Nuclear Engineering and Design 199 (2000) 203–214

Measurements of solid particle suspension concentrations inboiling pools

Abraham Dayan, Amos Ullmann *, Sylvia ZalmanovichDepartment of Fluid Mechanics and Heat Transfer, The Faculty of Engineering, Tel A6i6 Uni6ersity, Tel A6i6 69978, Israel

Received 14 December 1998; received in revised form 1 December 1999; accepted 4 January 2000

Abstract

An experimental study was performed to measure vertical particle suspension concentrations in contaminatedboiling pools. The study was conducted in a nucleate boiling regime. Tests were conducted with distilled water andsolid nickel particles ranging in size from 5 to 40 mm. The test apparatus was 30 cm wide and 120 cm high. Particleconcentrations were on the order of milligrams per cubic centimeter of slurry. Heat fluxes on the order of 100 kWm−2 were attained by electrical bottom heating. Corresponding superficial vapor velocities were on the order ofseveral centimeters per second. Measurements were aimed to reveal the dependence of dilute particle suspensiondistributions on the pool depth, heat flux and particle loading. The results indicate that only a fraction of the particleloading gets suspended. This fraction turns out to be largely dependent on the pool depth and heat flux, but isinsensitive to particle loading variations. The particle distribution within the suspension was analyzed with thedispersion–sedimentation model. The work demonstrates the applicability of this model for the conditions of boilingpools and partial particle suspensions. Furthermore, the results indicate that for shallow pools and small size particlesthe distributions are fairly uniform. Consequently, the suspension concentration is substantially a function of thefraction suspended. The work provides experimental data to evaluate this fraction for a range of heat fluxes and pooldepths. The knowledge of particle suspension concentrations has important industrial and environmental applicationsin the power generation, nuclear and chemical engineering industries. For example, the results could be used toevaluate the amount of particle released from a contaminated boiling-pool spill, or could be used to reduceconservatism applied in analyses of pools containing larger particles. © 2000 Elsevier Science S.A. All rights reserved.

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1. Introduction

The dispersion of solid particles in bubble andboiling columns is an important industrial andenvironmental problem. In the chemical industry,

bubble column slurry reactors often contain solidparticles, which could be catalysts, reactants andproducts. The dispersion of these particles influ-ences reaction rates and reactor efficiencies. In thepower generation industry, the dispersion of solidcontaminants in boiling pools could be haz-ardous, both, industrially and environmentally.Existence and carry over of solid impurities inworking fluids affects strongly the life of power

* Corresponding author. Tel.: +972-3-6408930; fax: +972-3-6407334.

E-mail address: ullmann@eng.tau.ac.il (A. Ullmann)

0029-5493/00/$ - see front matter © 2000 Elsevier Science S.A. All rights reserved.

PII: S0 029 -5493 (00 )00235 -1

A. Dayan et al. / Nuclear Engineering and Design 199 (2000) 203–214204

generation machinery. In the nuclear industry,during postulated emergency conditions, any pos-sibility of release of solid radionuclides from boil-ing pools is of critical importance. The concern isin the potential spread of activity by mechanismsof flooding or carry-over in vapor clouds. Suchreleases are highly dependent on the dispersion ofthe radionuclides in boiling pools and bubblecolumns. With such safety concerns, the currentresearch work was initiated with a focus on rela-tively shallow pools, which, potentially, could re-lease contaminants at the highest rates. Theconditions chosen for this study were aimed to-wards exploring nuclear safety concerns related tosource term evaluations of contaminated boilingpools.

