Journal of Nuclear Engineering

Objective neural network-based two-phase flow regime classifiers are developed for vertical, narrow, rectangular channels and a 1 inch round pipe using Kohonen Self-Organizing Maps. In the rectangular channel, the classifier uses five geometric inputs obtained from a two-sensor droplet-capable conductivity probe (DCCP-2): the bulk gas void fraction ${\alpha }_g$, ligament void fraction ${\alpha }_{\mathrm{lig}}$, normalized ligament chord length $y_{\mathrm{lig}}$, normalized large bubble chord length $y_{\ell ,\mathrm{bb}}$, and a droplet indicator. These parameters allow for the objective identification of bubbly/distorted bubbly, cap-turbulent, churn-turbulent, annular, rolling wispy, and wispy flow regimes, and yield quantitative transition boundaries in the plane for a densely populated test matrix. In the round pipe, a four-sensor droplet-capable conductivity probe (DCCP-4) provides the mean and standard deviation of droplet, bubble, and ligament chord length distributions, which are used as inputs to a Self-Organizing Map (SOM) classifier that separates rolling annular and wispy annular regimes at high void fractions. The resulting regime maps are discussed in terms of the associated phase geometries and their impact on interfacial area, drag, and entrainment, providing regime-dependent geometric inputs that can be used to improve Two-Fluid Model closures for reactor downcomers, core channels, and other nuclear thermal–hydraulic applications.

The neutron survival probability (and related quantities including probabilities of extinction and initiation) is a central element of the broader stochastic theory of neutron populations and finds application in fields including reactor start-up, analysis of reactor power bursts and criticality accidents, and safeguards. In a full neutron transport formulation, the equation governing the single-neutron survival probability is a backward or adjoint-like integro-partial differential equation with the added complexity of being highly nonlinear. Analogous formulations of this equation exist in the context of many approximate theories of neutron transport, with the point kinetics formulation having received significant theoretical attention since the 1940s. This work continues this tradition by providing a novel analysis of the single-neutron survival probability equation using the tools of boundary layer theory. The analysis reveals that the “fully dynamic” solution of the single-neutron survival probability equation—and some key probability distributions derived from it—may be cast as a singular perturbation around the underlying quasi-static single-neutron probability of initiation. In this perturbation solution, the expansion parameter is the ratio of the neutron generation time to a macroscopic time scale characterizing the overall system evolution; this interpretation illuminates some of the fundamental structural aspects of neutron survival phenomena.

The SCALE transport lattice code, Polaris, has been previously developed to generate few-group homogenized cross sections for whole-core nodal diffusion simulators in which the embedded self-shielding method (ESSM) is used for resonance self-shielding calculations to process cross sections. Although the ESSM capability has been very successful in light-water reactor analysis, it may require enhancements in computational efficiency; treatment of spatially dependent resonance self-shielding effects; and handling of interrelated resonance effects among fuel, cladding, and control rod materials. Therefore, this study focuses on improving computational efficiency by using a Dancoff-based Wigner–Seitz approximation combined with a material-based resonance categorization, through which a spatially dependent ESSM capability is developed to accurately estimate self-shielded cross sections inside the fuel. Benchmark results show that the new capability significantly enhances computational efficiency and accuracy for spatially dependent local zones within the fuel and through depletion.