An alternative method of increasing the incineration rate of the RBWR is to soften the neutron spectrum by increasing the H/HM ratio. The simplest way is to reduce the pin diameter while keeping the lattice pitch constant. This results in a lower discharge burn-up being achievable while satisfying the constraint that the VC must be negative. However, as the performance is most sensitive to achieving a hard neutron spectrum in the Th-TRU, one option is to preferentially harden the neutron spectrum in the Th-TRU using a variable pin diameter. The pin diameter of the Th-U3 pins is reduced to 9.5 mm (Fig. 6.13). This results in approximately double the H/HM ratio relative to the reference assembly design (but still only ~27% that of a conventional PWR). A multi-tier fuel cycle with 50 GWd/t burn-up in the first pass was implemented.
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Fig. 6.13. Variable pin diameter assembly design with 127 Th-TRU (blue) pins and 90 Th-U3
(green) pins.
By selecting the number of Th-U3 pins appropriately, it is possible to limit the power peaking in the assembly. As the Th-U3 pins are smaller, this leads to a higher burn-up rate in these pins. As the burn-up is clad-limited, it is sensible to utilize a seed-blanket-unit approach and pass the Th-TRU pins through the core twice as many times as the Th-U3 pins to achieve a roughly uniform burn-up. The Th-TRU reactivity is approximately constant with burn-up, as U3 is bred and 241Am and even isotopes of Pu are burned over the cycle, which compensate for the depletion of fissile Pu and accumulation of fission products. Assemblies with fresh Th-U3 and Th-TRU are shuffled according to the batch strategy in Fig. 6.1. The burned Th-U3 pins are replaced, and a further 4–5 passes are performed, with fresh Th-U3 assemblies being batch 1 (from Fig. 6.1), but having 4 or 5 times burned Th-TRU, and so on. The Th-TRU therefore resides in the core for 8–10 batches. As discussed in Chapter 5, separating the assembly in this manner is expected to be feasible.
Use of variable nozzle sizes and/or grid spacer design for variable loss coefficient within the assembly can compensate for linear heat rating and pin diameter variations across the assembly (Lindley et al., 2013c), although a more detailed thermal-hydraulic analysis is necessary to determine feasibility.
The reactor core was modelled as before. The core flow rate was increased from 7222 kg/s to 8000 kg/s to maintain a similar core-average VF to before. A core height of 120 cm was appropriate for the selected TRU reload fraction and equilibrium cycle burn-up. The performance is summarised in Table 6.7.
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Table 6.7. Performance of variable fuel pin diameter design.
Waste loading fraction in feed 52.7%
Waste incineration rate 202 kg/GWthyr
Assembly-average burn-up/pass 40.0 GWd/t
Average Th-U3 discharge burn-up 75.3 GWd/t
Average Th-TRU discharge burn-up 54.8 GWd/t
Average discharge burn-up 63.1 GWd/t
Cycle length 259 days
Reactivity swing over cycle 1805 pcm
By comparison with the RMPWR analysis (see Chapters 2, 5 & 7), the waste loading fraction, and therefore the waste incineration rate, is significantly larger than could be expected by a uniform reduction in pin diameter. However, the average discharge burn-up is somewhat lower than in Section 6.3, and given the complexity of the design, implementation may not be worthwhile.
The selected core configuration only achieves a cycle length of 9 months. This is likely to be unacceptably low, implying that a taller core with lower power density is necessary to achieve a minimum 12 month cycle. A single-tier fuel cycle is also likely to allow a longer cycle length. The radial and axial power peaking were both ~1.2.
Reliable values for the VC and DC were not found: using Eq. 6.1 a substantially negative VC was calculated but low (and in some cases positive) values for the DC were calculated, with variation depending on how RELAP5 was converged. Lattice calculations with fresh fuel and 0%, 53% and 95% VF give a DC of –2.5, –2.9 and –2.1 pcm/K respectively. The inconsistent values for the DC and VC are a cause for concern and reduce confidence in the analysis. This implies that there are problems with the methodology described in Section 6.1 for solving for the VC and DC based on perturbing the power and the flow, for example due to different values of the VC for different flow perturbations. It is also clear that convergence of RELAP5 is a problem – lack of convergence to an accurate solution to the flow under perturbed conditions leads to inaccurate values for the VC and DC. This is in part due to the time-marching solution in RELAP5, In future it is therefore recommended that statepoint or quasi-static calculations are carried out using a steady state thermal- hydraulic code instead of a time-marching code.
Due to the inaccurate values of VC and DC in this case, the change in reactivity with overpower and reduced-flow is instead presented in Table 6.8 for two different evaluations with different RELAP5 solutions. The different evaluations results in differences of around 3 pcm/% overpower and 3 pcm/% flow rate. The matrix solution method for calculating the VC and DC given in Equation 6.1 can exacerbate these uncertainties and lead to calculation of a positive DC, which is
161 unphysical. The overpower coefficient is around zero and may indeed be slightly positive, which indicates that the TRU loading may need to be reduced slightly. In general, if the fuel and coolant reactivity coefficients cannot be evaluated accurately, a significant margin for error is required.
Table 6.8. Overpower and reduced flow coefficients for variable pin diameter design.
Evaluation 1 Evaluation 2
SOC EOC SOC EOC
Overpower (pcm/% overpower) –15.5 +1.2 –13.3 –2.0
Flow rate (pcm/ % flow rate) –19.2 –13.1 –21.8 –10.2