Distinction should be made between bubblecolumns operating with continuous flow (liquidand gas) and those operating under batch orsemi-batch conditions (with no net flow at thebottom or with gas flow only, respectively). Whilecontinuous flow systems are more typical to nor-mal operation of chemical and power generationinstallation, the batch conditions are rather typi-cal to accident conditions (but not exclusively).For the nuclear industry, the batch conditions ofcontaminated boiling pools are of particular im-portance. Such conditions are generally associatedwith postulated hypothetical core disruptive acci-dents. More specifically, in accidents involvingfuel-coolant interactions. In such events, fragmen-tation of fuel material could produce substantialquantities of radioactive and toxic solid particles.Emergency cooling systems are expected to keepfuel debris in a submerged state. Nonetheless,pools containing those debris could be intenselyheated by sources such as: stored heat, chemicalreactions, and radioactive decay heat. The inten-sity of these sources is sufficiently strong to induceand sustain boiling conditions. Rising bubbleswithin boiling pools and vapor flow above thepools could suspend from the floor and expelparticles from the surface, respectively. It is,therefore, necessary to quantitatively assess thepotential of environmental contamination frommaterial releases of contaminated boiling pools.In this context, knowledge of the suspended parti-cle concentration at the pool surface is of major

importance because fluid spills and vapor inducedparticle emissions are mostly surface transportphenomena.

Particle distributions in bubble columns aresubstantially one-dimensional. To evaluate a dis-tribution one must know: (a) what portion of theparticle loading is in a suspension state; and (b)what is the vertical concentration distribution ofthe suspended particles. At the pool floor, parti-cles tend to settle due to the existence of gravita-tional slip velocities (between particles and fluid)and awing to impinging fluid circulation. Againstthat, particles are lifted from the floor at differentlocations. The upward transport from the floor isgoverned by: (1) particle entrainment in the risingdomains of circulation currents; (2) entrapment inbubble wakes; and (3) entrainment in swirlingflow patterns (‘tornado’ like). These mechanismswere observed in separate visualization experi-ments conducted in a rectangular bubble columncontaining distinct points of bubble injection(simulating nucleation sites). Once in suspension,particles are dispersed by the influence of fluidcirculation that acts against gravity. The determi-nation of how many particles gets suspended fromthe pool floor, for a given boiling rate, is yet to beexplored. At present, such a determination mustrely on experimental work. In contrast, the sub-ject of the dispersion distribution of already sus-pended particles has received considerableattention. In essence, models were developed toevaluate the rate of a pool bubble-induced fluidcirculation (Joshi et al., 1988; Viswanathan, 1988).These models were than extended to account forparticle drag effects as well as gravitation. Conse-quently particle transport equations were devel-oped for bubble columns. The equations showthat the particle dispersion mechanism is a turbu-lent diffusion process with a characteristic disper-sion coefficient. Several models were developedfor the evaluation of these coefficients. In general,dispersion coefficients are functions of the gassuperficial velocity (bubbling rate) and the pooldiameter (Joshi et al., 1988; Viswanathan, 1988;Saxena and Thimmapuram, 1992). They reflecteffects of two-dimensional cellular fluid circula-tion patterns on particle dispersion. These analy-ses demonstrated that multi-dimensional flow

A. Dayan et al. / Nuclear Engineering and Design 199 (2000) 203–214 205

circulatory patterns produce essentially one-di-mensional particle distributions, parallel to thegravitational field. Consequently, particle trans-port equations are one dimensional, and dependon a single dispersion coefficient which can beinterpreted as a vertical diffusion coefficient.

Dispersion coefficient models were developedprimarily for the chemical industry, in particularfor reactor performance characterizations. A com-prehensive survey on the subject can be found inthe publications of Mashelkar (1970), Chandahriand Ramachandran (1980), Shah et al. (1982) andSaxena and Thimmapuram (1992). Models existfor different fluid flow patterns, i.e. bubbly flow,churn turbulent and slug flow. In general, pres-ence of small particles has little influence on thedispersion characteristics of the column (Cova,1966; Kato et al., 1972).

Other studies were directed towards the deter-mination of critical gas velocities necessary forcomplete suspension of the solid particles (Roy etal., 1964; Narayanan et al., 1969). Critical gasvelocity criteria apply primarily to bubblecolumns operating continuously with gas sparg-ers. They are of prime importance to the chemicalindustry. Operation with supercritical gas veloc-ities implies that the entire particle loading is insuspension and the particle distribution is simplydetermined by the dispersion coefficient. There-fore, the subject of particle holdup for conditionsof partial particle suspension has not receivedmuch attention.

