Resuspension of Small Particles from Multilayer Deposits in Turbulent Boundary Layers

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1 Resuspension of Smll Prticles from Multilyer Deposits in Turbulent Boundry Lyers F. Zhng, *,, M. Reeks*, M. Kissne nd R. J. Perkins Institut de Rdioprotection et de Sûreté Nucléire, BP 3, St-Pul-lez-Durnce, Frnce * School of Mechnicl nd Systems Engineering, Newcstle University, Newcstle upon Tyne, NE1 7RU, UK Lbortoire de Mécnique des Fluides et d'acoustique, Ecole Centrle de Lyon, 36, venue Guy de Collongue Ecully, Frnce Keywords: remobiliztion, turbulence, multilyer resuspension, severe ccident Abstrct We present hybrid stochstic model for the resuspension of micron-size prticles from multilyer deposits in fully-developed turbulent boundry lyer. The rte of removl of prticles from ny given lyer depends upon the rte of removl of prticles from the lyer bove which cts s source of uncovering nd exposure of prticles to the resuspending flow. The primry resuspension rte constnt for n individul prticle within lyer is bsed on the Rock n Roll (R n R) model using non-gussin sttistics for the erodynmic forces cting on the prticles (Zhng et l., 1). The coupled lyer equtions tht describe multilyer resuspension of ll the prticles in ech lyer re bsed on the generic lttice model of Friess & Ydigroglu (1) which is extended here to include the influence of lyer coverge nd prticle size distribution. We consider the influence of lyer thickness on the resuspension long with the spred of dhesion within lyers, nd the sttistics of non-gussin versus Gussin removl forces including their timescle. Unlike its wek influence on long-term resuspension rtes for monolyers, this timescle plys crucil nd influentil role in multilyer resuspension. Finlly we compre model predictions with those of lrge-scle nd mesoscle resuspension test, STORM (Cstelo et l., 1999) nd BISE (Alloul-Mrmor, ). 1. Introduction In previous pper (Zhng et l., 1) we presented n improved version of the Rock n Roll model (Reeks & Hll, 1) for the resuspension of deposited prticles by turbulent flow. This model employs stochstic pproch to resuspension involving the rocking nd rolling of prticle bout surfce sperities induced by the moments of the fluctuting drg force cting on the prticle close to the surfce. It represented significnt improvement over the originl model becuse it used joint distribution of the moments of the drg force f (t) nd its derivtive f & (t) cting on the prticle bsed on DNS dt of the ner-wll strem-wise fluid velocity nd ccelertion in turbulent chnnel flow. Unlike the originl model in which both f (t) nd f & (t) re ssumed to hve Gussin sttistics, this improved non-gussin model ccounted for the influence of the highly non-gussin forces (ssocited with the sweeping nd ejection events in turbulent boundry lyer) on the resuspension rte. Anlysis nd model predictions were focused on the resuspension of smll prticles from microscopiclly rough surfces where even for nominl mcroscopiclly-smooth surfce

2 there is brod rnge of surfce moleculr dhesive forces. In ll cses the coverge of the surfce with prticles ws ssumed to be less thn monolyer, so tht individul prticles could be considered s isolted, i.e., ttched only to the surfce substrte nd not to other prticles. An importnt feture of resuspension from rough surfces is tht the resuspension tkes plce in two distinguishble phses, n initil short-term resuspension nd longer-term resuspension kin to erosion. The short-term resuspension tkes plces over period ~ timescle of the fluctuting removl forces when typiclly the erodynmic force ~ men dhesive force nd significnt frction of the prticles on the surfce my be detched. Those prticles tht remin on the surfce fter this initil phse re much more strongly ttched to the surfce nd re resuspended on much longer timescle. In fct the resuspension (erosion) rte for these prticles is found to vry lmost inversely s the exposure time nd is only very wekly dependent upon the timescle of the removl forces. Furthermore whilst the bsolute decy rte is dependent upon the spred nd men of the dhesive forces/erodynmic forces, these hve little effect on the inverse time decy. These re fetures tht re chrcteristic of stochstic pproch nd the existence of brod rnge of dhesive forces nd we investigted the dependence of the long-term erosion rte on the spred of the dhesion nd the distribution of the removl forces bout their men vlue (which ws strongly non-gussin) In this pper we focus on multilyer resuspension, i.e., the resuspension of prticles from multilyer deposits of erosol prticles by turbulent flow. This is the most generl cse for resuspension of deposited prticles nd the one most likely to rise in severe nucler ccident. It is lso common feture of lrge-scle severe ccident experiments involving both deposition nd resuspension of erosol prticles, e.g., the STORM experiments (Cstelo et l., 1999). To be more precise, we use the formul for the resuspension rte constnt given by the non-gussin R n R model in hybrid model for the multilyer resuspension bsed on the pproch used by Friess nd Ydigroglu (1). We then exmine how resuspension depends upon number of key prmeters: the number of lyers, the distribution of dhesive forces nd prticle size, coverge nd pcking within ech lyer, the influence of non- Gussin versus Gussin removl forces nd, perhps most importnt of ll, their timescle. Unlike their wek influence on long-term resuspension rtes for monolyers, the timescles ssocited with the removl forces ply crucil nd influentil role in multilyer resuspension. Throughout this study we will compre our predictions with those of monolyer. Most importntly we will lso compre model predictions with those of two lrge-to-medium scle resuspension tests, nmely STORM nd BISE We begin in the next section with brief description of the non Gussin R n R model focusing on the form given for the primry resuspension rte constnt. We then follow this in section 3 with description of vrious multilyer models tht hve been developed nd used in the pst, the prticulr focus being on the Friess nd Ydigroglu (FY) multilyer generic model which is used s the bsis of the hybrid model we present nd study here. In this section we lso show how the R n R model is incorported into the FY model nd present the set of equtions for the resuspension of prticles from ech lyer. In section 4 we consider their solution for the resuspension rte nd frction resuspended nd its dependence on the vrious prmeters we hve referred to previously. In sections 5 nd 6 we dpt the model to incorporte the influence of coverge (section 5) nd polydispersed deposit (section 6) i.e. prticle size distribution in ech lyer. Then in section 7 we show how these predictions compre with the ctul experimentl results for the frction resuspended in the two multilyer resuspension experiments, STORM (Cstelo et l., 1999) nd BISE (Alloul- Mrmor, ). Section 8 concludes with summry nd conclusions.

