The effect of cracking on the geometric surface

As mentioned in Section 5.2, the effect of cracking on the geometrical surface to volume ratio (SG) can be accounted for by the expected radial cracking pattern using equation 5. In Figure 6, the roughness factors have been calculated using the White et. al. diffusion coefficients both with and without the cracking correction of equation 5. The data shown are here running averages over 20 consecutive rating values for all 3 types of fuel taken together. Without correction the roughness factors vary by a factor of approximately 1.7 over the range of rating and this systematic is removed by the correction for radial cracking.

1 1.5 2 2.5 3 3.5 4 4.5

0 2 4 6 8 10 12 14 16 18 20

Rating (W/gU)

Roughness Factor

Crack Correction No Crack Correction

FIG. 6. Roughness Factors Calculated with and without Allowance for Fuel Cracking.

6. DISCUSSION

It is evident from the above analysis that with a suitable fuel densification model both the Belle algorithm and the Aronson data predict similar levels of roughness and therefore will predict adequately the overall levels of fission gas release. As the Belle form is more porosity sensitive the details of the densification model are more important for predictions in this case.

The temperature sensitivity of predicted roughness factor, noted above, is related to the densification model. If the White et. al. diffusion coefficients are used then the fission gas data shows roughness to be remarkably insensitive to temperature, indicating that the Aronson roughness is the more appropriate for the calculation of stable gas release.

Although the above prescription provides a suitable method for calculation pre-interlinkage gas release with some accuracy, there still remains one problem. If the Aronson data was used in estimating surface to volume ratios for the unstable release data used by White et. al., the diffusion coefficient so determined would be markedly changed, removing the agreement achieved above. For a resolution of this problem one must turn to an effect reported by White^[12]. He notes that if the unstable fission gas release data is analysed in detail, then the

release rate does not follow exactly the expected l^-½ relationship and attributes this to a change in the effective roughness of the surface with the lifetime of the species. He suggests for short-lived species the surface behaves in a fractal manner. Species with the shortest “range” (i.e.

have the shortest lifetime and are from the coolest parts of the fuel) are released from closest to the surface and therefore are more affected by the roughness of the surface. They thus exhibit the largest surface to volume ratio. It is not clear how such an approach could be extrapolated to stable isotopes but the magnitude and direction of this effect is consistent with the discrepancy found here.

The BET method measures surface areas on the molecular level and therefore on the basis of fractal theory should be most consistent with the release for shortest-lived fission products, exhibiting the greatest degree of roughness. For the release of stable isotopes, the surface will effectively appear much smoother and exhibit a lower roughness factor.

Aronson’s as-sintered data are, of course, BET measurements but made on what effectively is a smooth surfaced material. Cracked pellets must, to some extent, have a rough finish but this will not be evident in the gas release because of the smoothing effect mentioned above. Overall therefore, the agreement with Aronson’s as-sintered data may be somewhat fortuitous. But the change in roughness factor arises from a recognised physical phenomenon.

The differences between the Aronson data sets does raise questions as to the correct value to be attached to the free surface when interpreting unstable release experiments and thus calls into question the absolute accuracy of the diffusion coefficients currently being recommended.

7. CONCLUSIONS

1. Analysis of the Windscale fission gas release database of some 503 CAGR pins primarily from the Hunterston and Hinkley Point reactors has led to the development of a parametric equation describing the pre-interlinkage ("athermal") release. The equation is suitable for standard fuel pins with grain sizes in the nominal range 6 µm to 12 µm and with weak 20/25/Nb cladding. The data are well predicted with a random error of times/divide 1.2 (1s).

2. Detailed analysis of the data shows that the observed releases are consistent with current theoretical mechanisms with migration of fission gas to free surfaces being primarily controlled by vacancy migration.

3. The diffusion coefficients derived from analysis of unstable fission gas release in the Halden Reactor provide a good description of the observed release. The equations, in terms of the fuel temperature(T) and rating(R) are:-

D2 = 1.49 × 10^-17R^½exp(-10600/T) m²/s D3 = 7.67 × 10^-22R exp(-2785/T) m²/s

4. The free surface depends on the fuel cracking behaviour, which increases the free surface area, and on the degree of surface porosity, which enhances the overall roughness of the surface.

5. A simple algorithm based on the development of radial fuel cracks adequately describes the observed effects of cracking on release.

6. The BET data of Aronson on as-sintered fuel best describes the roughness effects.

Analysis of these data yields a porosity (p) dependent roughness factor given by the equation:-

-7. Differences between Aronson’s measurements on different fuel surface types gives some uncertainty on the absolute accuracy of current diffusion coefficient recommendations

ACKNOWLEDGEMENTS

The author acknowledges Scottish Nuclear Limited and the Health and Safety Executive for their support in the performance of this work.

REFERENCES

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[8] UKAEA Internal Document. 1981.

[9] BEATHAM N, HUGHES H, ELLIS W E AND SHAW T L. “Modelling of pellet-cladding interaction in thermal reactor fuel pins using the SLEUTH computer code.”

Nucl. Energy, 29, No. 2, 115-122. April 1990.

[10] BAKER C. Journal of Nucl. Mater. 66 , 283, 1977

[11] WHITE R J, TEMPEST P A and WOOD P. “An evaluation of diffusion coefficient data obtained from the start-up ramp of IFA 563 and comparison with data from the gas flow rigs IFA 504 and IFA 558.” Paper presented at the Enlarged Halden Programme Group Meeting, Storefjell Hotel, Gol, 7-12 March 1993.

[12] WHITE R J. The fractal nature of the surface of uranium dioxide: A resolution of the short-lived/stable gas release dichotomy. Paper presented at the Enlarged Halden Programme Group Meeting, Lillehammer, Norway, 15-20 March 1998.

CLAD MODELLING