Particle-gas flow in a cyclone separator used in a circulating fluidized-bed boiler is simulated using computational fluid dynamics software Fluent 6.2.36 and an Unsteady Reynolds-Averaged Navier-Stokes (URANS) method. A Lagrangian method is used for particle simulation and a one-way coupling between particles and gas is assumed. The effect of the turbulence model is studied using several turbulence models. Only the Reynolds stress model gives a physically reasonable flow field without adjusting parameters unknown beforehand

Ahlstedt, Hannu

Karvinen, Aku

Palonen, Marko

English

Engineering Conferences International

Engineering Conferences InternationalECI Digital Archives10th International Conference on CirculatingFluidized Beds and Fluidization Technology -CFB-10Refereed ProceedingsSpring 5-2-2011Simulation of Particle-Gas Flow in a Cyclone UsingURANSAku KarvinenTampere University of TechnologyHannu AhlstedtTampere University of TechnologyMarko PalonenMetso Power OyFollow this and additional works at: http://dc.engconfintl.org/cfb10Part of the Chemical Engineering CommonsThis Conference Proceeding is brought to you for free and open access by the Refereed Proceedings at ECI Digital Archives. It has been accepted forinclusion in 10th International Conference on Circulating Fluidized Beds and Fluidization Technology - CFB-10 by an authorized administrator of ECIDigital Archives. For more information, please contact franco@bepress.com.Recommended CitationAku Karvinen, Hannu Ahlstedt, and Marko Palonen, "Simulation of Particle-Gas Flow in a Cyclone Using URANS" in "10thInternational Conference on Circulating Fluidized Beds and Fluidization Technology - CFB-10", T. Knowlton, PSRI Eds, ECISymposium Series, (2013). http://dc.engconfintl.org/cfb10/27SIMULATION OF PARTICLE-GAS FLOWIN CYCLONE USING URANSAku Karvinen and Hannu AhlstedtTampere University of TechnologyPO Box 589, FI-33101 Tampere, FinlandMarko PalonenMetso Power OyPO Box 109, FI-33101 Tampere, FinlandABSTRACTParticle-gas flow in a cyclone separator used in a circulating fluidized-bed boiler issimulated using computational fluid dynamics software Fluent 6.2.36 and an UnsteadyReynolds-Averaged Navier-Stokes (URANS) method. A Lagrangian method is usedfor particle simulation and a one-way coupling between particles and gas is assumed.The effect of the turbulence model is studied using several turbulence models. Onlythe Reynolds stress model gives a physically reasonable flow field without adjustingparameters unknown beforehand.INTRODUCTIONinletoutletxyzFigure 1: Cyclone separator.Domain and coordinate sys-tem used in this study.Cyclone separators (Fig. 1) occur in many industries,e.g. in oil and gas industry, power generation, incin-eration plants, cement plants, coking plants and thefood industry. Compared to the other methods forparticle removal from gases the main advantages ofcyclone separators are: low capital investment andmaintenance costs, applicability under extreme pro-cessing conditions, no moving parts, and robustness.According to (1), the first studies of the cyclone flowwere undertaken in 1930-1950 (2) and (3). The firstCFD (computational fluid dynamics) simulations wereundertaken in the 80’s (4). In the 21st century, CFDsimulations have been made for example by Derksen(5) and by Wang (6). A more extensive review can befound in (7) and (1).CASE STUDIEDThe schematic of the case studied and the coordinate system used is given in Fig. 1.The flow gas is hot air. The cyclone body Reynolds number based on an average inletvelocity and the cyclone diameter (7) is Re = 634,000.METHODS AND MODELSThe Reynolds-averaged Navier-Stokes equations (RANS) for incompressible flow are∂ui∂xi= 0, (1)∂ui∂t+ uj∂ui∂xj= −1ρ∂p∂xi+ ν∂2ui∂xj∂xj+∂∂xj(−u′i u′j), (2)where the overbar denotes time averaging, and the prime denotes the fluctuating com-ponent. In the k-ε models and the k-ω models, the Boussinesq hypothesis is used inwhich the Reynolds stresses, −u′i u′j , are calculated from−u′i u′j = 2νtSij −23kδij , Sij =12(∂ui∂xj+∂uj∂xi). (3)In the standard k-ε model (8), the turbulence kinetic