Influence of coherent structures in the gas-particle circular cylinder wake flow

Ji et al. /J Zhejiang Univ SCI 2005 6A(10): 1132-1136Journal of Zhejiang University SCIENCEhttp://www.zju.edu.cn/jzusInfluence of coherent structures in the gas-particle circularcvlinder wake flowJI Feng(嵇峰), LIU Lan(刘兰), Fan Jian-ren(樊建人), CeN Ke-fa(岑可(Clean Energy d Environment Engineering Key Laboratory of Ministry of Education, Institute for Thermal Power Engineering,Zhejiang University, Hangzhou 310027, China)E-mail:fengjiren(@zju.edu.cn;fanjr@zju.edu.cnReceived Dec. 17, 2004; revision accepted Feb. 24, 200Abstract: To investigate the influence of coherent structures in the gas-particle wake flow, direct numerical simulation(DNSmethod was adopted to compute a two-dimensional particle laden wake flow, a high accuracy spectral element method (SEM)wasemployed to simulate the gas flow field and a Lagrangian approach was used to compute the particles movement. Numericalresults showed that at the same Stokes numbers, particles would be greatly impacted by the development of the coherent structureBut with different Stokes numbers, it can be seen that the large-scale vortex structures would influence the particle flow differentlyWhile under different Reynolds numbers(150 and 200), there are no great changes in the particle laden flowKey words: Direct numerical simulation(DNS), Wake flow, Coherent structures, Particle laden flowdoi:10.1631/jzus.2005.A1132Document code: ACLC number: TK16INTRODUCTIONphase turbulent flows were summarized by Crowe etal. (1996). In recent years direct numerical simulationTurbulent gas-particle flows are frequently (DNS) has become a powerful tool(Parviz andfound in natural phenomena and industrial processes. Krishnan, 1998 )for the study of fluid dynamicsCases of cylinders in cross flows with particles occur though it is sometimes used for solving some idealheat exchange equipment, includingand simple problems far from technical applicationzone of a fluidized-bed combustor, and in the primary levelsuperheaters, reheaters, and economizers of coal-firedRecent reports to predict the three-dimensionboilersfeatures of particle dispersion for a plane mixing layerCoherent structures oftenn the aboywere made by Fan(2001; 2003)and Marcu andmentioned gas-particle flow, and have great effect on Meiburg(1996). Simulation results showed thatsuch different systems, while some features of turstreamwise vortices produce additional effects thatbulent multiphase flow resemble those in sin- modify the dispersion patterns of particles Along thespanwise direction, particle dispersion also developsrence of coherent structures, the stretching of the into"mushroom'patterns, owing to intense 3D vortexstretching and foldgle-phase flow and multiphase flowChung and Troutt(1988)simulated the particleMany and various numerical models for multidispersion in an axisymmetric jet using a discretech with the interesting outcome'Corresponding authorwas that the ratio of particle dispersion to fluid agreedProject(No. 50236030)supported by the National Natural Sciencewell with experime中国煤化工Foundation of ChinAccordingYHlexitCNMHGJi et al. /J hejiang Univ SC/ 2005 6A(10): 1132-11361133(Karniadakis, 1999), wake is more complex to simu- where V is the velocity, p is pressure(density p=1)late than other shear flows(mixing layer and jet). The reynolds number Re is defined as Re=ood/,Slater and Young(2001) studied the particle flow with o the uniform stream velocity, d characteristicover a circular cylinder by using an Eulerian formu- length, and v kinematic viscosity. Linear dispersionlation. This paper presents the seldom studied before operator and nonlinear convection operator arethe coherent structures effect on complex gas-particlelow. DNS for calculating particle-laden wake flowL(D)=VV,N()=-[.V+V·(v)2was done in this paper, with emphasis placed onclarifying the impact mechanism of coherent struc- respectively represented in oblique symmetric form totures in the wake floweduce the anti-aliased erroA detailed description of the computational ap-proach and its validation is given in(Yao et al., 2003)MATHEMATICAL MODELIn this paper we focus on the particle movementanalysIsFlow configuration and simulationIn the direct numerical simulation, we