Unirradiated U0 2 Pellet
THERMAL DIFFUSIVITY MEASUREMENTS OF XA9847852 IRRADIATED UO 2 PELLETS
H. HAYASHI, M. KITAMURA
3. RESULTS AND DISCUSSIONS 1 Characterization Test
3.2 Thermal Diffusivity of Irradiated UO 2
The results are shown in Fig. 4 for UO2 samples irradiated up to 39.3 GWd/tU (1-3).
Solid line represents reported values for unirradiated UO2 [5, 6] and broken line is calculated 0.020
Eu
0.015
0.010
* 0. 005
E
0. 000
>
500 1000 1500 Temperature (K)
2000
FIG. 4. Thermal diffusivity for UO2 irradiated up to 39.3 GWd/tU.
0:1st Run, •: 2nd Run, A: 3rd Run, A: 4th Run, D: 5th Run
————: Unirradiated UOsfS.d], ————: SIMFUEL corresponding to 39.3 GWd/tU[8], -—•—: eq.(2), - —- :eq.(3).
values for simulated burnup fuel (SIMFUEL) [8]. According to reference [8], thermal diffusivity of SIMFUEL a^ was expressed by
a
where
'FP
"-FP
^FP / (Cp P)
A0 arctan(x) / x + CT3, [YodDcM2 + YFP D
(1)
Here, A.pp and X0 is thermal conductivity of SIMFUEL and pure UO2, respectively, Cp, heat capacity; p, density; T, temperature in K; yod, atomic fraction of gadolinium;
DGd coefficient; yFP, atomic fraction of simulated fission products; DFP, coefficient.
Thermal diffusivity decreased with increasing burnup. The first run data (o in Fig. 4:
below 750 K) for all samples were lower than the values calculated for SIMFUEL. Assuming that this deviation of thermal conductivity from SIMFUEL data was due to point defects induced by irradiation, k x yFP was substituted for ypp in eq.(l) to express the data as
a
where
FP+pd (2)
') Ix* + CT\
+ k X yFP DFP2]1/2A01/2.
Here, app+pd and kfp+pi is thermal diffusivity and thermal conductivity taking account of the effects of impurities and point defects induced by irradiation, respectively.
The calculated value was shown as a chain line in this figure at k = 5 and this agreed well with the data at the first run. This agreement was confirmed for the other samples (1-1, I- 2 and 1-4). The second run data (•) for samples experiencing below 750 K agreed well with the first run data, showing that thermal diffusivity recovery did not occur below 750 K.
Above 750K, thermal diffusivity deviated from the line by eq.(2) shown as a chain line. After experiments above 750 K, thermal diffusivity (A) recovered and had the same values as the SIMFUEL values after excursion above 1400 K (D). While thermal diffusivity decrease slightly by excursion above 1700 K.
According to Nogita and Une [3], point defects began to recover above 750 K, were almost recovered completely above 1100 K, and above 1400 K micro-bubbles grew to 8 to 10 nm. In this temperature range, no obvious swelling was observed. Above 1700 K, bubbles coarsened rapidly with swelling. This radiation damage recovery coincided with the thermal diffusivity recovery. Based on the results of Nogita and Une, Amaya and Hirai [26] proposed the thermal conductivity expression for irradiated UO2 by using Klemens' theory and the assumption that thermal conductivity (or thermal diffusivity) was degraded by
(1) fission product dissolved in the UO2 matrix,
(2) point defects induced by irradiation, which recover completely above 1 100 K, and (3) micro-bubbles, which grow above 1400 K.
According to them, thermal diffusivity for irradiated UO2 , am3d could be expressed by (3)
Here, A^ is thermal conductivity of irradiated UO2; E is burnup; A and tr are coefficient; a0 is thermal diffusivity of pure UO2 ; u, the group velocity of phonons in UO2; L, the mean free path of phonons in UO2. By using eq.(3), thermal diffusivity of irradiated UO2 was calculated and plotted as the dotted line in Fig. 4. The calculated value agrees with the obtained data successfully below 1700 K. Above 1700 K, data were slightly lower than the expected values.
This decrease in thermal diffusivity can be explained by the porosity change during experiments.
The thermal conductivities were derived from measured thermal diffusivities and were plotted in Fig. 5 for 1-3 sample with the values reported by several authors [9, 10, 18, 19].
Ross [9] and Daniel et al. [10] evaluated thermal conductivity by heat flow method and reported thermal conductivity hysteresis during the experiment. Recently, Nakamura et al.
[19] measured thermal conductivity by the laser flash method and found similar behavior.