Critical flow velocity criteria are of limitedvalue to analyses of a bottom heated boiling poolwhere no net bottom flow exists. In bottomheated boiling pools it is expected that only afraction of the particle loading is suspended. It isimportant to determine what is this fraction inorder to evaluate particle concentration distribu-tions. However, little is known on the parametersaffecting this fraction. The current work focusedon exploring what are those parameters and theirrelative importance. Additionally, the investiga-tion addressed the parameters affecting the sus-pended particle vertical distributions. As it turnsout, for shallow pools with small particles indilute concentrations, those distributions werefound to be close to uniform (this would not be

the case for larger particles and deeper pools).This fact was demonstrated theoretically and ex-perimentally. In the theoretical part, it was shownthat the fully batch conditions of boiling poolscan be modeled with dispersion coefficients thatwere originally developed for continuous flow andsemi-batch bubble columns.

1.1. Particles distribution

Particle concentration distributions in bubblecolumns are usually determined from the solutionof sedimentation–dispersion model (originallyproposed by Cova, 1966 and later by Suganumaand Yamanishi, 1966). In this model, the solidflux is obtained by superposition of a Fickian typedispersion flux and a sedimentation flux on theconvective slurry flux. The various publicationson the subject differ mainly in the selection of twogoverning parameters, namely, the solids settlingvelocity and the solids dispersion coefficient.

Concentration distributions can be derivedfrom the continuity equation (Cova, 1966) orfrom a differential mass balance equation (Smithand Ruether, 1985). Both approaches yield thesame final expression for the axial distribution ofsolid particles. For the case of steady-state batchoperation and under the assumption of constantdispersion coefficient, Es, and constant solids set-tling velocity, Ust, the axial distribution of thesolid particles is given by the following equation

Es

d2Cdz2 +Ust

dCdz

=0 (1)

Appropriate selection of models for dispersioncoefficients and effective settling velocities mustconform with batch operation conditions in abubbly flow regime. Numerous correlations weresuggested over the years for the dispersion coeffi-cient and the effective settling velocity of thesolids in the presence of gas and liquid phaseflows. A comprehensive review of different corre-lations for Es and Ust is given by Saxena andThimmapuram (1992).

Integration of Eq. (1) with the followingboundary conditions:

C=C0 as z�0

A. Dayan et al. / Nuclear Engineering and Design 199 (2000) 203–214206

C=0 as z�� (2)

yields

C=C0 exp�

−Ust

Es

z�

(3)

where C0 is the particle concentration just abovethe pool floor and z the height above the poolfloor. The equation indicates that: (1) particleconcentrations decrease exponentially with heightfrom the pool floor; (2) that heavier particleswould be more difficult to suspend due to theirlarge settling velocities; and (3) that strong disper-sion characteristics would produce more uniformdistributions.

As previously indicated, in pool boiling there isno net upward flow through the pool floor. There-fore, a complete suspension of all the particlesfrom the pool floor is quite unrealistic. Thus,under such conditions, the suspended particleconcentration near the pool floor, C0, depends onthe ratio K=M/M0 of the suspended particlemass, M, to the particle loading total mass M0.To derive this dependence, Eq. (3) is integratedover the volume of the pool to produce the sus-pended particle mass M (or KM0). Solving theresult for C0 yields

C0=KM0Ust

AEs

�1−exp

�−

Ust

Es

h�n−1

(4)

where A is the pool horizontal cross section area,and h the pool depth. The inspection of Eqs. (3)and (4) clearly shows that the particle concentra-tion is a function of Es, Ust, M0 and the fraction,K, of the particle loading that is suspended.

