thermal conductivity of compressed ceramic breeder pebble beds

Thermal conductivity of compressed ceramic breederpebble beds

J. Reimann �, S. Hermsmeyer

Forschungszentrum Karlsruhe, Postfach 3640, D-76021 Karlsruhe, Germany

Abstract

The effective thermal conductivity of pebble beds is an important parameter for the thermomechanical design of solid

breeder blankets operating at temperatures of up to 900 8C in breeder pebble beds and up to 700 8C in beryllium

pebble beds. Compressive stresses and creep might cause significant pebble deformations. The knowledge of the thermal

conductivity as a function of bed deformation, therefore, is of prime importance. For strongly deformed pebble beds,

only results for beryllium pebbles existed where the conductivity increased by a factor of about 5 for bed deformations

of about 1%. For ceramic breeder beds, the increase of the bed conductivity with increasing bed deformation is expected

to be much smaller. Quantitative results were missing. This paper presents results on the thermal conductivity of lithium

orthosilicate and different types of lithium metatitanate pebble beds (monsized and binary beds) for bed deformations

up to 4.5% and temperatures up to 800 8C using the pulsed hot wire technique. Most of the measurements at high

temperatures were performed in air; at ambient temperature, helium and argon were also used. A distinct increase of the

thermal conductivity with bed deformation was found: however, this effect is quite small compared to deformed

beryllium beds and might be neglected at high temperatures. The results for zero bed deformation agree well with

correlations from literature.

# 2002 Elsevier Science B.V. All rights reserved.

Keywords: Ceramic breeder material; Pebble beds; Thermal conductivity

1. Introduction

For the thermomechanical design of ceramic

breeder blankets the effective thermal conductivity

of pebble beds is an important design parameter.

Maximum temperatures in the breeder and the

beryllium pebble beds of power reactor blankets,

compare [1], are about 900 and 700 8C, respec-

tively. Large temperature differences between

pebble beds and the structural material, different

thermal expansion coefficients and irradiation

effects, give rise to compressive stresses in these

beds which might result in significant pebble

deformations. For the blanket design, therefore,

the dependence of the thermal conductivity on bed

deformation must be known.

An extensive data basis exists for the mechanical

behaviour of ceramic pebble beds (stress-strain

dependence, thermal creep) obtained by uniaxial

� Corresponding author. Tel.: �/49-7247-823498; fax: �/49-

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E-mail address: [email protected] (J. Reimann).

Fusion Engineering and Design 61�/62 (2002) 345�/351

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compression tests (UCTs), see e.g. [2,3]. Measure-ments of the thermal conductivity of ceramic

breeder pebble beds concentrated on uncom-

pressed pebble beds [4�/6]; only one investigation

was performed [7] where the bed was compressed

at ambient temperature up to a pressure of 1.4

MPa, however, without recording bed strains. Up

to now, heat conductivity measurements at differ-

ent temperatures combined with measurements ofbed pressure and strain were only performed with

beryllium pebble beds [8] using the hot wire

technique. Compared to uncompressed beds, the

conductivity increased by a factor of about 5 for

bed deformations of about 1%. A linear relation

between conductivity and bed strain was observed.

For ceramic breeder pebble beds, the conductiv-

ity increase with increasing pressure is expected tobe much smaller compared to beryllium pebble

beds because of the smaller conductivity ratio of

pebble material to gas atmosphere. In the experi-

ments [6], the change of conductivity with pressure

was negligible. However, no significant elastic and

plastic pebble deformations were expected to occur

which is different at high temperatures where large

strains due to thermal creep can be observed [2,3].Therefore, the present investigations were per-

formed both at ambient temperature and at

elevated temperatures (750 and 800 8C); the max-

imum pressure was 6.5 MPa.

2. Experimental set-up

In the present experiments the pulsed hot wire

method (HWM) was combined with an UCT. In

UCTs, pebble beds, filled in cylindrical containers,

are compressed in the axial direction and both the

axial pressure (identical to the uniaxial stress) and

the axial strain o (defined as ratio of axial

displacement to bed height H) are measured.

Fig. 1 shows the set-up already used in previousexperiments [2,3].

The pulsed HWM is a standard technique for

thermal conductivity measurement of poorly con-

ducting materials. In respect to ceramic breeder

blankets, the HWM has been extensively used by

Enoeda et al. [4,5].

