PREDICTION OF PARTICLE DEPOSITION IN TURBULENT INDOOR FLOWS WITH A 3D LAGRANGIAN MODEL

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1 PREDICTION OF PARTICLE DEPOSITION IN TURBULENT INDOOR FLOWS WITH A 3D LAGRANGIAN MODEL M Abadie 1,2, K Limam 2 and F Allad 2 1 Indoo Envionment Det., Lawence Bekeley National Laboatoy, Bekeley, CA, USA 2 LEPTAB, Univesity of La Rochelle, La Rochelle, Fance ABSTRACT This study descibes the develoment of a thee dimensional (3D) Lagangian code of aticle tansot in indoo tubulent flows. This aoach consists of integating tansot equations fo each aticle at each time ste to detemine successive ositions of the aticle. The fist challenge was to calculate instantaneous velocities of the aiflow. The mean comonent of these velocities was calculated by a classic CFD code. A stochastic ocess based on the Gosman and Ioannides method geneated the fluctuating comonent. Coections wee alied to bette fit exeimental esults. The second challenge was the detemination of the wall-aticle inteactions. These inteactions wee evaluated though the simulation of smallscale exeiments to measue aticles deosition on eal textues encounteed in building sufaces. Two kinds of bounday conditions wee tested: a aticle ebound obability and a citical velocity of ebound. The latte seems moe aoiate fo simulating the inteaction between textues and 5.0 µm aticles. INDEX TERMS Paticle, Deosition, Wall textue, Bounday condition, Numeical simulation, Lagangian modeling. INTRODUCTION The moden wok envionment has changed with technical develoment in ou society. Fench eole send 80 to 90% of thei time inside buildings (CSHPF, 1996), and thus ae moe exosed to the indoo envionment than the outdoos. Public awaeness of indoo bacteiological isks has ecently inceased due to U.S. anthax events. Indoo aticle ollution modeling tools ae imotant to assess a bette ediction of human exosue to aticle ollutants. Two levels of aticle disesion modeling exist in building envionment. The fist, based on a multizone aiflow model aoach (Cum and Seinfeld, 1981 and Nazaoff and Cass, 1989) consides the oom (o building) as a efectly well mixed zone. This model has a quick esonse fo fist analysis but it doesn t take into account the heteogeneity of aticle concentation within the zone. This can be done using the second kind of model, called Lagangian model, which calculates the tajectoy of each aticle based on the fluid chaacteistics. Paticle tansot though ai can be tacked and deosition location can be ecisely known. This study was aimed to develo a thee dimensional (3D) Lagangian code fo the simulation of aticle disesion in tubulent indoo flows. Fist, the eliability of the Gosman and Ioannides (1981) model alied to ecalculate the fluctuating comonent of the fluid velocity, which is needed to detemine the aticle tajectoy, is analysed. Then two kinds of wall- 1 Contact autho moabadie@lbl.gov 554

2 aticle inteaction ae descibed and comaed: a aticle ebound obability and a citical velocity of ebound. METHODOLOGY Lagangian modeling incile: In the Lagangian method, aticles ae teated individually by solving the aticle motion equation and the bulk of oeties of the aticulate hase is obtained by aveaging a significant numbe of aticles. The aticle motion equation, accoding to Hinze (1987), is: du π 3 π 2 3 d ρ Cd ρd U U 6 dt = ρ 8 6 π du du ( U U ) + Ca d + Fe whee d, ρ and U ae the diamete, the density and the instantaneous velocity of the aticle esectively; ρ and U ae the density and the instantaneous velocity of the fluid; C d is the dag coefficient; C a is the added mass coefficient and F e eesents the extenal foces. Fluid flow chaacteistics In ode to detemine the instantaneous velocities of the fluid, thee diffeent methods may be used to solve the Navie Stokes equations. The fist is the Diect Numeical Simulation (DNS) that has the advantage of solving these equations without any hyothesis but equies an extemely fine mesh. As such, it s only suitable fo simle o 2D geomety due to time intensive calculations. The Lage Eddy Simulation (LES), based on aveage tubulence theoy solves the Navie-Stokes equations using a coase gid, but needs additional equations to take into