3 . The non-gussin Rock n Roll (R n R) Model, Brief Description The geometry of the prticle-surfce contct in the R n R model is shown in Figure 1b in which the distribution of sperity contcts is reduced to simple two-dimensionl model of two-point sperity contct. Thus, rther thn the centre of the prticle oscillting verticlly s in the originl Reeks, Reed nd Hll (1988) (RRH) model, it will oscillte/ rock bout the pivot P until contct with the other sperity t Q is broken. When this hppens it is ssumed tht the lift force is either sufficient to brek the contct t P nd the prticle resuspends or it rolls until the dhesion t single-point contct is sufficiently low for the prticle to resuspend. In either sitution the rte of resuspension is controlled by the rte t which contcts re initilly broken. Figure 1 - Potentil well nd prticle couple system The formul for the resuspension rte hs the sme form s in the originl RRH model except tht couples re tken ccount of by replcing verticl lift forces by equivlent forces bsed on their moments. Tht is, referring to Figure 1b, the equivlent force F is derived from the net couple (Γ) of the system bove so tht 1 r Γ = FL + rfd F = FL + FD [1] where is the typicl distnce between sperities, r the prticle rdius, F L the lift force nd F D the drg force. The rtio r/ ~ 1 (bsed on Hll s experiment, Reeks & Hll 1) mening tht drg plys the dominnt role in prticle removl. We recll tht for the qusisttic cse in the R n R model, t the detchment point (i.e., point y d in Figure 1, referring to the ngulr displcement of the sperity contct t Q bout P s in Fig 1b), the erodynmic force cting on the prticle (which includes the men <F> nd fluctuting prts f(t)) is considered to blnce the restoring force t ech instnt of time (hence the term qusi-sttic). So, F + f ( t) + FA ( y) = [] where F A (y) is the dhesive restoring force s function of the ngulr deformtion (y) of the prticle. At the point of detchment (y d ) the dhesive pull off f (the force required to detch the prticle is = -F A (y d ). Following the trdition of previous uthors we refer to this force s the force of dhesion. In the presence of pplied men force F from Eq.[], the vlue of the fluctuting component of the equivlent erodynmic force required to detch the prticle (f d ) is given by f = f F [3] d

4 So s F(t) fluctutes in time, the dhesive force F A (y) nd hence y(t) chnges to blnce it ccording to Eq.[]; every time the vlue of f(t) exceeds the vlue of f d prticle is detched from the surfce. So the rte of detchment depends not only on the vlue of f d but on the frequency t which it is exceeded, i.e., upon the typicl timescle of the fluctuting erodynmic force f(t) nd its distribution in time. Bsed on their mesurements, the men drg nd lift force for sphericl prticle of rdius r is given by Reeks nd Hll (1) s 3 ruτ =.9 ruτ F D = ρ fν f F L ρ fν f [4] ν f ν f where ρ f is the fluid density, ν f the fluid kinemtic viscosity, nd u τ the wll friction velocity. The dhesive force is considered s scled reduction of the dhesive force on smooth surfce bsed on the JKR model (Johnson, Kendl nd Roberts, 1971). Thus, 3 f = πγ rr [5] where γ is the surfce energy nd r the normlised sperity rdius r / r where r is the sperity rdius. r is ssumed to hve log-norml distribution φ(r ) with geometric men r nd geometric stndrd devition σ. Physiclly, these two prmeters define the microscle roughness of the surfce. r is mesure of how much the dhesive force is reduced from its vlue for smooth contct with surfce nd σ describes how brod/ nrrow the distribution is. For convenience we cll r the reduction in dhesion nd σ the spred. Hll s experimentl mesurements of the distribution of dhesive forces on polished stinless steel surfce gve vlues of r ~.1 nd spred σ ~3. For log-norml distribution φ(r ) is given explicitly by [ ] ϕ ln( r r ) ( r = ) exp π r ln σ (lnσ ) [6] Bisi et l. (1) took the R n R model for resuspension nd dded n empiricl log-norml distribution of dhesive forces to reproduce the resuspension mesurements of number of experiments. Some dhesion-force prmeters were tuned to fit the dt of the most highlychrcterised experiments, i.e., those of Hll (Reeks & Hll, 1) nd Brten (1994). Then, for n enlrged dtset including STORM nd ORNL ART resuspension results, the best globl correltions for geometric men dhesive force nd geometric spred s function of prticle geometric men rdius (in microns) were obtined, nmely.545 r =.16.3r [7] 1.4 σ = r where r is the prticle rdius in microns. The resuspension rte constnt p, ccording to Reeks et l. (1988), is defined s the number of prticles per second detched from the surfce over the number of prticles ttched to the surfce. p = vp( y,v) dv d y d P( y,v) dydv where y is the displcement or deformtion of the centre of the prticle, v = dy / dt = y& nd P is the joint distribution of v nd y. The numertor is the prticle detchment flux t the point of detchment (Figure 1) whilst the denomintor is the number of prticles ttched to the surfce, i.e., in the potentil well..31 [8]

5 Referring to Eq.[] for the qusi-sttic cse, we note tht the ngulr deformtion or displcement y cn be written s n implicit function of the fluctuting erodynmic force, f(t), i.e., y( t) = ψ ( f ) nd so y& ( t) = f & ψ ( f ) [9] where ψ ( f ) is the first derivtive of ψ(f) with respect to f. Then f d p = fp & ( f, f& ) dv P( f, f& ) dfdf& ] [1] d where in the R n R model the joint distribution P of fluctuting erodynmic force f nd its derivtive f & is ssumed to be joint norml distribution with zero correltion between the force nd its derivtive. In the modified R n R model (Zhng, 11), new joint distribution is developed from DNS dt which compounded of Ryleigh distribution for z 1 nd Johnson SU distribution for z. More precisely, z1 + A 1 1 z1 + A1 B1 1 ( ( ( ) P z ) 1, z) = exp exp B 3 B1 ln z z 1 A A B π z + 1 [11] where A 1, A, B 1, B, B 3 nd B 4 re constnts depending on the wll distnce y + z 1 nd z is the fluctuting erodynmic force nd derivtive normlized on their r.m.s vlues, so f f& z1 =, z = [1] f f& Then the modified resuspension rte constnt is obtined z f& d p = z P( zd, z ) dz P( z1, z ) dz1dz f f& zd + A 1 1 zd + A1 1 zd + A1 = B exp 1 exp f& f A A A fd zd =. f In the originl R n R model the term erodynmic force, i.e., f frms F [13] f is expressed s frction f rms of the men = [14] As for the originl R n R model we write f& + uτ = ω [15] f ν f Vlues for the vrious dimensionless prmeters ssocited with the formul for p in Eq.[13] re given below for vlues of y + =.1 for DNS mesurements. DNS B & A 1 A ω + f = f F f rms

