Fusion Engineering and Design 81 (2006) 449–454

Thermal conductivity of compressed beryllium pebble beds

J. Reimanna,∗, G. Piazzab, H. Harschc

a Forschungszentrum Karlsruhe, Institut fur Kern- und Energietechnik, P.O. Box 3640, D-76021 Karlsruhe, Germanyb EFDA-CSU, Culham Science Centre, Building K1, Abingdon, Oxfordshire OX14 3DB, UK

c Goraieb Versuchstechnik, In der Tasch 4a, D-76227 Karlsruhe, Germany

Received 7 February 2005; received in revised form 1 June 2005; accepted 1 June 2005Available online 6 January 2006

Abstract

For helium cooled pebble bed blankets, the description of the thermal-mechanical interaction between pebble beds andstructural material requires the knowledge of the pebble bed thermal conductivityk as a function of temperatureT and deformationstate (pebble bed strainε).

Experimental results for the thermal conductivity of compressed beryllium pebble beds are presented. The pebble bedsconsisted of 1 mm NGK pebbles and are representative for dense pebble beds (packing factorsγ ≈ 63.5%). Measurements wereperformed in the temperature range between 200 and 650◦C, with maximum pressures of 3.6 MPa and pebble bed deformationsup to ε ≈ 3.5%. A correlation is proposed which is based primarily on measurements but uses conductivity values for non-deformed pebble beds predicted by the Schlunder Bauer Zehner model. It is argued that the proposed correlation is expected tobe applicable also for pebble diameters different from 1 mm and other packing factors than 63.5% as long as densified pebbleb

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eds are considered.Finally, a conductivity correlation is presented which is applicable up to the ultimate compaction to a solid body.2005 Elsevier B.V. All rights reserved.

eywords: Beryllium pebbles; Fusion reactor blanket; Pebble beds; Thermal conductivity

. Introduction

In many helium cooled pebble bed blankets forusion power reactors, the beryllium neutron multi-lier and the breeder material are used as pebbles

∗ Corresponding author. Tel.: +49 7247 82 3498;ax: +49 7247 82 4837.

E-mail address: joerg.reimann@iket.fzk.de (J. Reimann).

between cooling plates. Maximum temperaturethe breeder and beryllium pebble beds are abouand 750◦C, respectively. Temperature differencesdifferent thermal expansion coefficients betweenble beds and structural materials result in constrastrains, which cause elastic and plastic pebble defotions. These deformations influence significantlyeffective thermal conductivityk within the berylliumpebble beds[1] because of the large conductivity raof beryllium to gas.

920-3796/$ – see front matter © 2005 Elsevier B.V. All rights reserved.doi:10.1016/j.fusengdes.2005.06.377

450 J. Reimann et al. / Fusion Engineering and Design 81 (2006) 449–454

The modelling of the thermal-mechanical inter-action between pebble beds and structural materialbehaviour requires, therefore, as important input datathe dependence ofk as a function of temperatureTand deformation state (pebble bed strainε). Althoughpebble deformations are caused by stresses imposedon the pebbles, the stressσ (or an externally appliedpressurep) is not a useful parameter to be correlatedwith k because there is no unique relationship betweenσ andk due to the occurrence of thermal creep strainat elevated temperatures[2]. Therefore, the volumet-ric bed deformationε is considered as prime parameterand the dependence ofk as a function ofε and T isinvestigated.

For the investigation of pebble bed thermal con-ductivities, axi-symmetric set-ups, see e.g.[3,4], area preferred option primarily for non-deformed pebblebeds. However, the independent variation ofε andTcannot be realised with these devices. This goal can beachieved using uniaxial compression test (UCT) set-ups, if besides the piston pressure the displacement ofthe piston is also measured. In previous investigationswith UCT set-ups, only pressure measurement wereperformed[5,6]; both pressure and deformation weremeasured by[7,8].

Without the control of bed deformation, accurateconductivity measurements for non-deformed pebblebeds might be difficult to achieve for (local) temper-atures above 400◦C because of thermal creep strains[2].

r ah sed,o e ist at atedu turei ue,g seee nso iump asa beds

uc-t bleb peri-m ford

2. Experimental apparatus and procedure

A first version of the HECOP (HEat COnductivityin Pebble beds) facility was described by[10] and firstexperiments atT = 250 and 350◦C were presented. Ini-tiated by the failure of an important component, a newapparatus was built (HECOP II) based on the old designin respect to the thermal control system but improvingin respect to several features (displacement measure-ment system, bed container, temperature range, etc.).

Fig. 1 shows the HECOP II set-up. The pebblebed (diameterD = 130 mm, heightH = 60 mm) is posi-tioned between the pistons of a hydraulic press (maxi-mum pressure 3.6 MPa). Within the pebble bed, 4 cap-illaries (2 mm outer diameter) are located at differentbed heights; each of them containing 5 thermocouplesat different radial positions.

