1、4758 Comparison of Two Models for Particle Separation in a Vane-Induced Uniflow Cyclone Zhongchao Tan, PhD Student Member ASHRAE Yuanhui Zhang, PhD, PE Member ASHRAE ABSTRACT This paper compares two models that were developed independently for predicting the particle separation eficiency of a vane-i
2、nduced unijlow cyclone. The Zhang model was based on direct analysis and the Crawford model was based on indirect analysis. Both models were further derived to show that the particle separation eficiency depended on Reynolds number and particle property. Experimental data from a unijlow cyclone were
3、 collected to compare with the two models. Particle separation eficiencies of the unzj7ow cyclone were measured at three Reynolds numbers: 2.3x104, 4.1x104, and 5.910. The predictions using the Zhang model were closer to the experimental data. However, both models under- estimated the particle separ
4、ation eficiency compared with the experimental data. INTRODUCTION A large number of cyclones have been used for particulate air cleaning. Most cyclones fall into the following four basic categories: (1) reverse flow with a tangential inlet (involute), (2) reverse flow with a guide vane inlet (vane-a
5、xial), (3) uniflow with a tangential inlet, and (4) uniflow with guide vanes. In a reverse-flow cyclone, centrifugal force is intro- duced by a tangential inlet or guide vanes. Particles migrate to the wall and get separated from the gas stream; clean gas reverses direction and flows out through a c
6、entral gas outlet, and the collected particles exit at the bottom of the cyclone, In a uniflow cyclone, the gas and particles exit in the same direc- tion. Reverse-flow cyclones have longer residence time than uniflow cyclones; uniflow cyclones avoid the progressive leakage of gas into the central c
7、ore. Xinlei Wang, PhD Member ASHRAE The mainstream of cyclone history is dominated by reverse-flow cyclones. Most publications before the mid- 1990s dealt only with reverse-flow cyclones. Many models have been developed to predict the collection efficiency of reverse-flow cyclones under laminar or c
8、omplete mixing assumptions. These models have been summarized by Dirgo and Leith (1 985). Lapples (1 95 1) cut-size model based on the time flight approach and laminar flow assumption is often cited in the literature. Leith and Lichts (1 972) model is based on the assumption that flow is completely
9、and uniformly mixed. Crawford (1976) analyzed particle separation in a uniflow cyclone with a tangential inlet. He analyzed both laminar flow and complete mixing. Recently, Wang et al. (2002) proposed a fractional efficiency curve model to describe the fractional efficiency curves of reversed-flow c
10、yclones. This model assumed that the particle size distribu- tions were log-normally distributed. Then the cyclone frac- tional efficiency curves were generated from the inlet and outlet dust mass concentrations and the particle size distribu- tions. While reverse flow cyclones have been well invest
11、igated and commercialized, uniflow cyclones were rarely investi- gated-early investigations were done in the 1960s, leaving a great amount of uncertainties and unknowns. Uniflow cyclones are attractive due to their low pressure drops and simple structures. These advantages and the uncertainties enco
12、urage researchers to further investigate the particle sepa- ration mechanisms and to improve the performance. For a uniflow cyclone with tangential inlet, Summer et al. (1987) recommended an optimum separation length of around 1 cyclone diameter. Gauthier et al. (1990) found that the opti- mum lengt
13、h increased with the inlet air velocity. These Zhongchao Tan is an assistant professor in the Department of Mechanical and Manufacturing Engineering, University of Calgary, Calgary, Alberta, Canada. Yuanhui Zhang is a professor and Xinlei Wang is an assistant professor in the Department of Agricultu
14、ral and Biological Engineering, University of Illinois, Urbana-Champaign. 176 02005 ASHRAE. assumptions were validated by experiments of large particle separation in a small uniflow cyclone with tangential inlet. The diameter of the cyclone was 50 mm and the particles had a mean diameter of 29 pm. T
15、hese models might not apply for separation of fine particles in cyclones handling high airflow rates, where high turbulence and greater radial distance exist. Zhang et al. (2001) developed a vane-induced uniflow cyclone. This uniflow cyclone has been developed to achieve high collection efficiency a
16、t low pressure drop. The shape of its vanes and converging region were streamlined to minimize the turbulence intensity. Laboratory tests showed that the prototype was able to collect respirable dust particles at low pressure drop and high airflow rate. The total pressure drop across the prototype w
17、as 100 Pa at a gas flow rate of O. 136 m3/ s (288 cfm). The cut-size ofthe air cleaner was 4.5 pm in aero- dynamic diameter, measured using an aerodynamic particle sizer (APS). The total efficiency was 85% for particles with a mass median diameter of about 12 pm and geometric standard deviation of a
18、bout 1.6. This technology is being developed for agricultural indoor air quality control and emission reduction. This vane-induced uniflow cyclone is the subject of this paper. The purposes of this paper are to (1) analyze the factors that affect the performance of the uniflow cyclone and (2) compar
19、e two uniflow cyclone models, the Crawford (1976) model and Zhang (2003) model, using three sets of experi- mental data, and test if they are applicable for predicting the particle separation efficiency of uniflow cyclones. THEORETICAL ANALYSES Crawford (1976) Model Crawford (1976) derived indirectl
20、y the efficiency of the vane-induced uniflow cyclone. He first analyzed the cyclone flow in a straight tube with a tangential inlet. As shown in Figure 1, airflow enters the cyclone with an airflow rate of Q. The depth of the inlet is W (in a direction that is perpendicular to this piece of paper).
