Numerical Simulation of Particle Concentration in a Gas Cyclone Separator *

Transcription

1 2007 Petroleum Science Vol.4 No.3 Numerical Simulation of Particle Concentration in a Gas Cyclone Searator * Xue Xiaohu, Sun Guogang **, Wan Gujun and Shi Mingxian (School of Chemical Science and Engineering, China University of Petroleum, Beijing, , China) Abstract: The article concentration inside a cyclone searator at different oeration arameters was simulated with the FLUENT software. The Advanced Reynolds Stress Model (ARSM) was used in gas hase turbulence modeling. Stochastic Particle Tracking Model (SPTM) and the Particle-Source-In-Cell (PSIC) method were adoted for articles comuting. The interaction between articles and the gas hase was also taken into account. The numerical simulation results were in agreement with the exerimental data. The simulation revealed that an unsteady siral dust strand aeared near the cyclone wall and a non-axi-symmetrical dust ring aeared in the annular sace and under the cover late of the cyclone. There were two regions in the radial article concentration distribution, in which article concentration was low in the inner region (r/r0.75) and increased greatly in the outer region (r/r>0.75). Large articles generally had higher concentration in the near-wall region and small articles had higher concentration in the inner swirling flow region. The axial distribution of article concentration in the inner swirling flow (r/r0.3) region showed that there existed serious fine article entrainment within the height of 0.5D above the dust discharge ort and a short-cut flow at a distance of about 0.25D below the entrance of the vortex finder. The dimensionless concentration in the high-concentration region increased obviously in the uer art of the cyclone searation sace when inlet article loading was large. With increasing gas temerature, the article searation ability of the cyclone was obviously weakened. Key words: Cyclone searator, article concentration distribution, simulation 1. Introduction The turbulent flow field with strongly swirling flow in a cyclone is very comlex. The article flow and the interaction between articles and gas hase are even more comlicated. Many investigations on gas and solids flows in a cyclone searator have been conducted over the yearswu, et al.,1993; 1994a; 1994b; Wu and Shi, 2003; Cao, et al.,1994and a number of emirical models for estimation of the erformance of a cyclone were develoed, but these models are not always suitable for different cyclones. The article concentration in a cyclone is the basis for searation rocess study and new model develoment. However the exerimental data of the article concentration in the cyclones were rare and sarsely reorted in literature due to the difficulties in measurement, esecially for a cyclone at high temerature and high solids loading conditions. Along with the develoment of comuter technology, comutational fluid dynamics (CFD) codes have roved to be a useful tool for exloring the gas-solids flow in a cyclone, and may be a more generic way to know what is haening in the cyclones. The revious numerical research mainly aimed at the gas-hase flow field and the article-trajectory (Lin and Wang, 1999; Wang, et al., 2006), and only a little attention was aid to the article concentration in the cyclones (Xue, 2005). In order to gain some insights into the hysical characteristics of the cyclone searation rocess, the effects of inlet article loading, article diameter and gas temerature on the article concentration in a cyclone were numerical examined in resent study. 2. Model and method 2.1 Mathematical model For the unsteady and incomressible turbulent flow in cyclone, the Reynolds-stress Model (RSM) is frequently used for simulation (Lu and Zhou, 2003). This model was also used in this study. Besides the time-averaged continuity equation and momentum equation, the transort equation of the stress comonents is exressed as follows (Hu, et al., 2005): t ( ρuiu j ) + ( ρu k uiu j ) = Dij + Pij + Π ij ε ij x k (1) where, the left side of the equation is the local time derivative and convection term, resectively. D ij, P ij, ij and ε ij are stress diffusion, stress roduction, ressure-strain and stress dissiation rate terms, resectively. The closed model of ressure-strain term, ij, concerns the reasonableness of the rediction of Reynolds stress. After selecting from several available linear and nonlinear models, such as IPM (Gibson and * Suorted by the National Key Project of Basic Research of the Ministry for Science and Technology of P. R. China (Grant No. 2005CB ) ** Corresonding author: Prof. SUN Guogang. ggsun@163bj.com

