Search NASA⌕ Search

SEARCH · Search NASA

Results for “Code verification”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 631 records · Page 35
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Code validation for the simulation of supersonic viscous flow about the F-16XL

The viewgraphs and discussion on code validation for the simulation of supersonic viscous flow about the F-16XL are provided. Because of the large potential gains related to laminar flow on the swept wings of supersonic aircraft, interest in the applications of laminar flow control (LFC) techniques in the supersonic regime has increased. A supersonic laminar flow control (SLFC) technology program is currently underway within NASA. The objective of this program is to develop the data base and design methods that are critical to the development of laminar flow control technology for application to supersonic transport aircraft design. Towards this end, the program integrates computational investigations underway at NASA Ames-Moffett and NASA Langley with flight-test investigations being conducted on the F-16XL at the NASA Ames-Dryden Research Facility in cooperation with Rockwell International. The computational goal at NASA Ames-Moffett is to integrate a thin-layer Reynolds averaged Navier-Stokes flow solver with a stability analysis code. The flow solver would provide boundary layer profiles to the stability analysis code which in turn would predict transition on the F-16XL wing. To utilize the stability analysis codes, reliable boundary layer data is necessary at off-design cases. Previously, much of the prediction of boundary layer transition has been accomplished through the coupling of boundary layer codes with stability theory. However, boundary layer codes may have difficulties at high Reynolds numbers, of the order of 100 million, and with the current complex geometry in question. Therefore, a reliable code which solves the thin-layer Reynolds averaged Navier-Stokes equations is needed. Two objectives are discussed, the first in greater depth. The first objective is method verification, via comparisons of computations with experiment, of the reliability and robustness of the code. To successfully implement LFC techniques to the F-16XL wing, the flow about the leading edge must be maintained as laminar flow. Therefore, the second objective is to focus on a series of numerical simulations with different values of angle of attack, alpha, and Reynolds numbers. The purpose of the simulations is to study their effects on the two main factors which precipitate transition to turbulence at leading edges of highly swept wings (e.g., 'spanwise contamination' and 'crossflow instability').

Flores, Jolen↗
DOE OSTI2024

Security of quantum position-verification limits Hamiltonian simulation via holography

We investigate the link between quantum position-verification (QPV) and holography established in [1] using holographic quantum error correcting codes as toy models. By inserting the “temporal” scaling of the AdS metric by hand via the bulk Hamiltonian interaction strength, we recover a toy model with consistent causality structure. This leads to an interesting implication between two topics in quantum information: if position-based verification is secure against attacks with small entanglement then there are new fundamental lower bounds for resources required for one Hamiltonian to simulate another.

AdS-CFT Correspondence↗
DOE OSTI2021

Verification Testing For Solid-Element Material Models 11-19 in DYNA3D/ParaDyn

This technical report documents the creation and implementation of verification tests for solid-element material models 11 through 19 available in DYNA3D/ParaDyn. The verification tests covered all aspects of each material model, except for the Weibull distribution functionality in material models 15 and 19. General test cases were created to verify the elastic and plastic behavior of the material models. Other additional tests were developed to examine the intricacies of each material model. Each test involved the use a kinematic load case and specification of material parameters necessary to activate corresponding features of the material model. The load cases prescribed the full time history of the kinematic motion for the solid elements, and these loads are independent of the material model or element formulation. When possible, closed form solutions were then derived for each verification test in a continuum setting. The DYNA3D simulations for each test were carried out over a unit time interval, t ϵ [0, 1], and the as implemented DYNA3D response was compared to the closed form solutions evaluated at discrete points in time. A relative error measure was determined for each test to justify the proper implementation of the material model. The relative errors comparing the DYNA3D solution to the analytical solution were, in general, on the order of machine precision except where noted. This signifies the proper implementation of solid-element material models 11-19. In the development of these verification tests, six bugs were found and fixed in the source code. Additionally, this work generated eighteen DYNA3D input decks and answer extraction scripts in the DYNA3D/ParaDyn Software Quality Assurance test suite, which are comprised of a total of 285 solid-element tests. Testing for each material model utilizes two input decks and answer extraction scripts, where one focuses on the linear elastic response and the other examines the inelastic and remaining functionalities of the material model. In total, this work added 285 individual verification test problems in the DYNA3D/ParaDyn test suite.