6 y + = Tble 1 - Vlues of prmeters used in formul for resuspension rte constnt p 3. Multilyer Resuspension Models Resuspension of multilyer deposits of rdioctive prticles is n importnt phenomenon in nucler severe ccidents. However, most of the models used to predict the mount of resuspended prticulte re bsed on the resuspension of isolted prticles. There re only few models which consider the multilyer cse, nmely Fromentin (1989), Lzridis & Drossinos (1998) (referred to s LD) nd Friess & Ydigroglu (1) (referred to s FY). In this pper, the modified R n R model will be dpted for ppliction to multilyer deposits bsed on the FY multilyer pproch. Furthermore, the coverge effect of lyers on resuspension will be considered in this modified FY multilyer model in two wys: 1) introducing coverge fctor; ) considering the influence of distribution of prticle size within ech lyer. Finlly, the modified multilyer model resuspension predictions will be compred with the resuspension mesurements in the STORM SR11 test (Cstelo et l., 1999) nd the BISE experiment (Alloul-Mrmor, ). Fromentin s model is semi-empiricl model bsed on force-blnce methods nd the input prmeters re limited to those in the PARESS experiment upon which the model is bsed. The LD model is restricted to multilyer deposit in which the resuspension rte for ech prticle in the deposit is the sme. In contrst the FY model (1) tkes ccount of the fct tht the resuspension rte constnt cn vry ccording to the distribution of dhesive forces experienced by prticle in ech lyer. If we compre the two models in situtions where the resuspension rte constnt is the sme for ll prticles, there is difference in the wy the frction of prticles exposed to the flow is clculted. If the lyers re numbered 1,, 3...etc from the top lyer exposed to the flow, then the LD model tkes this frction in the ith lyer to be the number of prticles removed from the (i-1)th lyer over the initil number of prticles in the (i-1)th lyer. Thus it ssumes tht whenever prticle is removed from the (i- 1)th lyer prticle in the ith lyer is exposed nd is immeditely resuspended. Hence, the model is vlid for lrge resuspension rtes or, equivlently, it gives the mximum multilyer resuspension rte (i.e., if prticle is exposed it resuspends). In these circumstnces the FY model, on the other hnd, tkes the frction of exposed prticles in the ith lyer to be the rtio of the number of prticles in the (i-1)th lyer to the number of prticles in the ith lyer t time t. Thus dn i ni 1( t) = pni 1 i LD model dt ni 1() dn i ni 1( t) = pni 1 i FY model dt ni ( t) where n i is the number of prticles in the ith lyer t time t (i.e., the totl number of prticles in ith lyer t time t being the sum of those prticles exposed nd unexposed to the flow) nd p is the resuspension rte constnt. Since every prticle sits on top of prticle in the lyer below, this rtio gives the exct number of exposed prticles which the LD model does not provide. The FY model is not only exct in this sitution but, s we stted bove, more generlly pplicble since the resuspension rte constnt cn vry from prticle to prticle in ny given lyer nd from lyer to lyer. Since this is n importnt considertion in multilyer resuspension, the FY model is used s the bsis for the multilyer modelling which will be presented here. Let us now recll the essentil fetures of the FY model (Friess & Ydigroglu, 1) which

7 dels with the resuspension of deposit composed of regulr rry of identicl sphericl prticles. FY (1) first delt with n infinitely thick deposit, defining resuspension rte constnt p(ξ) for ech prticle exposed to the flow, where ξ is sttisticl vrible or number of vribles upon which p depends (e.g., dhesion rising from the contct of prticle with other prticles whose vlue controls the influence of the flow). The probbility density function (pdf) for the occurrence of ξ is given by n(ξ,t). It is ssumed tht every time prticle is removed (resuspended by the flow) nother prticle is uncovered nd exposed to the flow but with different ξ sy ξ with probbility distribution φ(ξ ) for uncovered prticles. The prticles re homogeneously distributed in the initil stte with n(ξ,) = φ(ξ). The rte t which prticles re exposed is given by Λ ( t) = p( ξ ) n( ξ, t) dξ [16] ξ nd the frction of those prticles exposed per unit time with vlues between ξ, ξ + dξ will be dξϕ( ξ ) p( ξ ) n( ξ, t) dξ ξ The eqution for n(ξ,t) is thus n( ξ, t) = p( ξ ) n( ξ, t) + ϕ( ξ ) p( ξ ) n( ξ, t) dξ t ξ [17] Therefore, for n L-lyer deposit, let n i (ξ,t)dξ denote the probbility of exposed prticles between ξ, ξ + dξ in the ith lyer t time t, the lyers being numbered sequentilly from the top lyer (totlly exposed to flow) downwrd s i = 1,, 3 L. Then the set of ODEs (ordinry differentil equtions) is n1 ( ξ, t) = p( ξ ) n1 ( ξ, t) t ni ( ξ, t) = p( ξ ) ni ( ξ, t) + ϕ( ξ ) p( ξ ) ni 1( ξ, t) dξ t ξ ( i ) [18] The resuspension rte for ith lyer is given by Λ ( t) = p( ξ ) n ( ξ, t) dξ [19] i ξ i 3.1 R n R Hybrid Model for Multilyer Resuspension Formultion using the Friess & Ydigroglu (FY) Generic Model (Hybrid Generic Model) The non-gussin R n R model is single prticle kinetic model bsed on the R n R model (Reeks & Hll, 1) (with the resuspension rte constnt p(ξ i ) ccounting for the prticlesurfce dhesive forces nd the non-gussin sttistics of the fluctuting erodynmic resultnt force obtined from DNS dt). We recll tht in the FY multilyer model, this distribution of normlized sperity rdii refers to the initil stte of the pdf of exposed prticles, n(ξ,), i.e., n( r,) = ϕ( r ) [] where the normlized sperity rdius r refers to the intrinsic sttisticl vrible ξ. The resuspension rte constnt p in the modified R n R model (Eq.[13]) is function of the normlized sperity rdius for fixed prticle size. Hence, p is referred to s p(r ). Therefore, the set of ODEs for the pdf of exposed prticles in deposit composed of i = 1,, 3 L lyers t time t is given by n1 ( r, t) = p( r ) n1 ( r, t) t

8 ni ( r, t) = p( r ) n ( r, t) + ϕ( r ) p( r ) n ( r, t) dr ( i ) t % % % [3] i i 1 The ϕ( r ) p( r% ) ni 1( r%, t) dr% prt is thus source term. It is considered s the extr source of prticle exposure rte (exposing prticles in given lyer by resuspending prticles from the lyer bove). The resuspension rte in the ith lyer is given by Λ ( t) = p( r ) n ( r, t) dr [4] i i For i = 1, the first lyer resuspension rte is given explicitly in the originl R n R model pproprite for monolyer becuse there is no source term from the prticles in the lyer bove, nmely ( ) 1( ) ( ) p r t t p r e ϕ( r ) dr Λ = [5] The initil vlue of exposed prticles from the second lyers downwrd n i (r,) = (i ) which mens ll the prticles in the lyer below re covered by the prticles from the lyer bove. Therefore, for the second lyer nd lyers below (i ) using the initil condition for n i (r,t), gives ni ( r, t) + p( r ) n ( r, t) = ϕ( r ) p( r ) n ( r, t) dr ( i ) t % % % i i 1 n ( r, t) e + p r n r t = e r p r n r t dr p( r ) t i p( r ) t ( ) ( i, ) ϕ( ) ( ) i 1(, ) t % % % t p( r ) t p( r ) t i (, ) ϕ( ) (% ) i 1( %, ) % t p( r ) t p( r ) t i ϕ i 1 e n r t = e r p r n r t dr dt % % % [6] n ( r, t) = ( r ) e e p( r ) n ( r, t ) dr dt ( i ) Substituting Eq.[6] in Eq.[4], the resuspension rte for the ith lyer is given by t p( r ) t p( r ) t i ( t) p( r ) ϕ( r ) e e p( r ) ni 1( r, t ) dr dt dr ( i ) % % % [7] Λ = Initilly it is ssumed s in the FY generic model tht the deposit is formed from identicl sphericl prticles s shown in Figure.