2 Vol.4 No.3 Numerical Simulation of Particle Concentration in a Gas Cyclone Searator 77 Launder, 1978), IPCM (Fu, et al., 1987), GL (Launder, 1989a), SSG (Launder, 1989b), FLT (Seziale, et al., 1991), the Isotroization of Production and Convection Model (IPCM) and the wall model were used. In order to redict the Reynolds stress better, an imroved model for strongly swirling flow (Hu, et al., 2004) was used, in which the model constant was otimized in consideration of the strongly swirling flow in the cyclone. The stochastic Particle Tracking Model describes the article motions by tracking article trajectories in a Lagrangian frame of reference. It is suitable for numerical simulation of dilute gas-article two-hase flows where the volume fraction of the article hase is small, which is similar to the article concentrations in most arts of a cyclone. Therefore, in this aer, the Stochastic Particle Tracking Model was selected to simulate the article trajectory, and the Particle-Sourcein-Cell (PSIC) method (Cen and Fan, 1990) is used to calculate the article concentration. Generally, the article concentration, C i, in the cyclone entrance is less than 10 kg/m 3 (C i 10 kg/m 3 ). The article volume fraction,ε C i / ρ b =0.37%-0.67%1%. Since the article concentration in most arts of a cyclone ( ε <<1%) belonged to the dilute hase excet in the wall region, the article-article interaction could be neglected. Only the gas-article interaction and the disersion of articles due to turbulence were taken into account. Therefore, the article motion equations in a Lagrangian frame of reference could be exressed as: Axial Radial du Tangential dt dv dt 1 = ( ug + ug u ) g τ 2 0 (2) 1 w = ( vg + vg v ) + (3) τ r dw dt 1 uw = ( wg + wg w ) (4) τ r where,, g stands for the articles and gas hase, resectively. r 0 is the radial osition of articles. τ stands for the relaxation time of articles., u g, v g and w are the fluctuation velocity comonents. g 2 ρ d 24 τ = (5) 18μ C Re where, is article density. d is article diameter. is the molecular viscosity of the gas. The drag coefficient, a2 a3 C D, can be obtained from C D = a1 + +, where 2 Re Re D 0 a 1, a 2 and a 3 are constants for smooth sherical articles over several ranges of Re given by Morsi and Alexander (Morsi and Alexander, 1972). Re is the article Reynolds number. From gas momentum equations, the influence of temerature on the gas flow field is shown by their influence on gas viscosity and density. Hence, the gas viscosity and density were exressed as the functions of temerature in the numerical simulation. The relationshi between gas viscosity and temerature is as follows: T μ T = μ 0 T (6) 0 where m is an exeriential exonential, which is for air. According to the gas law, gas density is exressed by m T0 P ρ T = ρ0 (7) T P0 2.2 Boundary conditions and grids Fig. 1 shows the geometry of the simulated cyclone. The gas inlet dimension is 176 mm84 mm. The body inner diameter is 300 mm. Structure grid was used for calculation, and the grid of the cyclone searator is shown in Fig. 2. The number of grid nodes is 978,653. The cyclone inlet air velocity was 20 m/s. The initial osition of articles was on the cross-section of the inlet of cyclone, with the distribution of all the articles being uniform. Particles were injected from every grid center with the same velocity of the inlet gas. The calculated article diameter (or diameter distribution), article concentration and the number of articles random tracks were all defined at the cyclone inlet cross-section It was assumed that there was no mass change and no heat transfer during the rocess of articles motion. The 325 mesh talcum owder with a density of about 2,700 kg/m 3 was selected as the simulation articles, and the diameter distribution of which is shown in Table 1. Table 1 Diameter distribution of 325 mesh talcum owder d, μm M D, % Assuming that the diameter distribution of articles satisfies the Rossin-Rammler distribution, the following equation for article size distribution can be obtained by regression of the data in Table 1:

3 78 Petroleum Science 2007 to be fully develoed, the cyclone exit tube was rolonged. The exit boundary condition of articles was assumed to be that when it ran into the exit the article could escae from the cyclone. A no-sli boundary condition was used at the wall in calculation of the gas-hase flow field. Standard wall functions were used to model the flow near the wall region. The article-wall boundary condition was considered as damed elastic collision. The coefficient of restitution was set as for the to annular sace of cyclone, for the middle searation sace and for the dust hoer. The QUICK discretization and SIMPLE-C algorithm were used to calculate the cyclone flow field, associated with unsteady article trajectory tracking calculations. The gas flow field and article trajectory were calculated alternately until a converged solution was achieved. Fig. 1 Schematic diagram of the cyclone 3. Results and discussion 3.1 Test of the simulation results To judge the creditability of the simulation results, the numerically calculated result was comared with the exerimental data in literature (Wu, et al., 1994a). Fig. 3 shows the measured and the calculated radial article concentration distribution on the cross section at a distance of 600 mm (Z=600 mm) below the vortex finder entrance. Fig. 4 shows the comarison of the measured and the calculated results of the axial article concentration distribution at the radial osition of r/r=0.3. The comarisons indicted that the calculated result of the article concentration distribution was satisfactory. Fig. 2 M D The grid of cyclone searator [ ( d 12. ) ] = ex 74 (8) The exit boundary condition of the continuous hase was considered as a fully develoed tube flow, assuming all the flow variables with a zero axial gradient on the ϕ exit cross-section, i.e. = 0. In order to ensure the flow Z Fig. 3 Simulated and measured radial article concentration distribution in searation sace (Z=600 mm)

4 Vol.4 No.3 Numerical Simulation of Particle Concentration in a Gas Cyclone Searator 79 Fig. 4 Simulated and measured axial article concentration distribution (r/r=0.3) 3.2 Basic characteristics of article concentration in a cyclone Figs. 5-6 show the simulated article concentration on the wall at two moments (t=2.7 and 3 s). Figs. 7-9 dislay the article concentrations in the annular sace, searation sace and dust hoer of the cyclone. Figs. 5-6 show the siral dust strand near the cyclone wall and its unsteady characteristics, and sace domains, which undulated with a frequency. But its dimensionless concentration did not change obviously, ranging from 15 to 30. Figs. 7-9 show that there existed dust rings in the uer art of the annular sace and the dust hoer, and the article concentration in the dust rings was not uniform nor axi-symmetric distribution. There existed a short-cut flow at a distance of about 0.25D below the entrance of the vortex finder. Fig. 10 shows that the articles were entrained seriously from the dust hoer in a range of about 0.5D above the dust discharge ort, and the secondary searation of articles due to the strongly swirling flow also occurred obviously in this region. The radial article distribution in the searation sace could be divided into the low-concentration region in the center and the high-concentration region near the wall. In most arts of the annular sace and of the searation sace, the low-concentration region was aroximately R and the high-concentration region was about ( )R. The articles concentration increased sharly at a distance of about 0.85R in the annular sace at 0orientation. In a range of 0.5D above the dust discharge ort, the article concentration was higher in the inner swirling flow region. In the dust hoer, there was a high-concentration region near the wall and under the to late of hoer, but no remarkable difference in article concentration in the other arts of the hoer. Fig. 5 Particle concentration on the wall at two moments Fig. 6 Axial article concentration distribution on the cyclone wall at two moments Fig. 7 Radial article concentration distribution in the annular sace of the cyclone

5 80 Petroleum Science 2007 Fig. 8 Radial article concentration distribution in the searation sace of the cyclone Fig. 11 Radial article concentration distribution of different article sizes at the distance of 20 mm and 600 mm under vortex finder Fig. 9 Radial article concentration distribution in the dust hoer Fig. 10 Axial article concentration distribution in the cyclone 3.3 Distribution of articles size Fig. 11 shows the radial articles concentration distribution of several article sizes in the searation sace of the cyclone. Fig. 12 is axial articles concentration distribution of different article diameters in the inner swirling flow region (r/r=0.3) of the cyclone. Fig. 12 Axial article concentration distribution of different article sizes in inner swirling flow region (r/r=0.3) It is seen from Fig. 11 that in the uer art of the cyclone, the dimensionless article concentration of different article diameters did not change greatly in the high-concentration region near the wall. While in the lower art of the cyclone, smaller articles always had higher concentration. The larger the articles (e.g. d >10 μm), the bigger the centrifugal force acting on the articles. Thereby the larger article moved faster towards the wall and resulted in a higher concentration near the wall region. While for the small articles, because of small centrifugal force and the effect of turbulent disersion, the searation was insufficient,