For thermal control, a system of 7 heaters (H1–H7)is used. The desired temperature gradient in the pebblebed is imposed by the heaters H2 and H4 at the bottomand by the heaters H1 and H3 at the top.

The heat fluxQ (W/m2) generated by H2 within adiameter of 80 mm is used to determine the thermal bedconductivity by

k (W/mK) = (Q − Qloss)�x

�T(1)

where�x (m) is the axial distance between bed ther-mocouples and�T (K), the corresponding temperaturedifference.Qloss is the residual heat loss.

sesb hatt ringt

owf lleds uplep tem-p atersH

oryc boxw

theF l ofo -c heatl d both

For the two types of set-ups, a heating rod oeated bottom and a cooled piston are usually uperated in steady-state condition. An alternativ

he simple “Hot Wire Technique” (HWT) wherehin wire, embedded in the pebble bed, is hep instantaneously and the wire surface tempera

s measured as a function of time. This techniqenerally used for non-deformed pebble beds,.g. [3], was also applied for the first investigatiof strongly deformed ceramic breeder and beryllebble beds[7,8]. The essential result obtained wlinear dependence of thermal conductivity on

train.The HWT is a standard technique for low cond

ivity materials but the accuracy for beryllium pebeds is questionable. Therefore, the HECOP exents, reported in the following, were performed;etails, see[9].

H3 and H4 are used to minimise radial heat losy controlling the heating power in such a way t

he temperature difference between two neighbouhermocouples becomes zero.

Heater H5 is used to minimise the axial heat flrom H2 to the press bottom plate, again controuch that the temperature difference of a thermocoair in H2 and H5 becomes zero. The highest bederatures are reached by additionally using the he6 and H7.The set-up is thermally insulated by refract

eramic fibre (Kerlane) and is operated in a gloveith a helium atmosphere of 0.1 MPa.Very detailed temperature calculations with

LUENT code were performed using a 3d modene quarter of the HECOP II facility[9]. These calulations showed that residual radial and axialosses are unavoidable. These heat losses depen

J. Reimann et al. / Fusion Engineering and Design 81 (2006) 449–454 451

Fig. 1. HECOP II set-up.

on mean pebble bed temperature and pebble bedconductivity.

As the test section weighs several kg, handling toolswere developed for movements of the test section andfilling procedures; for details, see[10]. The 1 mm NGKberyllium pebbles were poured into the cylindrical con-tainer and vibrated at 50 Hz in order to achieve densepackings, resulting in packing factors ofγ ≈ 63.5%.

After installing the pebble bed container in the press,the system was heated up at minimum piston pressureto the desired mean bed temperature. Because thermalconductivity values scatter considerably at very smallpressures, e.g. because of a non-homogeneous con-tact between pebble bed top and piston, conductivitymeasurements were only performed atp ≥ 0.3 MPa. Ingeneral, two bed temperature differences were applied:

�Tbed= 15 and 30◦C. Additionally, an isothermalexperiment at each pressure level was performed inorder to determine the heat lossQloss. The small�Tbedvalues required the careful calibration of the bed ther-mocouples during the isothermal experiments. Becauseof thermal creep, the measurements were generallytaken when creep rates had become negligible. Anexception was the experiment at the largest bed tem-perature of 650◦C.

3. Results

Fig. 2 presents the normalised thermal conductiv-ity k* = (k − k0SBZ)/k0SBZ as a function of bed strainε. k0SBZ is the conductivity value for non-deformed

452 J. Reimann et al. / Fusion Engineering and Design 81 (2006) 449–454

Fig. 2. Normalised thermal conductivityk* = f(ε,T).

pebble beds relevant forε = 0, calculated from theSchlunder Bauer Zehner (SBZ) model[11] with a con-tact area fractionρ2

k = 0 and an accommodation factorfor helium of≈0.22. This procedure, used first by[7]is well suited to demonstrate that: (i) thek0SBZ valuesappear to be reasonable values for the extrapolation tonon-deformed beds; and (ii) the conductivity increaseslinearly with strainε up to values of≈2%, expressedby:

k = k0SBZ(T )B(T )ε + k0SBZ(T ) (2)

For deformations larger than≈2%, the data becomesmaller than the values according to Eq.(2).

Without thermal creep, e.g. forT = 200◦C, the beddeformation at the maximum pressure of 3.6 MPabecomes≈0.8% which is in very good agreement withprevious results[7]. The larger values forT = 200◦Cwere obtained after first performing an experiment athigh temperature with thermal creep and then, keepingthe pressure constant, cooling down the test section to200◦C.

At T = 650◦C, thermal creep effects are veryexpressed.Fig. 3 shows the pressurep, the strainε,and the thermal conductivityk as a function of time.The pressure was imposed in several steps andk wascontinuously measured. Except for short time periodsafter the pressure increase, quasi-steady-state condi-tions existed. Heat losses were measured at distinctir el

Fig. 3. Transient experiment at 650◦C.

