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All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Multiphysics Coupling of PROTEUS-NODAL and SAM for Molten Salt Reactor Simulation

The purpose of this report is to document the new features and capabilities that have been implemented in the PROTEUS-NODAL code and the coupling procedure of PROTEUS-NODAL with SAM to analyze MSRs. This report is organized as follows. Section 2 presents the variational nodal P 1 solver for cylindrical geometries and its verification test results. Section 3 discusses the transient analysis capability implemented in the P 1 solvers of PROTEUS-NODAL. The solution methods for the coupled system of TFSP and precursor drift equations, the coarse mesh finite difference (CMFD) acceleration, the kinetics parameter evaluation method, and the thermal feedback are discussed. The verification test results against the SP 3 solutions are also discussed. Section 4 describes the coupling scheme of PROTEUS-NODAL and SAM under the MOOSE framework for MSR applications. The developed MOOSE applications named “TreeFrog” and “TreeKangaroo” are discussed. Verification test results for the coupled system are also discussed by comparing the MSFR steady state solution with that obtained from a manually coupled PROTEUS-NODAL and ANSYS CFX computational fluid dynamics (CFD) calculations and the MSFR transient analysis results with the open literature solutions and the PROTEUS-NODAL solutions obtained with the standalone thermal-hydraulics solver. Section 5 provides conclusions and future works.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2021

IC reports (2021)

We requested HPC support to continue research on the seismic waves generated by impacts. We used the following codes: (1) the Hybrid Optimization Software Suite (HOSS), developed at LANL. HOSS is based on a combined Finite and Discrete Element Method (FDEM). New material models are developed for the sedimentary rocks. HOSS has been recently benchmarked to iSale and FLAG codes. SPECFEM3D is an open-source code developed since the last 90s. It won the Gordon Bell award for best performance in 2003, was finalist again in 2008 for a run at 0.16 petaflops on 149,784 cores on the ‘Jaguar’ Cray system at Oak Ridge National Laboratory. It also won the BULL Joseph Fourier supercomputing award in 2010.; SW4 is a 4th-order finite difference code developed at LLNL which is currently actively developed to handle complex 3D models and to be ported on future exascale platforms. We assessed our need to a total of 3.9M CPU-hrs for year 1 and and 3.1 M for year 2.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Vibration-Based Sensor Design: A Grey-Box Approach

Knowledge of the internal structure of an object or device under investigation proceeds from the basic idea of constructing its dynamic behavioral relations governed by a set of differential/algebraic equations that characterize its response. These equations can be partial differential equations leading to finite element or finite difference relations requiring a complex numerical solution on a super computer or ordinary differential equations requiring sophisticated numerical integration techniques to obtain the desired solution. Discrete dynamic systems evolving from digitized data acquisition are typically captured by sampled-data (continuous-to-discrete) representations characterized by a set of difference equations specifying the underlying system dynamics. In any case, with a mathematical description in hand, Grey-Box modeling techniques have evolved, concerned with the estimation of model parameters embedded in a prescribed set of equations (the system) governing its behavior, while capturing the underlying physical phenomenology of the problem at hand.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Vadose and Saturated Zone Flow and Transport Model Package Report for the Active Trenches of the Low-Level Burial Grounds, Hanford Site, Washington