energy and its dissipation rateare obtained from the modeled transport equations, which are as follows:∂k∂t+ uj∂k∂xj=∂∂xj[(ν +νtσk)∂k∂xj]+ νtS2 − ε, (4)∂ε∂t+ uj∂ε∂xj=∂∂xj[(ν +νtσε)∂ε∂xj]+ C1εεkνtS2 − C2εε2k, (5)where S ≡√2SijSij . The turbulent viscosity is computed from νt = Cµk2/ε. Modelconstants used have the following values: Cµ = 0.09, C1ε = 1.44, C2ε = 1.92, σk = 1.0,and σε = 1.3.The transport equations for k and ε in the RNG k-ε model (9) are∂k∂t+ uj∂k∂xj=∂∂xj(αkνt∂k∂xj)+ νtS2 − ε, (6)∂ε∂t+ uj∂ε∂xj=∂∂xj(αενt∂ε∂xj)+ C1εεkνtS2 − C2εε2k−Cµη3 (1 − η/η0)1 + βη3ε2k, (7)where η ≡ Sk/ε, η0 = 4.38, β = 0.012, and νt is obtained in a similar way as inthe standard k-ε model. The model constants are: Cµ = 0.0845, C1ε = 1.42, andC2ε = 1.68.The RNG k-ε model in Fluent provides an option to account for the effects of the swirlin the mean flow by modifying the turbulent viscosity appropriately:νt,modified = νtf(αs, Ω,kε), (8)where Ω is a swirl number evaluated within Fluent and αs is a swirl constant thatassumes different values depending on whether the flow is swirl-dominated or mildlyswirling. The exact function for describing this dependency is not revealed in (10).The transport equations for k and ε in the realizable k-ε model (11), (10) are∂k∂t+ uj∂k∂xj=∂∂xj[(ν +νtσk)∂k∂xj]+ νtS2 − ε, (9)∂ε∂t+ uj∂ε∂xj=∂∂xj[(ν +νtσε)∂ε∂xj]+ C1εSε − C2εε2k +√νε, (10)where C1ε is now a variable. The turbulent viscosity is obtained in a similar way asin the standard k-ε model, but Cµ is no longer constant. The model constants are:C2ε = 1.9, σk = 1.0, and σε = 1.2.In the standard k-ω model (12), the turbulence kinetic energy, k , and the specificdissipation rate, ω, are obtained from the following transport equations:∂k∂t+ uj∂k∂xj=∂∂xj[(ν +νtσk)∂k∂xj]+ νtS2 − β∗∞fβ∗kω, (11)∂ε∂t+ uj∂ω∂xj=∂∂xj[(ν +νtσω)∂ω∂xj]+ωkνtS2 − βi fβω2, (12)and the turbulent viscosity is obtained from νt = k/ω. The model constants are: βi =0.072, β∗∞= 0.09, σk = 2.0, and σω = 2.0.The SST k-ω model (13) has a form similar to that of the standard k-ω model. Thetransport equations are given as follows∂k∂t+ uj∂k∂xj=∂∂xj[(ν +νtσk)∂k∂xj]+ min(νtS2, 10ρβ∗∞kω) − β∗∞kω, (13)∂ε∂t+ uj∂ω∂xj=∂∂xj[(ν +νtσω)∂ω∂xj]+ S2 − βiω2 + Dω, (14)where βi = F1βi ,1 + (1 − F1)βi ,2 and σk and σω are calculated in a similar way. Theturbulent viscosity νt = (k/ω)/ max[1, SF2/(a1ω)]. The model constants are: a1 = 0.31,β∗∞= 0.09, βi ,1 = 0.075, βi ,2 = 0.0828, σk ,1 = 1.176, σω,1 = 2.0, σk ,2 = 1.0, andσω,2 = 1.168.In the Reynolds stress model (RSM), there are the exact transport equations for thetransport of Reynolds stresses, −u′i u′j (14):∂u′i u′j∂t+∂∂xk(uku′i u′j)= −∂∂xk[u′i u′j u′k +p′ρ(δkju′i + δiku′j)]︸ ︷︷ ︸Dtij+∂∂xk[ν∂∂xk(u′i u′j)]−(u′i u′k∂uj∂xk+ u′j u′k∂ui∂xk)+p′ρ(∂u′i∂xj+∂u′j∂xi)︸ ︷︷ ︸φij− 2ν∂u′i∂xk∂u′j∂xk︸ ︷︷ ︸εij, (15)where Dtij , φij , and εij are modeled, see (10) for more details. The model constantsare: C1 = 1.8, C2 = 0.60, C1ε = 1.44, C2ε = 1.92, Cµ = 0.9, σk = 1.0, and σε = 1.3.Calculation Procedure and Computational GridAll the calculations are performed using commercial software Fluent 6.3.26 (10). Allterms in all equations are discretized in space using second-order central differencing,apart from the convection term, which is discretized using a second-order upwindscheme. Pressure-velocity coupling is achieved using the PISO algorithm.Time integration is done using a first order implicit method and adaptive time steppingwhere the first time step is very small (∆t0 = 10−6 s) and next time steps are chosen asfollows: If the solution has not converged after seven iterations, then ∆tnew = 0.9∆told,otherwise, ∆tnew = 1.1∆told.The simulation is initiated using a steady state solver. After several thousand itera-tions, the simulation is continued by running an unsteady solver and run until the flowbecomes statistically steady (30 s). After that, simulation is continued until statisticallystable data is gathered (30 s → 60 s).The computational grid consists exclusively of hexahedral cells (Fig. 2). Four differentgrid resolutions have been used such that the total number of control volumes usedis 72,978, 260,808, 785,819 or 1,802,564. All grids are constructed so that the grid isfiner for the wall-adjacent cells of all no-slip walls of the cyclone.