The ;;virtual density;; theory of neutronics

[摘要] 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;; method in 3-D coarse mesh models of the Fast Flux Test Facility (FFTF) and Jōyō benchmarks using the MATLAB-PETSc-SLEPc (MaPS) multigroup finite difference diffusion code, which we developed for this purpose. We model a panoply of non-uniform anisotropic swelling scenarios, including axial swelling of individual assemblies, axial swelling of each mesh cell in proportion to its fission power, and radial core flowering with arbitrary axial dependence. In 3-D coarse mesh Cartesian cores with explicit coolant gaps, we model individual assembly motion, assembly row motion with arbitrary axial dependence, and assembly row ;;s-shape;; bowing. In all cases, we find that ;;virtual density;; perturbation theory predicts reactivity coefficients that agree with ;;virtual mesh;; reference cases to within 0.01%. These reactivity coefficients are two to four orders of magnitude more accurate than those computed via boundary perturbation theory. We also develop the Pseudo-Seismic (PseuSei) Animator within MaPS to explore point-kinetic effects of arbitrary assembly motion for 3-D coarse mesh Cartesian cases. In general, this ;;virtual density;; perturbation method can precisely predict reactivity coefficients due to anisotropic swelling or expansion of any core region in any direction. Furthermore, we compute flux and power shift distributions due to geometry distortions. We find that our ;;virtual density;; formalism couples seamlessly with existing modal expansion perturbation theory (MEPT) formalism, and we use the resulting new hybrid method to compute flux and power shifts due to arbitrary anisotropic swelling of arbitrary core regions. We test this new method for a large, highly-heterogeneous Cartesian core, and we find that predicted (global and local) flux and power shift distributions typically agree with ;;virtual mesh;; reference cases to within a few percent. Development of the ;;Virtual Density;; Theory (VirDenT) industry code constitutes the culmination of this work. This parallelized Python code computes ;;virtual density;; reactivity coefficients given a DIF3D flux solution as input. VirDenT contains a flux reconstruction module that computes individual pin powers from a homogenized nodal diffusion solution. It also contains PyPinPlot, a high-resolution visualization tool for pin-level powers, fluxes, and current vector fields. Most importantly, VirDenT computes reactivity coefficients due to local anisotropic swelling of assembly zones (which direct diffusion theory cannot compute) in CPU seconds, while Monte Carlo (currently the only high-fidelity approach) requires CPU years to do the same.

[发布机构] Massachusetts Institute of Technology