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CFD analysis of flow field in square cyclones

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CFD analysis of flow field in square cyclones
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  Author's personal copy CFD analysis of    ow   eld in square cyclones Arman Raou  , Mehrzad Shams  , Homayoon Kanani Department of Mechanical Engineering, K.N. Toosi University of Technology, Pardis St., Mollasadra St., Vanak Sq., Tehran, Iran a b s t r a c ta r t i c l e i n f o  Article history: Received 19 August 2008Received in revised form 30 September 2008Accepted 6 November 2008Available online 27 November 2008 Keywords: CFDSquare cycloneTwo phaseFlow   eld In this study, computational   uid dynamic method is used to predict and evaluate the   ow   eld inside asquare cyclone. The   ow   eld is calculated using 3D Reynolds-averaged Naveir – Stokes equations. TheReynolds stress transport model (RSTM) is used to simulate the Reynolds stresses. The Eulerian – Lagrangiancomputational procedure is implemented to predict particle trajectory in the cyclone. The Newton's secondlaw is used to study the particle trajectory with modeling the drag and gravity forces acting on the particles.The velocity   uctuations are simulated using the discrete random walk (DRW). Two square cyclones whichhave different geometries are studied. The cyclones are simulated at different   ow rates. The details of the  ow   eld are studied in the cyclones and the effect of varying the   ow rates is observed. Tangential velocityis investigated in different sections inside the square cyclone. Contour of pressure and turbulence intensity isshown for different inlet velocities inside the cyclones. It is observed that different geometries, also differentinlet velocities, could affect on the pressure drop. The collection ef   ciency and the   ow patterns obtainednumerically are compared with the experimental data and good agreement is observed.© 2008 Elsevier B.V. All rights reserved. 1. Introduction Due torelative simplicity tofabricate, lowcost tooperate,and welladaptabilitytoextremelyharshconditions, cycloneshavebecomeoneof the most important gas – solid separators which are preferablyutilized in both engineering and process operations. Cyclone is a keypart for the circulating   uidized bed (CFB) boiler which has greateffects on the combustion ef   ciency, the circulation rate and thedesulfurizationef   ciencybythecirculationofthesolidparticlesinthefurnace.Theperformanceofacycloneiscriticaltotheboiler'ssafeandeconomic operation. The arrangement and structure of the cyclonehave in  uence on the overall arrangement of a boiler.Conventional cyclone which has circular cross section was thecommonly used cyclone for the CFB boiler. With the development of large CFB boilers, the huge bodyof the conventional cyclone became amajor shortcoming because of the thick refractory wall that needs along period to start the boiler. An alternative way to overcome theseproblems is the use of square cyclone. A square cyclone has moreadvantages over the conventional cyclone including convenientconstruction, easier membrane wall arrangement, shorter start – stoptime and at the same time easy integration with the boiler [17].A considerable number of experimental investigations have beenperformed on the square cyclones. Wang et al. [17] studied theseparation mechanism of a square cyclone at high inlet particleconcentration. They proposed an instantaneous separation modelbased on experimental observation and measurement. Junfu et al. [6]investigated the square cyclone at 75 t/h CFB boiler and presented amodel to study the cyclones. Effects of different parameters includinglength, diameter of vortex  nder, and inlet velocity onperformance of squarecycloneswerestudiedbyQiangetal.