The HWM is based on the use of a long, thin

wire embedded in the material to be investigated.

At the time t�/0, the electric power is switched on

and the measured temperature differences at two

times t2 and t1 are used to determine the con-

ductivity k by

k�q=(4p) ln(t2=t1)=(DT2�DT1) (1)

where q is the electrical power per unit length, q�/

Q /L , where L is the heated wire length. For dataevaluation it is convenient to plot the temperature

difference DT�/T (t )�/T (t�/0) versus the loga-

rithm of the time t . Then, Eq. (1) results in a

straight curve with the slope (DT2�/DT1)/ln(t2/t1).

Eq. (1) is valid for an infinitely long thin wire

with no thermal inertia and with no heat resistance

between wire and surrounding material. However,

Eq. (1) is also the asymptotic solution if thermalinertia of the wire and heat resistance wire/bed are

considered.

Fig. 2 (from [8]) shows characteristic HW

temperature signals for two types of pebble beds:

. an aluminium pebble bed characterised by a

large thermal conductivity of the pebbles and

significant plastic pebble deformations during

compression, and,

Fig. 1. Experimental set-up.

J. Reimann, S. Hermsmeyer / Fusion Engineering and Design 61�/62 (2002) 345�/351346

. an orthosilicate pebble bed, characterised by a

small pebble conductivity and negligible plastic

pebble deformations.

After switching on the electrical power in the

wire, the thermal response is dominated by the

heat resistance between heater and pebble bed.

Then, the heat conductivity of the surrounding

material becomes dominating and a fairly straight

curve in the half-logarithmic plot develops after

about 20 s for the Al pebble bed and after less than

10 s for the orthosilicate pebble beds. For a larger

conductivities (Al beds at 0.4 MPa), the slope of

the curve becomes quite flat and with this the

accuracy of the conductivity evaluation decreases.

In the experiments the hot wire consisted of an

indirectly heated element with 1-mm outer dia-

meter (diameter of the inner electrically heated

wire di�/0.3 mm, MgO insulator thickness of si�/

0.3 mm, thickness of outer stainless steel tube sS�/

0.1 mm, heated length within the pebble bed: 90

mm). This heater penetrated the cylindrical con-

tainer (diameter 60 mm, height 60 mm) horizon-

tally at a height of 30 mm, see Fig. 1. Two

thermocouples with a diameter of 0.25 mm, being

10 mm apart, were brazed on the heater surface.

The experiments at ambient and elevated tem-

peratures (750 and 800 8C) were performed in air

atmosphere at atmospheric pressure. In order to

vary the gas atmosphere, additional experimentswere performed at ambient temperature using a

helium or argon purged plastic hood.

There is one additional experiment with an

orthosilicate pebble bed in helium at 480 8C.

This experiment was performed in a similar test

facility positioned in a glove-box, used for ber-

yllium experiments [8].

The experiments were performed with orthosili-cate pebbles (Osi), developed by FZK and four

types of metatitanate pebbles (Ti�/D ect.), pro-

vided by CEA and JAERI; characteristic data are

given in Table 1, for details, see [3,9]. Pebble beds

with the first four types of pebbles are denomi-

nated as monosized pebble beds, although there is

a certain diameter variation; the type Ti�/J�/bin is a

binary pebble bed where after filling the largepebbles into the cavity, the small pebbles are

poured in.

3. Results

3.1. Parameter sensitivity analyses using SBZ-

Model

The Schlunder�/Bauer�/Zehner-Model (SBZ-

Model) [10] has been frequently used to predict

the thermal conductivity, k , of pebble beds. This

model takes into account the influences of para-

meters such as thermal conductivities of the pebble

material, kp, and gas, kg, pebble diameter d , bed

porosity, l, and normalised contact area between

pebbles, rk2 �/(dc/d )2, where dc is the diameter of

the contact area. In practice, the value of rk2 is not

known and is used to fit the model to experimental

data.

Fig. 3 contains the thermal conductivity of the

orthosilicate and metatitanate material and he-

lium, air and argon as a function of temperature.

