On using alternative perturbation theory methodologies in the evaluation of reactivity effects in ADS cores

Pelloni, S.; Coddington, Paul

doi:10.1016/j.anucene.2006.10.001

Cited by 7 publications

(4 citation statements)

References 13 publications

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“…Particularly noteworthy is the work by Pomraning, who laid out much of the general Since 2000, much less work has been done on variational methods applied to material density perturbations, although isolated papers occasionally appear for particular applications [32].…”

Section: Perturbation Theory and Variational Methods Applied To Matermentioning

confidence: 99%

The “virtual density” theory of neutronics

Reed¹,

Smith

Forget

2018

Annals of Nuclear Energy

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Sustainable nuclear energy will likely require fast reactors to complement the current light water reactor paradigm. In particular, breed-and-burn sodium fast reactors (SFRs) offer a unique combination of fuel cycle and power density features. Unfortunately, large breed-and-burn SFRs are plagued by positive sodium void worth. In order to mitigate this drawback, one must quantify various sources of negative reactivty feedback, among which geometry distortions (bowing and flowering of fuel assemblies) are often dominant. These distortions arise mainly from three distinct physical phenomena: irradiation swelling, thermal swelling, and seismic events.Distortions are notoriously difficult to model, because they break symmetry and periodicity. Currently, no efficient and fully generic method exists for computing neutronic effects of distortions. Computing them directly via diffusion would require construction of exotic hyperfine meshes with continuous re-meshing. Many deterministic transport methods are geometrically flexible but would require tedious, intricate re-meshing or re-tracking to capture distortion effects. Monte Carlo offers the only high-fidelity approach to arbitrary geometry, but resolving minute reactivities and flux shift tallies within large heterogeneous cores requires CPU years per case and is thus prohibitively expensive. Currently, the most widely-used methods consist of various approximations involving weighting the uniform radial swelling reactivity coefficient by the power distribution. These approximations agree fairly well with experimental data for flowering in some cores, but they are not fully generic and cannot be trusted for arbitrary distortions. Boundary perturbation theory, developed in the 1980s, is fully general and mathematically rigorous, but it is inaccurate for coarse mesh diffusion and has apparently never been applied in industry.Our solution is the "virtual density" theory of neutronics, which alters material density (isotropically or anisotropically) instead of explicitly changing geometry. While geometry is discretized, material densities occupy a continuous domain; this allows density changes to obviate the greatest computational challenges of geometry changes. Although primitive forms of this theory exist in Soviet literature, they are only applicable to cases in which entire cores swell uniformly. Thus, we conceive a much more general and pragmatic form of "virtual density" theory to model non-uniform and localized geometry distortions via perturbation theory.In order to efficiently validate "virtual density" perturbation theory, we conceive the "virtual mesh" method for diffusion theory. This new method involves constructing a slightly perturbed "fake" mesh that produces correct first-order reactivity and flux shifts due to anisotropic swelling or expansion of individual mesh cells. First order reactivities computed on a "virtual mesh" agree with continuous energy Monte Carlo to within 1-uncertainty.We validate "virtual density" theory via the "virtual mesh" me...

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Section: Perturbation Theory and Variational Methods Applied To Matermentioning

confidence: 99%

The “virtual density” theory of neutronics

Reed¹,

Smith

Forget

2018

Annals of Nuclear Energy

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“…The values obtained from the MCNP modeling and calculations are compared with the reference data, which is summarized in Table 3. The reference data have been calculated by Pelloni and Coddington (2006) with deterministic computational method. It can be seen that the calculated values are in good agreement with the reference data, and the relative errors of β eff and Λ are 1.6% and 2.4%, respectively.…”

Section: Verification Resultsmentioning

confidence: 99%

Icone23-1068 Calculation of Kinetic Parameters for Ads Cores With Minor Actinides by Using Monte Carlo Method

Luo

Wei

Zhao

2015

ICONE

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The most important kinetic parameters are effective delayed neutron fraction (β eff ), mean neutron generation time (Λ) and reactivity coefficient (α), which play a key role in nuclear reactor control and safety analysis. In this work, these kinetic parameters for the accelerator driven system (ADS) cores are calculated by using Monte Carlo method. The calculated values of β eff and Λ agree well with the reference data. In addition, the effect of minor actinides (MA) on kinetic parameters is investigated. Both uranium and plutonium mixed oxides (MOX) fuel and (U,Pu,MA)O 2 fuel are taken into account to load in the different cores. The results show that the values of β eff and Λ decreases with increasing the content of MA in the (U,Pu,MA)O 2 fuel. The results also demonstrate that prompt negative feedback effects, including Doppler feedback effect and Coolant feedback effect, would be weakened after loading a large amount of MA into the core.

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“…All the reference data are provided by some researchers (Pelloni and Coddington, 2006;Talamo and Gohar, 2008;Kiedrowski and Brown, 2009). The relative errors between the results of new method with reference data and prompt method for b eff are less than 1.0% and 3.1%, respectively.…”

Section: Benchmarks Verificationmentioning

confidence: 98%