Numerical Simulation of Particle-Gas Flow, in Order to Investigate the Effects of Dispersed Phase on Continuous Phase

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1 Internatonal Journal of Mnn, Metallury & Mechancal Enneern (IJMMME) Volume, Issue (015) ISSN (Onlne) Numercal Smulaton of Partcle-Gas Flow, n Order to Investate the Effects of Dsersed Phase on Contnuous Phase Zafar Namazan 1,, Amr Farhad Najaf 1, Seyyed Mohsen Mousavan 1 Abstract A numercal smulaton of the artcle-as flow n a vertcal turbulent e flow was conducted. The man objectve of the resent artcle s to nvestate the effects of dsersed hase (artcles) on contnuous hase (as). In so don, two eneral forms of Euleran-Laranan aroaches namely, one-way (when the flud flow s not affected by the resence of the artcles) and two-way (when the artcles exert a feedback force on the flud) coulns were used to descrbe the equatons of moton of the two-hase flow. Gas-hase veloctes whch are wthn the order of mantude as that of artcles, volume fracton, and Stokes number were calculated and the results were subsequently comared wth the avalable exermental data. The smulated results show that when two-way couln s used, the flud velocty s attenuated. Wth an ncrease n artcle volume fracton, artcle mass loadn and artcle Stokes number, velocty attenuaton also ncreases. Moreover, the results ndcate that an ncrease n artcles Stokes number reduces the secal lmted artcle volume fracton, accordn to whch one-way couln method yelds lausble results. Keywords Two-way Couln, Volume Fracton, Stokes Number, Dsersed Phase, Euleran-Laranan Aroaches. S I. INTRODUCTION usenson of artcles n a turbulent flud has been frequently observed n many mortant natural and technolocal stuatons such as crculatn fludzed bed reactors, aerosol transort and deoston, neumatc conveyance of sold materals, ulverzed coal and sray fuel combuston, and dserson of ollutants. In most of these alcatons, the turbulent behavor of the carrer hase lays a domnant role n transortn or mxn the artcles. To mrove the effcency of these rocesses and the qualty of the fnal roducts, t s necessary both to dscover and to redct the mechansms that nfluence the flow feld. The nteractons between the carrer hase (contnuous hase) and the artcle hase (dsersed hase) comrse a comlex ssue by themselves. No surrse that turbulence flow analyss has yet remaned a challenn toc for the classcal mechancs snce Osborne Reynolds ornally formulated the well-known closure roblem n the late 1800s. The ambuty of whch, however, s exected to ncrease follown the njecton of 1 Deartment of Mechancal and Enery Enneern, Shahd Behesht Unversty, Tehran, Iran Deartment of Mechancal Enneern, Yasuj branch, Islamc Azad Unversty, Yasuj, Iran (z.namazan@mal.com) artcles to a turbulent flow [1]. Turbulence ntensfes the dserson of artcles, and the artcles may n return affect the roertes of the carrer hase flow. The deree of couln between the artculates and the aseous carrer hase deends on the amount of exstn artculates []. For dlute flows (where the effect of artcle/artcle collson s nelble), 6 and for artcle volume fractons less than, the couln between hases s one-way, that s, the artculate moton s drven by as hase but the resence of the artculates does not nfluence the carrer hase flow. As the volume fracton of the artculate hase ncreases, the flud hase veloctes and turbulence characterstcs alter as a result of nteractn wth the artcles. Ths stuaton has been termed as two-way couln by Crowe []. Several revews on the artcle-laden turbulent flow have been ublshed durn the ast decade. [See Hetsron [4], Elhobash [], Crowe et al. [5], Mashayek and Pandya [6], Nasr and Ahmad [7], Dosneau [8] for