adopted Particle movement computationspectral element method to solve the gas flow fieldAssumptions: First, all particles are rigid spheresThe computational domain was set to 14x37(Fig. I). with the same diameter and density Second, at theAnd the computational time step was 0.01nitial time, particles are distributed uniformly in theflow and have the same dynamic characteristicsCircular cylinderSince the density ratio pp/pg> 1000, in the dilutetwo-phase flow the Basset force and the added forccan be neglected. The influence of the particles on thegas-flow and particle-particle interactions is ne-glected because of the low particle loadinIn addition the saffman force and magus forcee neglected in this simulation too. So, only the mostimportant drag force due to the relative velocity be-tween the phases is taken into account in this study ofTherefore, the non-dimensional motion equationbased on a particle is expressed asdv/dtf/St(U-vwhere V is the particle velocity, U is the fluid velocityat that particle position and f is a modification factorfor the Stokes drag coefficient, which is described byFig1(a)Sketch of computational domain;(b)Partial f=1+0. I5Rep, with Rep=0-Vdp/v. St namedStokes number for a particle is defined asSt(Ppdp /18)/(R/Uo). The velocity and position ofIncompressible viscous fluid flow N-s equationparticles can be obtained by integrating Eq 3)and conservative forms are normalized as followsParticle-wall collision modelGrant and Tabakoff (1975 )obtained the expres-aV--Vp+D-Lo)+N) in Q2 (1) sion of particle-wall collision by practical experI-V.=0H架Ji et al. /J Zhejiang Univ SCI 2005 6A(10): 1132-1136impact velocity and its incidence angleNUMERICAL RESULTS AND DISCUSSIONVn2/Vn=1.0-04159-0.499482+0.292月3(4)Fig 2 of the pressure contour for different rey-molds numbers in the whole computational domainV2V=1.0-212A+307752-11B(5) shows clearly the flow characteristics of circularwhere Vn and V, represent the particle velocity impactThe recirculating separation region shows verycomponents normal and tangential to the wall, re- low pressure in both instances. Obviously, mostspectively. Subscripts I and 2 refer to the conditions pressure values of Re-200 are higher than those ofbefore and after impact, respectively. In the above Re=150 according to the iso-pressure contour viewequations, B,(in radians)is the angle between the Lowest pressure exists in the recirculating regimeincident velocity and the tangent to the surface which because of the highest velocity existing thereis supposed to be smoothThe analysis of the results has to be consideredSo, if the detailed velocity history was known for with respect to the operative St numberparticle that ultimately strikes a surface, we canIn Fig 3 and Fig 4, the results indicate that co-compute the impact velocity from which the corre- herent structure exhibits in the particle flow field assponding incidence angle and incidence speed can be well as in the gas flow fieldomputedParticles with small Stokes number (St=0. 1)The Lagrangian approach yields a more detailed have low inertial and very rapid response to changesphysical description of the particle phase(such as in fluid velocity. The particle vector field shows thatindividual particle speeds, trajectories, and residence some particles had entered the vortex core. In contrast,times), compared to Eulerian description The particle particles with medium Stokes number (StD)aretrajectories are determined using an adaptive step size faithfully follow the flow and, in principle, can befourth order runge-Kutta methodused to visualize fluid motionFig 2 Comparative view of the pressure field for Reynolds numbers (instantaneous snapshot, 7-100)(a)Re=150;(b)Re=2001040-24-60Fig 3 Comparative view of the particle vector field for reynolds numbers (insta中国煤化工a)Re=150;(b)Re=200,St=0.1YHCNMHGJi et al. /J hejiang Univ SC/ 2005 6A(10): 1132-11361135Instantaneous particles movement (Fig3 and pairing interactions occur. The mechanism for theFig 4) shows that the small particles enter the inner particle dispersion in circular cylinder wake mainlyregions of the vortices but that the bigger cannot do depends on the repulsion force associated with thethe same. The following vertical dispersion function vortex sheet regions between