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Nuclear Engineering and Design 263 (2013) 500– 508

Contents lists available at SciVerse ScienceDirect

Nuclear Engineering and Design

jo u r n al hom epa ge: www.elsev ier .com/ locate /nucengdes

omputational and experimental prediction of dust production in pebble bedeactors—Part I

aziar Rostamiana,∗, Gannon Johnsona, Mie Hirutaa, Gabriel P. Potirnichea,bderrafi M. Ougouagb, Joshua J. Cogliatib, Akira Tokuhiroa

Department of Mechanical Engineering, University of Idaho, 1776 Science Center Drive, Idaho Falls, ID 83401, USAIdaho National Laboratory, 2525 N Fremont Avenue, Idaho Falls, ID 83401, USA

i g h l i g h t s

A nonlinear dimensionless wear coefficient is theoretically proposed.A material constant for the relation of asperity height and wear is introduced.A nonlinear modification of Archard wear formula is proposed.The graphite wear dust production in a typical pebble bed reactor is predicted.Experimental and computational wear results for graphite are presented.

r t i c l e i n f o

rticle history:eceived 3 November 2012eceived in revised form 16 April 2013ccepted 19 April 2013

a b s t r a c t

This paper describes the computational modeling and simulation, and experimental testing of graphitemoderators in frictional contacts as anticipated in a pebble bed reactor. The potential of carbonaceousparticulate generation due to frictional contact at the surface of pebbles and the ensuing entrainment andtransport into the gas coolant are safety concerns at elevated temperatures under accident scenarios suchas air ingress in the high temperature gas-cooled reactor. The safety concerns are due to the documentedability of carbonaceous particulates to adsorb fission products and transport them in the primary circuitof the pebble bed reactor, thus potentially giving rise to a relevant source term under accident scenarios.Here, a finite element approach is implemented to develop a nonlinear wear model in air environment.

In this model, material wear coefficient is related to the changes in asperity height during wear. Thepresent work reports a comparison between the finite element simulations and the experimental resultsobtained using a custom-designed tribometer. The experimental and computational results are used toestimate the quantity of nuclear grade graphite dust produced from a typical anticipated configuration.In Part II, results from a helium environment at higher temperatures and pressures are experimentallystudied.

. Introduction

The vast majority of today’s nuclear reactor designs, pre-ominantly light water reactors, have fixed fuel and coolantonfigurations. The pebble bed reactor (PBR), having neither ofhese, uses nuclear fuel encased in a random configuration of spher-cal fuel elements called ‘pebbles’ in a cylindrical ‘bed.’ While this

esign is capable of online refueling and high output temperatures,

ts design also creates specific modeling and design challenges forafety and licensing (IAEA, 2003). Of these challenges, one that is

∗ Corresponding author. Tel.: +1 208 310 9555.E-mail addresses: mrostamian@asme.org,

zram 22@yahoo.com (M. Rostamian).

029-5493/$ – see front matter © 2013 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.nucengdes.2013.04.019

© 2013 Elsevier B.V. All rights reserved.

specific to Graphite-Moderated Gas Cooled Reactors (GM-GCR) isthe phenomenon of carbonaceous particulate generation due tofrictional contact of graphitic components. Due to the number ofmoving carbonaceous components (i.e. fuel elements or ‘pebbles’),this is primarily a concern for pebble bed reactors for safety andoperation.

Safety concerns are focused around understanding transportand deposition of fission and activated products, and how the dustwill be transported during a Depressurized Loss-Of-Flow Cool-down accident (DLOFC). In particular, under DLOFC and similarhypothetical accidents, the main issues are as follows: quantifica-

tion of the inventory of dust, dust re-suspension off of surfaces inthe primary circuit, dust departure from a breached primary circuit,contamination levels associated with such an event (‘source term’),and assessment of the additional risks posed by any energetic

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echanisms of the graphite dust suspending into the surroundingir (NUREG/CR-6944).