nstance]. Gore and Crowe [9] demonstrated that n most cases, small artcles have a tendency to mnmze dsturbance whereas larer artcles ncrease turbulence levels. In the study of Kulck et al. [] n develoed turbulent flow n the channel, artcles smaller than the mcro scale were consdered. They showed that the flud turbulence decreases wth ncreasn number of artcles. Portela and Olemans [11] reorted that the resence of artcles leads to a decrease n turbulent eddy ntensty wthout snfcant chane n ther sze and shae. Strömren et al. [1] nvestated the dfference between one-and two-way couln for dfferent artcle volume fractons and artcle dameters. It was found that artcles wth a much hher densty than the flud substantally affect the as-hase n turbulent channel flow for artcle volume fractons as low as -4. They showed that two-way couln and the turbohoretc effect must be taken nto account n models even at relatvely low artcle volume fractons. Also n the other study, Mousavan et al. [1] showed that usn of two way couln model redct more accurate searaton erformance n the hydrocyclone due to hh sold concentraton n outlet. The obtaned exermental data for Partcle-laden turbulent flows, reorted addn the artcles wth ncreases and decreases turbulence. Tsuj and Morkawa [14, 15] showed that small artcles wth a dameter of about mcrometers reduce turbulence ntensty and velocty of the flud hase. Breuer and Alletto [16] nvestated the smulaton of artcle-laden two-hase flows based on the Euler Larane aroach. They used two-hase 46

2 Internatonal Journal of Mnn, Metallury & Mechancal Enneern (IJMMME) Volume, Issue (015) ISSN (Onlne) flows, the flud artcle nteracton (two-way couln) as well as artcle artcle collsons (four-way couln). Also In order to tackle comlex turbulent flows eddy-resolvn schemes (lare-eddy) s used. They found ood areement between comutatonal results and exermental measurements. Some researchers study the arorateness of modeln method of sold flud nteracton. Benra et al. [17] nvestated the dfferent roblems wth one-way and two-way couled methods and showed under what conons a one-way couln soluton ves lausble results. The resent study ntends to make a comarson between two eneral forms of Euler-Larane aroaches, namely one-way and two-way coulns. Ths analoy has been tested by the use of two well-known arameters, namely artcle Stokes Number and Volume Fracton. To serve ths urose, frst for each Stokes number, volume fracton s ncreased and then velocty n a secfc ont of the as flow-feld s determned both by one-way couln and two-way couln methods. In one-way couln, due to nelble effects of artcles on the as flow, flow-feld s not affected by the volume fracton, whereas n two-way couln, flow-feld chanes wth dfferent volume fracton. The ntrun ont observed n ths study s the devaton of the results of one-way couln from those of two-way couln whch s due to the ncreasn effects of artcles on contnuous hase when the volume fracton s rased. Tycally the use of one-way couln method can be justfed as a result of ts low comutatonal cost; hence, artcular lmted volume fractons have been secfed for several stokes numbers for whch, the use of oneway couln s lausble wthout any snfcant error. Fnally, areement of exstn exermental data [15] and redctons obtaned by the model n queston s comletely observable. II. ANALYSIS AND MODELLING A number of arameters whch are of mortance to turbulent flow susenson as well as those used n ths revew are defned below. The volume fracton of the dsersed hase (artcles) s: V (1) V Where V s the volume of the dsersed hase n the volume V of mxture. An adonal arameter that may have a snfcant nfluence on the flow s the artculate loadn rato. It may be