Criticality Data and Factors Affecting Criticality of Single Homogeneous Units.

Stratton, William

doi:10.2172/4178370

Cited by 8 publications

(8 citation statements)

References 10 publications

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“…(5,29) These conclusions lend additional support to our conclusions regarding the cube and the sphere.…”

supporting

confidence: 81%

“…Previous calculations in two earlier papers, one by W. R. Stratton (68) and also by C. B. Mills (69) show that by surrounding a single reactor unit of fissile material with a thick weakly absorbing reflector such as graphite, heavy water or beryllium, it is possible to affect a reduction increases rapidly with increased water density due to internal moderation, external reflection and enhanced interaction.…”

Section: Figure 30 Criticality Mass and Volume Of Unreflected Metal mentioning

confidence: 99%

“…(29,39) The effect is illustrated in Figure 19, where the critical mass of U(93.5) metal reflected by graphite and beryllium has been plotted against density of 235 U metal in the core. The critical mass is at first seen to increase, and then contrary to the usual expectation, the change reverses itself and the critical mass decreases with decreasing core density.…”

Section: External Moderationmentioning

confidence: 99%

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Anomalies of Nuclear Criticality, Revision 6

Clayton¹,

Prichard²,

Durst³

et al. 2010

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“…(5,29) These conclusions lend additional support to our conclusions regarding the cube and the sphere.…”

supporting

confidence: 81%

Section: Figure 30 Criticality Mass and Volume Of Unreflected Metal mentioning

confidence: 99%

Section: External Moderationmentioning

confidence: 99%

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Anomalies of Nuclear Criticality, Revision 6

Clayton¹,

Prichard²,

Durst³

et al. 2010

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“…Back then, performing an accurate eigenvalue calculation (even for extremely simple geometries) was laborious, and so this "density law" provided a simple way for them to know what would happen if they were to scale up (or down) the dimensions of a critical system. As described in a later report by Stratton, they knew that the critical radius of a system is inversely proportional to density and that the critical mass is inversely proportional to the square of density [89]. Stratton also states that the law applies precisely to the extrapolation distance in diffusion theory, which one would expect.…”

Section: Literature Reviewmentioning

confidence: 97%

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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“…1, the critical mass of plutonium metal mixed with water is illustrated as a function of the density of plutonium in the water. 6 The mixture is idealized to be only metal and water; actual solutions of plutonium compounds would differ but little. Both water-reflected (20-cm thickness) and unreflected (bare) systems are shown.…”

Section: Nuclear Criticality-simple Systemsmentioning

confidence: 99%