While there is limited data on these phenomena in the pub-ished literature from past GM-GCRs and R&D, it is not sufficientor the level of details expected under modern design review andicensing requirements of a pebble bed by the United States Nuclearegulatory Commission (US-NRC). This is further complicated byhe fact that some materials in the past GM-GCRs are either notsed in current designs (e.g. Inconel 617 being replaced by modernlloys), or available (e.g. nuclear graphite H-451) (Kissane, 2009).

panel of experts ranked the phenomena as “medium” in thehenomena Identification Ranking Table (PIRT) and the knowledgeevel as “low” (NUREG/CR-6944). The qualitative ratings in a PIRTf “high,” “medium,” and “low” are used to identify the impor-ance of expected phenomena and the level of understanding ofhose phenomena. The US Nuclear Regulatory Commission Regu-ation (NUREG) also identifies a need for graphite dust productionnd tribological data in a helium environment, as an anticipatedunction of temperature, pressure, and fluence.

In an effort to quantify the frictional wear of materials (fuel,on-fuel) used in the pebble bed, a custom tribometer was devel-ped to measure the wear of materials in helium atmosphere atressures and temperatures expected in a modern GM-GCR. Thisaper describes the design, deployment of the device and the ini-ial experimental data from several grades of nuclear graphite. Also,n this paper the analytical linear Archard model is modified toccount for the wear of brittle materials. In an attempt, the wearoefficient in this equation, which is conventionally assumed con-tant, is derived as a function of the surface asperity height. Thenite element computational model of contacting fuel pebbles iseveloped in ABAQUS.

. The computational analysis

Wear in metals is commonly in the form of microcracks ini-iating under high local plastic strains. In the contact region, theighest plastic strain is seen on the perimeter of the contact area.his is where microcracks are likely to initiate. Existence of a con-inuous contact stress can easily cause to propagate the microcrack.or plane stress, there are two major crack modes: mode I where aensile stress is normal to the plane of the crack, and mode II where

shear stress acts parallel to the plane of the crack and perpendic-lar to the crack front. Under the frictional contact condition, mode

is the possible crack type. Microcracks that are formed can propa-ate only if their stress intensity surpasses the critical crack stressntensity as formulated by Irwin (1957). If this criterion is satisfied,he cracks usually start to propagate perpendicular to the maxi-

um principal stress (Pook, 2007). If the contact stress continueso exist or if the segment under study goes through a high num-er of cycles, cracks on both sides of a 2D contact zone can meetne another at a certain depth underneath the contact zone. Thisechanism produces chips, which leads to abrasive wear. Abrasion

an be a form of wear in brittle materials. However, at very smallnter-pebble loadings present in PBRs, this needs to be investigated.ollowing a previous macro-level analysis (Rostamian et al., 2012),nd using eXtended Finite Element Method (XFEM), crack domainsere considered on the surface of two graphite pebbles in contact.onsidering the domain of applicability for the inter-pebble forces,hich is a range of 10–50 N (Cogliati and Ougouag, 2008; Rostamian

t al., 2012), crack initiations studies were performed. However, its revealed that the wear mechanism by plastic deformation and

rack initiation has an onset of 1000 N for IG-11 graphite pebblesith a diameter of 3 cm. Therefore, it is assumed that the wear in

rittle materials such as graphite under smaller loadings is causedy powder formation from the frictional contact between surface

g and Design 263 (2013) 500– 508 501

asperities. This is also seen in the experimental results where after60 m of frictional contact, only a small worn mass of approximately1 �g was accumulated (Johnson, 2012). Therefore, an analyticalmodel has been established to consider the effect of asperities ongraphite wear.

Most brittle materials including graphite have a linear wearbehavior for small sliding distances (Blau, 1992). However, for mostreal-life applications, the materials that are subject to frictionalcontact are used over long time periods, which means they undergolong sliding distances. In a previous work, it was attempted tomodel a 2-m sliding wear (Rostamian et al., 2012). The results werecompared with Cogliati’s results (Cogliati and Ougouag, 2010) andhis reviews on Xiaowei’s results (Cogliati et al., 2011). However, itis now attempted to model a much longer sliding length, so thatthe nonlinear wear map (i.e. wear versus distance variation) gen-erated from the experimental results can be predicted. In order tocapture this phenomenon, the linear Archard wear model has beenexamined, modified and adapted.