For a temperature increase from 25 to 800 8C, the

conductivities k of the pebble materials decreasefrom about 4 to 2 (for beryllium the values vary

between 160 and 80 W/mK!) whereas the helium

conductivity increases from 0.154 to 0.4.

The influence of the pebble deformation rk2 as a

function of temperature is shown in Fig. 4. For

zero deformation, rk2 �/0, k increases moderately

Fig. 2. Measured temperature response for Li4SiO4 and Al

pebble beds.

J. Reimann, S. Hermsmeyer / Fusion Engineering and Design 61�/62 (2002) 345�/351 347

with temperature T due to the increasing gas

conductivity. For a deformation of rk2 �/0.02, the

bed conductivity has increased; however, the

temperature effect is negligible due to the compet-

ing influence of the pebble material conductivity,

decreasing with temperature.

3.2. Pebble bed results

Fig. 5 shows measurements of the stress-strain

dependence (characteristic for UCTs) and the

values of the bed conductivities for metatitanate

(Ti�/D) at two temperatures. At ambient tempera-

ture the conductivity increases during stress in-

crease only by about 10%. In the experiment at800 8C, the pressure was kept constant after

having reached the maximum value of 6.4 MPa

and strain increased up to a value of about 4.5%

because of thermal creep. During the pressure

increase period the conductivity again increased

only moderately and a significant increase is also

not observed during the creep phase where strain is

supposed to be caused primarily by plastic defor-mation (during the pressure increase period strains

are partially caused by pebble relocation).

Fig. 6 summarises the results for orthosilicate

pebble beds for the pressure increase period:

similar to beryllium pebble beds [8], a linear

increase of conductivity with strain is observed,

however, this increase is quite small. Table 2

contains the coefficients of these relationships.For non-deformed pebble beds, the SBZ-model

with rk2 �/0 agrees fairly well with the experimental

results in air and helium at ambient temperature

but underestimates the conductivities at higher

temperatures. The measurement in helium at

485 8C agrees well with the prediction from Dalle

Table 1

Characteristic data of investigated granular materials

Type Association Pebble diameter d

(mm)

Density ratio d(%)

Grain size gs

(mm)

Sinter temperature Tsinter

(8C)

Packing factor g(%)

Osi FZK 0.25�/0.6 98 50 64

Ti�/D CEA 0.8�/1.2 90 1�/2 1050 63

Ti�/E CEA 0.8�/1.2 86 1�/5 1100 63.2

Ti�/J JAERI :/2 84 1�/3 1200 64.3

Ti�/J-

bin

JAERI 0.2�/2 84 1�/3 1200 81.2

Fig. 3. Thermal conductivity of ceramic breeder materials and

helium and air.

Fig. 4. Influence of temperature and contact area ratio on

pebble bed conductivity.


Donne et al. [6], established for helium at elevated

temperatures.

Fig. 7 presents the corresponding results for

metatitanate pebble beds: for small gas conductiv-

ities (air or argon atmosphere at ambient tempera-

ture) the increase of conductivity with strain is

more expressed than for orthosilicate pebble beds.

This might be caused by the larger surface rough-

ness and smaller sphericity of the titanate pebbles

compared to the orthosilicate pebbles [9]. During

stress increase, the surface roughness might be

decreased and the pebbles might relocate in such a

way that contact zones increase. However, these

influences become smaller with increasing gas

conductivity. Table 2 shows that for non-deformed

pebble beds the agreement between measurements

and SBZ-model is again quite good for air at

ambient temperature while the SBZ-model pre-

dicts too low values in the other cases. Enoeda et

al. [5] fitted the SBZ-model with a value of rk2 �/

0.0049 to their measurements for non-deformed

monodisperse metatitanate pebble beds in helium

at elevated temperatures. With this value, the

agreement is also quite good for the present

experiment in helium atmosphere, but the agree-

ment becomes worse for the experiments in air at

low temperatures. Comparing the results for

orthosilicate and monodisperse metatitanate peb-

ble beds it is seen that at high air temperatures the

metatitanate conductivity is higher by about 20%;

the increase of conductivity with strain is about

20% in both cases for a strain of 4.5%.