wrtten mathematcally as: m () m For systems wth ntermedate artculate loadns, estmatn the value of the Stokes number may contrbute to the selecton of the most arorate model. The Stokes number can be defned as a relaton between the artcle resonse tme and that of the system as follows St () s Whereas St 0, the artcle behaves as a flud tracer and as St, the artcle s unresonsve to the fluctuatons of the flow. Obvously, the most hyscally nterestn stuaton occurs when t aroaches the unty: artcles follow the lare scale flud moton. Fnally, the flow reme n the vcnty the artcles can be characterzed by means of the artcle Reynolds number as follows: u u d Re (4) At small values of Re vscous effects are domnant and the streamlnes are essentally symmetrcal around the artcle center, whereas at larer Re numbers t can be dsersed and a wake may develo behnd the artcle ath. When Re rases enouh, the wakes become turbulent. It has been ostulated by Hetsron [4] that Re can be used to determne whether artcles attenuate ( Re 0 ) or enhance ( Re 400 ) the flud turbulence level. In the resent work we have concentrated on shercal undeformable artcles of densty and dameter d smaller than all the flow lenth scales, and low values of the artcle Reynolds number. The Laranan artcle equaton of moton roosed by Basset [18], Boussnesq [19], and Oseen [0] and later exanded by Tchen [1] s most frequently used. That s, du V V C M 1 d CD u 4 u Du du Dt V V u u d CL V Du Dt t0 u t u u (5) The sx terms on the rht hand-sde of Eq.( 5) reresent, from left to rht, the buoyancy force, ressure radent force (excludn the ravty term that we ncluded n the buoyancy force), the Stokes dra force, the basset hstory force, added mass or vrtual mass force, and the lft force, resectvely. In most ractcal dlute flow alcatons, the flud-to-artcle densty ratos are n the order of. Under such a crcumstance, the added mass, the basset hstory force, and ressure radent force can be nelected [, ]. The lft force can also be nelected, snce t does not affect the artcle trajectory excet wthn the vscous sub layer [6]. Accordn to the assumton above, dra force s the most nfluental force on the movn of artcles and Eq. (5) wll be reduced to du And CD Re 4 u u t d u d (6) 47

3 Internatonal Journal of Mnn, Metallury & Mechancal Enneern (IJMMME) Volume, Issue (015) ISSN (Onlne) dx u III. DESCRIPTION OF THE FLOW (7) In Tsuj et. al s exerment [15], artcles were njected nto the flow by the use of an electromanetc feeder and hence assed around a horzontal-vertcal bend to enter the vertcal test secton as a two hase flow, as shown n F. 1. The e dameter chaned abrutly at the bend outlet from 40 mm to 0.5 mm. It made the artcles slde on the bend outer wall and become dsersed. The dstance between the bend outlet and the test secton was 5.11 m. At the end of the test, they made measurements usn Laser Doler Velocmetry (LDV) n the fully develoed reon of the lass e. There were fve knds of olystyrene artcles (four tyes of shercal and one cylndrcal shaes) utlzed n ther exerment. A wde rane of artcle szes (from 00 m ~000 m n dameter) wth denstes rann from 0 k/m to 0 k/m and loadn ratos rann from 0.5 to 5.0 were emloyed for shercal artcles. The 00 m and 500 m artcles were coated wth a chare-reventn substance to avod the electrostatc charn caused by the frcton between the artcles and the wall. The mean ar veloctes were raned from 8 to 0 m/s. Where CD s the dra coeffcent and for the sold artcles s exressed by Newton law: 4 Re 1 Re CD Re 1 Re 00 Re 0.44 Re 00 (8) For ncomressble steady flow overnn equatons are Naver-Stocks and contnuty equatons. The corresondn overnn equatons for flud hase are: Contnuty u 0 x (9) Momentum equaton uj u u 1 ( T (u, j u j, ) x j x x j x j () k j ) S For turbulence modeln standard k-ε Turbulence model s used. F. 1. Exermental set u of Tsuj et al [15] Turbulence knetc enery equaton T k k uj ( ) ( k j x j x j k x j T (u, j u j, )) IV. NUMERICAL SIMULATION In ths study, the system of equatons has been numercally solved by the alcaton of a D- axsymmetrc double recson model usn CFD code based on fnte volume rocedure. The equatons are dscreed usn Presto s scheme, whch s smlar to the staered-rd scheme wth a frst-order uwnd scheme for the convectve terms. The Smle alorthm s used to solve the couln between contnuty and momentum throuh ressure. The converence (11) u S k x j Turbulence dssaton enery equaton T uj ( ) C 1 ( k j x j x j x j k u T (u, j u j, )) C S x j k crteron n each case was ( 1) ( ) ( ) 8, where denotes the teraton number and could stand for any of the deendent varables. When alyn one-way couln smulatons, the contnuous-hase flow feld s solved and then the artcle trajectory for dscrete hase s determned. On the other hand, when we emloy two-way couln smulatons, the contnuous hase flow attern s macted by the dsersed hase (and vce versa); thus, teratve calculatons of contnuous hase and dsersed hase are erformed untl a convered couled soluton s obtaned. The artcle hase equatons are solved usn the mlct and the traezodal scheme. In all the smulatons, the hases are assumed to be ncomressble, and densty and vscosty are constant. The walls were adabatc and no-sl wall conons were used for (1) S, S k and S are the effect of artcles on momentum equaton, turbulence knetc enery and turbulence dssaton enery resectvely. 48

4 Internatonal Journal of Mnn, Metallury & Mechancal Enneern (IJMMME) Volume, Issue (015) ISSN (Onlne) none of the hases. A velocty nlet boundary conon was aled on the nlet, whle on the outlet ressure outlet boundary conon was aled. The quadrlateral mesh was used to smulate ths axsymmetrc vertcal e flow (F. ). Tests were conducted earler to ensure rd-ndeendent results and n the end, a non-unform rd of 00 0 was found to suffce. Amed to verfy the ndeendence of ntal conons from turbulence, dfferent turbulent knetc enery and turbulent dssated enery at the nlet of e are consdered, then ndeendence of results at the end of e are studed. Physcal doman was lon enouh to obtan fully develoed conon. The ntal veloctes of the as-hase were not rovded n the exerment of Tsuj et al. [15], therefore n order to obtan an averae velocty to be used as the nlet velocty, nteraton was erformed on the avalable velocty rofles for each test case [1]. (14) The averae artcle Reynolds number was calculated by solvn the non-lnear equaton as follows [1]: Re Re d 0 (15) Ths equaton was obtaned based on the defnton of the artcle Reynolds number. The ntal velocty of the artcles was set equal to those of the as hase. V. RESULTS AND DISCUSSION In order to valdate the relablty of the roosed model, obtaned numercal results were comared wth several exstn exerments. Therefore, for radal dstrbuton of axal velocty at the e outlet, we made a comarson between numercal (One-way and Two-way couln) and exermental results for cases I, II, and III, as llustrated n F.. As exected, comared to the smulaton results of the one-way couln, those of the two-way couln are n a better areement wth the exermental results for the axal veloctes. Moreover, t s observed that ncreasn the artcle sze leads to a decrease n the velocty attenuaton (see case I and case III).). F.. Mesh scheme used n the resent work The nlet velocty was consdered to be constant across the nlet lane. The artcles were njected wth a constant mass flow rate across the nlet secton. Actually, usn the follown equaton the nlet velocty was calculated based on a ven loadn rato ( ) (1) m ua The test cases n the artcle laden vertcal e flow by Tsuj et al. [15] are summarzed n Table 1. TABLE 1 A SUMMARY OF THE TEST CASES IN THE PARTICLE LADEN VERTICAL PIPE FLOW BY TSUJI ET AL [15] Quantty Case 1 Case Case d m k m s u m s m k Re The artcle volume fracton was calculated as [1].4 Case I Case II 49