[11].SuandMao[15]used a three-dimensional particle dynamic analyzer (3D-PDA) to under-stand the nature and characteristics of the suspension   ow in thesquare cyclone separator and found out the factors affecting particlemotion. The turbulent   ow   eld inside a square cyclone wasexperimentally investigated by Su [16] to study the mechanism of particle separation and provide guidance for the optimization of itsstructure. Junfu et al. [7] evaluated the performance of advancedwater-cooled square cyclone with curved inlet. The results werecompared with other cyclones through   y ash analysis and showedthat the overall performance of the square cyclone in such capacity iscompatible with the conventional cyclones.Laser Doppler anemometry (LDA) and hot-wire anemometry arefrequently employed to study the   ow pattern in the cyclonesexperimentally. Recently, research efforts by computational   uiddynamics are frequently carried out for the resolution of    ow   eldand dust particle behavior with different degrees of numerical andmodeling accuracy in order to assist in the time consuming experi-mental works. In conjunction with the complex   ow structure,numerical simulation is momentarily not able to completely sub-stitute experiments but can reduce, to a certain degree, experimentalcosts for design and optimization. Powder Technology 191 (2009) 349 – 357   Corresponding author. Tel.: +98 912 359 6236; fax: +98 21 88877273. E-mail address:  shams@kntu.ac.ir (M. Shams).0032-5910/$  –  see front matter © 2008 Elsevier B.V. All rights reserved.doi:10.1016/j.powtec.2008.11.007 Contents lists available at ScienceDirect Powder Technology  journal homepage: www.elsevier.com/locate/powtec  Author's personal copy CFD has a great potential to predict the   ow   eld characteristicsand particle trajectories inside the cyclone as well as the pressuredrop [4]. The complicated swirling turbulent   ow in a cyclone placesgreat demand on the numerical techniques and the turbulencemodels employed in the CFD codes. CFD was widely used toinvestigate   ow   eld inside conventional cyclones. It has beenshown in the previous works on the prediction of the cycloneperformance under different operating temperatures and inletvelocities (Gimbun et al., 2005). Raou   et al. [13] used computatio-nal   uid dynamics to simulate and optimize vortex   nder of conventional cyclones. Although many numerical works have beenconducted on the conventional cyclones, there is a little numericalstudy about square ones. As numerical investigations of squarecyclones could have an important role to better understanding of the   ow parameters, this study is intended to obtain detailed  ow information by CFD simulation within square cyclones. Twocases with different geometries are selected to study. Case 1 is thesquare cyclone studied by Wang et al. [17] with upward outlet.Also, a square cyclone investigated by Su and Mao [15] issimulated numerically, as case 2. The square cyclones are modeledat different   ow rates and   ow   elds are evaluated inside thesecyclones. Contours of pressure and turbulence intensity withinthe cyclones are shown. Tangential velocity pro  les and velocityvectors in different sections are investigated. The numerical resultsare compared with experimental data and good agreement isobserved. 2. Flow simulation For an incompressible   uid   ow, the equations of continuity andbalance of momentum for the mean motion are given as A u i A  x i =0  ð 1 Þ A u i A t   + u  j A u i A  x  j = − 1  ρ A  p A  x i + m A 2 u i A  x  j A  x  j −  AA  x  j R ij  ð 2 Þ where  u     i  is the mean velocity,  x i  is the position,  p      is the meanpressure,  ρ is the constantgasdensity,  v  is thekinematicviscosity, and R ij = u i ′ u  j ′ ¯¯¯¯¯ is the Reynolds stress tensor. Here,  u i ′ =u i − u     i  is the  i th   uid  uctuation velocity component. Fig. 1.  The geometry of cyclone for (a) case 1 and (b) case 2, unit: mm.350  A. Raou    et al. / Powder Technology 191 (2009) 349 –  357   Author's personal copy The RSTM provides differential transport equations for evaluationof the turbulence stress components i.e., AA t R ij  + u k AA  x k R ij  =  AA  x k v t  σ  k AA  x k R ij   −  R ik A u  j A  x k + R  jk A u i A  x k   − C  1 e k R ij − 23 δ ij k   − C  2  P  ij − 23 δ ij P    − 23 δ ij e ð 3 Þ where the turbulence production terms are de  ned as P  ij  = − R ik A u  j A  x k − R  jk A u i A  x k ;  P   = 12 P  ij  ð 4 Þ with P  beingthe  uctuationkineticenergyproduction. v t istheturbulent(eddy) viscosity; and  σ  k =1,  C  1 =1.8,  C  2 =0.6 are empirical constants [8].The transport equation for the turbulence dissipation rate,  ε  , is given as A e A t   + u  j A e A  x  j =  AA  x  j m +  m t  