2.1. The linear Archard wear model

The Archard wear equation is a linear model derived frompin-on-disk (perpendicular contact) and pin-on-pin (tangentialcontact) experiments by the French scientist, J.F. Archard, in the1950s (Archard and Hirst, 1956). In this model, the wear volumeis related to the material properties and the sliding distance in thefollowing form

V = KFL

H(1)

where K is the dimensionless wear coefficient or the proportional-ity constant, which is a material parameter; F is the force normal tothe contact point; L the sliding distance; and H the material hard-ness. It is seen that the wear volume is directly related to the normalforces and the sliding distance. By performing finite element sim-ulations at a macro-level, the Hertzian normal forces can be easilydetermined (Johnson, 1987). As a result, the relationship betweenthe wear volume/mass and the sliding distance can be obtained(Rostamian et al., 2010, 2011, 2012). However, this is only true forsmall sliding distances in the case of brittle materials. In order toaccount for the nonlinear wear rates or behavior of brittle mate-rials, one needs to consider the material surface at a micro-level,where asperities are considered as the real contact points. In thefollowing section, a micro-level study of the contact surface willbe considered and the role of asperity height in presented in thenewly introduced nonlinear version of the Archard model will beexplained.

2.2. Micro-level considerations

The height of asperities and the surface topology determine theroughness of the material surface. Let us consider two segmentsmade of one material; one of a rough surface and one of a smoothsurface. It is obvious that the material of a rougher surface has ahigher wear volume after a certain distance of sliding wear. This isalso seen in the air test experiment results from the tribometer atroom temperature. The wear ring around the pebbles is seen to have

been smoothed after the pebbles have been in contact (see Section3 and Fig. 6). Therefore, by a closer examination of the Archard wearmodel, we strive to assess the dependence of wear volume on theasperity height.

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.3. A new wear correlation

Based on the microlevel consideration above, we consider theolumetric wear rate (V = dV/dt) form of the Archard equation:

˙ = KFL

H(2)

Introducing the asperity height into this equation, we approxi-ate the volume by V = hA. Therefore,

hA = KFL

H(3)

here A is the contact area. The negative sign denotes that the timeate change of asperity height is negative, representing a decreasen asperity height with time. It should be noted that the contactrea can vary based on the component shape and the contact con-gurations. In order to generalize this equation for any contact areand component shape, we consider the contact stresses instead oformal forces. Then, Eq. (3) takes the form:

h = KPL

H(4)

here P is Hertzian contact stress. By performing computationalimulations in ABAQUS, contact stresses can be easily obtained atach node in the mesh. In Eq. (4), L is sliding distance rate or relativeelocity at contact. However, the time rate of change in the asperityeight, h, is unknown. To eliminate this unknown, we consider the

ollowing:

= h(t) = h(L(t)) (5)

hich denotes that the dependence of asperity height on time cane formulated as the dependence of asperity height on wear length.ere, the gas adsorption effects on graphite surface are not consid-red. In order to find h, the partial derivative of h with respect toime is used:

dh

dt= dh

dL· dLdt

⇒ h = dh

dL· L ⇒ h

L= dh

dL(6)

herefore,

H

P

dh

dL= K (7)

This is still a linear equation for the rate of change of the asper-ty height. However, it can now be argued that the asperity height

hich decreases with the sliding length can start to influence theaterial constant K. This material property is commonly consid-

red as a constant when the Archard equation is implemented forear calculations. In this work, we introduce a function, which take

nto account the effect of asperity height variations. This functionncorporates the effect of asperity height decrease into the linearrchard wear model for higher sliding distances. When the asper-

ty height decreases from its initial height, the surface becomesmoother, which indicates that the wear rate should decrease.efore introducing the asperity height function, we consider the

ollowing normalized parameters to simplify the equations.

∗ = L

Lmax, h∗ = h

hi(8)

here Lmax is the maximum sliding length and hi is the averagesperity height of the component unworn surface. Therefore, Eq.