42 ENGINEERING↗
NASA NTRS2018

SLS Navigation Model-Based Design Approach

The SLS Program chose to implement a Model-based Design and Model-based Requirements approach for managing component design information and system requirements. This approach differs from previous large-scale design efforts at Marshall Space Flight Center where design documentation alone conveyed information required for vehicle design and analysis and where extensive requirements sets were used to scope and constrain the design. The SLS Navigation Team has been responsible for the Program-controlled Design Math Models (DMMs) which describe and represent the performance of the Inertial Navigation System (INS) and the Rate Gyro Assemblies (RGAs) used by Guidance, Navigation, and Controls (GN&C). The SLS Navigation Team is also responsible for the navigation algorithms. The navigation algorithms are delivered for implementation on the flight hardware as a DMM. For the SLS Block 1-B design, the additional GPS Receiver hardware is managed as a DMM at the vehicle design level. This paper provides a discussion of the processes and methods used to engineer, design, and coordinate engineering trades and performance assessments using SLS practices as applied to the GN&C system, with a particular focus on the Navigation components. These include composing system requirements, requirements verification, model development, model verification and validation, and modeling and analysis approaches. The Model-based Design and Requirements approach does not reduce the effort associated with the design process versus previous processes used at Marshall Space Flight Center. Instead, the approach takes advantage of overlap between the requirements development and management process, and the design and analysis process by efficiently combining the control (i.e. the requirement) and the design mechanisms. The design mechanism is the representation of the component behavior and performance in design and analysis tools. The focus in the early design process shifts from the development and management of design requirements to the development of usable models, model requirements, and model verification and validation efforts. The models themselves are represented in C/C++ code and accompanying data files. Under the idealized process, potential ambiguity in specification is reduced because the model must be implementable versus a requirement which is not necessarily subject to this constraint. Further, the models are shown to emulate the hardware during validation. For models developed by the Navigation Team, a common interface/standalone environment was developed. The common environment allows for easy implementation in design and analysis tools. Mechanisms such as unit test cases ensure implementation as the developer intended. The model verification and validation process provides a very high level of component design insight. The origin and implementation of the SLS variant of Model-based Design is described from the perspective of the SLS Navigation Team. The format of the models and the requirements are described. The Model-based Design approach has many benefits but is not without potential complications. Key lessons learned associated with the implementation of the Model Based Design approach and process from infancy to verification and certification are discussed

Oliver, T. Emerson↗
DOE OSTI2025

Analysis of the impact of parallel magnetic fluctuations on linear gyrokinetic stability in NSTX-U and verification of gyro-fluid models

In this work, we use the CGYRO gyrokinetic code to analyze two L- and one H-mode discharges from the National Spherical Torus Experiment (NSTX) and NSTX-Upgrade (NSTX-U) selected due to their different mix of ion-scale driftwaves, ion temperature gradient (ITG) mode and trapped electron mode (TEM), and electromagnetic instabilities, kinetic ballooning mode (KBM), and micro-tearing mode (MTM) in the plasma core. It is found that the effect of parallel magnetic fluctuations is strongly destabilizing to the unstable KBMs compared to calculations with only perpendicular magnetic fluctuations. Two discharges have a mix of ITG/TEM and MTMs that are predicted to be dominant instability across the plasma radius. The parallel magnetic fluctuations are found to have little effect on the MTM stability but are destabilizing to ITG/TEM modes. To test the validity of the gyro-fluid linear stability codes TGLF and GFS at low aspect ratio, a database of linear growth rates has been created using the CGYRO gyrokinetic code. The database is comprised of various parameter scans around a standardized set of NSTX-U core parameters. It contains a group of electrostatic cases and an electromagnetic group that includes the effects of perpendicular and parallel magnetic fluctuations. Comparing the results from the GFS and TGLF models, we find that GFS exhibits the best agreement with the database of CGYRO linear growth rates. Comparing the model results for the electromagnetic scans shows that GFS captures the effects of parallel magnetic fluctuations accurately, while the TGLF model does not, as it lacks sufficient perpendicular energy resolution.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1981

Model verification studies using accurate measurements of spin up

The reliability and accuracy of the numerical code for spin up flows in a cylinder by comparing the numerical results against high resolution laser Doppler velocimeter (LDV) measurements of the azimuthal flows were checked. A computer code to generate numerical solution for axisymmetric rotating fluid in a cylinder was obtained and amended for routine use at MSFC. The numerical simulations used the Navier-Stokes equations in axisymmetric form and employed finite difference techniques on both constant and variable grids. The numerical solutions are analyzed to gain further insight into the fundamental questions analyzed in rotating fluid dynamics.