9 Figure - Geometry of the multilyer system with sme-size prticles 4. Hybrid Generic Model Predictions for Multilyer Resuspension In this section we present the prediction of the hybrid generic multilyer model for the resuspension frction nd resuspension rtes. In so doing the micro roughness for ll the prticles is ssumed to be the sme so the sme distribution of normlized sperity rdius φ(r ) is used for ll the prticles in the domin. In the clcultion below, the prmeters from the STORM SR11 experiment Phse 6 condition will be pplied (more informtion is provided in the next section). The prmeters used for Phse 6 re: Averge rdius (µm) Fluid density (kg.m -3 ) Fluid kinemtic viscosity (m.s -1 ) Wll friction velocity (m.s -1 ) Surfce energy (J.m - ) Reduction fctor (Geometric men) Spred fctor (Geometric stndrd devition) x Tble Vlues of prmeters in STORM SR11 Phse 6 where Bisi s correltion (Eq.[7]) is used for the dhesion distribution prmeters. The prticles in ech lyer re ssumed to be monodisperse with size given by the men prticle rdius in Tble. 4.1 Resuspension s Function of Lyer Number Loction nd Lyer Thickness Figure 3 shows the resuspension rte of prticles in lyers 1, 3, 5, 1 nd. The resuspension rte of the first lyer is identicl to tht of the isolted prticle model. For the second nd subsequent lyers, the initil resuspension rte t t = is zero. Strting from zero the resuspension rte rises to mximum during which time most of the prticles which re esily removed resuspend from given lyer (i.e., for these prticles the men effective erodynmic force > dhesive force), the reminder being removed over much longer period. The time to rech mximum my therefore be regrded s dely time for the prticles in given lyer to be exposed by removing prticles from ll the lyers bove it. Note tht the mximum resuspension rte decreses s the lyer number increses. Also note tht the resuspension rte of ech lyer beyond its mximum vlue, whilst being initilly less thn the lyer bove, eventully exceeds it so tht the integrted mount (frction resuspended) is the sme (close to unity) for ll lyers in the long-term (t ) (the numerics were checked to mke sure tht this ws the cse).

10 Figure 3 - Resuspension rte of ech lyer vs. time for the hybrid generic model using STORM test (SR11) Phse 6 conditions (see Tble ). The initil number of prticles is the sme in ech lyer normlized to unity. Then the frctionl resuspension rte for the domin (L lyers) is given by L Λi ( t) i= 1 Λ L ( t) = L which corresponds to the resuspension frction of n L-lyer deposit. f ( t) = Λ ( t ) dt [9] r L L t The modified R n R model incorporting the FY multilyer pproch will be referred to s the initil multilyer model since the model will lter on be extended to include the coverge effect. [8]

11 Figure 4 - Frctionl resuspension rte s function of number of lyers (prticle dimeter:.45µm) bsed on STORM test (SR11) Phse 6 conditions (see Tble ). Figure 5 - Predictions of the hybrid generic model for rtio of monolyer / multilyer resuspension rtes, bsed on STORM test (SR11) Phse 6 conditions (see Tble ).

12 Figure 6 - Hybrid generic model predictions for the resuspension frction s function of time nd lyer thickness bsed on STORM test (SR11) Phse 6 conditions (see Tble ). The frctionl resuspension rte is shown in Figure 4. The short term resuspension rte is considered finished when the exposure time t is round 1-4 s when s shown in the plot the long-term resuspension (pproximtely proportionl to 1/t) begins (we note tht 1/ω + which corresponds to timescle ~1-5 s). The initil frctionl resuspension rte decreses with incresing lyers when more prticles tend to be removed over longer period. Figure 5 shows how much the monolyer frctionl resuspension rte differs from tht of the multilyer resuspension (for the sme initil frction = 1, in ech cse). As the lyer number increses, the rtio of the resuspension rte between monolyer nd multilyer increses significntly in the short term. However fter given time which increses with the vlue of i, the resuspension rte for given lyer eventully exceeds tht for monolyer i = 1 t the sme time (the rtio < 1), nd in the long-term the rtio should converge to zero (see the cses for lyer i = 3 nd 5 in Figure 3). Figure 6 shows the resuspension frction of the whole deposit domin. It shows tht fter 1s 8% of the monolyer deposit is removed wheres only round 3% of the 1-lyer deposit is resuspended. 4. Influence of Adhesive Spred Fctor on Multilyer Resuspension In these predictions we fix the geometric men of the normlized sperity rdius t.15. The spred fctor vlues of 1.1, (bsed on the Bisi correltion) nd 4. re chosen for comprison (note tht the spred is the geometric stndrd devition nd > 1). Figure 7, Figure 8 nd Figure 9 show the comprison of resuspension frction for monolyer, 1-lyer nd 1-lyer deposits for different spred fctors, respectively. We note tht for monolyer, by virtue of the log-norml distribution, the time for 5% of the deposit to resuspend is independent of the spred fctor. For times smller thn this vlue, the lrgest spred fctor gives the gretest frction resuspended wheres beyond this time, the sitution is reversed.

13 1.9.8 Resuspension Frction monolyer, spred fctor = 1.1 monolyer, spred fctor = 1.8 monolyer, spred fctor = t (s) Figure 7 - Effect of dhesion spred fctor on monolyer resuspension frction (note tht the exposure for 5% resuspension is the sme for ll spred fctors (bsed on STORM test (SR11) Phse 6 conditions (see Tble )) lyers, spred fctor = lyers, spred fctor = lyers, spred fctor = 4. Resuspension Frction t (s) Figure 8 - Effect of dhesion spred fctor on 1 lyer deposit bsed on STORM test (SR11) Phse 6 conditions (see Tble ).

14 Figure 9 - Effect of dhesion spred fctor on 1 lyer deposit bsed on STORM test (SR11) Phse 6 conditions (see Tble ). We note tht spred of 1.1 corresponds to very nrrow distribution of dhesive forces ( vlue of 1. corresponds to zero spred) so in this cse there is only very smll mount of longer-term resuspension, most prticles being resuspended over period of 1 - s. As the number of lyers increses from 1 to 1 lyers, the resuspension is still reltively shrply defined but the onset of resuspension is delyed from 1-4 s to 1 - s, whilst occurring over period of sy 1-1 s. As the spred fctor increses the difference between the 1-lyer deposit nd the monolyer is much more mrked: for spred of 4 fter 1s, only % of the 1-lyer deposit hs resuspended compred with lmost 1% for the monolyer deposit. There is in fct no shrp distinction between short- nd long-term resuspension; in fct it is relly ll long-term resuspension in the multilyer cse.

15 1 Time to resuspend hlf of prticles (s) spred fctor = 1.1 spred fctor = Bisi(1.8) spred fctor = Lyer numbers (L) Figure 1 - Resuspension hlf-life vs. lyer thickness bsed on STORM test (SR11) Phse 6 conditions (see Tble ). Figure 1 shows the resuspension hlf-life for different spred fctors. With incresing dhesive spred fctor, the hlf resuspension time increses drmticlly s the deposit becomes incresingly multilyer.