7) takes the form

˛dh∗

dL∗= K (9)

g and Design 263 (2013) 500– 508

where = (hiH)/(LmaxP). Now, by introducing the following asper-ity height power-law function, we strive to model the effect ofsurface smoothing:

(h∗) = R(h∗)n (10)

where R is an ‘asperity model constant’ to be obtained by compar-ing the analytical model with the computational data and n is theexponent of the power-law function, also to be determined througha fit of the computational results. Substituting the asperity heightfunction (h∗) into Eq. (9), we will have:

⎧⎪⎪⎨⎪⎪⎩

−˛dh∗

dL∗= K, h = hi (11a)

−˛dh∗

dL∗= K (h∗)︸ ︷︷ ︸

K ′

= KR · (h∗)n, h < hi (11b)

where K ′ = KR(h∗)n is a varying dimensionless wear coefficient,which depends on the variation of asperity height with wear lengthand on the material properties. By rearranging and integrating, thevarying wear coefficient, K ′, can be derived as a function of thesliding length, L*, and the constants R and n. There follows,

K ′ ={

KR

[(1 − n)˛L∗]n

}1/(1−n)

. (12)

The wear coefficient thus derived depends on two parameters:the asperity model constant, R, and the power law coefficient n.These material constants are determined through a fitting processdescribed here. The finite elements computational model pre-sented in Section 2.4 allows the determination of asperity heightas a function of wear length. The FEA model is used repeatedly toobtain a function describing the height, h, of a given asperity versusthe wear length, L, as it is varied between 0.0 and 2.0 m. The deriva-tive of that function is proportional to K ′. Knowing the computed(L, K ′) pairs and introducing the L values into Eq. (12) for K ′, “model”values for K ′ are obtained for various values of the parameters R andn. This process allows the formulation of a fitting problem for theR and n parameters, based on minimizing the difference betweenthe computed K ′ and the “model” K ′. The values of R and n that areretained in this work are the first pair found that results in a max-imum absolute error below 10−6 for K ′. The parameters obtainedin this way from computational model data up to 2.0 m of wearlength are then used for predicting the wear performance for upto 1200 m of wear length. The analytical model predicts experi-mental data with remarkable accuracy and fidelity as detailed laterthrough comparison with the experimental results. All the fittingwork described here assumed the properties of graphite IG-11.

2.4. The computational analysis

The finite element software ABAQUS v6.11 has been used to con-duct simulations of the micromechanics of wear (ABAQUS user’smanual). Primarily, 3D spherical asperities were considered tobe modeled using the implicit module of ABAQUS known as the‘ABAQUS Standard’. However, given the demanding nature of con-tact conditions, the nonlinear geometry of the asperities, severedeformations, and most importantly, the overlapping of asperi-ties, the implicit module of ABAQUS faced convergence issues. Analternative was taken by applying the same methodology in the

explicit solver of ABAQUS known as the ‘ABAQUS Explicit’, whichis very robust in handling contact problems. This module howeverdemands higher run times. As a result, it was decided to switchfrom spherical to cylindrical asperities.

M. Rostamian et al. / Nuclear Engineerin

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chosen for the asperity model. Here we have used a damagemodel and have included damage evolution to visualize the degra-dation of the fully damaged elements. Material failure refers tothe complete loss of load-carrying capacity, which results from

Fig. 1. A meshed asperity of radius 3 �m and thickness 0.04 �m.

.4.1. Finite element modelFig. 1 shows the finite element mesh used for the cylindrical

sperity model. This asperity model was made of linear hex-hedral elements (C3D8R). ‘R’ stands for ‘reduced-integration’,hich uses fewer number of Gaussian points when solving the

ntegral. The advantage of the reduced integration elementss that the strains and stresses are calculated at the loca-ions that provide optimal accuracy; the so-called Barlow pointsBarlow, 1976). A second advantage is that the reduced numberf integration points decreases CPU time and storage require-ents.In the case of cylindrical asperities which is considered

n this study, it would be common sense to conduct theimulation in 2D considering shell elements. However, sincelement removal is sought in these simulations, the ele-ents which are originally within the interior of the asperity

an start to interact with the opposing asperity as a con-act surface. This feature is only avalibale in ‘general contactlgorithm’ in ABAQUS, which requires the use of 3D solidlements. Thus, a 3D model of cylindrical asperities was con-tructed.