This model package report (MPR) documents the development of the integrated vadose and saturated zone flow and transport model developed for the performance assessment of Trenches 31 and 34 in the low-level burial grounds (LLBGs). This modeling capability is intended for use in addressing the analysis requirements outlined in DOE O 435.1, Chg 1, Radioactive Waste Management1. The overall objective of the modeling effort is to provide a basis for making informed disposal decisions pertinent to Trenches 31 and 34. The purpose of the MPR is to document the development of the three-dimensional numerical vadose zone and saturated flow and transport model test case and evaluate its adequacy to support the LLBG performance assessment. The purpose is not to present results for DOE 435.1 decision making. The use of the model to perform base case and sensitivity analysis for the LLBG performance assessment, including inputs and results, is documented separately in subsequent environmental calculation files. This report discusses the development and translation of the conceptual model for flow and contaminant transport into the LLBG performance assessment three-dimensional numerical flow and transport model evaluated using the Subsurface Transport Over Multiple Phases (STOMP©) simulator. The development of representative geologic framework is described along with the implementation of waste release models used to represent contaminant release from waste disposed in the trenches. The report also provides the technical basis for specific model parameters and boundary conditions, along with description of modeling assumptions. This MPR includes certain calculations that are necessary to demonstrate the soundness of the model. Results provided by the model include vadose zone and saturated zone flow fields, and estimates of the possible future concentration in groundwater of technetium-99 and iodine-129 as example test cases. As an evaluation of the test cases, the model estimates of current vadose conditions are compared to available and analogous field and laboratory data, and compared to the results from the original performance assessment model (WHC-EP-0645, Performance Assessment for the Disposal of Low-Level Waste in the 200 West Area Burial Grounds 2 ). The features, events, and processes applicable to vadose zone and saturated zone flow and transport model are identified, and representative initial estimates for various parameters are documented. Note that the parameter estimates presented in this MPR are for illustration purposes, and may or may not reflect values selected for eventual performance assessment. Several key topical discussions (i.e., basis for recharge estimates, basis for vadose zone modeling, basis for saturated zone model development, and calibration) are included, which serve as the groundwork for confidence building for the groundwater pathway modeling and results. Numerical simulation results based on an example test case are included to illustrate the use of the combined saturated-unsaturated model in performance assessment calculations. Sensitivity and uncertainty results are not included in this MPR. Those results will be included in future environmental calculation files. The inclusion of the trapezoidal trench geometry and construction details in the finite difference grid introduces some gross simplifications regarding the trench and liner systems. The model test case presented in this MPR includes the assumption that the trench liner system does not affect flow through or around the trenches after the liner system is assumed to fail. This MPR also includes results of other test cases that involve alternate assumptions about how to incorporate the hydraulic effects of the trenches into the vadose zone of the model. These alternate cases do not attempt to account for the presence of the liner system after its assumed failure either. None of these cases is considered to be the base case at this time. Analysis and alternate cases that attempt to account for the presence of the liner system in greater detail, and its effect on flow through and around it, are to be documented in subsequent environmental calculation files. Depending on the results of those analyses and alternate cases, the eventual base case may involve more detailed inclusion of the effects of the liner system hydraulics.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2021

An efficient method to estimate the probability density of seismic Green's functions

We present a computationally efficient method to approximate the probability distribution of seismic Green's functions given the uncertainty of an Earth model. The method is based on the Karhunen-Loève (KL) theorem and an approximation of the Green's function (or seismogram) covariance. Using Monte Carlo (MC) simulations as a control case, we demonstrate that our KL-based method can accurately reproduce a probability distribution of seismograms that results from an uncertain Earth model for a MC-derived seismogram covariance. We then describe a method to estimate the covariance of the seismograms resulting from those Earth models that is not based on MC simulations. We use the estimated Green's function covariance in conjunction with our KL-based method to produce a Green's function probability distribution, and compare that distribution to a Green's function probability distribution produced using a MC finite difference method. We find that the Green's function probability distribution approximated using our KL-based method generally mimics that produced using the MC simulations, especially for direct-arriving body waves. However the accuracy of the KL-based method generally decreases for later times in the simulated Green's function distribution.

58 GEOSCIENCES↗
DOE OSTI2021

Hexagonal Geometries in MPACT

The MPACT code is a high-fidelity light-water reactor analysis code using whole-core pin-resolved neutron transport calculations on modern parallel-computing hardware. MPACT uses the 2D/1D method to solve 3D neutron transport problems by decomposing the problem into a stack of 2D slices, each of which is solved independently using the method of characteristics (MOC). The slices are then coupled axially using the P3 nodal expansion method (NEM-P3) for the 1D axial calculations. MPACT also employs the coarse mesh finite difference (CMFD) method to accelerate calculations. This manuscript details work supporting advanced reactor designs using hexagonal pins and hexagonal assemblies such as the VVER-1000. If performed correctly, MOC is geometry agnostic. However, MPACT previously had optimizations in place for Cartesian geometries, specifically in the modularization and current calculations. Sections 2 and 3 detail the changes made to MPACT to support MOC and CMFD calculations on hexagonal geometries. Section 4 reports results demonstrating solution consistency for problems run with and without CMFD acceleration, results demonstrating solution consistency when run in serial and parallel, and pincell results using the Monte Carlo code, McCard’s benchmark results.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

