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|
[email protected]. × |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.