Hyun, J. M.↗
NASA NTRS1986

A verification of unsteady Navier-Stokes solutions around oscillating airfoils

A finite difference solution code for the two dimensional Navier-Stokes equations was combined with a moving-grid system. The thin layer Navier-Stokes equations with a turbulence model are solved in a time-accurate manner in order to study the unsteady aerodynamics around airfoils undergoing small amplitude pitching or heaving motions in the transonic regime. The accuracy of the solutions obtained by the use of the present moving-grid technqiue is investigated. The effects of the minimum grid size and the integrating time-step size on the solutions are also checked. Some of the solutions obtained by the present method are compared with experimental results. It is demonstrated that the unsteady aerodynamics around oscillating airfoils can be predicted fairly well by the present code for cases in which the dynamic angle of attack or displacement is small.

Nakamichi, J.↗
NASA NTRS1995

The formal verification used for the AAMP5 and AAMP-FV

The main goal of the project was two-fold: First, to investigate the feasibility of formally specifying and verifying a complex commercial microprocessor that was not expressly designed for formal verification. Second, to explore effective ways to transfer the technology to an industrial setting. The choice of the AAMP5 satisfied the first goal since the AAMP5 was not designed for formal verification, but to provide a more than threefold performance improvement while remaining object-code-compatible with the earlier AAMP2, which is used in numerous avionics applications, including the Boeing 737, 747, 757, and 767. To satisfy the technology transfer objective, we had to develop a suitable verification methodology and a formal infrastructure to make the technology usable by practicing engineers. This infrastructure includes techniques for decomposing the microcompressor verification problem into a st of verification conditions that the engineers can formulate and strategies to automate the proof of the verification conditions. The development of the infrastructure was one of the key accomplishments of the project. Most of the infrastructure and methodology are general enough to be reused for other microprocessors, certainly in the verification of another member of the AAMP family. This methodology was used to formally specify the entire microarchitecture and more than half of the instruction set and to verify a core set of eleven AAMP5 instructions representative of several instruction classes. However, the methodology and the formal machinery developed are adequate to cover most of the remaining AAMP5 instructions. Although PVS was the vehicle of the experiment, the methodology is applicable to other sufficiently powerful theorem provers.

Srivas, Mandayam↗
DOE OSTI2018

The Influences of Neutron Irradiation on Aggregate Induced Degradation of Concrete