16 1 1 1 sf = 1.1, m =.75 sf = 1.1, m =.15 sf = 1.1, m=.15 sf = 1.8, m=.15 sf = 4., m= Rtio lyer numbers Figure 11 - Rtio of short-term (<1-4 s) to long-term resuspension frction where the longterm resuspension frction is 1 the short-term resuspension frction (bsed on STORM test SR11 Phse 6 conditions - see Tble ) (m: geometric men of normlized sperity rdius, sf: spred fctor) Figure 11 shows the resuspension frction short-term to long-term rtio for the flow nd dhesion prmeters for the STORM SR11 test shown in Tble. The short term is considered s the period before the resuspension rte becomes pproximtely proportionl to 1/t. It cn be observed in Figure 4 tht fter round 1-4 s the curves become stright lines. Therefore, short term finishes ~1-4 s (~1 in wll units). For the geometric men in dhesion of.15, it is cler tht s the number of lyers increses, i.e., s the deposit thickness increses, the short term resuspension contributes less nd less to the totl resuspension since most of the prticles covered re not so esily removed. For the sme number of lyers L, whilst the rtio of short-term to long-term resuspension frction increses with incresing dhesive spred fctorσ, the chnges in the rtio diminish s σ increses. In contrst the rtio decreses with n inverse power lw decy with incresing lyer thickness tht is independent of the spred fctorσ. In the cse defined by the prmeters in Tble, the short term resuspension is very smll since it is cse where the men erodynmic force < the geometric dhesive force. By contrst Figure 11 lso shows the opposite cse for geometric men dhesion of.75 when the geometric men dhesive force < the men erodynmic force. In this cse, the short/long term rtio increses significntly to ~1. Significntly the power lw decy of the rtio with incresing lyer thickness remins the sme independent of dhesive spred. More precisely these observtions imply tht log( Rtio) = log [ f ( σ )] + slope log( L) [3] slope Rtio = f ( σ ) L

17 where the slope is very close to -1. f(σ ) is function of σ nd is plotted in Figure 1 for vlues of σ >1.5, the vlue for mcroscopiclly smooth polished surfce (Reeks nd Hll, 1). Below this vlue there is no trnsition from short to long term resuspension f(σ ') dt fitted curve σ ' Figure 1 - f(σ ) vs. σ see Eq.(3) for the prmeters given in Tble For The function f ccording to Figure 1 is fitted to f ( σ ) = 1.5exp(.9 σ ) +.65 [31] Note the sympotic vlue of.65 for σ. 4.3 Comprison of Gussin nd non-gussin R n R Models in Multilyer Resuspension The mjor difference between Gussin nd non-gussin R n R models is reflected in the formul for the resuspension rte constnt; we recll Reeks nd Hll (1) for the Gussin cse, 1 f & 1 exp f dh dh 1 f p = + erf π f f f nd the non-gussin cse Eq.[13] f& zd + A 1 1 zd + A1 1 zd + A1 p = B exp 1 exp f& f A A A with the sme vlues of the rms coefficient f rms nd the typicl forcing frequency ω +, f& + uτ f = frms F, = ω. f ν f

18 The frctionl resuspension predicted by of the multilyer model using these two R n R formul for the resuspension rte constnt ws clculted. In the comprison, the typicl forcing frequency ω + nd the rms coefficient f rms re chosen to be the sme for both Gussin nd non-gussin cses (ω + =.413 nd f rms =.). Therefore, the difference between the curves in Figure 13 is due only to the Gussin nd non-gussin distributions (the distributions of erodynmic resultnt force nd its derivtive) used to derive the resuspension rte constnt. Resuspension Frction monolyer, Gussin 5 lyers, Gussin 1 lyers, Gussin ω + =.413, f rms =. monolyer, non-gussin 5 lyers, non-gussin 1 lyers, non-gussin Figure 13 - Comprison of multilyer model with the rte constnt bsed on Gussin nd non-gussin R n R model, STORM test SR11 Phse 6 conditions (see Tble ) Figure 13 shows tht the non-gussin model lwys results in more resuspension thn the Gussin cse t ll times except one point. As time increses, the difference becomes greter nd greter. It is noted tht the time of the contct point (round 1-3 s in the plot) depends on the wll friction velocity, typicl forcing frequency nd the rms coefficient; it is independent of the number of lyers. t (s)

19 5. Influence of Lyer Coverge on Multilyer Resuspension We now consider chnges to the FY generic model effect due to coverge. We ssume now tht prticles re not regulrly spced s in the lttice of the FY generic model but rndomly spced with the sme distribution for ll lyers. Thus in ny given lyer prt from the top lyer when no prticles re removed from the lyer bove, n re corresponding to the prticles projected cross section re is reveled within which prticles re exposed to the flow. Here new prmeter α i (the coverge coefficient) is introduced to describe the number rtio of prticles exposed to the flow in given lyer (i + 1) due to removl of prticles from the lyer bove (i), nmely ni + 1 i = f Ai [3] ni where f Ai is the prticle occupied-re frction (the frction of prticles projected re in horizontl plne prllel to the wll) in lyer i nd n i is the initil verge number of prticles in the ith lyer. In other words, ll the prticles in lyer i would therefore cover f Ain i + 1 prticles in lyer i + 1. It is noted tht the verge number of prticles in ech lyer is the sme, therefore ni + 1 ni =1. Also it is ssumed tht the coverge coefficient is the sme for ll lyers (use α insted of α i ). The prticle occupied-re frction is defined s the rtio of the totl (remining) prticle cross-section re to the whole re of the lyer. Apini f Ai = [33] A where i A is the verge prticle projected re (for sphericl prticle, this is pi the verge prticle rdius in lyer i) nd A i is the totl surfce re of lyer i. π r i nd r i is The verge number of prticles in the ith lyer cn be determined s Vi fv i ni = [34] V pi where V i is the totl volume of lyer i. f Vi is the prticle volume frction in the ith lyer nd V is the verge single prticle volume in the ith lyer. The volume frction is relted by pi definition to the porosity, nmely fvi = 1 ς i [35] It is noted tht, strictly, this porosity ought to be different for different lyers. Here, it is ssumed tht the porosities for ll the lyers re the sme (henceforth we use ς). The verge thickness of the ith lyer is ssumed to be the verge dimeter of prticles in tht lyer. Therefore, the prticle occupied re frction is given by Apini ApiVi fv i Api ri f Ai = = = ( 1 ς ) [36] A AV V i i pi pi As stted bove, the verge number of prticles in ech lyer is the sme so the coverge coefficient cn therefore be derived s n A 1 pi r i+ i = f Ai = ( 1 ς ) [37] n V i pi For deposit composed of sphericl prticles, π ri ni π ri Ai ri fvi 3 3 f Ai = = = f 3 Vi = (1 ς ) [38] A A π r 4 i i 3 i