two adjacent vortexintroduced (Ling et al., 1998)structures with opposite sign, which is namedstretching processl/2That is to say, it is obvious that particles followD()=2()-X()2nhe gas flow and do not collide with the front face ofthe cylinder when the particle size is small But whenwhere n, is total particle number in the computationalSt equals l, almost no particle enters the core. Thesedomain when time is t, yAt) is the ith particle instaresults showed that particle flow of medium Stokestaneous vertical displacement, Ym(O is mean vertical number is more influenced by gas flow than the smalldisplacement of total particles at that time. ThiStokes numberWhen Re equals 200, the perturbation is strongerParticle dispersion function in vertical direction than that when Re equals 150. So particles flow dyis quantitatively and instantaneously plotted in Fig. 5 namic characteristics have ditferent aspects. But un-showing that decreases with increase of particle der the different Reynolds numbers 150 and 200Stokes number. For the circular cylinder wake, two there are no great changes in the particles flow. Forsymmetrical vortices with opposite sign are sepa- examples, when both of Stokes numbers are 0. 1,therately and alternately generated. They are convected irregularities of particle flow vortex structure areand diffused away from the cylinder but no vortex similar1022-64202468101214161822242628Fig 4 Comparative view of the particle vector field for Reynolds numbers(instantaneous snapshot, T-100)a)Re=150;(b)Re=200,S=1S=0.1251525354555657585955152535455565758595Fig5 Time-dependent particle dispersion in the vertia)Re=150;(b)Re=200TYH任Ji et al. /J Zhejiang Univ SCI 2005 6A(10): 1132-1136CONCLUSIONFan, J.R., Zheng, Y Q, Yao, J, Cen, K.F.simulation of particle dispthreng layer. Proc. R. SocWe have presented a numerical study of gas2151-2166particle wake flow. Simulations were performed to Fan, J.R, Luo, K, Zheng, Y Q. Jin, H.H., Cen, KF, 2003gain more insight into the flow dynamics than couldModulation on coherent vortex structures by dispersedbe obtained from previous experiments. For the nsolid particlesthree-dimensional mixing layer.Physical review E. 68: 036309merical integration of the governing equations a Grant, G, Tabakoff, W, 1975. Erosion prediction in turbo-high-order spectral element method (sEM)was emmachinery resulting from environmental solid particles. Jployedof Aircraft, 12: 471-478The present results show that the change trends Karniadakis, G.E., 1999. Simulating turbulence in complexof particle flow are sometimes similar with differentgeometries. Fluid Dynamics Research, 24: 343-362Reynolds numbers. Stokes numbers have determininLing, w, Chung, J N, Troutt, T.R., Crowe, C.T., 1998. Directnumerical simulation of a three-dimensional temporalnfluence on overall features of the gas flow.mixing layer with particle dispersion. Journal of fluidFuture work needs to be done in several areasMechanics. 358: 61-85There is more to be done in studying the feedback of Marcu, B, Meiburg, E, 1996. Three-dimensional features ofparticles on gas flow, after which, we can investigateparticle dispersion in a plane mixing layer. Phys. Fluids,how particles influence the coherent structures of gas Parviz, M,Krishnan, M, 1998. Direct numerical simulationflow(called two-way couplinga tool in turbulence research. Annu. Rev. Fluid mech30:539-578ReferencesSlater, S.A., Young, J B, 2001. The calculation of inertialChung, J N, Troutt, T.R., 1988. Simulation of particle dispparticle transport in dilute gas-particle flows. Internasion in an axisymmetic jet J. Fluid Mech., 186: 199-222tional ournal of Multiphase Flow, 27: 61-87.rowe, C.T., Troutt, T.R., Chung, J N, 1996. Numerical Yao, J, Feng, J, Liu, L, Fan, J.R., Cen, K.F., 2003. Directmodels for two-phase turbulent flows. Annu. Rev. Fluidnumerical simulation on the particle flow in the wake ofMech.,28:11-43ircular cylinder, Progress in Natural Science, 13(5)379-394:Welcomevisitingourjournalwebsitehttp://www.zju.edu.cn/jzusWelcome contributions subscription from all over the worldThe editor would welcome your view or comments on any item in theournal or related mattersPlease write to: Helen Zhang, Managing Editor of JZUsE-mail: jzus zju. edu.cn Tel/Fax: 86-571-87952276中国煤化工CNMHG