Reactor cavity concrete, the primary support structure for the reactor pressure vessel (RPV), is exposed to chronic neutron/gamma radiation during normal operation. During long term operation, the interaction of neutron irradiation with the concrete’s constituents may cause premature degradation of the concrete structure, as highlighted by a review of concrete properties in nuclear power plant environments. At high fluence levels, as in biological shielding, neutron irradiation may cause amorphization of the crystalline components of concrete, i.e., mineral aggregates, and volume changes, which are typically expansive in nature. Volume expansion can generate tensile stresses within concrete which can induce microcracking and/or result in debonding of aggregate with the matrix. On the other hand, structural disordering can result in changes in the stability of the phase in aqueous environments. This report presents the findings of investigations performed over 3 years through the collaboration of researchers from University of California, Los Angeles, Arizona State University, and Oak Ridge National Laboratory. The first part of the study addresses the effect of neutron irradiation on the durability of aggregates. Comparisons of aqueous dissolution rates, as a function of pH and temperature, were performed for aggregates that are either pristine (i.e., non-irradiated) or exposed to Ar+ ion irradiation at specified doses. These experimental results were coupled with molecular dynamics simulations of atomic scale changes in the crystallographic structure of the mineral and any resulting changes in physical properties (e.g., density) that result. The second section focuses on macroscopic effects of such changes in aggregate behavior in concrete degradation, primarily through changes in the concrete’s microstructure. Particularly, the effects akin to those originating from alkali-silica reaction (ASR) were evaluated. The project is structured to encompass 6 main tasks, as follows: Task 1: Selection of aggregates in relation to their abundance and mineralogy, and their irradiation Task 2: Molecular dynamics (MD): The effects of irradiation on the atomic disordering of aggregates Task 3: The influences of irradiation on aggregate reactivity Task 4: Reactive-transport simulation of expansive product formation in concrete microstructures Task 5: X-FEM-based modeling of damage evolution due to irradiation-induced aggregates reactions Task 6: Benchmarking, verification and validation of the simulation modules Thus, a rigorous understanding of irradiation-assisted mineral alterations was used to develop a mechanistic degradation model for concrete exposed to neutrons, while considering aspects of: chemical reaction (dissolution and precipitation), mass and ion transport, and damage evolutions. The models developed were embedded in a multi-physics aging code for nuclear components and structures called Grizzly, which allows for benchmarking, verification, and validation against expansion data acquired on concrete undergoing alkali-silica reaction, a physically/chemically equivalent form of degradation that develops in the absence of radiation. These findings provide insight into the sensitivities of minerals to irradiation, by highlighting characteristics of concretes and power plants subject to such risks. The research will aid the nuclear power industry to anticipate and mitigate such risks in light of second license renewals.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Initial development and verification of a primary load design method based on elastic-perfectly plastic analysis

This report describes a new primary load design method to supplement the current design-by-elastic-analysis rules in Section III, Division 5, Subsection HB, Subpart B of the ASME Boiler and Pressure Vessel Code, covering the design and construction of Class A high temperature nuclear structural components. The main objectives for the new design method are to provide a procedure that can be applied to components with complicated geometries and to simplify the primary load design process by providing rules more compatible with modern finite element analysis. The report includes a complete set of design rules, presented as a draft ASME Code Case, as well as a commentary on the rules and a set of verification problems. The verification design problems demonstrate the new primary load design rules produce safe, efficient components when compared to the current Division 5 approach, while greatly simplifying the design analysis process.

42 ENGINEERING↗
DOE OSTI2024

Uranium measurements in the field using high-resolution cadmium zinc telluride detectors

A new generation of cadmium zinc telluride (CZT) detectors has become available and is being evaluated by the International Atomic Energy Agency (IAEA) for safeguards verifications in the field. The new CZT detector, model M400, is a room temperature spectrometer manufactured by H3D, Inc. The M400 demonstrates superior energy resolution, effective isotope identification capabilities, and convenient usability features when tested in a controlled laboratory environment. These characteristics define the M400 as a potential platform for IAEA field detection applications, which could become suitable for nuclear material characterization (e.g., enrichment verification) and nuclear safeguards missions. The capabilities of gamma spectrometry codes including Fixed energy, Response function Analysis with Multiple efficiencies (FRAM) from Los Alamos National Laboratory, CZT for Uranium (CZTU) from Lawrence Livermore National Laboratory, and Gamma Detector Response and Analysis Software (GADRAS) from Sandia National Laboratories were adapted for M400 spectra, and the performance of the codes has been validated. This was reported in a prior work. To further validate the performance of the high-energy resolution CZT detector and the isotopic analysis codes, a field measurement campaign consisting of uranium hexafluoride (UF 6 ) cylinder measurements was conducted at a fuel fabrication facility. A total of 34 Type 30B cylinders containing UF6 were measured using three different M400 CZT detectors. Each detector was outfitted with a custom rectangular collimator and shield made out T-Flex®, a tungsten-impregnated polymer. Measurements were performed at three different locations of the cylinder, ensuring that the measurement geometry satisfied the infinite thickness criterion. The spectra from the M400 CZT were analyzed using the code General Enrichment Meter (GEM). For analyzing the gamma-ray spectra from UF 6 cylinder, the GEM code is the appropriate tool since it relies only on the gamma-ray emissions from 235 U and not from other isotopes. Results from the spectral analysis were compared with the known abundance of 235 U in the cylinders, as well as with the International Target Values 2020 (ITV2020). The suitability of the different underlying techniques used by the various codes for UF 6 analysis is discussed. The challenges of measuring UF 6 contained in cylinders and mitigation strategies are highlighted.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2024