3D orthorhombic earth model effects on seismic source characterization

Most earth materials are anisotropic with regard to seismic wave-speeds, especially materials such as shales, or where oriented fractures are present. However, the base assumption for many numerical simulations is to treat earth materials as isotropic media. This is done for simplicity, the apparent weakness of anisotropy in the far field, and the lack of well-characterized anisotropic material properties for input into numerical simulations. One approach for addressing the higher complexity of actual geologic regions is to model the material as an orthorhombic medium. We have developed an explicit time-domain, finite-difference (FD) algorithm for simulating three-dimensional (3D) elastic wave propagation in a heterogeneous orthorhombic medium. The objective of this research is to investigate the errors and biases that result from modeling a non-isotropic medium as an isotropic medium. This is done by computing “observed data” by using synthetic, anisotropic simulations with the assumption of an orthorhombic, anisotropic earth model. Green’s functions for an assumed isotropic earth model are computed and then used an inversion designed to estimate moment tensors with the “observed” data. One specific area of interest is how shear waves, which are introduced in an anisotropic model even for an isotropic explosion, affect the characterization of seismic sources when isotropic earth assumptions are made. This work is done in support of the modeling component of the Source Physics Experiment (SPE), a series of underground chemical explosions at the Nevada National Security Site (NNSS).

58 GEOSCIENCES↗
DOE OSTI2022

MPACT Software Management Plan (V.4.3)

The MPACT code solves a discretized form of the Boltzmann transport equation on a wide variety of geometries and is distributed with a multigroup neutron cross section library. MPACT provides an advanced geometrically resolved neutral-particle transport capability to solve the flux distribution throughout the entire problem geometry, and it can model the isotopic depletion, decay, and activation of materials. The flux solution in MPACT is provided using a 2D/1D synthesis method within the framework of the 3D coarse mesh finite difference (CMFD) method for which axial and radial correction factors are obtained from 2D method of characteristics (MOC) and 1D nodal expansion method (NEM), PN, or SN. Other key characteristics of the MPACT code include the subgroup method and the embedded self-shielding method (ESSM) for resonance treatment, depletion capability based on the ORIGEN exponential matrix method, and a simplified thermal-hydraulics method for temperature/fluid feedback. The sole purpose of the simplified feedback model is to provide a mechanism for testing during code development and to provide a limited capability for educational applications. Work performed at the code level supports the VERA-QA-001, quality assurance program plan (QAPP) and VERA-QA-002, VERA Software Quality Assurance Plan.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Expedited Real Time Processing for the NETL HYPER Cyber-Physical System (Final Report)

The primary objective of the proposed project was to provide the National Energy Technology Laboratory’s Hybrid Performance (Hyper) Facility the needed numerical methods algorithm(s), software development and implementation support to enact real time cyber-physical systems (CPSs) that simulate process dynamics on the order of five milliseconds or smaller. The proposed paths forward comprised three distinct approaches to hasten transient simulations. They fell under the numerical methods categorical options of: 1) optimizing key parameters within the facility’s pre-existing real time processing scheme; 2) introducing an “informed” processing approach wherein a priori computations expedite real time attempts; and 3) implementing alternatives to the employed explicit-implicit blended finite difference (spatio-temporal) approach. Each of these three classes were proposed independently as options for improvement, yet in some cases one class of approach could have complemented another.

20 FOSSIL-FUELED POWER PLANTS↗
DOE OSTI2023

Design of a Nanophotonic Hybrid Coupler

This project aims to design and simulate a nanophotonic hybrid coupler for detecting vacuum ultraviolet (VUV) light with higher efficiency. VUV light is of significant interest because of its applications ranging from high energy physics to space science and electronic industry. However, current VUV photodetectors have very low efficiencies because most materials absorb in the VUV region (100-200 nm). To address this challenge, I have designed a plasmonic-dielectric coupler with wavelength shifting properties, enabling high Purcell enhancement and far-field confinement. The coupler consists of a cylindrical cSi resonator on top of a thin ZnO layer, and Ag and SiO2 are used as substrates. Simulations are done using the finite-difference time domain method to solve Maxwell’s equations, and specifically with Meep and Lumerical. The effectiveness of the coupler is characterized by the Purcell factor and far-field radiation. The Purcell factor reaches a maximum near 390 nm and is in the o rder of 10^4. Furthermore, the coupler also allows partial control of the directionality of the far-field radiation. With the presence of the resonator, the radiation is directed towards the coupled metalens. Overall, our design combines the advantages of plasmonic and dielectric couplers, along with the intrinsic wavelength shifting properties of materials to enhance VUV detection significantly, and such a device can be used in, for example, the DUNE project.