6 Vol.4 No.3 Numerical Simulation of Particle Concentration in a Gas Cyclone Searator 81 resulting in a high-concentration in the region under the vortex finder and in the inner swirling flow region of the cyclone searation sace. Meanwhile, the simulation revealed that most articles entrained from the dust discharge ort were of less than 10 μm in diameter. Particles larger than 6 μm in diameter could be searated again by the secondary searation in the zone above the dust discharge ort. However articles less than 5 μm were hard to be searated in the secondary searation zone. This is one reason of low efficiency of searation for small articles. 3.4 Effect of inlet article loading Fig. 13 and Fig.14 show the article concentration distribution at different cyclone inlet articles loadings. When inlet article loading increased (e.g. C i >2 kg/m 3 ), the center low-concentration region decreased to about r0.5r and the high-concentration region increased to 0.5R r R (see Fig. 13). The dimensionless concentration in the high-concentration region increased obviously in the uer art of the cyclone searation sace when inlet article loading was large. But in the cyclone conical art, the influence of inlet articles loading on article concentration was not obvious. It indicated that when inlet article loading was high, searation was mainly carried out in the uer searation sace. Thereby, in order to imrove the searation efficiency, the cyclone body should be rolonged aroriately. The short-cut flow region below the entrance of vortex finder still maintained in the range of 0.25D, but the dimensionless article concentration would increase obviously. The range of the article entrainment region above the dust discharge ort would reduce to less than 0.5D with article concentration decreasing significantly. Thus, increasing the cyclone searation sace height and reducing the exit short-cut flow are of significance for a better searation. Fig. 13 Radial article concentration distribution at a distance of 600 mm under the vortex finder Fig. 14 Axial article concentration distribution in the inner swirling flow region (r/r=0.3) 3.5 Effect of gas temerature on article concentration Figs dislay the article concentration distributions at different gas temeratures. With increasing gas temerature, the article searation ability of the cyclone was obviously weakened. This is mainly because the viscosity of the gas increased with increasing temerature and the drag force acting on the article also increased. Meanwhile, when the temerature rose, the turbulent fluctuation of the gas obviously was strengthened too, causing increased turbulent disersion of the fine articles. So, the searation ossibility of the articles was significantly reduced. When temerature rose, the dimensionless article concentration in the high-concentration region did not change obviously in the uer area of the cyclone searation sace. However it increased significantly in the near wall area of the conical art of the cyclone searation sace. It indicated that at a high temerature, the article searation rocess was not finished in the annular sace and the uer art of the searation sace of a cyclone and continued in its lower conical art of the cyclone searation sace. Thereby, resent simulations suggested that a cyclone for high-temerature oeration should have a higher ratio of height to body radius. From the calculations, it was also seen that the uer short-cut flow region and the bottom article entrainment region were obviously increased at a high temerature (T1273 K). And the two regions even overlaed, resulting in sharly worsened searation erformance. 4. Conclusion 1) The article concentration distribution in a cyclone was numerically investigated with the Particle-Source-In-Cell (PSIC) method and incororation of gas-article interaction. The calculation results were in good agreement with the measured data in literature (Wu, et al., 1994a).

7 82 Petroleum Science 2007 the dust rings were not uniform nor axi-symmetric. A short-cut flow aeared below the entrance of the vortex finder. The articles were entrained seriously from the dust hoer, but the secondary searation of articles due to the strongly swirling flow was also obvious in the conical art. Fig. 15 Radial article concentrations at a distance of 20 mm below the vortex finder Fig. 16 Fig. 17 Radial article concentrations at a distance of 600 mm below the vortex finder Radial article concentrations at a distance of 824 mm below the vortex finder 2) The radial distribution of article concentration was divided into the low-concentration region in the center and the high-concentration region near the wall in the cyclone searation sace. The article concentration near the cyclone wall was simulated as an unsteady siral dust strand. High-concentration dust rings existed in the cyclone annular sace and under the cover late of the dust hoer, and the concentrations in Fig. 18 Axial article concentrations in the inner swirling flow region (r/r=0.3) 3) As the inlet article loading increased, the radial low-concentration region decreased and the high-concentration region increased. The dimensionless concentration in the short-cut flow region increased obviously with increasing inlet solids loading. 4) The searation efficiency of cyclone generally decreased with increasing gas temerature. The uer short-cut flow region and the bottom article entrainment region would link u together and even overla at a high temerature. Nomenclatures C Particles concentration, kg/m 3 C i Inlet articles concentration, kg/m 3 D Cyclone searator diameter, mm d Particle diameter, mm M D Particle cumulative rate P Pressure, Pa P 0 Normal conditions ressure, Pa r Cyclone searator radial osition, mm R Cyclone searator radius, mm T Temerature, K T 0 Normal conditions temerature, K Y Radial coordinate, mm Z Axial coordinate, mm μ0 Normal conditions gas viscosity, Pa s μt Gas viscosity at high temerature, Pa s ρ0 Normal conditions gas density, kg/m 3 ρ Gas density at high temerature, kg/m 3 T