21、The inner and outer diameters are RI and R, respectively. Crawford (1 976) derived the efficiency equations for two conditions, laminar flow and complete mixing. When airflow travels a degree of , the particle separation efficiencies under laminar flow and complete mixing conditions are as follows:
22、W18qR2(R2 - R,)ln(R2/Rl) (Complete mixing) Then Crawford extended the above analysis to the appli- cation for vane-induced uniflow cyclones. He gave the follow- ing two relationships: Q 111 II Figure 1 Cyclone pow pattern in the Crawford (1976) model. “2 Q Figure 2 Schematic of Zhung S (2003) physic
23、al model. 8, = -tan(a) L R2 (3) (4) where a is the exit angle at R, when air exits the vanes. The efficiency under laminar flow conditions was not given. He used this value to obtain the collection efficiency in turbulent flow. Following Crawfords direction, we can get the effi- ciency of a vane-ind
24、uced uniflow cyclone under complete mixing condition: 2 (5) Qp,gLtan Q 36q nR:(R2 - Ri) In (R2/R , ) Zhang (2003) Model Similar to Crawfords (1 976) analysis, Zhang (2003) analyzed the particle separation in a straight annular tunnel under laminar flow and complete mixing conditions. As shown in Fig
25、ure 2, instead ofthe straight tube with a tangential inlet, he started directly from a uniflow cyclone with axial inlet airflow rate, Q. The length of the tunnel is L; the radii of the inner and outer cylinder of the tunnel are R, and R, respec- tively. The vane exit angle is a. ASHRAE Transactions:
26、 Research 177 Under laminar flow condition, it was assumed that air did not move in the radial direction. Particles entering the cyclone travel outward only. The particle separation efficiency equa- tion was where C, is a function of particle diameter. For a turbulent flow condition, as in Crawfords
27、 analysis, a conservative assumption of complete mixing flow was made. The effi- ciency equation was given as sc = 1 -exp (complete mixing). (7) Further Analysis of the Models In the above equations, a large number of variables are involved. Therefor, it is desirable to classify these parameters and
28、 to ascertain whether it is possible to describe the separa- tion efficiency in terms of dimensionless parameters. In models for reversed-flow cyclones, dimensionless geometric parameters are frequently defined. In this paper, Reynolds number is considered. Reynolds number for flow inside a round du
29、ct is defined as UD 11 Re = -, where U is the fluid velocity in ds, D the characteristic dimension of the system in which the flow occurs (m), and the kinematic viscosity of the fluid (m2/s). Here the fluid velocity is defined as inlet air velocity, V,. It is determined by inlet airflow rate, Q. The
30、 kinematic viscosity is 1.8 1 x 1 O-5 m2/s for room air at 2OoC and 1.01310 Pa. For the annular tunnel, the characteristic dimension is a diameter of a round duct that has an equal open area as the annular tunnel. Then we have D = 2,/=. (9) Then the Reynolds number in this paper is 2 V,/R; - R f Re
31、= The Crawford (1 976) equation can be expressed in terms of Reynolds number: cc = 1-exp -Re I 1 I 2 Ltan (a) 72Ri(-) In(R2/R1) R2+R1 1/2 R2 -Ri (Complete mixing) The Zhang (2003) equations can also be written as: c 2 Cc = 1 - exp -Re Ltan (2!/p4cCl (13) 18(R; - Ri) (Complete mixing) In the above th
32、ree equations, value in the first brackets after “Re” is determined by the cyclone geometry, while the value in the second brackets after “Re” is determined by the properties of the particle. In order to achieve high efficiency, the length (L) should be long, the vane angle (a) should be as large as
33、 practical, while the open area (R22-R,2) should be as small as practical. Note that particle separation efficiency is only one of several parameters that determine the overall performance of an air cleaner. These parameters include pres- sure drop, airflow rate, weight of the unit, and space availa
34、bil- ity. After the geometry is decided, the efficiency of a uniflow cyclone is determined by two factors, particle property (the density and size) and Reynolds number. Furthermore, for separation of a given particle in a cyclone with fixed geometry, the Reynolds number is the only parameter that de
35、termines its efficiency. All three equations show that the higher the Reynolds number, the higher the efficiency. This is disputable at a high Reynolds number when air turbulence intensity is high. In this case, the bouncing effect and reentrainment of particles may become significant. Consequently,