Daniel and Cohen [18] evaluated the 'effective1 thermal conductivity under irradiation by measuring fuel center temperature. They reported no thermal conductivity hysteresis, but they had data scattered within the hatched region in Fig. 5. The present results were within these reported values. In particular, the tendency for thermal conductivity recovery agreed well with data of Nakamura et al. From the results, it was confirmed that thermal conductivity of UO2
irradiated in a commercial reactor was consistent with the previous data measured for samples irradiated in a test reactor.
Thermal diffusivity is shown in Fig. 6 for the R-l sample after being power ramped up to 512 W/cm. Thermal diffusivity in Fig. 6 was higher than the values expected by eq.(3) and does not show obvious hysteresis, contrary to the results for base irradiated samples.
10
r 6
>.*-»
(J
•g 4 2
Ou
<0
J=
FIG. 5.
500 1000 1500 Temperature (K)
2000
Thermal conductivity for UO2 irradiated up to 39.3 GWd/tU.
O: 1st and 2nd Run, A: 3rd Run, D: 4th and 5th Run
———— : Unirradiated UO2[5,6], - - - - : SIMFUEL corresponding to 39.3 GWd/tU [8], — w — : Ross [9], ———— : Daniel et al. [10]
- - - • - : Nakamura et al. [19], ^^^^ : Daniel & Cohen [17].
0.020
§ 0 . 0 1 5
0.010
0. 005
0.000
\D
500 1000 1500 Temperature (K)
2000
FIG. 6. Thermal diffusivity for UO2 ramped to 512 W/cm for 4 hours after base irradiation up to 43.1 GWd/tU.
0:1st Run, •: 2nd Run, A: 3rd Run, A: 4th Run, D: 5th Run
————: Unirradiated UO^S.e], -•-•-: SIMFUEL corresponding to 43.1 GWd/tU [8], - - — : eq. (3).
Thermal diffusivity estimated for base irradiated sample experiencing a temperature above 1100 K was quite similar to that for the power ramped sample. The latter was prepared from a position with a relative radius (R / R0) of 0.6 to 0.9 and was estimated to experience a temperature up to 1300 K. The base irradiated samples 1-1 to 1-4 were estimated to have experienced temperatures below 1100 K. Nogita and Une [3] reported that the lattice dilation mainly due to fission induced point defects was recovered completely by annealing at about 1150 K and also that the lattice parameters of power ramped samples in this region were smaller than those of base irradiated samples because of higher irradiation temperature during the ramp test. Therefore, radiation damage recovery during the power ramp test was considered to cause higher thermal diffusivity than obtained for the samples as base irradiated.
In other words, thermal diffusivity degradation was suggested to be due to solution of fission products into the matrix and accumulation of radiation damage during irradiation and not after it.
4. CONCLUSIONS
Thermal diffusivity was measured by a laser flash method for micro samples prepared from UO2 pellets irradiated in a commercial reactor. Thermal diffusivity decreased with increasing burnup at lower temperature, which began to recover above 750 K, and recovered completely above 1400 K, becoming quite similar to the value for SIMFUEL. The recovery stage of thermal diffusivity corresponded with that of the radiation damage. Good predictions were made by using the thermal conductivity expression considering the radiation damage effect by Amaya and Hirai. Obtained thermal conductivity was consistent with reported values for samples irradiated in test reactors. The power ramped sample showed higher thermal diffusivity than base irradiated sample and the former had no obvious thermal diffusivity hysteresis. From these results, thermal diffusivity degradation was suggested to be caused mainly by solution of fission products and accumulation of radiation damage during irradiation and not after it.
ACKNOWLEDGEMENTS
This study was sponsored by the Ministry of International Trade and Industry (MITI).
The authors wish to acknowledge the aid of the many persons who co-operated in this study.
They would particularly like to thank Dr. Katsumi Une and Mr. Kazuhiro Nogita for many valuable suggestions and helpful discussions.
REFERENCES
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DISCUSSION
(Questions are given in italics)
For clarification, you mentioned HOOK as base irradiation temperature. Is this temperature calculated at the micro-sample location? Does it take into account modifications of diametrical gap and thermal conductivity during base irradiation? What is the best estimation of the temperature evolution of this 11OOK average temperature with burnup?
That temperature is the right specimen temperature.
For modeling purpose it is necessary to have the lowest curve with the maximum degradation.
But this is depending upon the fuel power history. The condition is to have a low power irradiation in order to accumulate the maximum of damage and gases in the matrix.
The average irradiation power is bout 250W/cm. I agree with you that the effect depends on power history.
THE EFFECTS OF IRRADIATION ON THE THERMAL XA9847853