Research on Quadratic Depletion Method for Reaction Rate Based on NECP-X
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摘要: 在燃耗计算中，尤其是针对含钆燃料，每个燃耗步往往需要预估校正的2次输运计算，但是在高保真计算中，2次输运计算会大大降低计算效率，导致燃料循环计算的时间成本过高。本文基于高保真程序NECP-X采用了反应率二阶插值燃耗（QD）方法。在燃耗计算中省去预估步的输运计算，并通过预校正的方法，修正预估步的7种钆同位素的原子核密度，并在校正步中对钆的反应率使用二阶插值，以提升含钆燃料燃耗计算的准确性。针对含钆单组件和多组件问题分别使用传统预估校正方法和反应率二阶插值燃耗方法进行燃耗计算并比较，计算结果表明新燃耗方法不仅可以在精度上提升至少1倍，而且还能将计算效率提升约30%。因此，本文采用的反应率二阶插值燃耗方法可以很好地应用在含钆燃料的燃耗计算中。Abstract: In depletion calculations, especially for gadolinium-bearing fuels, each burnup step often requires two flux calculations for predictor and corrector. However, in high-fidelity calculations, performing two physical calculations significantly reduces computational efficiency, leading to excessively high time costs in fuel cycle calculations. In this paper, quadratic depletion (QD) method is adopted in high-fidelity code NECP-X. The flux calculation in predictor is skipped, and a post-correction method is adopted to correct the number densities of seven gadolinium isotopes. In the correction step, quadratic interpolation is used for the reaction rates of gadolinium isotopes to improve the accuracy of depletion calculations of gadolinium-bearing fuels. Comparative depletion calculations are performed for both single-assembly and multi-assembly Gd-bearing fuel cases using traditional predictor-corrector method and quadratic depletion method. The results show that the quadratic depletion method cannot only improve the accuracy by at least a factor of 2, but also increase the efficiency by approximately 30%. Therefore, the proposed QD method can be well applied in Gd-bearing fuel depletion calculations.
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Key words:
- Depletion method /
- Gadolinium isotopes /
- Reaction rate /
- Predictor-Corrector
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图 3 不同子步数下QD方法临界硼偏差曲线
Figure 3. Deviation Curves of Critical Boron Concentration under Different Substep Numbers in QD Method
图 4 燃耗步长为500 MW·d·t−1(U)时单组件算例临界硼浓度偏差曲线
Figure 4. Deviation Curves of Critical Boron Concentration for the Single-assembly Case at a Burnup Step of 500 MW·d·t−1(U)
图 5 燃耗步长为250 MW·d·t−1(U)时单组件算例临界硼浓度偏差曲线
Figure 5. Deviation Curves of Critical Boron Concentration for the Single-assembly Case at a Burnup Step of 250 MW·d·t−1(U)
图 6 单组件算例QD方法与LELI方法在8 GW·d·t−1(U)下的功率分布偏差
Figure 6. Power Distribution Deviation between QD and LELI for the Single-assembly Case at 8 GW·d·t−1(U)
图 8 3×3多组件算例QD方法和LELI方法临界硼浓度偏差对比
Figure 8. Comparison of Critical Boron Concentration Deviation between QD and LELI for the 3×3 Multi-assembly Case
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