7 and 8), which considers the grade collection efficiency. In this case, it is possible to use the strategy proposed by Yuan (1996), where the design is based only on the global collection efficiency.

The global efficiency obtained with the three different configurations studied can be observed in Figures 4 and 5. The experimental results correspond to the predicted by the neural network, showing that when the overflow diameter is decreased, the collection efficiency increases. However, it could be noted by the experimental results that this increase is more significant when configurations (**1)** and (**2)** rather than when configurations (**2)** and (**3)** are compared.

It is possible to note from Figure 6 that the pressure drop increases with the flow rate increase, as expected. In this case the equation 3 is very good to describe the pressure drop.

**CONCLUSIONS**

It was confirmed through the Neural Network prediction and by the equation proposed by Shephered and Lapple (1939) that the decrease in the overflow diameter of small cyclones leads to an increase in the pressure drop and in the collection efficiency. The experimental results show that below a certain ratio (D_{e}/D_{c}), the increase in the collection efficiency is small when compared to the increase in the pressure drop.

**NOMENCLATURE**

a | cyclone inlet height [L] |

b | cyclone inlet width [L] |

B | cyclone lower (dust) outlet diameter [L] |

d_{p} | diameter of the particle to be separated [L] |

D | cylindrical section diameter [L] |

D_{c} | cylindrical section diameter [L] |

D_{e} | cyclone outlet diameter [L] |

D* | cut diameter of the equipment [L] |

D | diameter correspondent to X=0.632 [L] |

h | cyclone cylinder height [L] |

H | cyclone height [L] |

K | dimensionless constant [-] |

m | model RRB dispersion [-] |

N_{H} | dimensionless parameter [-] |

Q | flow rate [L^{3}/q ] |

S | cyclone gas outlet pipe length [L] |

v | velocity at the cylindrical section of the cyclone [L/q ] |

v_{i} | inlet velocity [L/q ] |

X | mass fraction of particles with diameter smaller than D [-] |

b | dimensionless constant [-] |

DP | pressure drop between the feed and the overflow [M/Lq ^{2}] |

global collection efficiency [-] | |

h(d_{p}) | grade collection efficiency [-] |

m | fluid viscosity [M/Lq ] |

r | fluid density [M/L^{3}] |

r_{s} | particle density [M/L^{3}] |

**ACKNOWLEDGEMENTS**

This work is part of the project entitled "Modelagem, Simulação e Controle de Processos Químicos", FAPERJ number E-26/150.970/99. Halasz would also like to acknowledge CNEN for the scholarship.

**REFERENCES**

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Büttner, H., Investigation on Particle Collection in Small Cyclones, J. Aerosol Science, V. 17, No. 3, p.537-541, Great Britain, (1986). [ Links ]

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Griffiths, W.D. and Boysan, F. , An Assessment of the Application of Computational Fluid Dynamics (CFD) to Model the Performance of a Range of Small Sampling Cyclones, J. Aerossol Science, V. 23, Suppl. 1, p. S587-S590, Pergamon Press Ltd., (1992). [ Links ]

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*To whom correspondence should be addressed