account the enegy tansfes between small and lage eddies. LES models need to be futhe develoed to bette suit aiflow simulation in buildings. The last model is the Reynolds Aveaged Navie-Stokes model. The method fo this model consists of intoducing time aveages of each vaiable (velocities, essue and temeatue) into the Navie-Stokes equations, and adding additional equations in ode to solve the equations system. These models ae suitable fo comlex geomety and ae less time consuming than the othe, and fo this eason ae fequently used to model aiflow attens in indoo saces. Numeous twoequation (k-ε) models exist and diffe fom one to anothe in the tansot equations of the tubulent chaacteistics and in thei alicability (Chen, 1995). Accoding to Chen, the Renomalization Gou Theoy (RNG) model is moe accuate then othe k-ε models fo aiflow in buildings because it takes into account small and lage scales of tubulence diffeently, although it equies moe calculations (iteations) than the standad model to achieve a good convegence. In this study, all the mean quantities, such as the mean fluid velocities, the tubulent kinetic enegy, k, and the kinetic enegy dissiation ate, ε, ae comuted by a Comutational Fluid Dynamics (CFD) code using a RNG model. Detemination of the fluctuating comonent of the velocity In ode to obtain the instantaneous velocity of the fluid, we have to calculate at each time ste and fo each location of a aticle the fluctuating comonent of the fluid velocity based on the tubulent chaacteistics of the fluid flow. Seveal models exist and diffe in the stochastic method alied. The Gosman and Ioannides (1981) model has seved as the basis fo numeous authos (Dust, Milojevic and Shonung, 1984 and Mostafa and Mongia, 1987). It calculates the fluctuating comonent of the fluid velocity fom a andom vaiable whose standad deviation, σ, is ootional to the tubulent kinetic enegy. dt dt (1) 555

3 2 σ = k (2) 3 The aticle motion equation (equation 1) is solved fo the entie time that the aticle inteacts with the tubulent eddy. This time is defined as the minimum between the eddy lifetime and the time equied by the aticle to ass though the eddy. The eddy lifetime, t e, is a function of the tubulent kinetic enegy, k, and its dissiation, ε: 2 3 Le t = and k e L e = C (3) ε ( 2k 3) 1 2 whee C is a constant equal to 0.46 (Chen and Cow, 1983) and L e is the eddy chaacteistic length. The time equied by the aticle to ass though the eddy is given by the following exession: t L ρ e = τ ln 1 τ U U and d 2 τ = (4) 18µ whee τ is the aticle elaxation time and µ is the dynamic viscosity of the fluid. The elaxation time, t, is the time equied by the aticle to eact to a change in the fluid flow, thus it is well adated to measue the effect of flow tubulence on aticle behavio. The highe the aticle elaxation time is, the lowe the flow tubulence effect. Wall-aticle inteaction The wall-aticle inteaction is a comlex henomenon because it involves many aametes. Dahneke (1971) and moe ecently John (1995) studied this ocess intensively. When a aticle collides with a wall, it can stick to the wall o ebound, deending on the intensity of the adhesion foce. This foce is difficult to evaluate because it deends on the wall and aticle suface chaacteistics (geomety, hadness and electostatic olaity) and ai dyness. To detemine if a ebound occus, we have defined two ebound citeia. The fist one is the stochastic aamete obability of ebound, P. If N aticles hit a wall, only P N will stick to the wall; the othes will ebound. By calculating a andom numbe at each collision and comaing it to the obability of ebound value (a function of the consideed wallaticle coule), the aticle behavio is detemined. This citeion has no hysical value but is well adated to the Lagangian method (moe ecisely to the Gosman and Ioannides (1981) scheme) because the Lagangian method also equies a lage numbe of aticle tajectoy calculations. The second citeion is the citical velocity below which the aticle sticks to the wall. As with the fist citeion, it deends on the consideed wall-aticle coule. It should be added that elastic ebound without enegy loss was taken as a fist aoximation fo both citeia to calculate the ost-collision aticle osition. RESULTS Befoe studying the wall-aticle inteaction, effot was made to detemine the eliability of the Gosman and Ioannides (1981) model to edict aticle tajectoy. The Snyde and Lumley (1972) exeiment was simulated in ode to comae the behavio of thee kinds of aticle intoduced in a homogeneous tubulent flow. Comaison with the numeical esults shows that the model tends to undeestimate the aticle axial disesion. Coections to the 556