2. Experimental

Tests were conducted with nickel powder inboiling water at atmospheric pressure. The testapparatus, seen in Fig. 1, consisted of a stainlesssteel cylinder, 30 cm in diameter and either 60 or120 cm in height (through the addition or removalof a 60-cm modular extension). The choice of a30-cm pool diameter for bubbles of �1 cm di-ameter insures measurement of ‘flat’ pool boilingcharacteristics with minor side effects. To provideeven bottom heating, nine electrical heaters wereinserted into the bottom plate, which in turn wasmade of a 3-cm thick aluminum plate. Each elec-trical heater had a rating of 1 kW. A transparenttube was used for level measurements. The con-tainer was thermally insulated to minimize, both,power consumption and side effects. A diffuserwas installed above the pool to collect and vent

Fig. 1. Experimental boiling pool apparatus.

A. Dayan et al. / Nuclear Engineering and Design 199 (2000) 203–214 207

the vapor through a blower. Make up water wasmonitored by a rotameter. The vapor flow ratewas determined from the supply rate of the makeup water.

Heat fluxes up to 12.7 W cm−2 were attainedby powering all the nine heaters. This range ofheat fluxes is within the limit of the nucleateboiling regime. For nuclear safety considerations,this limit corresponds to characteristic heat fluxesof hypothetical core disruptive accidents. For in-stance, the decay heat of a 1000 MW (thermal)core in a late stage of the fuel cycle would be onthe order of 10 MW, an hour after shutdown. Ifthe core debris spread on a circular surface areaof 10 m diameter, they would produce a heat fluxof 12.7 W cm−2. This rate would represent amaximum from which the decay heat would di-minish thereafter.

The experiments were conducted with deionizedwater and nickel powder with particle size rangingfrom 5 to 40 mm. The particle size distributionclosely follows a log–normal distribution with amass median diameter (MMD) of 14.5 mm and ageometric standard deviation (sg) of 1.5. A maxi-mum particle loading of 200 g was used in theexperiments. A loading of this magnitude pro-duced particle concentrations on the order ofmilligrams per cubic centimeter of slurry.

The choice of the particle size range conformswith the goal of data collection of suspendableparticles (within and above the pool). Metallicparticles larger than 40 mm have excessive settlingvelocities and therefore pose limited hazards. Thechoice of nickel powder material has a twofoldmerit: (a) it reflects densities close to those ofnuclear core materials as well as those of chemicalreaction catalysts; and (b) it provides a chemicallyinert substance. The particle loading was keptwithin reasonable limits so as not to mask thebubble-particle entrainment characteristic by theinfluence of a particle bed formation on the poolfloor.

Samples from the pool were collected by sub-merging a 6 cc syringe to desired depths. Thevolume of the fluid drawn into the syringe, reflect-ing several bubble wakes volume, was largeenough to provide measurements of average localconcentrations. The samples were analyzed, both,

with a Coulter counter and in an atomic absorp-tion spectrometer. The Coulter counter providedparticle size distributions and the atomic absorp-tion spectroscopy provided measurements of par-ticle overall mass concentrations. The results werequite reproducible and each data point in thefigures represents an average of several measure-ments. The standard deviation of the samples forany given point was usually smaller than 10% ofthe median (closer to 7%).

Measurements were taken along the pool depthat different radial locations. The particle concen-tration data was sensitive to the depth and insen-sitive to the radial sampling position. We avoidedsampling the immediate vicinities of the pool sur-face and bottom. Concentration distributions atthese interfaces are influenced by irregular localphenomena such as, radial flow currents, wavyfree surface at the top, and uneven spread ofnucleation sites at the bottom. Therefore, localmeasurements at these locations would not neces-sarily reflects lateral averages. Alternatively, itwas assumed that data could be extrapolatedfrom their neighborhoods to obtain approximateinterface concentrations. In this respect, we ob-tained reproducible concentration measurementsfew centimeters away from each interface andtherefore considered the data as representative ofconcentration averages.