Zhou, Jiayang↗
DOE OSTI2024

Pore-scale visualization of natural hydrate-bearing sediments

Accurate modeling of gas hydrate reservoir productivity and geomechanical risks associated with subsurface dissociation of natural gas hydrates (NGH) requires the determination of model parameters through physical testing on natural hydrate-bearing sediments (HBS). This involves investigating the hydro-mechanical behavior of undisturbed hydrate samples from nature under in situ conditions using pressure core characterization and analysis, which provides a unique opportunity for research. By employing state-of-the-art micro computed tomography imagery on cryogenically preserved, hydrate-bearing sediment samples, we can determine hydrate saturation as well as permeability with and without the presence of hydrates in the sediment. Furthermore, utilizing a machine learning based image segmentation technique, it is possible to extract pore space and grain information. Subsections of the entire image volume were used to determine anisotropic permeabilities using a finite-difference method Stokes solver (FDMSS). Additionally, permeability measurements on whole pressure and temperature preserved hydrate-bearing core were analyzed by utilizing the National Energy Technology Laboratory’s (NETL) Pressure Core Characterization and X-ray CT Visualization Tool (PCXT) to manipulate, cut, and analyze pressure preserved sediment. Permeabilities were measured under a broad range of vertical stress states to simulate expected pressure changes during production scenarios, and the results show that permeabilities derived from images are in agreement with those from traditional core derived experiments. The collected stress-dependent permeability, permeability anisotropy, and corresponding gas hydrate saturations provide valuable input into numerical simulations of reservoir productivity. These properties have been proven to be key parameters determining a long-term reservoir response under depressurization.

Liu, Mengwei [Oak Ridge Institute for Science and ↗
DOE OSTI2024

Determining Exact RANS Operators with the Macroscopic Forcing Method (Final Report)

This report contains a compilation of key results and findings from the ACT project “Determining Exact RANS Operators with the Macroscopic Forcing Method.” The Macroscopic Forcing Method (MFM), a numerical tool for determining closure operators, is used to measure eddy diffusivity moments in Rayleigh-Taylor (RT) instability. It is first applied to low-Atwood 2D RT instability; that work is then extended to 3D RT at different finite Atwood numbers. It is found that nonlocality is important for modeling the mean scalar transport closure operator in RT mixing. Additionally, work is done to improve the statistical convergence of MFM for chaotic problems like RT mixing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Verification of the PERSENT Software

Ongoing commercial design activities require a thorough verification of the Argonne Reactor Computation codes be performed. DIF3D is central to this system and substantial work has been done to verify its accuracy on several identified commercial needs. This manuscript details the verification work done on PERSENT which relies upon the DIF3D code for its forward and adjoint flux solution. Previous work identified the PERSENT features required to be verified to support commercial design activities, features of which are generally applicable to hexagonal-Z fast reactor designs. The scope of this verification effort includes verifying PERSENT’s ability to correctly calculate four key quantities: perturbation worth distributions, kinetics parameters, sensitivity coefficients, and cross section uncertainty quantification. This manuscript provides the verification tasks and their results with respect to these quantities needed for commercial design activities. For the perturbation worth distributions, hand calculations are deployed to verify the PERSENT calculated results. Similarly, hand calculation of the PERSENT computed kinetics parameters is also used to verify the PERSENT results. In both of these, the input to PERSENT is manipulated to ensure the hand calculation exactly matches the equations PERSENT is calculating. The sensitivity coefficients involve calculating the derivatives of a parameter (such as reactivity worth), with respect to the cross section data. Direct finite difference calculations with DIF3D are used to verify the PERSENT calculated results. For the uncertainty quantification, manufactured input to PERSENT is used to allow an exact hand calculation to reproduce the PERSENT calculated results. The work detailed in this report verified that significant issues were identified for earlier versions of PERSENT for sensitivity coefficients which were corrected in this work and thus version 12.1.0 of PERSENT must be used to reproduce all of the verified work in this report.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