36、 the particle separation efficiency decreases with Reynolds number. To compare the above models, an example calculation is given in Figure 3. It is known that the curve under laminar flow condition is the upper boundary of the efficiency, but the lower boundary of the efficiency remains uncertain. F
37、igure 3 shows that the efficiency calculated using the Crawford (2003) model is always lower than with the Zhang (2003) model. EXPERIMENTAL SETUP A schematic of the experimental setup is shown in Figure 4. The aerosol from the dry disperser is diluted in the mixing chamber upstream of the cyclone. T
38、he airflow rate is adjusted with a variable transformer connected to the fan. The fan is downstream of the air cleaner. Upstream and downstream particle concentrations were measured under isokinetic sampling conditions. Particle separation fractional efficien- cies were calculated from the measured
39、concentrations of particles of different sizes. Prototype A diagram of the prototype is shown in Figure 5. The diameters of the inner and outer tubes were Ri=0.084 m and R2=0. 123 m, respectively. The overall length of the unit length of the cyclone was 1.27 m (50 in.). The straight section after th
40、e vanes was L=l .O m. Vane exit angle was a=60. 178 ASHRAE Transactions: Research Instruments and Sampling System Particle-sizing instruments include an Aerosizer DSP powder system (DSP) and an aerodynamic particle sizer (APS). The measurement particle size ranges are 0.5-20 pm and 0.2-700 pm for th
41、e APS and DSP, respectively. To achieve isokinetic sampling conditions, six sets (12 in total) of commercial isokinetic sampling nozzles were employed. Downstream rotational airflow was conditioned to an acceptable uniformity. As it has been proved that it is not prac- tical in the laboratory to eli
42、minate possible measurement errors attributed to swirl simply by using long ducts (Talbot 1954; Kreith and Sonju 1965; Laribi et al. 2001), an airflow conditioner was used downstream of the cyclone. This Bow conditioner has four vanes that were made of galvanized sheet metal with smooth surfaces. Th
43、e open ratio of a conditioner was greater than 98%. Considering the large open ratio and smooth surface of the vanes and small nonsticky particles downstream, the particle loss introduced by the airflow condi- tioner was expected to be minimal. The particle mass concen- trations after the now condit
44、ioner were measured at five locations to check the uniformity. The variation was less than 3% (Tan et al. 2003). Re=5.9xI O6 100% I I _- I -*I I / /- .- 0 25% 0% / / ,*- I 0 - - - - .Crawford I I I - Bang-CompMix - - - - .Crawford Il I , O 5 IO 15 20 Parcle aerodynamic diameter (pm) Figure 3 Compari
45、son between the Crawford (1976) model and the Zhang (2003) model (R2=0.123 m, R,=0.084 m, L=I.O m, a=60, Re=5.9xlO ). 4 Dust Dispersion Fully dispersed aerosols are required in order to evaluate the performance of air cleaning devices. The most widely used method for generating solid-particle test a
46、erosols is dry disper- BIO- fM haSS to exhaust Fan speed control step rnOtM Figure 4 Schematic of the experimental setup. ASHRAE Transactions: Research 179 Converging Straight region , region I l - / Bunker U Figure 5 Diagram of the prototype. sion. The basic requirements for all dry dispersers are
47、(1) a means of continuously metering a powder into the disperser at a constant rate and (2) a means of dispersing the powder to form an aerosol. When testing an air cleaner, it is usually not critical which dry dispersing method is used as long as the desired particle size and concentration remain c
48、onstant for the duration of measurement (Hinds 1998). This is compatible with the fact that many researchers develop their own dry dispersers for specific applications. As shown in the lower part of Figure 4, a dry disperser metered the dust using a turntable with a pressure manifold. To achieve a m
49、ass concentration less than 15 mg/m3, only a small amount of dust was needed. It was found extremely challeng- ing to feed a small amount ofpowder particles less than 1 O ym into a small groove and keep a constant bulk density. There- fore, an eight-way manifold was designed to divide the total dust flow rate. The exits of the manifold were evenly distrib- uted on the same cross section that was perpendicular to the direction of the entering airflow. It overcame the pressure difference problem. Dust was fed into the groove in the turn- table. A scrape
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