3. Results and discussion

Particle distributions within the pool were mea-sured as a function of particle loading, pool depthand vapor flow rate (presented as superficial gasvelocities). For the aforementioned heat fluxes,measurements were conducted with superficial gasvelocities ranging from 4 to 7.2 cm s−1 (saturatedvapor at 100°C).

Data on particle concentration distributions ina pool 50 cm deep for four different particleloadings are shown in Fig. 2. The area below eachcurve multiplied by the pool cross section arearepresents the amount of suspended particles. Thefraction of the particle loading that gets sus-pended, K, is simply the ratio of the amount ofsuspended particles divided by the particle load-

A. Dayan et al. / Nuclear Engineering and Design 199 (2000) 203–214208

Fig. 2. Effect of particle loading on the axial distribution of particles in a 50-cm deep pool.

ing. Inspection of the results revealed that �80%of the total particle population was suspended bythe boiling action (K=0.8), regardless of theloading. This conclusion can be observed directlyfrom the inspection of Fig. 2. Doubling the parti-cle loading entailed a doubled suspension. Toexplain this observation, attention is directed tothe migratory path of the particles. The particlesare subject to basically three distinct transportregimes; one at the pool floor, the other at thepool surface, and the third within the pool fluiditself. If one follows over time the path of a singleparticle, it is reasonable to expect that the particlewill have three characteristic residence times thatwould correspond to the three distinct pool zones.For instance, one may find that 20% of the totalobservation time the particle is on the floor,79.9% in the pool fluid, and 0.1% at the poolsurface. If the observation period is long enoughand the test is conducted with a mono-size parti-cle population in dilute concentrations, it isjustified to invoke the ‘ergodic hypothesis’. Inother words, an ensemble of many particles wouldexhibit the same average properties in space aswhat a single particle exhibits over time. Hence,regardless of the number of particles (or particle

loading), 20% would be on the floor, and the restsuspended in the pool. It is important to note thatthe tests were conducted with dilute particle volu-metric concentrations on the order of 10−4. It isrecognized that the percent suspended is a func-tion of the particle size. However, the same argu-ment holds for a system of few particles ofdifferent sizes and a multiple of such systems.Based on this explanation, it becomes clear whythe observed fraction of suspended particle isbasically independent of the loading.

The solid lines depict predicted particle distri-butions according to Eqs. (3) and (4), with anexperimental value for K. The slope of each solidline on the logarithmic plot represents the ratio ofthe effective settling velocity to the solids disper-sion coefficient. The effective settling velocity wascalculated according to the following correlationreported by Kato et al. (1972) for semi-batchbubble columns:

Ust=1.33U t0.75Ug

0.25oL2.5 (5)

where Ut is the terminal velocity of a single parti-cle in a quiescent liquid (calculated for a particlewith a diameter equal to the mass median diame-ter of the suspended particles), Ug is the superfi-

A. Dayan et al. / Nuclear Engineering and Design 199 (2000) 203–214 209

cial gas velocity, and oL is the fractional liquidholdup in the slurry (which, for low solid concen-tration as studied in the present work, approachesunity). This correlation is valid for superficial gasvelocities extending from 3 to 20 cm s−1 (Smithand Ruether, 1985; Smith et al., 1986).

The dispersion coefficient; according to Kato’scorrelation (Kato et al., 1972) which is valid forparticles smaller than 100 mm and 0.025BFrB0.18, is

Pes=13Fr1+0.009RepFr−0.8

1+8Fr0.85 (6)

where the Peclet number is defined as Pes=UgD/Es, the Froud number by Fr=Ug/(gD)1/2, theReynolds number by Rep=Utd/n, g the gravita-tional acceleration, d the particle diameter and Dthe pool diameter. The ratio Ust/Es turned out tobe 0.15574 for superficial gas velocity of 7.2 cms−1, a value that was confirmed by incorporatingother correlations, such as those of Smith andRuether (1985), Smith et al. (1986) and O’Dowdet al. (1987). Being a fairly constant parameter,independent of the particle loading, the slope ofall curves is similar. As seen, the sedimentation–dispersion model and the correlations developedoriginally for semi-batch reactors could be suc-

cessfully applied to the batch conditions of poolboiling. Furthermore, it is seen that the appli-cability holds for partial particle suspension.

