Comprehensive Adjoint Sensitivity Analysis Methodology Research Articles

Application of the Second-Order Comprehensive Adjoint Sensitivity Analysis Methodology to Compute First- and Second-Order Sensitivities of Flux Functionals in a Multiplying System with Source

This work presents an application of the Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) to the neutron transport Boltzmann equation that models a multiplying subcritical system comprising a nonfission neutron source to compute efficiently and exactly all of the first- and second-order functional derivatives (sensitivities) of a detector’s response to all of the model’s parameters, including isotopic number densities, microscopic cross sections, fission spectrum, sources, and detector response function. As indicated by the general theoretical considerations underlying the 2nd-ASAM, the number of computations required to obtain the first and second orders increases linearly in augmented Hilbert spaces as opposed to increasing exponentially in the original Hilbert space. The results presented in this work are currently being implemented in several production-oriented three-dimensional neutron transport code systems for analyzing specific subcritical systems.

A Paradigm-Shifting Methodology for Sensitivity Analysis of Critical Multiplying Nuclear Systems

Dispensing with the traditional approach to solving the equations modeling multiplying critical nuclear systems as an eigenvalue system, this work proposes a new and comprehensive mathematical framework (C-Framework) that eliminates the need for solving eigenvalue problems when computing the forward and adjoint neutron flux distributions in critical reactors. Consequently, the C-Framework enables the mathematical and computational analysis of critical and noncritical multiplying systems, with or without external sources, in a unified manner. By eliminating the need for solving eigenvalue problems, the C-Framework also enables the use of more efficient numerical methods (than currently used) for computing the forward and adjoint neutron flux distributions in critical reactors. Furthermore, the C-Framework also enables the application of the Comprehensive Adjoint Sensitivity Analysis Methodology (C-ASAM) as a replacement for the so-called generalized perturbation theory (GPT). The C-ASAM is much simpler to apply than the GPT, while not only yielding all of the results that the GPT can deliver, but also delivering results for all of the many—and not “GPT-allowable”—nonlinear responses of interest in reactor analysis that do not satisfy the very restrictive orthogonality relations required by the GPT’s underlying generalized adjoint equation. By dispensing with the need for solving eigenvalue problems involving the inversion of singular operators, the C-ASAM is vastly more general and more efficient than the GPT. These conclusions are underscored by exact analytical results presented for paradigm illustrative problems, which include problems that are solvable using the GPT (e.g., the system’s multiplication factor, ratios of reaction rates responses), and problems that are not solvable using the GPT (e.g., absolute reaction rates, equilibrium xenon concentration responses); all of these problems are shown to be solvable exactly and most efficiently within the C-ASAM framework.

Predictive Modeling of a Buoyancy-Operated Cooling Tower Under Saturated Conditions—I: Adjoint Sensitivity Model

A cooling tower discharges waste heat produced by an industrial plant to the external environment. The amount of thermal energy discharged into the environment can be determined by measurements of quantities representing the external conditions, such as outlet air temperature, outlet water temperature, and outlet air relative humidity, in conjunction with computational models that simulate numerically the cooling tower’s behavior. Variations in the model’s parameters (e.g., material properties, model correlations, boundary conditions) cause variations in the model’s response. The functional derivatives of the model response with respect to the model parameters (called “sensitivities”) are needed to quantify such response variations changes. In this work, the comprehensive adjoint sensitivity analysis methodology for nonlinear systems is applied to compute the cooling tower’s response sensitivities to all of its model parameters. These sensitivities are used in this work for (1) ranking the model parameters according to the magnitude of their contribution to response uncertainties; (2) propagating the uncertainties in the model’s parameters to quantify the uncertainties in the model’s responses. In an accompanying work, these sensitivities are subsequently used for predictive modeling, combining computational and experimental information, including the respective uncertainties, to obtain optimally predicted best-estimate nominal values for the model’s parameters and responses, with reduced predicted uncertainties.