Despite being robust for large deformations and saving exten-ive amounts of run time, the reduced-integration solid and shelllements used in ABAQUS are prone to zero-energy modes. These

odes, commonly known as hourglass modes, are oscillatory in

ature and result in mathematical states that are physically unfea-ible. They typically have no stiffness and give a zigzag appearanceo the mesh known as hourglass deformations as seen in Fig. 2. The

Fig. 2. A schematic of hourglass deformation.

g and Design 263 (2013) 500– 508 503

occurrence of hourglass deformations in an analysis can invalidatethe results and should always be minimized. Therefore, hour-glass control is used to overcome this deficiency. This formulationprovides improved coarse mesh accuracy with slightly higher com-putational cost and performs better at high strain levels. Hourglasscontrol is an embedded feature in ABAQUS v6.11.

Plane strain is simulated in this 3D model by constrainingthe front and back planar faces of the asperity as symme-try (i.e. uz = 0, urx = ury = 0). In this way, the model behavesas a plane strain slice. A prescribed velocity was primarilyused for the movement of the upper asperities, and the lowerasperity was kept fixed as its base. Hence, to simulate the move-ment of both pebble surfaces, the relative tangential velocity isapplied to the upper asperity. In a later attempt, it was foundout that prescribing velocities to both upper and lower asper-ities in opposite directions provides more realistic results forthe two asperities. Therefore, the actual tangential velocity ofpebbles at contact was applied to upper and lower asperitybases.

2.4.2. Mass scalingModeling using an explicit procedure can take a considerable

amount of time for the simulation to converge. This is due to thefact that the minimum stable time increment is small. Using appro-priate mass scaling, the computational efficiency is improved whileretaining the necessary degree of accuracy required for a particularclass of problems.

Mass scaling was introduced into the material model in mul-tiple steps. This means that in every step, an artificial masswas added and the simulations were performed. After assess-ing the results, if inertial effects were not seen as comparedwith the results of no artificial mass, then some more masswas introduced. Otherwise, mass scaling would not be contin-ued.

2.4.3. Material modelThe material properties for nuclear grade graphite IG-11 were

Fig. 3. Elastic–plastic behavior with hardening for nuclear graphite IG-11.

5 eering and Design 263 (2013) 500– 508

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rogressive degradation of the material stiffness. An undam-ged constitutive behavior of the material (i.e. elastic-plastic withardening) is determined (Yokoyama et al., 2008) as seen inig. 3.

Then, a damage initiation criterion is determined (point A). Thiss followed by damage evolution (paths A–B) and finally the choicef element removal (point B).

In the absence of any experimental data for the damageoftening part of the curve (A–B), a simple linear damage evo-ution law was used to degrade the material stiffness to zero

here the equivalent total strain reaches 0.05 (point B inig. 3). When an element reaches point B on the curve, its stiff-ess has fully degraded, and the element is removed from theesh.

.4.4. The finite element analysisThe finite element analysis of asperity contact in ABAQUS

xplicit revealed that asperities undergo very high deforma-ions. As the material reaches a total strain of 0.05, thelements are removed and the degradation leads to mate-ial removal from the asperity. In Fig. 4, the degradationnd material removal from asperities of 3 �m high are pre-ented.

The height of the worn asperity from the first simulation wassed to perform the next simulation on this asperity after one fullotation of the graphite pebble. This process continued to derive theight hand side of Eq. (11b), which is needed to derive the ‘asperityodel constant’, R.

. The experiment

The basic sample design conceived for testing to mimic theeometry of the pebble bed with the apparatus is a graphiteisk machined into 2.54 cm tall disks with a 3 cm outer contourJohnson, 2012).

.1. The experimental apparatus

The test data used in this paper is at room temperature andtmospheric pressure. This is because the material properties foruclear graphite are only available at room temperature. Also, there

s no test data for graphite matrix or graphite at the tempera-ures and pressures expected in a pebble bed. As a result, a customest apparatus was designed. In the following section, the exper-mental setup is explained in brief. The motion requirements forolling and sliding between two spherical objects led to the selec-ion of a twin disk tribometer. Because no off-the-shelf twin-diskribometer could operate at the temperature and pressure require-

ents of PBR, a custom apparatus had to be designed. However,nly the results at room temperature and atmospheric pressurere reported in the present paper. High temperature and pres-ure results are presented in a parallel but different work (PartI). The samples were also measured before and after the experi-

ents on an analytical balance for a separate method to measurehe average wear rate of the samples for comparison. A schematicf the tribometer with the pebbles in contact is presented inig. 5.