As previously explained, particles could belifted from the pool floor, either, by entrapment inwakes of rising bubbles (Dayan and Zal-manovitch, 1982) or by circulatory flow entrain-ment. These mechanisms dominate the extent ofthe suspension particle population. For a givenpool diameter, these mechanisms are dependenton the vapor flow rate and the pool depth. Effectsof this dependence are described subsequently.

The influence of the heat flux, or the vapor flowrate, on particle vertical distributions in a 50-cmpool can be observed in Fig. 3. Clearly, a higherboiling rate enhances both the total bubble wakedrag capacity and the pool circulation currents.Consequently, the suspended particle populationis increased. Here the calculated solid line slopesare −0.15574 and −0.15763 for the superficialgas velocities of 7.2 and 4.0 cm s−1, respectively.

The trend of increased suspended particle popu-lation can also be observed in the test results of apool 105 cm deep, shown in Fig. 4. Here, at thehighest boiling rate, evidence exists for the forma-tion of distinct circulation cells, known to form intall columns (Joshi and Sharma, 1979; Joshi,

Fig. 3. Effect of superficial gas velocity on the axial particle distribution in a 50-cm deep pool.

A. Dayan et al. / Nuclear Engineering and Design 199 (2000) 203–214210

Fig. 4. Effect of superficial gas velocity on the axial particle distribution in a 105-cm deep pool.

Fig. 5. Effect of pool depth on the axial particle distribution.

1980). The evidence of three circulation cells in apool with a depth of 105 cm and a diameter of 30cm confirms Joshi’s assumption that the height ofthe circulation cell is about the column diameter.

The increase in pool depth from 50 to 105 cm

for given heat flux and particle loading, as seen inFig. 5, depressed substantially the population ofthe particle suspension. The augmented depth en-tails: (1) a larger fluid inertia opposing the samedisturbance rate of bubble formation and detach-

A. Dayan et al. / Nuclear Engineering and Design 199 (2000) 203–214 211

ment; (2) a higher hydrostatic pressure at the poolfloor (both, smaller bubble volumes and wakes);and (3) an increased pool wet wall surface area(more friction). These factors, though not fullyunderstood, are likely to act adversely on theboiling pool capacity to suspend particles fromthe floor.

The influence of the pool depth on the particlesuspension is so pronounced that the increase ofpool depth diminished the fraction of the sus-pended particles, K, from 0.80 to 0.46. This effectcan be observed in Fig. 6 as well. Here, for a fixedheat flux (corresponding to Ug=7.2 cm s−1), thesensitivity of the fraction of suspended particles topool depth variations is demonstrated. The sensi-tivity is so apparent that doubling the pool depthfrom 0.4 to 0.8 m, for instance, cuts the suspendedparticle fraction by more than half. The datashown is taken from experiments with variousparticle loadings. As previously indicated, the sen-sitivity of the curve to the particle loading is quitelimited. This fact is most pronounced at a depthof 0.5 m where four data points coincide. Thedata spread around the solid line is quite ‘ran-dom’, a feature that supports the claim that theloading is not influential. Excluding two data

points, the deviations from the solid curve is quitelimited. The noticeable deviation of the twopoints occurred in the region that is most sensitiveto pool depths, and thus is not surprising.

Similar experiments were repeated for two addi-tional heat fluxes for which the results are shownin Figs. 7 and 8. To demonstrate the trend simi-larities, the curves of Figs. 6 and 7 were added toFig. 8 (without their data points). Fig. 8 alsoexhibits the relative sensitivity of the suspendedparticle fraction to variations of pool depth andsuperficial gas velocity. This sensitivity is confinedto the range of intermediate pool depths. Fordeep pools, changes in pool depths would, per-centage wise, entail smaller changes in the particlelifting characteristics of the boiling pool. There-fore, the curve slope levels off at increased pooldepths. For very shallow pools the particle sus-pension is at its maximum. The maximum concen-tration depends primarily on the boiling rate andless on pool depth. The data unveil a slight reduc-tion of the suspended particle concentration atdepths shorter than the pool diameter. This couldbe attributed to the corresponding reduction ofthe turbulent characteristic mixing length fromthe pool diameter to the pool depth.