VARI3D & PERSENT: Perturbation and Sensitivity Analysis

The nodal diffusion method is one of the most widely used approaches in modern reactor analysis. In the nodal diffusion method, a coarse multi-group set of “homogenized” parameters is constructed such that the complex geometry of a reactor core along with the energy dependence of neutron and gamma ray cross sections in a nuclear reactor are conserved in the simpler geometry. The homogenization is typically done on a fuel assembly level as is the case in the DIF3D code developed at Argonne National Laboratory. The nodal methodology is used primarily to predict fuel cycle behavior of nuclear systems of which there is a substantial amount of validation in the literature. Another use of the nodal method is to obtain reactivity coefficients and kinetics parameters for use in a safety analysis of a given nuclear reactor. While there are many ways to obtain reactivity worth and kinetics parameters, the work presented in this manuscript is unique as it provides the user with the ability to compute reactivity worths, kinetics parameters, and cross section sensitivities with a Cartesian and hexagonal geometry based transport code. This manuscript serves as a single manual for two separate codes: VARI3D and PERSENT. The VARI3D code (VARIational 3D) is based upon the classic finite difference diffusion theory solver available in DIF3D. The PERSENT code (PERturbation and SENitivity for Transport) is based upon the variational nodal method employed in DIF3D termed VARIANT. The VARIANT solver was added to DIF3D in 1995 and has seen continued development and use for the last 18 years. Because VARI3D primarily uses deprecated coding practices, rather than incorporating the perturbation and sensitivity treatments for transport within VARI3D, a new coding development was built using modern Fortran coding. The primary purpose of this manual is to describe the theory behind PERSENT (and by convenience, that of VARI3D) and discuss the input and output of PERSENT along with giving potential users an idea of how to use it. While this manuscript does describe the input and output of VARI3D, the PERSENT code is intended to be the replacement capability of VARI3D as PERSENT can generate nearly identical (if not superior) diffusion theory results. In this manuscript, the relevant aspects of generalized perturbation theory and exact perturbation theory that apply to both VARI3D and PERSENT are covered. The input and output of VARI3D is displayed by excerpting several of the example problems. Similarly, the input and output of PERSENT is displayed along with tips on how best to use the code. Note that the input and output of the inhomogeneous solver wrapped around DIF3D (DIF3D_IFS) is also discussed as it is needed to carry out some of the sensitivities in PERSENT such as reaction rate ratios. This manuscript describes several perturbation and sensitivity problems, and the results computed using PERSENT. From these sections, potential users should find that PERSENT provides not only the typical tables of numbers desired in perturbation and sensitivity analysis work, but also can visually plot the result for a more thorough understanding of the space and energy distribution (Section 5). Overall, PERSENT is observed to produce accurate reactivity worths and sensitivities for the displayed set of test problems and clearly demonstrates the need to have a transport-based sensitivity capability as evident from the thousands of percent errors observed in the 21-group hexagonal fast reactor problem (covered in Section 7). The uncertainty calculation capability is described in Section 3 and demonstrated in Section 7.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Hypercomplex Automatic Differentiation in the Eulerian Hydrocode PAGOSA

Enabling the computation of partial derivatives or sensitivities in production hydrocodes is beneficial for design, optimization, sensitivity analysis, and uncertainty quantification. Traditional finite difference approximations of these sensitivities are inefficient since convergence studies of the step size is required for each parameter of interest. For these reasons, HYPercomplex Automatic Differentiation (HYPAD) was implemented in the Eulerian hydrocode PAGOSA. HYPAD is analogous to forward-mode automatic differentiation except hypercomplex numbers (numbers with multiple imaginary parts) are used instead of dual numbers. Accurate partial derivatives can be computed of all state variables with respect to multiple input variables in a single run. The method was implemented using operator overloading to handle hypercomplex algebra. HYPAD was demonstrated and verified on Sod’s shock tube problem to compute derivatives of the state variables with respect to a material parameter, initial conditions, and geometry.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