σ  e    A e A  x  j   − C  e 1  e kR ij A u i A  x  j − C  e 2  e 2 k  :  ð 5 Þ In Eq. (5),  k =  12 u  V i u  V i  is the   uctuation kinetic energy, and  ε   is theturbulence dissipation rate. The values of constants are  σ  ε  =1.3, C  ε  1 =1.44 and  C  ε  2 =1.92.The dispersion of small particles is strongly affected by theinstantaneous  uctuationof   uidvelocity.Theturbulence  uctuationsare random functions of space and time. In this study, a discreterandom walk (DRW) model is used for evaluating the instantaneousvelocity  uctuations. The values of   u ′ ,  v ′  and  w ′  that prevail during thelifetime of the turbulent eddy,  T  e , are sampled by assuming that theyobey a Gaussian probability distribution. In this model the instanta-neous velocity in the  i th direction is given as u  V i = f  ffiffiffiffiffiffiffiffiffiffiffi u  V i u  V i : q   ð 6 Þ In Eq. (6),  ζ   is a zero-mean, unit-variance, normally distributed,random number,  ffiffiffiffiffiffiffiffiffi u  V i u  V i q   is the local root mean-square (RMS) Fig. 2.  Generated mesh of the cyclones for (a) case 1 and (b) case 2.  Table 1 False time steps used for the simulationParameters False time stepPressure 0.2 u  (  x -velocity) 0.4 v  (  y -velocity) 0.4 w  (  z  -velocity) 0.4 k  (turbulent kinetic energy) 0.5 ε   (turbulent dissipation rate) 0.5Reynolds stresses 0.5  Fig. 3.  Comparison of numerical, mathematical and experimental [17] result forcollection ef   ciency in the case 1.351  A. Raou    et al. / Powder Technology 191 (2009) 349 –  357   Author's personal copy  uctuation velocity in the  i th direction; and the summation conven-tion on  i  is suspended.The characteristic lifetime of the eddy is de  ned as a constantgiven by T  e  =2 T  L   ð 7 Þ where  T  L   is the eddy turnover time given as  T  e =0.3( k/  ε  ) in the RSTM.The other option allows for a log-normal random variation of eddylifetime that is given by T  e  = − T  L   log  r  ð Þ ð 8 Þ where  r   is a uniform random number between 0 and 1. The particle isassumed to interact with the   uid   uctuation   eld, which stays   xedovertheeddylifetime.Whentheeddylifetimeisreached,anewvalueoftheinstantaneousvelocityisobtainedbyintroducinganewvalueof  ζ   in Eq. (6).There are two main approaches to modeling multiphase   owsthat account for the interactions between the phases. These are theEulerian – Eulerian and the Eulerian – Lagrangian approaches. Theformer is based on the concept of interpenetrating continua, forwhich all the phases are treated as continuous media with propertiesanalogous to those of a   uid. The Eulerian – Lagrangian approachadopts a continuum description for the liquid phase and tracks thediscrete phases using Lagrangian particle trajectory analysis.Inpresent study, onewaycoupling method is used to solve of two-phase  ow and the Eulerian – Lagrangian approach is implemented forsimulationofseconddiscretephase(particles).Inthismodel,theairisthe continuous phase and the particles are treated as the disperseddiscrete phase. The volume-averaged and steady state Navier – Stokesequation is solved for the gas phase. The particle motions aresimulated by the Lagrangian trajectory analysis procedure. Forcesacting on the dispersed phases include drag and gravity. The discrete-phase equations are solved with the Runge – Kutta for particles.To calculate the trajectories of particles in the   ow, the discretephase model (DPM) was used totrackindividual particles through thecontinuum   uid. The particle loading in a cyclone separator istypically small, and therefore, it can be safely assumed that the Fig. 4.  Contour of static pressure (Pa) for two cyclones at different inlet velocities. Case 1 (a)  v =22, (b)  v =30 and case 2 (c)  v =20, (d),  v =28.32, unit: m/s.352  A. Raou    et al. / Powder Technology 191 (2009) 349 –  357   Author's personal copy presence of the particles does not affect the   ow   eld (one-waycoupling).The equation of motion of small particles, including the effects of nonlinear drag and gravitational forces, is given by du P i dt   =3 vC  D Re p 4 d 2 S  u i − u P i   +  g  i  ð 9 Þ dx i dt   = u P i  :  ð 10 Þ Here,  u i P is the velocity of the particle and  x i  is its position,  d  is theparticle diameter,  S   is the ratio of particle density to   uid density, and  g  i  is the acceleration of gravity. The buoyancy, virtual mass and Bassetforces are negligible because of the small   uid-to-particle densityratio. The  rsttermon theright-handside (RHS)ofEq.