5 Internatonal Journal of Mnn, Metallury & Mechancal Enneern (IJMMME) Volume, Issue (015) ISSN (Onlne) Case III F. Comarsons of redcted radal dstrbuton of axal mean velocty w.r.t the exermental data of Tsuj et al. [11], Re,000 Cases I, II, and III. In ths secton, the smulaton results for flud veloctes as well as the dscreancy between two-way and one-way coulns for dfferent artcle volume fractons and Stokes numbers are resented. The smulatons were erformed for D-Axsymmetrc uward fully develoed e wth the dameter and lenth of 0.5 mm and 5.11m lon, resectvely. We assumed the values of T, and for ar to be as: 5 T K, Ns m and 1.77k m, resectvely. Fure 4 comares the axal mean as velocty redcted by one-way wth those of two-way coulns at the end of the centerlne of e secton n dfferent artcle volume fractons for Case II. couln from those of two-way couln; ths s due to cumulatve effects of artcles on the contnuous hase whle the volume fracton s ncreased. Fure 5 llustrates the ercentae of the devaton of axal mean as velocty at the end of centerlne of e secton redcted by one-way and two-way coulns. The smulatons were erformed at m s velocty of nlet ar and 400 m artcles sze n dfferent artcle volume fractons and Stokes numbers. As llustrated n Fure 5, velocty redcted devaton s hhly deendent on the Stokes number and volume fracton. Wth a smle observaton, t could be erceved that the velocty obtaned devaton ncreases wth an ncrease n the volume fracton, whch s due to ncreasn the number of artcles, at constant Stocks number. In adon, t can be seen at a secfc volume fracton, the obtaned velocty devaton rows wth ncreasn the Stokes number. Ths may be due to the fact that ncreasn the stock number at constant artcle dameter s equal to an ncrease n the artcle densty,.e. heavy artcles wth more nfluence on contnuous hase. (a) F 4. Comarson between the axal mean as velocty at the end of centerlne of e secton redcted by one-way and two-way couln for Case II. In one-way couln, because of nelectn the effects of artcles on the as flow, flow-feld s not affected by the volume fracton, n two-way couln, however, flow-feld chanes n dfferent volume fractons. The nterestn ont of ths nvestaton s devaton of the results of one-way (b) Fure 5. Percent of devaton of axal mean as velocty at the end of the centerlne e secton obtaned by one-way and two-way 4 couln for 400 m artcles; (a) 5, (b)

6 Internatonal Journal of Mnn, Metallury & Mechancal Enneern (IJMMME) Volume, Issue (015) ISSN (Onlne) [1] Strömren T., Brethouwer G., Amber G., Johansson A., 01, Modelln of turbulent asartcle flows wth focus on two-way couln effects on turbohoress, Powder Technoloy, Volume 4, Paes 6 45 [1] Mousavan S.M., Ahmadvand M., Najaf A.F., 009, One-Way and Two-Way Couln Analyses on Three Phase Flows n Hydrocyclone searator, Journal of aled mechancs, 009, vol. 76, No 6 [14] Tsuj, Y, and Morkawa, Y, 198, LDV Measurements of an Ar-Sold Two-Phase Flow n a Horzontal Pe, J. Flud Mech,,. 