Paul J. Turinsky

In-Core Nuclear Fuel Management Optimization for Pressurized Water Reactors Utilizing Simulated Annealing

This paper reports on an in-core nuclear fuel management code for pressurized water reactor reload design developed that combines the stochastic optimization technique of simulated annealing with a computationally efficient core physics model based on second-order accurate generalized perturbation theory. The approach identifies the placements of feed fuel, exposed fuel with assembly orientations, and burnable poisons within the core lattice that optimize fuel cycle performance or thermal margin according to one of the following objectives: maximization of k{sub eff} at a target end-of-cycle (EOC) burnup, minimization of the maximization radial power peaking over the cycle, or maximization of region average discharge burnup, and subject to constraints on radial power peaking, discharge burnup and moderator temperature coefficient.

FORMOSA-B: A Boiling Water Reactor In-Core Fuel Management Optimization Package III

As part of the continuing development of the boiling water reactor in-core fuel management optimization code FORMOSA-B, the fidelity of the core simulator has been improved and a control rod pattern (CRP) sampling capability has been added. The robustness of the core simulator is first demonstrated by benchmarking against core load-follow depletion predictions of both SIMULATE-3 and MICROBURN-B2 codes. The CRP sampling capability, based on heuristic rules, is next successfully tested on a fixed fuel loading pattern (LP) to yield a feasible CRP that removes the thermal margin and critical flow constraint violations. Its performance in facilitating a spectral shift flow operation is also demonstrated, and then its significant influence on the cost of thermal margin is presented. Finally, the heuristic CRP sampling capability is coupled with the stochastic LP optimization capability in FORMOSA-B—based on simulated annealing (SA)—to solve the combined CRP-LP optimization problem. Effectiveness of the sampling in improving the efficiency of the SA adaptive algorithm is shown by comparing the results to those obtained with the sampling turned off (i.e., only LP optimization is carried out for the fixed reference CRP). The results presented clearly indicate the successful implementation of the CRP sampling algorithm and demonstrate FORMOSA-B’s enhanced optimization features, which facilitate the code’s usage for broader optimization studies.

Efficient Subspace Methods-Based Algorithms for Performing Sensitivity, Uncertainty, and Adaptive Simulation of Large-Scale Computational Models

Abstract This paper introduces the concepts and derives the mathematical theory of efficient subspace methods (ESMs) applied to the simulation of large-scale complex models, of which nuclear reactor simulation will serve as a test basis. ESMs are intended to advance the capabilities of predictive simulation to meet the functional requirements of future energy system simulation and overcome the inadequacies of current design methods. Some of the inadequacies addressed by ESM include lack of rigorous approach to perform comprehensive validation of the multitudes of models and input data used in the design calculations and lack of robust mathematical approaches to enhance fidelity of existing and advanced computational codes. To accomplish these tasks, the computational tools must be capable of performing the following three applications with both accuracy and efficiency: (a) sensitivity analysis of key system attributes with respect to various input data; (b) uncertainty quantification for key system attributes; and (c) adaptive simulation, also known as data assimilation, for adapting existing models based on the assimilated body of experimental information to achieve the best possible prediction accuracy. These three applications, involving large-scale computational models, are now considered computationally infeasible if both the input data and key system attributes or experimental information fields are large. This paper will develop the mathematical theory of ESM-based algorithms for these three applications. The treatment in this paper is based on linearized approximation of the associated computational models. Extension to higher-order approximations represents the focus of our ongoing research.

Automatic determination of pressurized water reactor core loading patterns that maximize beginning-of-cycle reactivity within power-peaking and burnup constraints

Computational capability has been developed to automatically determine a good estimate of the core loading pattern, which minimizes fuel cycle costs for a pressurized water reactor (PWR). Equating fuel cycle cost minimization with core reactivity maximization, the objective is to determine the loading pattern that maximizes core reactivity while satisfying power peaking, discharge burnup, and other constraints. The method utilizes a two-dimensional, coarse-mesh, finite difference scheme to evaluate core reactivity and fluxes for an initial reference loading pattern. First-order perturbation theory is applied to determine the effects of assembly shuffling on reactivity, power distribution, end-of-cycle burnup. Monte Carlo integer programming is then used to determine a near-optimal loading pattern within a range of loading patterns near the reference pattern. The process then repeats with the new loading pattern as the reference loading pattern and terminates when no better loading pattern can be determined. The process was applied with both reactivity maximization and radial power-peaking minimization as objectives. Results on a typical large PWR indicate that the cost of obtaining an 8% improvement in radial power-peaking margin is approx. =2% in fuel cycle costs, for the reload core loaded without burnable poisons that was studied.

Nuclear Fuel Management Optimization: A Work in Progress

The focus of this overview for this issue of Nuclear Technology, which contains papers presented at the American Nuclear Society Advances in Nuclear Fuel Management III (ANFM-III) 2004 topical meeting, is to introduce the subject of nuclear fuel management for light water reactors. A total of 23 papers was presented on this topic at ANFM-III. Nuclear fuel management involves making the so-called out-of-core and in-core decisions. Simply put, the out-of-core decisions address the attributes of the new (fresh) fuel that will be fabricated and the partially burnt (shuffled) fuel to reinsert into the core for additional energy production. The in-core decisions address where the fresh and burnt fuel along with burnable poisons should be located in the core. The above applies to batch refueling strategies, e.g., pressurized water reactors and boiling water reactors (BWRs). For BWRs, additional in-core decisions enter to address control rod pattern paired with core flow rate as a function of burnup. It is obvious that the out-of-core and in-core decisions are coupled. The objective of nuclear fuel management is to minimize the cost of electrical energy generation subject to operational and safety constraints. Since fuel resides in the core for several cycles, a multicycle assessment is required to make nuclear fuel management decisions. For nearly four decades there has been an effort to develop automated computational capability to assist the reload core nuclear design engineer in making nuclear fuel management decisions. This development has ranged from employment of heuristic rules to utilization of mathematical optimization approaches. This overview reviews the development of nuclear fuel management optimization capabilities by first defining the problem, then describing current capabilities, and finally projecting where future capabilities need to be developed to support the needs of reload core nuclear design engineers.