(a) In inlet andcyclone walls.(b) In middle of cyclone barrel inpositive quadrant.Figure 2: Grid 785,819.GRID INDEPENDENCY TESTThe grid independency test shows that velocity profiles of the RSM in the middle of thecyclone barrel do not change significantly when the grid is made finer than 785,819cells (Fig. 3). A grid of 785,819 cells is therefore used exclusively in the turbulencemodel comparison. A dimensionless wall unit y+ in a cyclone barrel is in an acceptablerange (within the log-law layer) when a 785,819 grid is used (Fig. 3(d)).Grid 72,978Grid 260,808Grid 785,819Grid 1,802,564y/Ru/vel inlet0 0.2 0.4 0.6 0.8 1.000.51.01.52.0(a) Radial mean velocity in middle of cyclonebarrel.Grid 72,978Grid 260,808Grid 785,819Grid 1,802,564y/Rv/vel inlet0 0.2 0.4 0.6 0.8 1.0−202468(b) Tangential mean velocity in middle ofcyclone barrel.Grid 72,978Grid 260,808Grid 785,819Grid 1,802,564y/Rw/vel inlet0 0.2 0.4 0.6 0.8 1.0−10123(c) Axial mean velocity in middle of cyclonebarrel.t/Rz/Rinlet−5 −4 −3 −2 −1 0 10.00.51.01.52.02.5 75757575100100100125125 125150(d) Dimensionless wall unit y+ in cyclone barrel lookedinside out. Grid 785,819.Figure 3: Grid independency test.TURBULENCE MODEL COMPARISONSeveral papers, e.g. (7) and (1), show that there is rigid body rotation in the core of thecyclone and almost friction free flow in the outer part of the cyclone. Tangential velocityprofiles complying with these assumptions are shown in Fig. 4(b) by the dashed lines(constants are adjusted according to the results of the RSM).Because of the highly anisotropic turbulence caused by the high curvature of thestreamlines and the high swirl intensity, two equation models cannot predict the flowfield correctly – they predict almost rigid body rotation in the whole flow field. Only theRSM gives a physically reasonable flow field.The RNG k-ε model with swirl modification implemented in Fluent gives usable results,but the modification contains an adjustable parameter which was unknown before thesimulations. The default value of the parameter is αs = 0.07, which turns out to be toosmall, as can be seen in Fig. 4(b). This makes the modification difficult to use.Std. k -εRNG k -ε (αs = 0)RNG k -ε (αs = 0.07)RNG k -ε (αs = 0.35)Real. k -εStd. k -ωSST k -ωRSMy/Ru/vel inlet0 0.2 0.4 0.6 0.8 1.0−0.500.51.01.52.02.5(a) Radial mean velocity.Std. k -εRNG k -ε (αs = 0)RNG k -ε (αs = 0.07)RNG k -ε (αs = 0.35)Real. k -εStd. k -ωSST k -ωRSMv = C1y + D1v = C2/y + D2y/Rv/vel inlet0 0.2 0.4 0.6 0.8 1.0−6−4−20246810(b) Tangential mean velocity.Std. k -εRNG k -ε (αs = 0)RNG k -ε (αs = 0.07)RNG k -ε (αs = 0.35)Real. k -εStd. k -ωSST k -ωRSMy/Rw/vel inlet0 0.2 0.4 0.6 0.8 1.0−2−101234567(c) Axial mean velocity.Figure 4: Turbulence model comparison.PARTICLE TRAJECTORY SIMULATIONBecause the only turbulence model that gives a reasonable flow field without any ad-justable parameter is the RSM, particle trajectory simulation is only done using thatmodel. Particles of different size are released from the bed and the particle trajectoriesare calculated assuming one-way coupling (particles do not affect the flow field). Themean flow field is used and no turbulence effects on particles are taken into account.The collision chart in the cyclone barrel is shown in the Fig. 5(a). The collision area ofthe largest particle corresponds well with the largest measured erosion (Fig. 5(b)).d < 50 µmd = 50 ... 100 µmd = 100 ... 150 µmd = 150 ... 