85. [15] Tsuj, Y., Morkawa, Y, and Shnom H, 198, LDV Measurements of Ar-Sold Two-Phase Flow n a Vertcal Pe, J. Flud Mech, 19, [16] Breuer M., Alletto M., 01, Effcent smulaton of artcle-laden turbulent flows wth hh mass loadns usn LES, Internatonal Journal of Heat and Flud Flow, Volume 5, June 01, Paes 1 [17] Benra K., Dohmen H., Pe J., Schuster S., Wan B., 011, A Comarson of One-Way and Two-Way Couln Methods for Numercal Analyss of Flud-Structure Interactons, Journal of Aled Mathematcs Volume 011, Artcle ID 85560, 16 aes [18] Basset, A.B., 1888, a Treatse on Hydrodynamcs, vol., Dehton, Bell and Co., Cambrde, (Chater 5) [19] Boussnesq, J., 190, Théore Analytque de la Chaleur, vol., Gauther-Vllars, Pars. [0] Oseen, C.W., 190, Hydrodynamk, Lez. [1] Tchen, C.M., 1947, Mean Value and Correlaton Problems Connected wth the Moton of Small Partcles Susended n a Turbulent Flud, Ph.D. Thess, Delft Unvercty, The Netherlands. [] Hodson, S.M., 1999, Turbulence Modulaton n Gas-Partcle Flows: A Comarson of Selected Modeles, Master Thess, Unversty of Toronto. [] Rudner, G., 1980, Hand Book of Power Technoloy, vol.: Fundamentals of Gas-Partcle Flow, Elsever Scentfc Publshn Comany, Amsterdam Because of low comutatonal cost of one-way couln, ths method s commonly referred. Therefore, secfyn secal conons n whch artcle effects are nelble are enerally accentuated. In ths study, the lmtatons of volume fracton were ndcated n several Stoke numbers where the one-way couln method can be used wthout any snfcant error. For examle, Table has been obtaned for 1% devaton. TABLE SPECIAL LIMITED PARTICLE VOLUME FRACTION FOR DIFFERENT STOKES NUMBERS FOR 1% DEVIATION Stokes number Volume fracton VI. CONCLUSION In the resent study, we erformed CFD analyss on nternal turbulent artcle-as flow. The Laranan model has been used to track the artcles. In order to valdate the numercal model, comarsons between exermental and numercal results have been made. Thus, n order to secfy the mortance of artcle flud nteracton, one-way and two-way couln methods have been comared. The results have shown when the artcle volume fracton and artcle Stokes number are ncreased, the two-way couln method leads to more accurate redcton of axal mean as velocty comared to one way couln method n whch the artcles-as nteracton s nelected. In other words, consderatons of asartcle nteracton aear to be more snfcant at hher volume fractons, artcle Stokes numbers and artcle mass loadn. The results also ndcate that artcle Stokes number enhancement reduces the volume fracton lmtaton. REFERENCES [1] Fushen yan, B.Sc, and M. Sc. (Northeastern Unversty, Chna) 006, Numercal Study on Turbulence Modulaton n Gas-Partcle Flows, Ph.D. Thess, McMaster Unversty, The Netherlands. [] Elhobash, S., 1994, On Predctn Partcle-Laden Turbulent Flows, Alled Scentfc Research, 5, [] Crowe, C.T., 198, Revew: Numercal Models for Dlute Gas-Partcle Flows, J. Fluds Enr, 79, [4] Hetsron, G., 1989, Partcles-Turbulence Interacton, Int. j. Multhase Flow, 15, [5] Crowe, C.T., Troult, T, and Chun, J, 1996, Numercal Models for TwoPhase Flows, Annu. Rev. Flud dyn, 8, [6] Mashayek, F, and Pandya, R, 00, Analytcal Descrton of Partcle/Drolet-Laden Turbulence Flows, Pro. Enery Combust. Sc, 9, [7] Nasr, H, and Ahmad, G, 007, The effect of two-way couln and nter-artcle collsons on turbulence modulaton n a vertcal channel flow, Internatonal Journal of Heat and Flud Flow [8] Dosneau F., Sbra A., Duays J., Murrone A., Laurent F., Massot M., 01, An effcent and accurate numercal stratey for two-way couln n unsteady olydserse moderately dense srays: alcaton to Sold Rocket Motor nstabltes, Journal of Proulson and Power 14 [9] Gore, R.A, and Crowe, C.T, 1991, Modulaton of Turbulence by a Dsersed Phase, Trans. ASME. I: J. Flud En, 11, [] Kulck, J.D., Fessler, J.R. and Eaton, J.K., 1994, Partcle Resonse and Turbulence Modfcaton n Fully Develoed Channel Flow, J. Flud Mech. 77, [11] Portela, L.M, and Olemans, R.V.A, 00, Euleran- Laranan DNS/LES of Partcle-Turbulence Interactons n Wall-Bounded Flows, Int. J. Number. Meth. Fluds, 4,