Nuclear Engineering - Ph.D. / Sc.D.
http://hdl.handle.net/1721.1/7854
2014-07-15T09:26:16ZThe "virtual density" theory of neutronics
http://hdl.handle.net/1721.1/87497
The "virtual density" theory of neutronics
Reed, Mark Wilbert
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.
Thesis: Sc. D., Massachusetts Institute of Technology, Department of Nuclear Science and Engineering, 2014.; Cataloged from PDF version of thesis. Vita.; Includes bibliographical references (pages 461-478).
2014-01-01T00:00:00ZDevelopment of accelerator based spatially resolved ion beam analysis techniques for the study of plasma materials interactions in magnetic fusion devices
http://hdl.handle.net/1721.1/87495
Development of accelerator based spatially resolved ion beam analysis techniques for the study of plasma materials interactions in magnetic fusion devices
Barnard, Harold Salvadore
Plasma-material interactions (PMI) in magnetic fusion devices pose significant scientific and engineering challenges for the development of steady-state fusion power reactors. Understanding PMI is crucial for the develpment of magnetic fusion devices because fusion plasmas can significantly modify plasma facing components (PFC) which can be severely detrimental to material longevity and plasma impurity control. In addition, the retention of tritium (T) fuel in PFCs or plasma co-deposited material can disrupt the fuel cycle of the reactor while contributing to radiological and regulatory issues. The current state of the art for PMI research involves using accelerator based ion beam analysis (IBA) techniques in order to provide quantitative measurement of the modification to plasma-facing surfaces. Accelerated ~MeV ion beams are used to induce nuclear reactions or scattering, and by spectroscopic analysis of the resulting high energy particles (s', p, n, a, etc.), the material composition can be determined. PFCs can be analyzed to observe erosion and deposition patterns along their surfaces which can be measured with spatial resolution down to the -1 mm scale on depth scales of 10 - 100 pim. These techniques however are inherently ex-situ and can only be performed on PFCs that have been removed from tokamaks, thus limiting analysis to the cumulative PMI effects of months or years of plasma experiments. While ex-situ analysis is a powerful tool for studying the net effects of PMI, ex-situ analysis cannot address the fundamental challenge of correlating the plasma conditions of each experiment to the material surface evolution. This therefore motivates the development of the in-situ diagnostics to study surfaces with comparable diagnostic quality to IBA in order resolve the time evolution of these surface conditions. To address this fundamental diagnostic need, the Accelerator-Based In-Situ Materials Surveillance (AIMS) diagnostic [22] was developed to, for the first time, provide in-situ, spatially resolved IBA measurements inside of the Alcator C-Mod tokamak. The work presented in this thesis provided major technical and scientific contributions to the development and first demonstration AIMS. This included accelerator development, advanced simulation methods, and in-situ measurement of PFC surface properties and their evolution. The AIMS diagnostic was successfully implemented on Alcator C-Mod yielding the first spatially resolved and quantitative in-situ measurements of surface properties in a tokamak, with thin boron films on molybdenum PFCs being the analyzed surface in C-Mod. By combining AIMS neutron and gamma measurements, time resolved and spatially resolved measurements of boron were made, spanning the entire AIMS run campaign which included lower single null plasma discharges, inboard limited plasma discharges, a disruption, and C-Mod wall conditioning procedures. These measurements demonstrated the capability to perform inter shot measurements at a single location, and spatially resolved measurements over longer timescales. This demonstration showed the first in-situ measurements of surfaces in a magnetic fusion device with spatial and temporal resolution which constitutes a major step forward in fusion PMI science. In addition, an external ion beam system was implemented to perform ex-situ ion beam analysis (IBA) for components from Alcator C-Mod Tokamak. This project involved the refurbishment of a 1.7 MV tandem linear accelerator and the creation of a linear accelerator facility to provide IBA capabilities for MIT Plasma Science and Fusion Center. The external beam system was used to perform particle induced gamma emission (PIGE) analysis on tile modules removed after the AIMS measurement campaign in order to validate the AIMS using the well established PIGE technique. From these external PIGE measurements, a spatially resolved map of boron areal density was constructed for a section of C-Mod inner wall tiles that overlapped with the AIMS measurement locations. These measurements showed the complexity of the poloidal and toroidal variation of boron areal density between PFC tiles on the inner wall ranging from 0 to 3pm of boron. Using these well characterized ex-situ measurements to corroborate the in-situ measurements, AIMS showed reasonable agreement with PIGE, thus validating the quantitative surface analysis capability of the AIMS technique.
Thesis: Sc. D., Massachusetts Institute of Technology, Department of Nuclear Science and Engineering, 2014.; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 214-218).