DIF3D-VARIANT 12.0: Updates and New Features

The DIF3D code has been a workhorse of fast reactor analysis work at Argonne National Laboratory for over 40 years. In 1995, a transport option called VARIANT was added to DIF3D to improve the flux solutions for fast reactor problems which we term DIF3D-VARIANT today. DIF3D-VARIANT performs nodal neutron transport calculations using P N or SP N theory in Cartesian and hexagonal two- and three-dimensional geometries. The limited computing capabilities of the time restricted DIF3D-VARIANT to use at most a 6 th order spatial approximation combined with a P3 flux approximation and P1 scattering kernel for a 33 group structure on most studied reactor problems. Computer capabilities have increased steadily since 1995 and today much larger space-angle-energy approximations are possible. This manuscript serves as an update to the theory section of the original DIF3D-VARIANT manual and details more than twenty years of changes made to DIF3D to make version 12 which was released on November 1 st , 2024. The primary focus of the initial work was to extend the space-angle approximations available in DIF3D-VARIANT such that the error due to transport approximations could be better understood. This work was started and completed in 2002 and marked the official version 10. Unfortunately, those higher order approximations could not be used at that time due to the memory constraints of the BPOINTER part of DIF3D (limited to 2 GB). In version 11, completed in 2012, BPOINTER was circumvented in DIF3D-VARIANT for the largest arrays by introducing a Fortran 90 module called LMA (Large Memory Array). This seamlessly replaces all of the functionality of the BPOINTER concept, but it allows 64 bit addressing for every array such that they can be larger than 2 GB. It is now common for DIF3D-VARIANT jobs to consume 50 GB of memory on modern workstations when using high order space-angle approximations and a large number of groups. Many improvements were made to version 11 from 2012 to 2022 when work to create version 12 started. For version 12, several parts of DIF3D were updated to improve performance and thread parallelism was introduced to further reduce the runtime. Numerous minor bugs were discovered in DIF3D-VARIANT as part of the process of creating the perturbation and sensitivity code PERSENT. All of these algorithmic problems were identified in the transition from version 10 to version 11 which prevented DIF3D-VARIANT from running efficiently and reliably. Firstly, the coarse mesh rebalance scheme would routinely diverge and a study detailed in this report demonstrates how it was also typically not effective. This is not a failure of the coarse mesh rebalance methodology, but a failure of its implementation in DIF3D-VARIANT for hexagonal geometries. The fission source extrapolation algorithm was also found to be unreliable on larger group structure problems, leading to divergence in some cases and a negligible improvement in performance overall. Finally, the “Omega” acceleration applied to the partial current solver routine of DIF3D-VARIANT was found to cause DIF3D-VARIANT to converge to the wrong answer. To resolve these issues, both the coarse mesh rebalance and fission source extrapolation were permanently disabled in version 11. The Tchebychev acceleration was put in as a temporary reliable alternative but it is generally inferior to coarse mesh rebalance or coarse mesh finite difference. For the Omega acceleration, the factor was restricted to guarantee that it would not cause follow-on errors in PERSENT. Due to limited funding to support maintenance and development of DIF3D in the last 10 years, no effort was spent since to resolve the outer iteration acceleration. Except for the threading work, all of the changes discussed in this manuscript refer to changes made between version 10 and version 11. Performance comparisons are done to demonstrate the improvements from version 9 to version 12. As will be demonstrated, the updated versi

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Implementation of Perturbation Theory and Sensitivity Capabilities in Griffin

Griffin is a Multiphysics Object-Oriented Simulation Environment (MOOSE) based reactor Multiphysics analysis application, jointly developed by Argonne and Idaho National Laboratories under the DOE-NE NEAMS program. This fiscal year, capabilities for reactivity and sensitivity evaluation using perturbation methods were implemented and verified. The First Order Perturbation Method (FOPT) was employed to compute reactivity worth resulting from small perturbations in input parameters, while the Generalized Perturbation Theory (GPT) was used to evaluate sensitivities of a range of response types, including reaction rate ratio, k-eigenvalue, neutron generation time, and effective delayed neutron fraction. These perturbation methods enable users to quantify how response quantities change due to a perturbation in a input parameter without explicitly performing an additional transport simulation for each perturbed state. In particular, the GPT formulation accounts for indirect effects arising from flux changes by solving generalized inhomogeneous equations, for which a Neumann series-based iterative solution method was developed and implemented in Griffin. The implemented reactivity and sensitivity evaluation capabilities were verified using two test problems: an infinite homogeneous system and a two-dimensional hexagonal core. The results showed excellent agreement with reference solutions obtained by a direct method based on finite difference approximation as well as GPT-based results from the PERSENT code, confirming the accuracy of both reactivity and sensitivity evaluations. Additionally, preliminary uncertainty quantification (UQ) results were obtained by combining the sensitivity values computed using GPT and external covariance data, demonstrating that the implemented sensitivity results can be reliably used for uncertainty calculations. To further demonstrate the generality and practical strength of the implementation, the sensitivity evaluation capability was successfully applied to the Empire microreactor with a geometrically complex design that poses significant modeling challenges. The results confirm that Griffin enables sensitivity evaluations even for irregular and highly heterogeneous reactor configurations, thereby establishing a foundation for UQ applications in advanced reactor designs and analyses.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