8 Vol.4 No.3 Numerical Simulation of Particle Concentration in a Gas Cyclone Searator 83 References Cao Y., Sun T. and Shi M. X. (1994) Study on fine article entrainment from dust hoer of the cyclone searator, Proc. 2nd China-Jaan Joint International Conference on Filtration & Searation, Cen K. F. and Fan. J. R. (1990) Engineering gas-solid multihase flow theory and calculation. Hangzhou: Zhejiang University Press (in Chinese) Fu S., Launder B. E. and Leschziner M. A. (1987) Modeling strongly swirling recirculating jet flow with Reynolds-stress transort closures. In Sixth Symosium on Turbulent Shear Flows, Toulouse, France. Gibson M. M. and Launder B. E. (1978) Ground Effects on ressure fluctuations in the atmosheric boundary layer. J. Fluid Mech., 86, Hu L. Y., Shi M. X., Zhou L. X. and Zhang J. (2004) Numerical simulation of 3-D strongly swirling turbulent flow in a cyclone searator. Journal of Hsinghua University, 44(11), (in Chinese) Hu L. Y., Zhou L. X., Shi M. X., et al. (2005) A modified ressure-strain model for simulating strongly swirling flows in a cyclone searator. Engineering Mechanics, 22(5), Launder B. E. (1989a) Second-moment closure and its use in modeling turbulent industrial flows. International Journal for Numerical Methods in Fluids, 9, Launder B. E. (1989b) Second-moment closure: Present and future? Inter. J. Heat Fluid Flow, 10(4), Lin W. and Wang N. N. (1999) Numerical simulation of three dimensional and two hase flow in a cyclone searator, Power Engineering,19(1), (in Chinese) Lu Y. J. and Zhou L. X. (2003) Numerical simulation of fluid flow and oil-water searation in hydrocyclones. Chinese Journal of Chemical Engineering, 11(1), Morsi S. A. and Alexander A. J. (1972) An investigation of article trajectories in two-hase flow systems. J. Fluid Mech., 55(2), Seziale C. G., Sarkar S. and Gatski T. B. (1991) Modelling the ressure-strain correlation of turbulence: an invariant dynamical systems aroach. J. Fluid Mech., 227, Wang B., Xu D. L., Xiao G. X., et al. (2006) Numerical study of gas-solid flow in a cyclone searator. Alied Mathematical Modelling, 30, Wu X. L., Huang X. D. and Shi M. X. (1993) Exerimental study on article concentration distribution in cyclone searator. J. of University of Petroleum, 17(4), (in Chinese) Wu X. L., Cao, Y. and Shi M. X.. (1994a) Exerimental study on article concentration distribution in PV cyclone searator, Proc. Chinese Chemical Engineering Annual Meeting (in Chinese) Wu X. L., Sun T. and Shi M. X. (1994b) The influence of configuration and oeration arameters on article concentration distribution in cyclone searator, The 2nd China-Jaan Joint International Conference on Filtration & Searation, Wu X. L. and Shi M. X. (2003) Visualization of the rocessing vortex core in a cyclone searator by PIV. Chinese Journal of Chemical Engineering, 11(6), Xue X. H. (2005) Numerical investigation on the gas-article two-hase flow behavior in the full sace of the cyclone searator, Ph.D. Thesis, China University of Petroleum, Beijing (in Chinese) About the first author Xue Xiaohu was born in He received his PhD from the China University of Petroleum (Beijing) in As a Professorial Senior Engineer, he now works at China National Petroleum Cororation Services & Engineering Ltd, with his interests in the field of numerical simulation of gas-article two-hase flow. xuexh@ctdc.cnc.com.cn (Received January 22, 2007) (Edited by Zhu Xiuqin)