NORTH DAKOTA CARBONSAFE PHASE III: SITE CHARACTERIZATION AND PERMITTING OF GEOLOGIC STORAGE OF CARBON DIOXIDE

The Energy & Environmental Research Center (EERC), in partnership with Minnkota Power Cooperative Inc. (Minnkota), SLB, and Computer Modelling Group Ltd. (CMG), supported wide-scale deployment of carbon capture and storage (CCS) as part of the U.S. Department of Energy (DOE) National Energy Technology Laboratory Carbon Storage Assurance Facility Enterprise (CarbonSAFE) Initiative Phase III. This phase included the acquisition, analysis, and development of information to fully characterize two storage complexes to demonstrate viable storage resources for commercial volumes of CO2 (defined by DOE as a minimum of 50 million tonnes [MMt] of CO2 within a 30-year period) (National Energy Technology Laboratory, 2024). Phase III also involved the preparation, submission, and approval of North Dakota underground injection control (UIC) Class VI storage facility permits (SFPs)—required precursors to applications for Class VI injection well permits. The presumed viability of commercial-scale CCS, situated adjacent to Minnkota’s Milton R. Young Station (MRYS), is validated by Minnkota’s continued pursuit of Project Tundra—an initiative to build the world’s largest lignite-based CCS project in central North Dakota (www.projecttundrand.com). Project Tundra comprises two scopes of work, Tundra Capture (installation of postcombustion CO2 capture at MRYS) and Tundra SGS (secure geologic storage). The efforts of North Dakota CarbonSAFE Phase III, Site Characterization and Permitting, supported Tundra SGS. Extensive site-specific characterization activities included a successful multimeasurement geophysical approach and drilling a stratigraphic test well (J-ROC 1, subsequently renamed Liberty-1) adjacent to MRYS. Core collection and analyses, downhole testing and fluid sampling, and geophysical logging were performed on J-ROC 1 and on a nearby stratigraphic test well (known as J-LOC 1), which was drilled, cored, and tested under a complementary project funded by the North Dakota Lignite Research Program. The injection tests performed on J-LOC 1 positively impacted the CarbonSAFE project, resulting in fewer proposed injection wells and significant construction, operations, and monitoring cost savings. The characterization data collected and analyses performed were integrated into geologic models, and successive numerical simulations were run to determine CO2 plume extent and subsurface pressure buildup associated with the planned CO2 injection rate of nearly 4 MMt per year. The latter doubles the CarbonSAFE Initiative goal with an estimated 100 MMt of CO2 stored in 20 years. Application of the U.S. Environmental Protection Agency’s (EPA’s) method for estimating the Class VI Rule area of review (AOR) to the overpressurized Broom Creek Formation inspired an alternative method of calculation, called risk-based AOR delineation. This peer-reviewed method was applied for the first time during the storage facility-permitting process. The two SFP applications submitted in 2021 successfully resulted in North Dakota Industrial Commission (NDIC) orders in 2022 authorizing the creation of the storage facility areas and amalgamation of pore space as well as establishing financial responsibility requirements. After approval of the SFPs, Minnkota filed in 2022 applications for permits to reenter the J-ROC 1 well and to drill two new wells—all with the intended purpose to become Class VI injection wells. To establish eligibility under the Internal Revenue Code for Section 45Q tax incentives, a monitoring, reporting, and verification (MRV) plan was prepared and submitted by Minnkota to EPA in 2022, resulting in the first such plan approved in North Dakota. Also in 2022, under the National Environmental Policy Act (NEPA), Minnkota prepared and submitted an environmental information volume (EIV) describing the proposed CCS project and associated potential environmental impacts. Based on the EIV, DOE determined that the proposed construction project required an environmental assessment, and Minnkota submitted the first draft in 2023 and a revised draft in 2024. Both submissions were followed by a public comment period. Subsequently, DOE issued a finding of no significant impact (FONSI) on September 13, 2024. A successful outreach program, strongly based in the production, presentation, and dissemination of informational material, fostered an environment to aid stakeholders in making informed decisions regarding the planned project. Opportunities for public input were provided at various steps along the way, including at county planning and zoning meetings, before and during the SFP administrative hearing, and during environmental assessment public comment periods. In addition, land/pore space owners and mineral owners had various points of contact, including granting access rights, securing pore space leasing, and mineral owner notifications. Based upon the successful storage facility permitting issued by NDIC, approval of the MRV plan by EPA, and receipt of a FONSI under the NEPA, Minnkota is continuing its pursuit of Project Tundra. In December 2023, the Office of Clean Energy Demonstrations under its Carbon Capture Demonstrations Projects Program announced funding for the capture system (Office of Clean Energy Demonstrations, 2023) and a proposal for CarbonSAFE Phase IV: Construction funding was submitted in March 2024 for the storage project. A go/no-go decision to proceed with construction and operations in the Broom Creek Formation is anticipated in 2024. References National Energy Technology Laboratory, CarbonSafe Initiative, https://netl.doe.gov/carbon-management/carbon-storage/carbonsafe (accessed August 2024). Office of Clean Energy Demonstrations, 2023, OCED selects three projects in CA, ND, and TX to reduce harmful carbon pollution, create new economic opportunities, and advance carbon reducing technologies, December, www.energy.gov/oced/articles/oced-selects-three-projects-ca-nd-and-tx-reduce-harmful-carbon-pollution-create-new (accessed August 2024).