4. Correlations for the thermal conductivity ofdense beryllium pebble beds

Fitting the temperature dependencies of the exper-imentally determined slopes B(T) and the calculatedSBZ valuesk0SBZ(T) by

B = 5.18− 0.0035T (◦C) (3)

k0SBZ(W/mK) = 1.81+ 0.0012T (◦C) − 5

× 10−7T (◦C)2 (4)

the thermal conductivityk can be expressed as:

k (W/mK) = 1.81+ 0.0012T (◦C) − 5

× 10−7T (◦C)2 + (9.03− 1.386

× 10−3T (◦C) − 7.6 × 10−6T (◦C)2

+ 2.1 × 10−9T (◦C)3)ε(%) (5)

Fig. 4 shows the ratio ofk according to Eq.(5) tothe measured data: 83% of the values are within±10%,which is considered to be a satisfactory agreement.

ntervals and interpolated for the evaluation ofk. If theesults were included inFig. 2, the agreement with thinear curve is excellent.

Fig. 4. Ratio ofkcorr to kmeas.

J. Reimann et al. / Fusion Engineering and Design 81 (2006) 449–454 453

For fusion reactor blankets, pebble diameters differ-ent from 1 mm are also envisaged; furthermore, pack-ing factors in blanket relevant geometries are not wellknown yet. Therefore, some comments are made forthe use of these correlations for other parameter valuesthan presently investigated:

(a) Packing factorγ: it is known since long[12] thatthe maximum packing factor, achieved for bedsdensified by vibration, increases with the ratio ofcontainer diameterD to pebble diameterd andreaches a constant value forD/d > 100. The ulti-mate value depends on pebble shape, pebble sur-face and size distribution; for mono-sized spheresvalues of about 63% were reported[12]; differentpebble diameters and deviations from sphericitycan increase this value.

The reason for decreasing packing factors withdecreasing container dimensions is the increasinginfluence of container walls: the packing factorclose to walls is significantly smaller than thebulk value. Therefore, packing factors obtainedfor experimental set-ups might not always be rele-vant for the bulk-packing factor where the thermalconductivity is determined. Additionally, internalcomponents like thermo-couple rakes representalso local disturbances, which decrease the globalpacking factor.

(b) Pebble diameterd: for non-deformed pebble beds,the SBZ model predicts for 2 mm pebbles at

rm-r a

-

n-ofon-om

mp rdero ofc ro-cp

Fig. 5. Thermal conductivity correlation for large deformations.

is the conductivity of the solid material andεmax is(1− γ).

This type of relationship predicts unsatisfactory val-ues at small deformations. Therefore, a correlation ofthe type

y = a(x + x0)b − y0 (6)

is looked for, satisfying the following conditions:

• x = 0: k = k0SBZ and slope taken from Eq.(3)• x = 1: k = ks, and slope as in the correlation proposed

by [13].

For 650◦C withks = 94 (W/mK), the following rela-tionship is obtained:

k

ks

= 2.78

(ε

εmax+ 0.22

)0.24

− 1.92 (7)

presented inFig. 5. Using the data for other tempera-tures, corresponding relationships can be easily deter-mined.

5. Conclusions

New results are presented for the thermal conduc-tivity k of compressed beryllium pebble beds. Thepebble beds consisted of 1 mm NGK pebbles and arerepresentative for dense pebble beds (packing factorsγ ≈ 63.5%). Measurements were performed for meantp a andε

T = 500◦C a conductivity which is≈24% largethan that for 1 mm pebbles. With increasing copaction, this difference decreases rapidly: Focontact surface ratioρ2

k ≈ 0.007, which corresponds to a pebble bed compaction ofε ≈ 1%,the difference becomes 4%, for details, see[9].The valueε ≈ 1% might be characteristic for blakets at the begin of live. From this pointview, Eq. (5) is expected to predict also reasable values for pebble diameters different fr1 mm.

During blanket operation, swelling of berylliuebbles might result in bed deformations of the of 10%. Correlations applicable up to the stateomplete compaction are of interest in sintering pesses. A relationship of the typey = axb was pro-osed[13] with y = k/ks and x = (ε/εmax), where ks

emperaturesT between 200 and 650◦C, and maximumressures and pebble bed deformations of 3.6 MP≈ 3.5%, respectively.

454 J. Reimann et al. / Fusion Engineering and Design 81 (2006) 449–454

A correlation k = f(ε,T) was proposed, primarilybased on measurements but using the conductivity val-ues for non-deformed beds predicted by the SchlunderBauer Zehner model,

It was argued that this correlation might be applica-ble also for pebble diameters different from 1 mm andthat a packing factors of≈63.5% is generally represen-tative for the bulk of densified pebble beds.

Finally, a correlation was proposed which has areduced accuracy at low bed deformations but givesreasonable values up to the ultimate compaction to asolid body.

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