2014-01-01T00:00:00ZModeling radiation-induced mixing at interfaces between low solubility metals
http://hdl.handle.net/1721.1/87493
Modeling radiation-induced mixing at interfaces between low solubility metals
Zhang, Liang, Ph. D. Massachusetts Institute of Technology
This thesis studies radiation-induced mixing at interfaces between low solubility metals using molecular dynamics (MD) computer simulations. It provides original contributions on the fundamental mechanisms of radiation-induced mixing and morphological stability of multilayer nanocomposites under heavy ion or neutron radiation. An embedded atom method (EAM) interatomic potential is constructed to reproduce the main topological features of the experimental equilibrium phase diagram of the Cu-Nb system in both solid and liquid states. Compared with two previously available EAM Cu-Nb potentials, the phase diagram of the current potential shows better agreement with the experimental phase diagram. The newly constructed potential predicts that the Cu-Nb liquid phase at equilibrium is compositionally patterned over lengths of about 2.3 nm. All three Cu-Nb potentials have the same solid phase behavior but different liquid phase properties, serving as a convenient set of model systems to study the effect of liquid phase properties on radiation-induced mixing. To study radiation-induced intermixing, a specialized MD simulation is developed that models multiple 10 keV collision cascades sequentially up to a total dose of ~5 displacements per atom (dpa). These simulations are comparable to experiments conducted at cryogenic temperatures. Mixing is modeled using all three Cu-Nb potentials and found to be proportional to the square root of dose, independent of interface crystallography, and highly sensitive to liquid phase interdiffusivity. It occurs primarily by liquid phase interdiffusion in thermal spikes rather than by ballistic displacements. Partial de-mixing is also seen within thermal spikes, regardless of liquid phase solubility, which is explained by segregation of impurities into the liquid core of the thermal spikes. Additional MD and phase field simulations are carried out on Cu-Nb multilayered nanocomposites with individual layer thicknesses above 1 nm. These simulations demonstrate that Cu-Nb multilayers with individual layer thicknesses above 2-4 nm remain morphologically stable when subjected to 100 keV collision cascades, characteristic of neutron or heavy ion irradiation. The probability of morphological instability rapidly increases as the layer thickness decreases to 1 nm, which is due to overlap of zones of liquid-like interdiffusion inside radiation-induced thermal spikes at neighboring interfaces in the multilayer. This work shows that to design morphologically stable radiation-tolerant nanocomposites, it is desirable to a) choose low solubility metals with small liquid phase interdiffusivity as the constituents, and b) use a microstructural length scale larger than twice the size of the interdiffusion zone inside thermal spikes.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Nuclear Science and Engineering, 2014.; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 123-139).
2014-01-01T00:00:00ZPredicting the equilibria of point defects in zirconium oxide : a route to understand the corrosion and hydrogen pickup of zirconium alloys
http://hdl.handle.net/1721.1/87492
Predicting the equilibria of point defects in zirconium oxide : a route to understand the corrosion and hydrogen pickup of zirconium alloys
Youssef, Mostafa Youssef Mahmoud
The performance of zirconium alloys in nuclear reactors is compromised by corrosion and hydrogen pickup. The thermodynamics and kinetics of these two processes are governed by the behavior of point defects in the ZrO₂ layer that grows natively on these alloys. In this thesis, we developed a general, broadly applicable framework to predict the equilibria of point defects in a metal oxide. The framework is informed by density functional theory and relies on notions of statistical mechanics. Validation was performed on the tetragonal and monoclinic phases of ZrO₂ by comparison with prior conductivity experiments. The framework was applied to four fundamental problems for understanding the corrosion and hydrogen pickup of zirconium alloys. First, by coupling the predicted concentrations of oxygen defects in tetragonal ZrO₂ with their calculated migration barriers, we determined oxygen self-diffusivity in a wide range of thermodynamic conditions spanning from the metal-oxide interface to the oxide-water interface. This facilitates future macro-scale modeling of the oxide layer growth kinetics on zirconium alloys. Second, using the computed defect equilibria of the tetragonal and monoclinic phases, we constructed a temperature-oxygen partial pressure phase diagram for ZrO₂. The diagram showed that the tetragonal phase can be stabilized below its atmospheric transition-temperature by lowering the oxygen chemical potential. This work adds a new explanation to the stabilization of the tetragonal phase at the metal-oxide interface where the oxygen partial pressure is low. Third, using the developed framework, we modeled co-doping of monoclinic ZrO₂ with hydrogen and a transition metal. Our modeling predicted a volcano-like dependence of hydrogen (proton) solubility on the first-row transition metals, which is consistent with a set of systematic experiments from the nuclear industry. We discovered that the reason behind this behavior is the ability of the transition metal to p-type-dope ZrO₂ and hence lower the chemical potential of electron. Therefore, the peak of the hydrogen solubility in monoclinic ZrO₂ also corresponds to an increased barrier for hydrogen gas evolution on the surface. This explanation opens the door to physics-based design of resistant zirconium alloys, and qualitatively consistent with the monoclinic ZrO₂. Finally, we uncovered the interplay between certain hydrogen defects and planar compressive stress which tetragonal ZrO₂ experiences on zirconium alloys. The stress enhances the abundance of these defects, while these same defects tend to relax the stress. This interplay was used to propose an oxide fracture mechanism by which hydrogen is picked up.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Nuclear Science and Engineering, 2014.; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 172-178).
2014-01-01T00:00:00Z