4 Gosman and Ioannides (1981) model wee added by eeating the simulations multilying the fluctuations by a daming coefficient, K GI, evaluated fo each aticle in ode to match the exeimental esults. Moeove, a diect coelation was detemined between this new coefficient, K GI, and the aticle elaxation time, τ. GI ( τ) = 4 ( 1 4 τ ) K (5) Figue 1 esents the aticle lateal disesion as a function of time. As exected, numeical and exeimental esults look simila. The coected esults obtained using this coection facto is shown fo the s-elaxation time aticle as an examle; the uncoected numeical method leads to a quasi non-disesion, which is in diect contadiction with the exeimental esults. Lateal Disesion (cm²) Exeiment Pollen de maïs (τ = E s) Exeiment t = 58.1 (τ = s) Exeiment Cuive - E (τ = s) Numeical Pollen de maïs (τ = Ds) Numeical Vee - 3D(τ = s) Numeical Cuive - 3D(τ = s) Uncoected Seies1 Num eical (τ = s) Time (s) Figue 1. Lateal disesion of thee aticle elaxation times vesus time. 100% Exeiment Pobability Citical Velocity Pecentage of global deosition 80% 60% 40% 20% Figue 2. 0% Smooth Wallae Rough Wallae Caet Linoleum Glazing Textue 5.0 µm aticle deosition on floo as a function of textue. 557

5 The Abadie (2000a, 2000b and 2001) exeiment was modeled to evaluate the wall-aticle inteaction and moe ecisely to detemine the ebound obability and the citical velocity values fo a given wall textue-aticle coule. This exeiment consists of a confined cubic enclosue whose hoizontal and vetical walls can be coveed by vaious textues. The selected wall suface anel fo the esent study is made u of five kinds of textues: fom the smoothest and hadest ones like glazing, linoleum and smooth wallae, to the oughest and softest like ough wallae, and caet (with cut velvet). A thee-bladed oelle susended fom the cente of the scale model ceiling and blowing towads the ceiling is emloyed as a tubulent souce. Exeimental constants of deosition wee detemined by egession-fitting of the concentation exonential decay cuves. This aamete was used as a efeence to calculate the deosition on walls using the global model of Cum and Seinfeld (1983). This global model is a efeence to detemine aticle deosition location in tubulent vessels. By vaying the value of the numeical citeion and by comaing the obtained constant of deosition with the exeimental value, one can identify the citeion value fo the desied textue-aticle coule. Figue 2 esents the 5.0 µm-aticle deosition on floo as a function of textue fo both wall-aticle citeia and fo the exeiment. If the tendencies fo both citeia ae the same as the global model, the citical velocity citeion seems to be moe aoiate to model the wall-aticle inteaction. DISCUSSION The develoment of the 3D Lagangian code of aticle disesion bought out two main oints. Fist, the integation of a coected coefficient to the Gosman and Ioannides (1981) model is consistent with the hysics involved in the aticle disesion. The calculation of the fluctuation by the Gosman and Ioannides (1981) model deends only on the fluid chaacteistics, and its exclusive goal is the detemination of the fluctuating at of the velocity without the esence of a solid body. As a esult, the fluid instantaneous velocity is the same egadless of the aticle tye. With the intoduction of the coefficient K GI, the esence of the aticle is then taken into account. Fo examle, the fluid fluctuating velocity is lowe fo a high elaxation time aticle than fo a low one. The second oint is that the method emloyed to evaluate the wall-aticle inteaction intensity seems eliable and emits an initial aoach to model this comlex ocess. Results show that the method clealy highlights the diffeence in inteactions between the textues and thei