Large eddy simulation of the gas-particle turbulent wake flow

http://ww.zju.educn/jzus:E-mail:jzus@zju.edu.cnsN 1009-3095 Journal of Zhejiang University SCIENCE V5 No. 1 P 106-110 Jan, 2004Large eddy simulation of the gas-particle turbulent wake flowLUO KuL(罗坤), JIN Han-hu(金晗辉)FaN Jian-ren(樊建人y, cen Ke-f(岑可法yInstitute for Thermal Power Engineering, Zhejiang University, Hangzhou 310027, China)(2 College of Materials Science and Chemical Engineering Zhejiang University Hangzhou 310027, ChinaReceived Dec 3 2002, revision accepted Apr 29 2003Abstract: To find out the detailed characteristics of the coherent structures and associated particle dispsion in free shear flow large eddy simulation method was adopted to investigate a two-dimensional particleladen wake flow. The well-known Sub-grid Scale mode introduced by Smagorinsky was employed to simulatethe gas flow field and Lagrangian approach was used to trace the particles. The results showed that the typicallarge-scale vortex structures exhibit a stable counter rotating arrangement of opposite sign and alternately formfrom the near wall region, shed and move towards the downstream positions of the wake with the developmentof the flow. For particle dispersion, the Stokes number of particles is a key parameter. At the Stokes numbersof 1. 4 and 3. 8 the particles concentrate highly in the outer boundaryWhile the particles congregatedensely in the vortex core regions at the Stokes number of 0. 15 and the particles at Stokes number of 15 as-semble in the vortex braid regions and the rib regions between the adjoining vortex structuresKey words: Large eddy simulation Plane wake Coherent structures, Particle dispersionDocument code: ACLC number: TK16INTRODUCTIONcorresponding particle dispersion patterns in thegas-solid two-phase plane wake flow with largePlane wake flow is one type of free shear eddy simulation, and try toance forflow and exists widely in nature and many engi- the associated industrial applicationsneering systems. To understand the kinetic chaacter of the large-scale coherent vortex structures MATHEMATICAL MODELand particle dispersion in plane wake flow ishelpful for improving many processes in energyengineering, chemical engineering and material 1. Flow configurationengineeringThe sketch of plane two-dimensional wakesimulation and Reynolds-averaged approache\ flow is shown in Fig. 1. The thickness of theLarge eddy simulation involves both directsplitter plate is 2=31. 5 mm and the velocityMethods have been developed in recent years to of free stream from each side of the plate for thesolve the problem of instantaneous gas flow field wake is Uo=3. 3 m/s. We assume that the gasand to simulate high Reynolds number turbu-ence on the basis of actual computer level. Diflow is incompressible and the fluid propertiesrect simulation techniques are applied to simulate are constant, The Reynolds number of the flowlarger scale anisotropic flows and time-average- can!中国煤化工S/U=6500, where vCNMHGof the fluid. In thesmaller scale isotropic flowscenterline of the plate the particles at density of4. The major objective of this work was to study np =4. 7 x 10" /m are injected at velocity of Ularge-scale vortex structure dynamics and =0. 4 m/s from a 3. 175 mm diameter hole intoLarge eddy simulation of the gas-particle turbulent wake flowthe wake flow. All geometrical lengths are scaled expressed ad( Fan et al., 2001with s. The characteristic flow time is obtaineddvas the characteristic length s, divided by thedt =f/S U-v)(3)characteristic velocity Uwhere v is the non-dimensional velocity of theparticle , U is the non-dimensional velocity ofthe fluid at the particle position t is the non-di2S Uo=3.3m/smensional time and st is the Stokes number de-fined as S=ppd2/18!f is the modification2x04mfactor for Stokes drag coefficient described by f1+0.15RUo=3, 3m.Reynolds number for particles and is defined asRe=IU-vi d.Fig 1 Sketch of plane wake flowNUMERICAL METHOD AND BOUNDARY CON-Flow-field simulationDITIONSIn large eddy simulation we adopt the wSub-grid Scale modeluce by Sma-In our simulation a two dimensional finitegorinsky( 1963 )to simulate the gas flow field. volume incompressible code based on xxyThe two-dimensional continuum equation and N- 302 x 401 staggered cells covering thS equations can be described as follows( Jin et tional domain is used to solve the flow field. Thespan of the computational domain covers x yContinuum equat=40S×30Smm2(1) Crank-Nicolson difference scheme in time isused. Sommerfeld boundary conditions( OrlansMomentum equationski,1976)at the outlet and free stream conditions in transverse direction are assumed. In parUi ulPticle dispersion simulation we choose the partiaicle diameter of 10um 30um 50um, 100um re-dudu(2)spectively to examine the disD-t Ddifferent size particles in the plane wake. Thecorresponding particle Stokes numbers are 0. 