Fig. 6. Effect of pool depth on the fraction of suspended particles for a superficial gas velocity of 7.2 cm s−1.

A. Dayan et al. / Nuclear Engineering and Design 199 (2000) 203–214212

Fig. 7. Effect of pool depth on the fraction of suspended particles for a superficial gas velocity of 5.6 cm s−1.

Fig. 8. Effect of pool depth and superficial gas velocity on the fraction of suspended particles.

The figures provide an essential data for particleconcentration evaluations as function of heat fluxand pool depth. For safety analyses, when uncer-tainty exits with respect to particle size, or heat flux

or pool depth, the data provided here could beconsidered as conservative. This stems from the factthat it represents the extreme conditions of largeheat fluxes, shallow pools and small size particles.

A. Dayan et al. / Nuclear Engineering and Design 199 (2000) 203–214 213

4. Conclusions

The phenomenon of particle dispersion in boil-ing pools was studied experimentally. The studywas conducted in a nucleate boiling regime. Thetests were conducted with small size particles indilute concentrations and reveal their distribu-tions. The results provide data for calculatingparticle distributions in boiling pools for a rangeof heat fluxes and pool depths. They can beincorporated in a variety of environmental safetyanalyses.

The experiments indicate that only a part of theparticle loading gets suspended from the poolfloor. The fraction of the particle loading that gotsuspended was found to be strongly dependent onthe pool depth and heat flux. Augmented particlesuspensions were observed either at higher heatfluxes or shallower pools. For a given heat fluxand pool depth, the fraction does not depend onthe particle loading.

The work demonstrates that the suspended par-ticle vertical concentration distributions in boilingpools (batch conditions) can be determined by thesedimentation–dispersion model. Specifically, itshows that dispersion coefficient correlations thatwere developed for semi-batch bubble columnswith supercritical gas velocities are applicable.

The results indicate that for shallow pools verti-cal dispersion distributions are of secondary im-portance. Surface concentrations follow quiteclosely the overall suspension concentrations. Thelargest particle suspensions were found in theshallowest pools and highest heating rates (ex-cluding pools shorter than their diameters). Con-sequently, it is concluded that shallow pools posethe highest risk for pollution and turbo machinerydamage by solid contaminant releases.

For the nuclear industry, the results are ofsignificance for nuclear safety assessments of hy-pothetical core disruptive accidents involving fuelcoolant interactions. The study identified thedominant parameters affecting the concentrationof small core debris at the surface of boilingpools. The information can be applied in evalua-tion studies of environmental contamination ow-ing to pool fluid releases by mechanisms offlooding, foaming and droplets’ emission from

those pools. For larger particles, the results can beused to reduce the level of conservatism applied insafety analyses. Furthermore, the results provide abasis for future studies aimed to model releaserates of airborne particulate from boiling pools.

Appendix A. Nomenclature

horizontal cross-section area of theApool

h depth of the poolC particle concentration

particle concentration near the poolC0

floorD pool diameterd particle diameter

dispersion coefficientEs

K ratio of suspended particlesFroud number Ug/(gD)1/2Frgravitational accelerationgsuspended particle massMparticle loading total massM0

mass median diameter of the particleMMDpopulation

Pes Peclet number UgD/Es

Reynolds number of particles Utd/nRep

superficial gas velocityUg

Ust settling velocityterminal velocityUt

Z vertical distance from the pool floor

Greek lettersoL liquid holdup in the slurrysg geometric standard deviation of the

particle populationkinematic viscosityn

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