20 Therefore, the coverge coefficient for the deposit of sphericl prticles ccording to Eq.[3] nd Eq.[38] is given by 3 α = (1 ς ) [39] Note: α vries from to 1.5. α = 1 mens tht if one prticle is removed from the lyer bove only one prticle in the lyer below will be exposed to the flow. Friess nd Ydigroglu () demonstrted tht in STORM SR11 experiment conditions, their deposition nd resuspension model with the porosity between.6 nd.71 gve the closest results to the experimentl dt. Therefore, putting these vlues into Eq.[39], the resulting vlue of α in STORM SR11 experiment conditions is clculted to be from.44 to.57. α is the number rtio of prticles exposed to the flow of the lyer below to the current lyer nd thn it cn be derived s the rte rtio since the exposure rte is pproximtely the number of prticles multiplied by the rte constnt. Thus, ni 1 n& + i+ 1 = f Ai f Ai [4] ni n& i Therefore, Eq.[3] is redefined by including the exposure-rte rtio in the source term. n1 ( r, t) = p( r ) n1 ( r, t) t ni ( r, t) = p( r ) ni ( r, t) + α ϕ( r ) p( r ) ni 1( r, t) dr ( i ) t % % % [41] Frctionl Resuspension Rte no coverge effect, monolyer no coverge effect, 1 lyers no coverge effect, 1 lyers lph=.5, monolyer lph=.5, 1 lyers lph=.5, 1 lyers t (s) Figure 14 - Effect of exposure-rte rtio on frctionl resuspension rte, bsed on STORM test SR11 Phse 6 conditions (see Tble ) Figure 14 nd Figure 15 show the resuspension-rte nd frction comprison between the initil multilyer model nd the model including the coverge coefficient. As one cn observe from the resuspension-rte comprison, the monolyer cse is unffected by the coverge

21 coefficient s expected while for the multilyer cse (1 nd 1 lyers) the resuspension rte with no coverge effect (with α = 1) is very close to the resuspension with α =.5 in the short term (i.e., <1-4 s) exposure time (since this is minly due to resuspension of the top lyers where the reduced coverge effect hs hrdly ny impct: only in the long-term (i.e., >1-4 s) does the coverge effect strt to dominte by drmticlly reducing the resuspension rte. This cn lso be observed in Figure 15 which is the comprison of resuspension frction s function of time. A coverge coefficient α =.5 reduces the frctionl mount by round hlf fter 1s. However, this coverge coefficient is determined by the porosity of ech lyer nd in relity the porosity for ech lyer is different nd this porosity vries s time goes on. In the next section, this rtio constnt will be replced with prticle size distribution which will be more physiclly correct no coverge effect, monolyer no coverge effect, 1 lyers no coverge effect, 1 lyers lph=.5, monolyer lph=.5, 1 lyers lph=.5, 1 lyers Resuspension Frction t (s) Figure 15 - Effect of exposure-rte rtio on resuspension frction, bsed on STORM test SR11 Phse 6 conditions (see Tble )

22 6. Multilyer Resuspension with Prticle Size Distribution in Ech Lyer In order to study the behviour of deposit structure in prticle resuspension, the clustering of prticles within given lyer nd between lyers (the clustering effect) is n importnt considertion. However, little informtion is to be found on the cluster nd deposit structure in bed of prticles. In this section, simple ddition is introduced to the set of multilyer equtions to include the influence of prticle size distribution in the initil multilyer model where the clusters re considered simply s different size prticles. The interction between the prticles in the sme lyer is not explicitly considered, but the coverge effect from the lyer bove to the lyer below will be included. The distribution ψ(r) of the prticle rdius r is considered s log-norml with geometric men r nd geometric stndrd devition σ r, i.e [ ln( r r )] ψ ( r) = exp [4] π r lnσ r (ln σ r ) Since the resuspension rte constnt p nd exposure pdf n is function of prticle size, then the formul for the pdf of exposed prticles (Eq.[3]) becomes n1 ( r, r, t) = p( r, r ) n1 ( r, r, t) t ni ( r, r, t) = p( r, r ) ni ( r, r, t) + ψ ( r) ϕ( r ) p( r, r ) ni 1( r, r, t) dr dr ( i ) t % % % % % % [43] r Note: the integrtion in the source term of the second eqution for prticle size distribution is tken from the current prticle rdius r to infinity. In other words, in order to expose the current prticle of rdius r to the flow, the rdius of the prticle from the previous lyer must be lrger thn the current prticle rdius. Ech deposit lyer is ssumed s the formtion of distribution of sphericl prticles s shown, Figure 16 - Geometry of the multilyer system with polydisperse prticles The resuspension rte in the ith lyer is thus defined s Λ ( t) = p( r, r ) n ( r, r, t) dr dr [44] i i The roughness condition for ll the prticles is ssumed to be the sme. The sme distribution of normlized sperity rdius (φ(r )) is used for ll the prticles in the domin. Lyer

23 thickness is determined by the men prticle dimeter nd they re ssumed to be the sme for every lyer. In the clcultion below, the prmeters from the STORM SR11 experiment Phse 6 conditions will be pplied together with Bisi s correltion for the prmeters of the dhesion distribution. Averge rdius (µm) Geometric stndrd devition of rdius Fluid density (kg.m -3 ) Fluid kinemtic viscosity (m.s -1 ) Wll friction velocity (m.s -1 ) Surfce energy (J.m - ) x Tble 3 - Prmeters in STORM SR11 Phse 6 for polydisperse model The verge prticle size nd geometric stndrd devition re tken from those used in n nlysis with the SOPHAEROS code (Cousin et l., 8). Figure 17 - Frctionl resuspension rte vs. time for model with polydisperse prticles, STORM test SR11 Phse 6 conditions (see Tble 3) The frctionl resuspension rte (clculted by Eq.[8]) for the polydisperse prticles is shown in Figure 17. Compred to the results for monodisperse prticles (Figure 14), the longterm resuspension rte in this cse substntilly decreses when the number of lyers increses. Below, Figure 18 compres the monodisperse nd polydisperse resuspension results for erosols hving the sme geometric men size (Eq.[4]). Interpreting Figure 18, the comprison of the frctionl resuspension rtes shows tht the frctionl resuspension of the polydisperse prticles in the short term is greter thn tht for the monodisperse prticles due to the fct the resuspension rte is bised towrds lrger-size prticles. After the initil resuspension nd the lrger prticles (> the geometric men) hve been removed, the remining polydispersé prticles re bised towrds prticle sizes < the geometric men which re hrder to remove thn those with the geometric men size. Note tht the long-term

24 resuspension rte of the polydisperse cse is severl orders of mgnitude less thn tht of the monodisperse cse Frctionl Resuspension Rte monodisperse, monolyer monodisperse, 1 lyers monodisperse, 1 lyers polydisperse, monolyer polydisperse, 1 lyers polydisperse, 1 lyers t (s) Figure 18 - Comprison of frctionl resuspension rte vs. time for two multilyer models, STORM test SR11 Phse 6 conditions (see Tble 3) Figure 19 - Resuspension frction vs. time for polydisperse prticles, STORM test SR11 Phse 6 conditions (see Tble 3)