consequences on the deosition location. Desite these encouaging esults, deosition on floo is still ove-evaluated comaed to global model ediction. One imovement will be to conside the enegy loss duing the wall-aticle contact by intoducing a estitution coefficient. Taking into account both citical velocity and estitution coefficient would ovide a bette modeling of the wall-aticle inteaction. CONCLUSION AND IMPLICATIONS A 3D Lagangian code of aticle disesion in tubulent flows was develoed in this study. A coection to a classical model of velocity fluctuating comonent geneation was alied to bette fit exeimental esults. Additional imovement to this at of the code would consist in testing othe models of velocity fluctuating comonent geneation o using anothe aoach; fo examle, Lage Eddy Simulation modeling (Chen, Jiang, Beghein et al., 2001) would emit avoiding the use of the atificial velocity fluctuating comonent calculation. The most imotant develoment fom this study concens the aoach used to evaluate the wall-aticle inteaction. The fist ste of this method consists of exeimentally measuing the constant of deosition fo a desied wall-aticle coule. Then, using the cuent database 558

6 (available fo 5.0 µm-aticle) o simulating the exeiment fo a new kind of aticle, the citical velocity (o ebound obability) can be detemined. This imlies that wall-aticle inteaction (and aticle deosition) fo evey indoo wall textue can be simulated using both the exeimental facility and the numeical code we develoed. This tool is suitable to detemine aticle disesion in buildings, to evaluate the main aths followed by aticles, to detemine the deosition locations and to assess a bette ediction of human exosue to aticle ollutants. ACKNOWLEDGEMENTS This study is at of the PhD dissetation Contibution to the study of aticle ollution: ole of the walls, ole of the ventilation (Abadie, 2000b) financed by the Agency of the Envionment and the Enegy Management (ADEME) and the Poitou-Chaentes Region. REFERENCES Abadie M, Limam K, and Allad F. 2000a. Indoo aticle ollution: effect of wall textues on aticle deosition. Roomvent 2000 Intenational Confeence, Vol. 1, Abadie M. 2000b. Contibution à l étude de la ollution aticulaie : ôle des aois, ôle de la ventilation. PhD dissetation. Univesité de La Rochelle, Fance. Abadie M, Limam K, and Allad F Indoo aticle ollution: Effect of wall textues on aticle deosition. Building and Envionment. Vol. 36 (N7), Chen PP, and Cow CT On the Monte-Calo method fo modeling aticle disesion in tubulence. Poceedings of Gas-Solids Flows, New Yok. Vol. 10, Chen Q Comaison of diffeent k-ε models fo indoo aiflow comutations. Numeical Heat Tansfe. Vol. 28(B), Chen Q, Jiang Y, Beghein C, and Su M Paticulate disesion and tansotation in buildings with Lage Eddy Simulation. Lincoln Laboatoy-Massachusetts Institute of Technology, Final Reot MA Cum JG, and Seinfeld JH Tubulent deosition and gavitational sedimentation of an aeosol in a vessel of abitay shae. Jounal of Aeosol Science. Vol. 12 (5), CSHPF Pollution atmoshéique à l'intéieu des bâtiments: Souces, Exositions et Risques Sanitaies. Conseil Suéieu d'hygiène Publique de Fance, section de l'evaluation des isques de l'envionnement su la santé. Ed. Lavoisie Tec&Doc. Dahneke B The catue of aeosol aticles by sufaces. Jounal of Colloid Inteface Science. Vol. 37, Dust F, Milojevic D, and Shonung B Euleian and Lagangian edictions of aticulate two-hase flows: A numeical study. Alied Mathematical Modeling. Vol. 8, Gosman AD, and Ioannides E Asects of comute simulation of liquid-fuel combusto. AIAA 19 th Aeosace Science Meeting. Vol Hinze JO Tubulence. McGaw-Hill Book Comany, Inc. John W Paticle-suface inteactions: Chage tansfe, enegy loss, esusension, and deagglomeation. Aeosol Science and Technology, Vol. 23 (1), Mostafa AA, and Mongia HC On the modeling of tubulent evaoating says: Euleian vesus Lagangian aoach. Intenational Jounal of Heat Tansfe. Vol. 30, Nazaoff WW, and Cass GR Mass-tansot asects of ollutant emoval at indoo sufaces. Envionment Intenational. Vol. 15, Snyde WH, and Lumley JL Some measuements of aticle velocity autocoelation functions in a tubulent flow. Jounal of Fluid Mechanics. Vol. 48,