(10)isthedragforce due to the relative slip between the particle and the   uid. Thedrag force is, generally, the dominating force. According to [5], thedrag coef   cient,  C  D , is given as C  D  = 24 Re P for  Re P b 1  ð 11 Þ C  D  = 24 Re P 1+ 16 Re 2 = 3P    for 1 b Re P b 400  ð 12 Þ where, Re P  is the particle Reynolds number de  ned asRe P  = d j u  j − u P  j  j m :  ð 13 Þ The particle equation of motion requires the instantaneousturbulent   uid velocity values at particle locations. The mean liquidvelocity was evaluated by the use of the Reynolds stress transportturbulence model (RSTM) and the   uctuation velocity componentswere calculated from Eq. (6). The drag coef   cient for sphericalparticles is calculated by using the correlations developed by Morsiand Alexander (1972). The ordinary differential equation (Eq. (10)) isintegrated along the trajectory of an individual particle. Collectionef   ciency statistics are obtained by releasing a speci  ed number of monodispersedparticlesat theinletof thecycloneand bymonitoringthe number escaping through the under  ow. Collisions betweenparticles and the walls of the cyclone were assumed to be perfectlyelastic (coef   cient of restitution is equal to 1) [13]. Also, particle – particle collision is negligible. 3. Results Thesimulationsareperformedfortwocyclonetypeswithdifferentgeometries which have been studied experimentally by [17,15]. Fig. 1 shows the geometry and dimension of the studied cases. As seen inFig.1 (a) the cyclone of case 1 has an upwardoutlet that also plays therole of vortex   nder. The particles size range is 0 – 2 mm of a materialwhose density and average diameter are respectively 0.205 mm and2550 kg/m 3 [17]. The simulations are performed at inlet velocities of 22, 26, 30 and 34 m/s.As indicated in Fig.1 (b), the exhaust gas went through downwardexit in case 2. The particle used was glass beads of mean diameter of 30 – 40    m and density of 2400 kg/m 3 [15]. This cyclone is studied atinlet velocities of 20, 25.3 and 28.32 m/s.Foranalyzing the  ow in the cyclones, the numbersof 186,298 and258,976 hexahedral cells are generated for cases 1 and 2, respectively.Fig.2 shows thedetailsof thecomputationalgrid forthecyclones.Thehexahedral computational grids are generated by dividing the wholecyclone geometry into a numberof blocks. A  “ velocity inlet ”  boundarycondition is used at the cyclone inlet. A fully developed boundarycondition is used at the outlet. Grid re  nement tests are conducted inorder to make sure that the solution is not grid dependent. The   nitevolume methods have been used to discretize the partial differentialequation. The SIMPLE method is used for pressure – velocity couplingand the second-order upwind scheme is implemented to interpolatethe variables on the surface of the control volumes. Turbulence  uctuations are simulated using Reynolds Stress Transport Model(RSTM). The computation is continued until the solution convergedwith a total relative error of less than 0.0005. The Lagrangian methodis used for tracking of particles in the simulation. For investigation of particles trajectory inside the cyclones, seven and nine millions of particles are released at the inlet of cases 1 and 2, respectively. Thechoice of the time step in  uences the convergence behavior: if takentoo large the simulations diverge, if taken too small the computationtimes go up. For steady-state problems, the time steps are false timesteps. False time steps used for simulation of    ow   eld are broughtin Table 1. Time step of 0.2 ms is used for calculation of particletrajectories in the numerical model.It is dif   cult to understand the cyclone separation behaviorwithout some information about the   ow   eld. CFD is a very usefultool to obtain details of the  ow inside a cyclone. Fig. 3 shows the CFD Fig. 5.  Pressure drop in the cyclones at different inlet velocities. (a) Static pressure dropand (b) Dynamic pressure drop.353  A. Raou    et al. / Powder Technology 191 (2009) 349 –  357 
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