Fig. 7 contains also results for binary metatita-

nate pebble beds in air atmosphere at ambient

temperature. Compared to the monodisperse bed

the conductivity is higher by a factor of approxi-

mately 2 for non-deformed beds. For blanket

relevant conditions, however, this difference be-

comes significantly smaller. According to the SBZ-

model this factor reduces to approximately 1.3 for

T�/600 8C and a helium atmosphere. A factor of

:/1.3 was also observed in [5] for the difference

between binary and monosized Al2O3 pebble beds

in helium at 600 8C.

Fig. 5. Stress�/strain dependence and measured conductivities

for orthosilicate pebble beds in air at T�/25 8C and at

800 8C.

Fig. 6. Thermal conductivity k�/f (o) for Li4SiO4 pebble beds.


A part of the experiments at 750 and 800 8Cwere performed in such a way that after the

termination of the creep period the pebble bed

was stepwise cooled-down under load, therefore,

keeping the maximum strain constant. Fig. 8

shows the corresponding results: The measurement

at the highest temperature was used to adjust the

SBZ-model by using for rk2 a value of approxi-

mately 0.02. For metatitanate pebble beds, the

conductivity stays fairly constant during tempera-

ture decrease; the SBZ-model predicts the same

tendency. For the orthosilicate pebble bed the

measurements are lower; one reason could be that

pebble contacts get lost during cooling-down due

to the much higher thermal expansion coefficient

of orthosilicate compared to metatitanate.

4. Conclusions

Measurements of the thermal conductivity of

considerably deformed ceramic breeder pebble

Table 2

Correlations for thermal conductivity of deformed ceramic breeder pebble beds

Granular material Gas T (8C) k (W/mK)�/a�/bo(%) kSBZ rk2 �/0 k

a b

Orthosilicate Helium 485 1.02 0.045 0.84 1.0a

Helium 25 0.72 0.045 0.74 0.78a

Air 25 0.24 0.038 0.27

Air 750 0.59 0.036 0.45

Air 800 0.56 0.025 0.46

Ti�/D Air 800 0.64 0.034 0.49 0.59b

Ti�/D Air 25 0.25 0.14 0.25 0.36b

Ti�/D Helium 25 0.98 0.046 0.86 1.00b

Ti�/J Air 25 0.28 0.13 0.26 0.37b

Ti�/J-bin Air 25 0.58 0.18 0.54 0.61b

a With: k (W/mK)�/0.768�/4.96�/10�4 T (8C)[6]b SBZ with rk

2 �/0.0049 [5].

Fig. 7. Thermal conductivity k�/f (o) for Li2TiO3 pebble beds.

Fig. 8. Thermal conductivity k�/f (T ) for constant large strains

(SBZ fitted at Tmax).


beds were performed at pressures up to 6 MPa andtemperatures up to 800 8C. At the maximum

temperature the thermal conductivity increases

only by about 20% for an air atmosphere; for a

helium atmosphere this value is expected to be

even smaller. With decreasing temperatures, this

effect is somewhat more expressed. Correlations

are given for the thermal conductivity as a func-

tion of strain and temperature.For non-deformed pebble beds in helium at

elevated temperatures, the correlation of Dalle

Donne et al [5] for orthosilicate beds is confirmed,

for metatitanate pebble beds the SBZ-model with

the value for rk2 as used by Enoeda et al. [5] is

recommended.

References

[1] S. Hermsmeyer, U. Fischer, K. Schleisiek, Improved

helium cooled pebble bed blanket, 21st Symposium on

Fusion Technology, Madrid, Spain, September 11�/15,

2000.

[2] J. Reimann, G. Worner, Thermal Creep of Li4SiO4 Pebble

Beds, 21st Symposium on Fusion Technology, Madrid,

Spain, September 11�/15, 2000.

[3] J. Reimann, G. Worner; Thermal creep of ceramic breeder

pebble beds, CBBI-9, Toki, Japan, September 27�/29,

2000.

[4] M. Enoeda, K.H. Furuya, S. Takatsu, T. Kikuchi,

Hatano, Effective thermal conductivity measurements of

the binary pebble beds by hot wire method for the breeding

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IEA collaboration program, CBBI-8, Colorado Springs,

CA, Oct. 6�/8, 1999.

[6] Dalle Donne et al., Measurements of the effective thermal

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[8] J. Reimann, S. Hermsmeyer, G. Piazza, G. Worner,

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thermal conductivity of compressed ceramic breeder pebble beds

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