Core Physics of Pebble Bed High Temperature Nuclear Reactors

To more accurately predict the temperature distribution inside the reactor core of pebble bed type high temperature reactors, in this thesis we investigated the stochastic properties of randomly stacked beds and the effects of the non-homogeneity of these beds on the neutronics and thermal-hydraulics in the core of pebble bed reactors. To investigate the stacking properties of randomly stacked beds, we measured the average packing fraction and the radial and axial packing fraction profiles of a bed containing 5400 pebbles. In a second experiment, three-dimensional X-ray tomography was used to determined the pebble locations of a bed containing 8900 pebbles. Results were used to validate a computational method to generate pebble bed stackings based on the removal of overlaps. Different stacking properties were found near the wall than in the bulk of the bed, indicating the stacking is anisotropic here, forming ordered layers parallel to the wall with hexagonal-like stacking properties. This results in strong fluctuations in the radial packing fraction close to the wall, and a significantly higher porosity next to the wall than in the rest of the bed, rising to unity at the wall. As a result, the average porosity of randomly stacked beds depends on their volume to surface ratio, with larger beds having a lower average void fraction than smaller bed. We also found strong variations in the local porosity throughout the pebble bed, resulting in small clusters of densely packed pebbles. To investigated the effect of the non-homogeneity of pebble bed on neutron transport, we compared $k_{eff}$ calculations for a model with uniform porosity, a zones model including density fluctuations, and an exact model with all pebbles modelled individually. Calculations were performed for an infinite cylinder and for a model of the PROTEUS facility. For the infinite cylinder we found a 71 pcm higher $k_{eff}$ for the zones model than for the uniform porosity model, showing the effect of density fluctuations at the wall to be very small. However, the same comparison for PROTEUS showed an increase of 649 pcm due to the low packing fraction near the top of the pebble bed, resulting in a much lower average packing fraction in the uniform porosity model. The effect of neutron streaming through the void space in between the pebbles was calculated by comparing the zones model with the exact model, and was found to decrease $k_{eff}$ by 606 pcm for the infinite cylinder, and by 1240 pcm for PROTEUS, showing neutron streaming is an important effect in small pebble bed reactors. Changing the Dancoff factor in the outer part of the pebble bed to compensate for the lower probability of neutrons to enter other fuel pebbles caused no significant changes in $k_{eff}$.%, showing that variations in Dancoff factor in pebble bed reactors can be ignored. Next we derived a thermal-hydraulics model for pebble beds based on turbulence modelling for porous media. Calculation results agreed well with measurements from two SANA experiments and with calculation results from THERMIX for the HTR-PM, showing the model's capability to accurately predict the flow and temperature distribution for both natural circulation and during full power operation. Comparison of results for a uniform porosity distribution with results for a nonuniform distribution with lower porosities near the walls showed the importance of the wall-channelling effect, resulting for the two SANA experiments in increased natural circulation and a better match with measurements. Finally, we investigated the effects of non-uniformities in the porosity distribution for the HTR-PM during normal operation and DLOFC and PLOFC transients, using coupled thermal-hydraulic and neutron transport calculations. We found that earthquakes can cause only a small change in porosity in pebble bed reactors, limiting the reactivity increase due to an earthquake for the HTR-PM to 94 pcm, which is too small to pose a significant safety risk. The occurrence of a cluster of densely packed pebbles was shown to result in no significant increase in the maximum fuel temperature during normal operation, and only very small increases in the maximum fuel temperature of 3.5 \textdegree C in the DLOFC transient and 0.25 \textdegree C in the PLOFC transient. Comparison of calculations taking into account the higher porosity at the boundaries with a uniform porosity distribution showed a strong increase of the mass flow next to the wall during normal operation, resulting in a decrease of the mass flow through the bulk of the pebble bed. Combined with the slightly higher power density in the centre of the bed due to the lower porosity, this caused a modest increase of the maximum fuel temperature in the centre of the bed of 21.5 \textdegree C during steady state. The increased steady state temperature and power density at the centre of the bed also caused a small increase in the peak maximum fuel temperature of 7 \textdegree C for the DLOFC and of 13 \textdegree C for the PLOFC transient. During the PLOFC transient, natural convection was almost identical to the case with uniform porosity, as flow still had to circulate up through the densely packed centre of the bed, where flow resistance is large. We conclude that taking into account the lower porosity near the boundary causes a strong increase in the mass flow next to the wall, but for large cylindrical pebble beds such as the HTR-PM will cause only a small increase of the maximum fuel temperature during steady state, and will hardly affect heat transfer during transients. However, as we expect the temperature increase to be much larger for smaller pebble beds , and as we expect the lower porosity near the inner wall to result in a decrease in the maximum fuel temperature for annular pebble beds, we recommend further research for these types of pebble bed reactors.Radiation Science and TechnologyApplied Science