15Where U, =( CSA)ISI, ISI=(2 Si Si ) Si 1.4 13.8 and 15, respectively. Our numericalsimulation procedure was done according to the△=(△x△Cs=0. 15 model mentioned aboveIs used InRESULTS AND DISCUSSIONS3. Particle dispersion simulationSince the density ratio Pp/pg>1000, theBasset force and the added force, can be ne1. Flow fieldglected. The collisions between the particles canFig 2 shows the vorticity contour at nonalso be ignored because of low particle loading. menn addition, the saffman force and the Magnus comforce are neglected in this simulation too. So, chaiH中用千4and56 in the whole- lows clearly the flowC N MH Gcluding the formingonly the drag force due to the relative velocity developing and shedding process of the large-between the two phases is taken into account in scale vortex structures. A recirculating separa-study of the particle dispersion. Without considion exists near the downstream of theering theforce of the particles the non- plate trailing edge. The front part of the recircudimensiion equation for the particle is lating area expands rapidly and the vorticity con-108LUo Kun, JIN Hanhui et algregates gradually. In the big air bubble area ea new vorticity being continually injected intothat then comes into being, two eddy cores the two eddy cores causes the two edee aremerge and seems to be axially symmetric( T= eas to become larger and larger till th20). With the development of the air bubble ar-( T=32)0.10.05060.050.05-00-0.1020.30.40.50.6Fig. 2 The vorticity contour at non-dimensional time of 20 32 A4 and 56 in the whole flow field(a)T=20;(b)T=32;(c)T=44;(d)T=56In the recirculating regime there exists a tion resultse circurmfluence the vorticity produced by each side of the plate fills the trianglar area, so, the triangular area becomes smallerand smaller and the gas cling to the wall finallyWith further development of the air bubble areaand the regurgitant area near the wake the typial large-scale vortex structures present betweenthble counter-rotating opposite signalternately form from the near wall region shedand move towards the downstream positions ofthe wake with the development of the flow T'Fig 3 Contour of instantaneous vorticity obtained44andT=56)by large eddy simulationFig 3 is the vorticity contour in the nearwake flow covering the initial region of the wakedevelopmen(0<*<11,-3<2<+3)ob3. TH中国煤化工CN MH GStribution of particlestained by large eddy simulation. The figure is with Stokes number of 0. 15 at T=78 in thelar to the typical instantaneous streak- wake flow shows that the particles follow the fluline patterns at the same region with the same id flow closely and that most particles congregateconditions obtained from experiment( Yang et in the vortex core regions of the large-scale vor-al., 200a WtlEh verified the numerical simula- tex structures. Some particles also distribute inLarge eddy simulation of the gas-particle turbulent wake flow109the banded region connecting with the adjacent vortex structures and particles accumulate partlys a whole rthe in the rib or saddle regions between the adjacentparticles disperse in vortex core-vortex braid- vortex structures. The particles, however,arevortex core pattern, similar to the large-scale extremely few in the central region of the vortexcoherent structures of the fluid. This dispersion structures. The reason is that the particles withpattern is associated with the smaller aerodynam- Stokes number of 1. 4 are affected apparently byic response time of particles. As the aerodynam- the centrifugal force of these large-scale vortexic response time of particles is small enough the structures compared with the particles withrticles can almost follow the gas with no relStokes number of 0. 