The Scanning Electron Microscopy (SEM) images (Fig. 6) fromhe graphite samples, after an approximate sliding distance of000 m show a wear scar of 1.7 mm wide with a smooth andlean surface. This is while outside of wear scar, a rough sur-

ace from the fabrication process is observed. This indicateshat the asperities were polished and leveled by the rotating

otion.

Fig. 4. Equivalent plastic strain contour: the degradation and material removal pro-cess from asperities at: (a) t = 0.000325 s, (b) t = 0.0013 s, (c) t = 0.002275 s and (d)t = 0.00325 s for a tangential speed of 0.08 m/s.

M. Rostamian et al. / Nuclear Engineering and Design 263 (2013) 500– 508 505

Fig. 5. Tribometer (left) and its schematic (right) with peb

Fig. 6. The SEM images of graphite sample (a) wear scar zone (b) interface betweenthe scar (lower) and rough zone (upper).

bles in contact and the modular analytical balance.

4. Results and discussion

The wear mass results from the tribometer are presented inFig. 7. The wear mass was recorded every 200 m. It is clearly seenthat the primary wear rates are reduced as the sliding lengthincreases. The wear coefficient obtained from the analytical modelis compared in Fig. 8a to the computational results, and in Fig. 8bto the experimental data. The analytical model exponent and ‘theasperity model constant’ were derived by fitting with the compu-tational results. The model thus obtained is then compared withthe experimental data for verification purposes. The exponent, n, iscomputed to be −1.38 and the dimensionless microlevel asperitymodel material constant, R, is 2.5 × 10−4.

It is clearly observed in Fig. 8b that the proposed analyticalmodel, which stems from the computational data, predicts a higheroverall wear coefficient than the actual wear coefficient derivedfrom experimental data. This is because the natural lubricatingproperties of graphite surface have not been considered (Czichos,

1978). As explained earlier, when two graphite surfaces are in con-tact, powder formation is the main form of wear. The powder is thencapable of filling in the surface valleys, which causes the surface

Fig. 7. Wear mass loss from the tribometer air-tests for ∼1100 m.

506 M. Rostamian et al. / Nuclear Engineering and Design 263 (2013) 500– 508

Fig. 8. Comparison of analytical K with (a) computational results and (b) experi-mental data with respect to the dimensionless sliding length, L*.

tmal(ifUwrba

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Fig. 9. Instantaneous and cumulative wear mass for one graphite pebble withrespect to wear length, L.

o become smoother than what is incorporated into our ABAQUSodel. A plausible explanation is that the uneven distribution of

sperity height on an actual surface could cause a different non-inear wear coefficient than what is predicted here. The minimumfinal) asperity height, as predicted by this model, is 12.45% of thenitial average asperity height. This indeed indicates that the sur-ace has become smoother and thus the wear coefficient smaller.sing the new varying wear coefficient, the wear results, whichere predicted before based on a constant coefficient, can now be

ectified. As seen in Fig. 9a, the initial wear rate starts to decreasey wear distance and the cumulative wear is extremely small forir-tests.

The predicted wear mass using the proposed analytical models compared to the experimental results in Fig. 9b. As anticipated,ue to the difference between the predicted and actual dimension-

ess wear coefficients, the predicted wear mass is approximately0% higher than the actual wear mass. It is clearly observed

n Fig. 9b that the proposed wear model shows a significantmprovement in comparison to the Archard wear equation. Therror bars indicated on the graph in Fig. 9b are from the uncer-ainty associated with the scale with which the experimental

ata was recorded. This indicates that the analytical model hasredicted reliable results that fit in within the uncertainty lim-

ts.

