Methodology for Sensitivity Analysis of Homogenized Cross-Sections to Instantaneous and Historical Lattice Conditions with Application to AP1000® PWR Lattice

Dean Price,Krishna Garikipati,Thomas Folk,Matthew Duschenes,Brendan Kochunas

doi:10.3390/en14123378

Abstract

In the two-step method for nuclear reactor simulation, lattice physics calculations are performed to compute homogenized cross-sections for a variety of burnups and lattice configurations. A nodal code is then used to perform full-core analysis using the pre-calculated homogenized cross-sections. One source of uncertainty introduced in this method is that the lattice configuration or depletion conditions typically do not match a pre-calculated one from the lattice physics simulations. Therefore, some interpolation model must be used to estimate the homogenized cross-sections in the nodal code. This current study provides a methodology for sensitivity analysis to quantify the impact of state variables on the homogenized cross-sections. This methodology also allows for analyses of the historical effect that the state variables have on homogenized cross-sections. An application of this methodology on a lattice for the Westinghouse AP1000® reactor is presented where coolant density, fuel temperature, soluble boron concentration, and control rod insertion are the state variables of interest. The effects of considering the instantaneous values of the state variables, historical values of the state variables, and burnup-averaged values of the state variables are analyzed. Using these methods, it was found that a linear model that only considers the instantaneous and burnup-averaged values of state variables can fail to capture some variations in the homogenized cross-sections.

Highlights

From the millimeter that may separate the fuel pellet from the cladding to the few meters that may make up the diameter of the core, nuclear reactors contain geometric features that span large scales
The present study presents a new methodology for sensitivity analysis to quantify the effect of instantaneous state variables, and the effect of the past values of these state variables on the HXS
Some analysis is presented that offers guidance on how complex of a history should be considered by looking into the sensitivity of HXS to burnup-averaged state variables

Summary

Introduction

From the millimeter that may separate the fuel pellet from the cladding to the few meters that may make up the diameter of the core, nuclear reactors contain geometric features that span large scales. As such, techniques such as cross-section homogenization must be used to perform full-scale core design calculations. The lattice calculations are often performed with computer codes written to approximate solutions to the neutron transport equation. Often, these codes are coupled with solvers for the Bateman equations [4]

Methods

Results

Conclusion