Thermal expansion of a compressed Li2TiO3 pebble bed

CBBI-14 6 September 2006Petten, The Netherlands

H. Tanigawa, T. Hatano, M. Enoeda and M. Akiba

Blanket Technology Group, JAEA

Thermo-Mechanical properties of a pebble bed

Neutron flux

Tritium breeder

NeutronMultiplier

Temperature distributionThermal expansion

Deformation, Stress

Thermal conductivity

Packing state

Interaction

Purpose of the study

Difference in thermal expansion between pebble bed and structural materials

Thermal stress and deformation

Thermal expansion of a Li2TiO3 pebble bed is investigated.

There is few data of thermal expansionfor packed pebble beds

Series of studies for thermo-mechanical analysis of blanket module

Finite element calculation code (ABAQUS)

Stress-Strain property

Thermal conductivity

Effective thermo-mechanical properties

Thermal expansion

reported inCBBI11, 12

Empirical continuum modelfor the pebble bed

reported in CBBI13, 14

Test apparatusINSTRON

IRfurnace

quartz tube

aluminacontainerpebble

bed

coolant

upperload rod

lowerload rod

actuator

load cellThermal expansion measured at the actuator includes that of load rods and the alumina container.

Thermal expansion of system is calibrated

3.93×10-3 (mmK-1) × T (K)

estimated expansion of system

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

200 400 600 800 1000Temperature / K

Ther

mal

exp

ansi

on /

mm

whole system

load rods and containor

copper column

measured expansion

calculated expansion

pebblebed

Cu column

45.0, h: 50.4mm: 60.0, h: 60.0mm

75.0, h60mm

Experimental conditions

R.T. ~ 973KTemperature

Atmosphere He; 1atmpurge rate; 30ccm

Sample Li2TiO3 pebble; 2mm81.1% of T.D.

Initial packing factor 65.0 ~ 68.0% (hand tapping)

Dimensions of packed bed 75mm, h60mm; 265.1cm3

0.44kN - 0.1MPaLoad on the bedduring heating (friction of O-rings; about 0.03kN)

Definition of words in the present studyStress

loadcross section of bed

Packing factor (P.F.)

Vall

defined at R.T.

Vpebble (Mpebble/density)

Average coefficient ofthermal expansion (CTE)

|dL|

L@R.T. × |973-R.T.|

dL

L

0.1MPa

@R.T.P.F.= a

dL

@973K

dL’

@R.T.P.F.= a’

L L’

inheating

incooling

Thermal expansion of Li2TiO3 pebble bed

compaction

thermal expansionin

heating cooling

heating cooling

heat treatment

heat treatments

initial packing state

<

~

Bed is thermally treated in 3times.

compaction

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

200 400 600 800 1000 1200Temperature of pebble bed / K

Hei

ght o

f peb

ble

bed

/ mm

1st heating1st cooling2nd heating2nd cooling3rd heating3rd cooling

Relationship between CTE and P.F.

1.25E-05

1.30E-05

1.35E-05

1.40E-05

1.45E-05

65.0 65.5 66.0 66.5 67.0

1st heating1st cooling2nd heating2nd cooling3rd heating3rd cooling

Ave

rage

ther

mal

exp

ansi

on c

oeff

icie

nt /

K-1

Packing factor / %

After a few heat treatments, the expansion coefficients in both heating and cooling processes have close values, and an increase of the packing factor becomes small.

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

200 400 600 800 1000Temperature of pebble bed / K

Hei

ght o

f peb

ble

bed

/ mm

1st heating1st coolingcompression2nd heating2nd cooling

Thermal expansion of pre-loaded bed

compactionheat treatment

heat treatments

initial packing state

loading up to 10MPa 5times,loading at 0.1MPa

thermal expansionin

heating cooling>

relaxation

Relaxation of residual deformation

relaxationcompression

for 4 beds with different P.F.relaxation ratio:

0.33 ~ 0.79

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

200 400 600 800 1000Temperature of pebble bed / K

1st heating1st coolingcompression2nd heating2nd cooling

The compressive deformation of the pebble bed and its relaxation are affected by the friction among a large number of pebbles. This effect is considered to work statistically.

ratchet-like deformation

heating

relaxation

excessstress

competitiveprocess

Correlation between CTE and P.F. (reported in CBBI-13)

1.0E-05

1.1E-05

1.2E-05

1.3E-05

1.4E-05

1.5E-05

1.6E-05

1.7E-05

1.8E-05

66.8 67.0 67.2 67.4 67.6 67.8 68.0

heating

cooling

Packing factor / %

Ave

rage

ther

mal

exp

ansi

on c

oeffi

cien

t / K

-1

equilibriumP.F.

higherP.F.

lower P.F.

heattreatment

heattreatment

thermalexpansion

small

constant

CTE ∝ P.F.

large

1.0E-05

1.2E-05

1.4E-05

1.6E-05

1.8E-05

65.0 66.0 67.0 68.0 69.0

heatingcooling

In larger region of P.F., CTEs are constantA

vera

ge th

erm

al e

xpan

sion

coe

ffic

ient

/ K

-1

Packing factor / %

in each seriesfor fresh packing

CTE ∝ P.F.

for all data withdifferent P.F. andloading histories

CTE ~ const.1.4±0.2×10-5K-1

1.0E-05

1.2E-05

1.4E-05

1.6E-05

1.8E-05

2.0E-05

65.0 66.0 67.0 68.0 69.0

Thermal expansion is explained by considering progress of compaction and its relaxation

Ave

rage

ther

mal

exp

ansi

on c

oeffi

cien

t / K

-1

Packing factor / %

1st heating: small

1st cooling: large

1st heating for loaded bed: large

others:

progress of compaction

progress of compaction

relaxation of residual deformation

All data are classified into four

about 1.4×10-5 K-1

Summary

For the beds with different packing factors and loading histories, average thermal expansion coefficients are 1.4±0.2×10-5K-1.

A residual deformation in the bed caused by a previous loading can be annealed when the bed is heated without the load.

The thermal expansion behaviour of pebble beds is explained by taking into account progress of compaction and its relaxation.

Thermal expansion behaviour of Li2TiO3 pebble bed has been studied. In the temperature range from R.T. to 973K, thermal expansion of the pebble beds is measured under compressive load of 0.1MPa.