25 monodisperse, monolyer monodisperse, 1 lyers polydisperse, monolyer polydisperse, 1 lyers Resuspension Frction t (s) Figure - Resuspension frction vs. time for polydisperse nd monodisperse prticles with the sme geometric men size, STORM test SR11 Phse 6 conditions (see Tble 3) Figure 19 shows the resuspension frction for different numbers of lyers for the polydisperse cse. It is noted tht s the number of lyers increses to more thn 1, less thn 1% of the deposit is removed fter 1s. It lso shows tht the resuspension frction for ech cse is exponentilly proportionl to the time in the long-term fter 1-4 s. The comprison of the resuspension frction for the polydisperse prticles nd the monodisperse prticles with the sme geometric men size nd is shown in Figure. This confirms wht ws sid bove tht, compred to the monodisperse resuspended frction, the polydisperse cse gives slightly more resuspension thn the monodisperse cse in the short initil period since popultion of lrger-thn-verge-size prticles is considered in the polydisperse model nd these re esier to remove thn smller ones. After tht initil period, the resuspension frction of polydisperse prticles becomes less nd less compred to tht of the monodisperse prticles since the remining polydisperse prticles re smller nd incresingly hrder to remove.

26 5.5 Rtio of Resuspension Frction monolyer 3 lyers 5 lyers 1 lyers lyers 5 lyers 1 lyers t (s) Figure 1 - Rtio of resuspension frction between initil monodisperse model nd model with polydisperse prticles, STORM test SR11 Phse 6 conditions (see Tble 3) Figure 1 shows the rtio of the resuspension frction of the monodisperse prticles with tht of the polydisperse prticles. All the curves strt with similr vlues due to the resuspension of the top lyers; lso in the short term (<1-4 s) the resuspension of the polydisperse prticles is greter thn tht of the monodisperse prticles since the 5% of the polydisperse prticles with sizes > tht of the monodisperse prticles re esier to resuspend. As the number of lyers increses the difference between the monodisperse nd polydisperse prticles becomes significnt. For 1 lyers, the resuspension frction of the monodisperse prticles fter 1s is ~4.5 times tht of polydisperse prticles. And for the 1 lyers cse, the rtio increses to round 5 fter 1s. This is ll consistent with the Figures provided for the resuspension rte comprison. It is noted here tht in the clcultions of the multilyer polydisperse prticles, Bisi s correltion of the prmeters for the distribution of dhesive forces ws used for ech prticle in the size distribution; so the geometric men of normlized sperity rdius nd dhesive spred fctor is different for every prticle size. To exmine the effect of spred fctor, the vlue of the geometric men normlized dhesive rdius is now fixed ( vlue of.15 is used) nd we consider the influence of spred fctors of 1.1 ( very nrrow spred), (Bisi s originl vlue) nd 4. with the sme size distribution s before in Figure 19.

27 monolyer, spred fctor = 1.1 monolyer, spred fctor = 1.8 monolyer, spred fctor = 4. Resuspension Frction t (s) Figure - Effect of dhesive spred fctor on monolyer resuspension for polydisperse prticles, STORM test SR11 Phse 6 conditions (see Tble 3) lyers, spred fctor = lyers, spred fctor = lyers, spred fctor = 4..1 Resuspension Frction t (s) Figure 3 - Effect of dhesive spred fctor on resuspension of polydisperse prticles in 1-1-lyer multilyer deposit, STORM test SR11 Phse 6 conditions (see Tble 3)

28 lyers, spred fctor = lyers, spred fctor = lyers, spred fctor = 4..1 Resuspension Frction t (s) Figure 4 - Effect of dhesive spred fctor on resuspension of polydisperse prticles in 1-lyer multilyer deposit, STORM test SR11 Phse 6 conditions (see Tble 3) Figures, 3 nd 4 show the effect on the frction resuspended of spred fctors for rnge of lyer thicknesses in the deposit. It is observed in Figure tht the monolyer model with lrger spred initilly gives more resuspension due to the fct tht there is more lrge size prticles involved in the distribution hving lower dherence nd these re esier to remove. After certin period (1-3 s), the model with the lrger dhesive spred predicts less nd less resuspension becuse the prticles left re much hrder to remove. However, s the number of lyers increses the difference between the resuspension for different spred fctors becomes less nd less becuse the coverge effect is incresingly influentil in mking prticles re hrder to remove in the thicker deposit. It is noted tht in Figures 7, 8 nd 9, the curves for the smll dhesive spred fctor (1.1) re quite different to the others with lrger spred fctors even for lrge lyer numbers (the curve for smll spred fctor being closer to step function). However, this phenomenon is not reproduced here. The reson for this is becuse when prticle size distribution is considered, there exists lrge probbility of smll prticles (rdius smller thn the verge rdius). Therefore, no mtter how smll is the rnge of dhesive force is, there is still lrge frction of prticles needing to be removed over much longer period.

29 1 spred fctor = 1.1 spred fctor = 1.8 spred fctor = Rtio lyer numbers Figure 5 - Rtio of resuspension frction between short term (<1-4 s) nd long-term (note tht the long-term resuspension is 1 the short-term resuspension) bsed on STORM test SR11 Phse 6 conditions (see Tble 3) Figure 5 shows the rtio of short-term to long-term resuspension frction. The short term is considered to be the period before the resuspension rte becomes pproximtely proportionl to 1/t. It is observed in Figure 17 tht fter round 1-4 s the curves become stright lines. Therefore, short term finishes round 1-4 s. As the number of lyers increses, in other words the deposit becomes thicker nd thicker, the short term resuspension contributes less nd less to the totl resuspension becuse most of the prticles were covered nd not esy removed. Also, for the lrge spred fctor (i.e., 4) the rtio of short-term to long-term resuspension frction is lwys higher thn the model with smll spred fctor though the difference is less significnt when the number of lyers is very lrge. The reson for this is the wide rnge of dhesive force where the prticles with smll dhesive force being more esily removed in the short term nd this ffects the lyers on the top more thn the lyers below. Also, Figure 5 indictes tht the slopes re the sme for the rnge of spred fctors. It is noted tht the slopes re close to -1.1.