15. Impacted by the centrif-tive slip. In this case the coherent vortex struc- ugal force the particles are thrown out from thetures of gas play a dominant role in the particle vortex core regions and congregate in the outerdispersionboundary regions of the large-scale vortex strucFig 5 of the spatial distribution of particles tures. This result is in good agreement with prewith Stokes number of 1. 4 at T=78 in the wake vious numerical result( Tang et al., 1992) andflow shows that most particles congregate densely recent experimental results Yang et alin the outer boundary regions of the large-scale 2000)0.10.05-0.05634^6Fig 4 Spatial distribution of particles with St =0.15Fig 5 Spatial distribution of particles with St=1.4Compared with dispersion patterns of parti- structures the particles are still thrown out fromcles with Stokes number of 1. 4, particles with vortex core regions and congregate in the outerStokes number of 3. 8 are affected apparently by boundary regions of vortex structures and rib re-the centrifugal force of coherent vortex struc- gion between the adjoining vortex structures. Thetures, but on the other hand these particles be- particles disperse more apparently and distribgin to show their inertia effects. Fig. 6 shows the more evenly along the streamwise direction andspatial distribution of particles with Stokes num- the transverse direction due to their inertia ef-ber of 3. 8 at T=78 in the wake flow. Befectsof the dominant action of large-scale vortexFig. 7 shows the spatial distribution of particles with Stokes number of 15 at =78 in thewake flow. These particles cover almost all theregions of large-scale vortex structures and haveno similar distribution pattern of coherent eddystructures with the gas phase. But in the braidreglH中国煤化工and rib regiontweetures, due to the effectCNMHGvortex structures andinertia of particles, the particle concentrationsareelative higher. In this case, the inertial ef0.40.5more remarkable and the effect on particle mo-Fig.6列痱数揶 stribution of particles with St=3.8tion by large-scale vortex structures is mainly to110LUo Kun, JIN Hanhui et alchange the particle motion direction and form the 1. 4 and 3.8 concentrate highly in theouterfolding pattern of particle distributionboundary regions i The particles with smallerStokes number of 0. 15 congregate densely in the0.1vortex core regions of the large-scale vortexstructures ;While the particles with larger Stokesnumber of 15 assemble in the vortex braid regions and the rib regions between the adjoiningultssimulation agreed well with previous resultYang et al. 2000; Tang et al. 1992)ReferencesFan ,J. R., Zheng,Y. Q., Yao,J. and Cen,K. FFig 7 Spatial distribution of particles with St= 152001. Direct simulation of particle dispersion in a threedimensional temporal mixing layer. Proc R Soc Lond A457:2151-2166Jin, h. h. luo k. Fan. R. and Cen, K. FCONCLUSIONS2002. Large eddy simulation of a particle-laden turbu-lent plane jet. Journal of Zhejiang University Science ,3Large eddy simulation method is used to Orlanski, I, 1976. A simple boundary condition for un-study the gas-solid two-phase plane wake flowbounded hyperbolic flows. Journal of ComputationalThe Sub-grid Scale mode of Smagorinsky is used Smagorinsky, J., 1963. General circulation experimentsto simulate the gas flow field and Lagrangian apth the primitive equations. I. The basic experimentproach is used to trace the particle motion. FirstMon. Weather Rev.,91(3): 99and the moving towards downstream positions ar Tang, L, Wen, F, Yang,Y, Crowe,CT.,Chungly the formation the developing, the sheddingN. and Troutt,T. R., 1992. Self-organizing particlethe large-scale vortex structures in the planedispersion mechanism in a plane wake. Phys. FluidsA,410):2244-2251wake are shown. Then, the results of particle Yang, Y, Crowe, C. T., Chung ,JI Troutt t. Rdispersion show that the Stokes number of parti2000. Experiments on particledispersion in a planeey parame responding particlewake. Int. Journal of Multiphase Flow 26: 1583dispersion. The particles with Stokes number ofWelcome visiting our journal websitehttp:/www.zju.educn/jzusWelcome contributions subscription from all over the worldThe editor would welcome your view or comments on any item inthe journal or related matters中国煤化工Please write to: Helen Zhang,man丿sCNMHGizus zju. edu. cn I el/Fax 86-571-87952276