The varying wear rate of graphite is shown in Fig. 10.It is seen that the wear rate decreases as graphite asper-ity height decreases with increasing wear length. The reportedwear rate in (Johnson, 2012) was a constant 8.45 × 10−8. Thisvalue is the same as the initial rate predicted in the presentstudy. However, in the present study, the rate is shown to bevarying over time. It must be noted that the present resultsare for air test at room temperature and atmospheric pres-sure.

Using the dimensionless wear coefficient K ′ obtained in thiswork, it is attempted to derive the wear mass for one pebblethrough 2.06 m of HTR-10 wear length as in (Rostamian et al., 2012).By performing wear calculations as carried out by Cogliati et al.(2011) based on the air-test results of Xiaowei et al. (2005a), thewear mass produced by inter-pebble forces (Cogliati and Ougouag,2008) is calculated. Estimates for HTR-10 and AVR are reportedusing the present model. The wear mass for one pebble is esti-mated to be 0.235 mg. For HTR-10 with an inventory of 27,000pebbles and a pebble flow rate of 125 pebble per day, the wear

mass is predicted to be 5.36 g/year. As explained by Rostamianet al. (2012), the estimated wear mass for AVR would then be63.55 g/year.

M. Rostamian et al. / Nuclear Engineerin

thwP

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oitt

Fig. 10. Wear rate for one graphite pebble with respect to wear length, L.

In Part II of this paper, helium-test experimental data at higheremperatures and pressures will be reported. It is known thatigher temperature and pressure have significant impacts on theear properties of graphite. These effects will be discussed in

art II.

. Conclusions

In the present work, we investigated the generation of car-onaceous particulate due to frictional contact at the surface ofraphite pebbles. Such particulates can give rise to safety issues atlevated temperatures, under accident scenarios for a high temper-ture gas-cooled reactor. Specifically, the adsorbed fission productsnto the ‘graphite dust’ represent a source-term concern. Here, aicro-level approach is undertaken to investigate the microme-

hanics of wear of nuclear graphite IG-11. The effect of the heightf surface asperities is introduced into the wear formula, and

correlation between dimensionless wear coefficient and sur-ace asperity height is obtained. We learned that the likelihoodf chip/particulate formation that is the major source of wear inetals is not dominant for porous, carbon-chain materials such as

uclear grade graphite.The constants in the proposed analytical wear model are

btained by fitting with the computational results. Then, the models used to predict experimental data. In this way, the accuracy ofhe proposed model is assessed. The computational results revealedhat there is approximately 20% difference between the results of

g and Design 263 (2013) 500– 508 507

obtained from the analytical model and the experimental data.This is attributed to the lack of a surface-level lubrication com-ponent in the model, thought to be induced by gas adsorptionas well as relocation of surface-adhering graphite particulates. Itis known that graphite acts as a good lubricant. Thus it couldbe surmised that when particulates are formed due to wear,they primarily relocate in the valleys between asperities. Thisincreases the smoothness of the surfaces, which in turn decreasethe wear coefficient. The lamellar structure of graphite facilitatesthe establishment of smooth surfaces between sliding contacts,and the presence of adsorbed gases may further improve thequality of these surfaces. Since these artifacts are not consideredin the finite element simulations, the predicted wear coefficientis slightly larger than that attributed to the experimental data.However, it is seen that the proposed model is capable of repre-senting the nonlinear wear rates as seen in experimental resultsand that it falls within the limits of the experimental data uncer-tainty.

The proposed model and the experimental results show thatthe wear mass for air environment at room temperature andatmospheric pressure is small and on the order of grams peryear for a reactor. Therefore, it is predicted that the presence ofhelium environment at higher temperature and pressures, actu-ally contributes to increased wear. It was shown by Xiaoweiet al. (2005b) that the wear rate of graphite at elevated tem-peratures is much higher than that at room temperature. Hightemperature/pressure tests in helium gas were also tested usingthe custom-designed tribometer. The results of these studiesare reported in Part II as a continuation of the work presentedhere.

Acknowledgement

We express our gratitude to DOE, under NEUP09-151, “TheExperimental Study and Computational Simulations of Key PebbleBed Thermomechanics Issues for Design and Safety” for providingfinancial support for this study.

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