30 7. Vlidtion of Multilyer Models In this finl section, model predictions re compred with the results of two experiments: the STORM SR11 test (Cstelo et l., 1999) nd the BISE experiment (Alloul-Mrmor, ). The former is probbly the best experiment for multilyer deposit resuspension in the nucler sfety re nd the ltter is the ltest experiment for multilyer resuspension for which the experimentl dt hve been compred with R n R model predictions. 7.1 STORM Test SR11 The STORM (Simplified Test of Resuspension Mechnism) experiements were crried out by the Joint Reserch Centre of the Europen Commission (EC/JRC) t Ispr, Itly. The erosol used throughout the tests ws composed of tin oxide (SnO ) prticles produced by plsm torch. In ll, 13 tests were undertken, the first 8 tests only for erosol deposition nd the rest of the tests included supplementry resuspension phse. The 5 resuspension tests were identified s SR9, SR1, SR11, SR1 nd SR13 (Bujn et l., 8). SR11 is lso the bsis of n Interntionl Stndrd Problem (ISP-4, in fct; Cstelo et l., 1999). It took plce in April 1997 nd included two distinct phses, the first concentrting on erosol deposition mostly by thermophoresis nd eddy impction (turbulence) nd the second on erosol resuspension under stepwise incresing gs flow. We note tht the dominnt deposition mechnisms should in the STORM conditions not hve fvoured deposition of ny prticulr size in the cse of thermophoresis (i.e., polydisperse deposit) but tht turbulent deposition must hve strongly fvoured lrge-prticle deposition (much reduced polydispersity). Figure 6 - The STORM fcility (Cstelo et l., 1999) The STORM test fcility is shown in Figure 6. The test section (in the blue box) ws 5.55m long stright pipe with 63 mm internl dimeter. In the deposition phse, the crrier gs nd erosols pssed through the mixing vessel followed by stright pipe into the test section nd then finlly to the wsh nd filtering system. In the resuspension phse, the clen

31 gs ws injected through the resuspension line directly into the test section nd the resuspended SnO erosols were collected on the min filter before the gs goes through the wsh nd filtering system (Cstelo et l., 1999). The resuspension phse ws divided into six steps of incresing gs velocity; the crrier gs ws pure nitrogen (N ) t 37 ºC; the flow rtes, fluid men velocity, fluid density nd kinemtic viscosity for ech step re given in the Tble 4 below. Step Mss flow Fluid men Fluid density Fluid kinemtic Wll friction rte (kg/s) velocity (m/s) (kg/m 3 ) viscosity (m /s) velocity (m/s) x x x x x x Tble 4 - Conditions of STORM test SR11 While the mss flow rte ws mesured in STORM test SR11, the fluid men velocity, density nd kinemtic viscosity re obtined from the SOPHAEROS code (Cousin et l., 8); SOPHAEROS is the module of the Europen integrl code ASTEC (Accident Source Term Evlution Code) tht hs been used by Bujn et l. (8) nd others to nlyse the experimentl results of the STORM resuspension tests. The wll friction velocity is clculted s τ w u τ = ρ f where τ w is the wll sher stress, whose vlue cn be obtined from 1-D therml-hydrulic system code simultion, using the formul f fric τ w = ρ fv [45] 8 where V is the fluid men velocity nd f fric is the friction fctor which in the STORM cse is pproximtely.16 (Komen, 7). The size of prticles collected fter deposition in the STORM test cn be reproduced by lognorml distribution nd in the SOPHAEROS code the geometric men dimeter (GMD) is given s.454µm nd the geometric stndrd devition 1.7. The SnO erosol ws generted during the deposition phse. The totl mss of the erosol deposited in the test pipe ws estimted to be.16kg. The time nd mss t the end of ech resuspension step nd the resuspension frction re shown in the Tble 5 below. Step Time t the end of Mss t the end of Frction ech step (s) ech step (kg) resuspended Tble 5 - Resuspension result of STORM SR11 test

32 The surfce energy of SnO ccording to Yun et l. () vries from.47 J/m to.51 J/m t 37 ºC. Here.5 J/m is used for the model clcultion..8 Resuspension frction Experimentl dt Monolyer, monodisperse lyers, monodisperse 3 lyers, monodisperse Monolyer, polydisperse lyers, polydisperse 3 lyers, polydisperse t (s) Figure 7 - STORM SR11 test nd model results comprison (using Bisi s correltion [Eq.7] for the dhesive forces) For the purposes of comprison, two multilyer models were used to clculte the frction of prticles resuspended t the end of ech time step: the monodisperse multilyer model (referred to s the monodisperse cse) nd the polydisperse multilyer model (referred to s the polydisperse cse). The vlues of the prmeters used in the model predictions re those given in Tbles 4 nd 5. Bisi s correltion for the dhesive force distribution ccording to ech prticle size ws used to obtin the results shown in Figure 7. Figure 7 shows the model comprisons of the resuspension frction with the STORM test SR11 results. It is observed tht for the monolyer resuspension both polydisperse nd monodisperse cses give more resuspension thn the experimentl dt. However, the polydisperse cse gives results very close to the experimentl dt in the first nd finl steps. Compring ll cses, the monodisperse cse with lyers gives the best results. This would imply tht the size-selective deposition of turbulent deposition significntly reduced the polydispersity of the deposit.

33 Resuspension frction Experimentl dt Monolyer, monodisperse 5 lyers, monodisperse 1 lyers, monodisperse Monolyer, polydisperse lyers, polydisperse 3 lyers, polydisperse t (s) Figure 8 - STORM SR11 test nd model results comprison (geometric men (reduction in dhesion) =.1, dhesive spred fctor = 1.5) However, it is reclled tht Bisi s correltion for the dhesive forces is bsed on the originl R n R model which is n isolted prticle model for resuspension. Therefore, it is strictly not suited for the multilyer deposit cse. In order to check the sensitivity of the resuspension to the vlues of the dhesion prmeters, geometric men (reduction in dhesion) ws chosen to be.1 ccording to Hll s experiment (Reeks & Hll, 1) with two different spred fctors (1.5 nd 4.) used for comprison. The smll spred cse is shown in Figure 8; one cn observe tht, this time, the polydisperse cse with 3 lyers is in much closer greement with the experimentl mesurements thn the monodisperse cse.

34 Resuspension frction Experimentl dt Monolyer, monodisperse lyers, monodisperse 3 lyers, monodisperse Monolyer, polydisperse lyers, polydisperse 3 lyers, polydisperse t (s) Figure 9 - STORM SR11 test nd model results comprison (geometric men (reduction =.1, dhesive spred fctor = 4.) In the cse of the resuspension for the lrge spred fctor (4.), Figure 9 shows poor comprison with the experimentl dt for both monodisperse nd polydisperse cses. The trends of the curves re quite different from those of the experimentl dt.

35 7. BISE Experiment The BISE (Bnc de mise en Suspension pr Ecoulement) experiment ws performed by Alloul-Mrmor () t IRSN/Scly in Frnce with the purpose of studying the resuspension of non-rdioctive polydisperse prticles on surfce in fully-developed chnnel ir flow. Figure 3 Schemtic digrm of the BISE experiment pprtus The principl zone of the instlltion is composed of two Plexigls prtitions. The one on the left in Figure 3 is horizontl right-ngled prllelepiped conduit 4cm in length, 1cm wide nd 7cm high. There ws n experimentl surfce towrds the end of the chnnel, s shown below. The crrier flow ws dry ir t room temperture with rnge of men velocities from.5m/s to 1m/s (friction velocities from.4m/s to.5m/s). The time intervl for ech experiment ws 9s. Figure 31 - Representtion of experimentl surfce Alumin (Al O 3 ) sphericl reltively monodisperse prticles were used in the experiment. 5 prticle sizes were considered from 4.6µm to 58.7µm (MMD) nd the resuspension of two of them were compred to R n R model predictions. In the model comprison, only one prticle size from these two hs been chosen (58.7 microns) becuse the resuspension frction ws