Peck, Wesley↗
NASA NTRS1991

Application of direct inverse analogy method (DIVA) and viscous design optimization techniques

A direct-inverse approach to the transonic design problem was presented in its initial state at the First International Conference on Inverse Design Concepts and Optimization in Engineering Sciences (ICIDES-1). Further applications of the direct inverse analogy (DIVA) method to the design of airfoils and incremental wing improvements and experimental verification are reported. First results of a new viscous design code also from the residual correction type with semi-inverse boundary layer coupling are compared with DIVA which may enhance the accuracy of trailing edge design for highly loaded airfoils. Finally, the capabilities of an optimization routine coupled with the two viscous full potential solvers are investigated in comparison to the inverse method.

Greff, E.↗
NASA NTRS1991

Probabilistic Structural Analysis Methods (PSAM) for select space propulsion system components

This annual report summarizes the work completed during the third year of technical effort on the referenced contract. Principal developments continue to focus on the Probabilistic Finite Element Method (PFEM) which has been under development for three years. Essentially all of the linear capabilities within the PFEM code are in place. Major progress in the application or verifications phase was achieved. An EXPERT module architecture was designed and partially implemented. EXPERT is a user interface module which incorporates an expert system shell for the implementation of a rule-based interface utilizing the experience and expertise of the user community. The Fast Probability Integration (FPI) Algorithm continues to demonstrate outstanding performance characteristics for the integration of probability density functions for multiple variables. Additionally, an enhanced Monte Carlo simulation algorithm was developed and demonstrated for a variety of numerical strategies.

Source record↗
DOE OSTI2024

SAM: A Modern System Code for Advanced Non-LWR Safety Analysis

The System Analysis Module (SAM), developed at Argonne National Laboratory and by collaborators at other organizations, is for advanced non–light water reactor safety analysis. SAM aims to provide fast-running, modest-fidelity, whole-plant transient analysis capabilities that are essential for fast-turnaround design scoping and engineering analyses of advanced reactor concepts. To facilitate code development, SAM utilizes the MOOSE object-oriented application framework, its underlying finite element library, and linear and nonlinear solvers to leverage modern advanced software environments and numerical methods. SAM aims to solve tightly coupled physical phenomena, including fission reaction, heat transfer, fluid dynamics, and thermal-mechanical responses in advanced reactor structures, systems, and components with high accuracy and efficiency. Finally, this paper gives an overview of the SAM code development, including goals and functional requirements, physical models, current capabilities, verification and validation, software quality assurance, and examples of simulations for advanced nuclear reactor applications.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2018