200 µmd > 200 µmt/Rz/Rinlet−5 −4 −3 −2 −1 0 10.00.51.01.52.02.5(a) Simulated collision chart. RSM.t/Rz/Rinlet−5 −4 −3 −2 −1 0 10.00.51.01.52.02.5(b) Measured erosion in target zone. Darkest graydenotes largest erosion.Figure 5: Simulated collision chart and measured erosion.CONCLUSIONSAn extensive grid independency test is achieved using the Reynolds stress model(RSM). The number of the cells in grids varies between 72,978 and 1,802,564. Thegrid independency test shows that a grid consisting of about 800,000 cells gives ac-ceptable results.An effect of the turbulence model is studied using six different turbulence models. Be-cause of the highly anisotropic turbulence caused by the high curvature of the stream-lines and the high swirl intensity, two equation models cannot predict the flow fieldcorrectly. Only the RSM gives a physically reasonable flow field. Also the RNG k-εmodel with a swirl modification implemented in Fluent gives usable results, but themodification contains an adjustable parameter which was unknown before the simu-lations. When the RSM is used, the collision area of the largest particle correspondswell with the largest measured erosion.ACKNOWLEDGMENTThe authors gratefully acknowledge the support from Metso Power Oy and from TheFinnish Graduate School in Computational Fluid Dynamics.NOTATIONCµ, C1, C2, C1ε, C2ε model constant in turbulence modelsDtij turbulent diffusive transport tensor in RSMDω cross-diffusion term in RNG k-ε modelF1, F2 blending functions in SST k-ω modelPij stress production tensor in RSMR radius of cyclone barrelRe cyclone body Reynolds numberS mean rate-of-strain tensord particle diameterfβ∗ , fβ auxiliary functions in standard k-ω modelk turbulent kinetic energyp mean pressuret time, tangential coordinate∆t0, ∆told, ∆tnew first, old and new time stepsu, v , w mean velocity componentsvelinlet average mean velocity in beginning of inlety+ dimensionless wall unitΩ mean rate-of-rotation, characteristic swirl numberαk , αε inverse effective Prandtl numbersαs swirl constant in RNG k-ε modelβi , β∗∞, βi ,1, βi ,2 model constants in turbulence modelsδ Kronecker deltaε dissipation rate of turbulent kinetic energyεij dissipation tensor in RSMν, νt molecular and turbulent kinematic viscosityνt,modified modified turbulent kinematic viscosityφij pressure-strain tensor in RSMρ densityσk , σε, σω, σk ,1, σk ,2, σω,1, σω,2 model constants in turbulence modelsσk , σω auxiliary functions in SST k-ω modelREFERENCES1. C. Cortés and A. Gil. Modeling the gas and particle flow inside cyclone separa-tors. Progress in Energy and Combustion Science, 33(5):409–452, 2007.2. R. M. C. K. Alexander. Fundamentals of cyclone design and operation. Proceed-ings of the Australasian Institute of Mining and Metallurgy, 152:208–228, 1949.3. A. J. Linden. Investigation into cyclone dust collectors. Proceedings of the Insti-tution of Mechanical Engineers, 160:233–251, 1949.4. F. Boysan, W. H. Ayers, and J. Swithenbank. A fundamental mathematical mod-elling approach to cyclone design. Transactions of the American Institute ofChemical Engineers, 60:222–230, 1982.5. J. J. Derksen, S. Sundaresan, and H. E. A. van den Akker. Simulation of mass-loading effects in gas-solid cyclone separators. Powder Technology, 163:59–68,2006.6. B. Wang, D. L. Xu, K. W. Chu, and A. B. Yu. Numerical study of gas-solid flow ina cyclone separator. Applied Mathematical Modelling, 30:1326–1342, 2006.7. A. C. Hoffmann and L. E. Stein. Gas Cyclones and Swirl Tubes: Principles,Design and Operation. Springer, Berlin, 2002.8. B. E. Launder and D. B. Spalding. Lectures in Mathematical Models of Turbu-lence. Academic Press, London, 1972.9. V. Yakhot and S. A. Orszag. Renormalization group analysis of turbulence. Phys-ical Review Letters, 57:1722–1724, 1986.10. Fluent Inc. FLUENT 6.3 User’s Guide. Lebanon, 2006.11. T.-H. Shih, W. W. Liou, A Shabbir, Z. Yang, and J. Zhu. A new k-ε eddy viscositymodel for high Reynolds number turbulent flows. Computers and Fluids, 24:227–238, 1995.12. D. C. Wilcox. Turbulence Modeling for CFD. DCW Industries, Inc., La Canada,California, second edition, 1998.13. F. R. Menter. Two-equation eddy-viscosity turbulence models for engineeringapplications. AIAA Journal, 32:1598–1605, 1994.14. M. M. Gibson and B. E. Launder. Ground effects on pressure fluctuations in theatmospheric boundary layer. Journal of Fluid Mechanics, 86:491–511, 1978.

Simulation of Particle-Gas Flow in a Cyclone Using URANS

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Simulation of Particle-Gas Flow in a Cyclone Using URANS

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