Pressurized water reactor core maneuvering utilizing optimal control theory

The computational capability of automatically determining the optimal control strategies for pressurized water reactor core maneuvering, in terms of an operating strategy generator (OSG), has been developed. The OSG was developed for use with an on-line, three-dimensional core simulator and applies optimal control theory. To reduce computer run time, the optimization engine employs a one-dimensional axial core model. A method has been developed for generating a consistent one-dimensional axial core model from the three-dimensional on-line core simulator based on the consistent collapse methodology. From the one-dimensional, model-based, optimal control strategy, the associated axial offset versus time is obtained. These axial offsets are subsequently used in the three-dimensional simulator to determine with enhanced accuracy the associated control rod insertions and boration/dilution operations versus time. Various operational objectives are defined as the performance index to be minimized. The axial flux difference limit constraint and the maximum boration/dilution limit constraint are treated as penalty functions added to the performance index. The control rod insertion/withdraw limit constraint is treated as a hard constraint on the control variable. The optimality condition is obtained by applying Pontryagins maximum principle for constrained optimization. The resulting nonlinear, two-point boundary-value problem is solved via an iterative approach based on the first-order gradient method. Several sample OSG maneuvering problems have been studied to assess the robustness and efficiency of the optimization search and nonlinear iterations. The algorithm exhibited excellent control of the axial power distribution during maneuvering. For the cases of minimizing the boron system duty during maneuvering, the optimal strategies produced reduced volumes of primary water generated by dilution and boration operations of 12% for beginning-of-cycle cases and 10% for end-of-cycle cases over the volumes generated using heuristic rules.

A Second-Derivative-Based Adaptive Time-Step Method for Spatial Kinetics Calculations

In solving few-group neutron kinetic equations in multidimensions, one must select time-step sizes as a function of time such that the temporal truncation error introduced by the discrete time derivative approximation is limited to ensure the desired fidelity. When using the Euler backward finite difference to approximate the first derivative of the flux--a popular approximation because it ensures numerical stability--the truncation error is known to be O({Delta}t{sup 2}) and proportional to the second derivative. By employment of the double-time-step-size technique, modified to reduce the frequency that double-time-step-size solutions are required, an estimate of the second derivative can be obtained, leading to an efficient computational algorithm for determining the near-optimum time-step-size sequence to ensure the desired fidelity.

ADVANCES IN MULTI-PHYSICS AND HIGH PERFORMANCE COMPUTING IN SUPPORT OF NUCLEAR REACTOR POWER SYSTEMS MODELING AND SIMULATION

Significant advances in computational performance have occurred over the past two decades, achieved not only by the introduction of more powerful processors but the incorporation of parallelism in computer hardware at all levels. Simultaneous with these hardware and associated system software advances have been advances in modeling physical phenomena and the numerical algorithms to allow their usage in simulation. This paper presents a review of the advances in computer performance, discusses the modeling and simulation capabilities required to address the multi-physics and multi-scale phenomena applicable to a nuclear reactor core simulator, and present examples of relevant physics simulation codes’ performances on high performance computers.

Higher Order Generalized Perturbation Theory for Boiling Water Reactor In-Core Fuel Management Optimization

Boiling water reactor (BWR) loading pattern assessment requires solving the two-group, nodal form of the neutron diffusion equation and drift-flux form of the fluid equations simultaneously because these equation sets are strongly coupled via nonlinear feedback. To reduce the computational burden associated with the calculation of the core attributes (that is, core eigenvalue and thermal margins) of a perturbed BWR loading pattern, the analytical and numerical aspects of a higher order generalized perturbation theory (GPT) method, which correctly addresses the strong nonlinear feedbacks of two-phase flow, have been established. Inclusion of Jacobian information in the definition of the generalized flux adjoints provides for a rapidly convergent iterative method for solution of the power distribution and eigenvalue of a loading pattern perturbed from a reference state. Results show that the computational speedup of GPT compared with conventional forward solution methods demanding consistent accuracy is highly dependent on the number of spatial nodes utilized by the core simulator, varying from superior to inferior performance as the number of nodes increases.

Many-Group Cross-Section Adjustment Techniques for Boiling Water Reactor Adaptive Simulation

Abstract Computational capability has been developed to adjust multigroup neutron cross sections, including self-shielding correction factors, to improve the fidelity of boiling water reactor (BWR) core modeling and simulation. The method involves propagating multigroup neutron cross-section uncertainties through various BWR computational models to evaluate uncertainties in key core attributes such as core keff, nodal power distributions, thermal margins, and in-core detector readings. Uncertainty-based inverse theory methods are then employed to adjust multigroup cross sections to minimize the disagreement between BWR core modeling predictions and observed (i.e., measured) plant data. For this paper, observed plant data are virtually simulated in the form of perturbed three-dimensional nodal power distributions with the perturbations sized to represent actual discrepancies between predictions and real plant data. The major focus of this work is to efficiently propagate multigroup neutron cross-section uncertainty through BWR lattice physics and core simulator calculations. The data adjustment equations are developed using a subspace approach that exploits the ill-conditioning of the multigroup cross-section covariance matrix to minimize computation and storage burden. Tikhonov regularization is also employed to improve the conditioning of the data adjustment equations. Expressions are also provided for posterior covariance matrices of both the multigroup cross-section and core attributes uncertainties.