EFFECT OF DISCRETIZATION ERROR ON THE QUANTIFICATION OF MODEL UNCERTAINTY IN TWO-PHASE FLOW SIMULATIONS

Verification, validation and uncertainty quantification (VVUQ) have become a common practice in thermal-hydraulics analysis. In general, these activities deal with propagations of uncertainties in computer code simulations, e.g., through system analysis codes. However, most existing such activities in thermal-hydraulics analysis have been primarily focused on input and model uncertainties, while numerical errors were largely overlooked. Numerical errors can appear in many different forms, e.g., round-off error, statistical sampling error, and discretization error. In thermal-hydraulics analysis, especially two-phase flow simulations commonly encountered in reactor safety analysis, the lack of consideration of discretization error is mainly due to the difficulty in estimating them. Accurate estimations of discretization error require continuous mesh refinement and/or implementation of high-order numerical schemes in system analysis code, both of which are difficult to achieve in existing codes. In this work, we will build a computer code that incorporates both first-order and second-order numerical methods to solve the two-phase flow problems. The first-order method resembles the one used in many existing system analysis codes; and the second-order method works as the reference to estimate numerical errors. Numerical verification of spatial discretization schemes will be presented in the form of mesh convergence study. It will also be demonstrated via case studies that, in practical scenarios, discretization errors can be as large as, or even larger than, model uncertainties.

42 ENGINEERING↗
DOE OSTI2019

REBUS-PC v1.5 Verification Test Summary

Motivated in part by its usage for analysis of the University of Missouri Research Reactor (MURR), the verification of the REBUS-PC software for θ-R-Z geometries is discussed and displayed in this manuscript. Of particular importance is to show that the eigenvalue, flux, power, and burnup outputs of the software given a user problem is correct. REBUS-PC contains many features and MURR only makes use of some of those aspects. As an example, the use of region specific cross section sets, interpolation of the cross section data with respect to burnup, and automatic movement of control rods during the fuel cycle is discussed and displayed. To demonstrate the accuracy, 22 verification tests based upon 7 physical geometries are discussed. Geometry descriptions are provided in Section 2 and the REBUS-PC results for each verification test are discussed in Section 3. These verification tests consist of both analytic problems with known solutions and a more complicated input consistent with usage of REBUS-PC on the MURR reactor itself called STRZ. In this verification test summary report, the REBUS-PC software is repeatedly demonstrated to reproduce, or closely match, the eigenvalue, flux, and power distributions from analytic test problem solutions, demonstrating that the implemented finite difference approximation in θ-R-Z is working as intended. Several additional REBUS-PC features are tested, such as control rod movement by detailed comparisons of the results against reference solutions obtained using an auxiliary implemented MatLab program. As expected, the REBUS-PC software produces results that are 100% consistent with the stated capabilities and thus the verification exercise is completed. These verification tests should be executed with each re-compilation of the REBUS-PC source and after any source code changes. All output results from any such new work should be rigorously compared against the stored output of the 22 verification tests cited in this report that forms the basis of the verification process.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Computation of linear MHD instabilities with the multi-region relaxed MHD energy principle

Over the last decade, a variational principle based on a generalisation of Taylor's relaxation, referred to as multi-region relaxed magnetohydrodynamics (MRxMHDs) has been developed. The numerical solutions of the MRxMHD equilibria have been constructed using the Stepped Pressure Equilibrium Code (SPEC) (Hudson et al 2012 Phys. Plasmas 19 112502). In principle, SPEC could also be established to describe the MRxMHD stability of an equilibrium. In this work, a theoretical framework is developed to relate the second variation of the energy functional to the so-called Hessian matrix, enabling the prediction of MHD linear instabilities of cylindrical plasmas, and is implemented in SPEC. The negative and positive eigenvalues of the Hessian matrix predict the stability of an equilibrium. Verification studies of SPEC stability results with the M3D-C 1 code and the tearing mode $\Delta^{^{\prime}}$ criterion have been conducted for ideal and resistive MHD instabilities, respectively, in a pressureless cylindrical tokamak, and have shown good agreement. Overall, our stability analysis is a critical step towards understanding the MHD stability of three-dimensional MHDs where nested flux surfaces, magnetic islands and stochastic regions co-exist.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