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DOE OSTI2017

Application of the new IAPWS Guideline on the fast and accurate calculation of steam and water properties with the Spline-Based Table Look-Up Method (SBTL) in RELAP-7

The numerical simulation of thermalhydraulic processes in nuclear power plants requires very accurate and extremely fast algorithms for calculating the thermophysical properties of water and steam. In order to provide such algorithms, the International Association for the Properties of Water and Steam (IAPWS) has adopted the new “IAPWS Guideline on the Fast Calculation of Steam and Water Properties with the Spline-Based Table Look-Up Method (SBTL)”. In this article, the SBTL method is applied to property functions of specific volume and specific internal energy (v,e) based on the scientific formulation IAPWS-95 and the latest IAPWS formulations for transport properties. From the newly generated SBTL functions, thermodynamic and transport properties as well as their derivatives and inverse functions are calculable in the fluid range of state for pressures up to 100 MPa and for temperatures up to 1273 K, including the metastable liquid and the metastable vapor regions. The SBTL functions reproduce the underlying formulations with an accuracy of 10–100 ppm and significantly reduced computing times. The SBTL method has been implemented into the nuclear reactor system safety analysis code RELAP-7 [2] to consider the real fluid behavior of water and steam in a novel 7-equation two-phase flow model.

42 ENGINEERING↗

DOE OSTI2014

RELAP-7 Beta Release: Summary of Capabilities

RELAP-7 is a nuclear systems safety analysis code being developed at the Idaho National Laboratory (INL). Building upon the decades of software development at the INL, we began the development of RELAP-7 in 2011 to support the Risk Informed Safety Margins Characterization (RISMC) Pathway. As part of this development, the first lines of RELAP-7 code were committed to the software revision control repository on November 7th, 2011. The overall design goal of RELAP-7 is to take advantage of the previous thirty years of advancements in computer architecture, software design, numerical methods, and physical models in order to provide capabilities needed for the RISMC methodology and to support nuclear power safety analysis. RELAP-7 is built using the INL’s modern scientific software development framework, MOOSE (Multi-physics Object Oriented Simulation Environment). MOOSE provides improved numerical calculations (including higher-order integration in both space and time, yielding converged second-order accuracy). The RELAP-7 code structure is based on multiple physical component models such as pipes, junctions, pumps, etc. Each component can have options for different fluid models such as single- and two-phase flow. This component-based and physics-based software architecture allows RELAP-7 to adopt different physical models for different applications. A relatively new two-phase hydrodynamic model, termed the ''7-Equation model'' for two phasic pressures, velocities, energies, and volumetric fraction, is incorporated into RELAP-7 for liquid-gas (water-steam) flows. This new model allows second-order integration because it is well-posed, which will reduce the numerical error associated with traditional systems analysis codes. In this paper, we provide a RELAP-7 capability list describing analysis features, range of applicability, and reactor components that will be available for the December 15th, 2014 beta release of the software.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2015

RELAP-7 Development Updates

RELAP-7 is a nuclear systems safety analysis code being developed at the Idaho National Laboratory, and is the next generation tool in the RELAP reactor safety/systems analysis application series. RELAP-7 development began in 2011 to support the Risk Informed Safety Margins Characterization (RISMC) Pathway of the Light Water Reactor Sustainability (LWRS) program. The overall design goal of RELAP-7 is to take advantage of the previous thirty years of advancements in computer architecture, software design, numerical methods, and physical models in order to provide capabilities needed for the RISMC methodology and to support nuclear power safety analysis. The code is being developed based on Idaho National Laboratory’s modern scientific software development framework – MOOSE (the Multi-Physics Object-Oriented Simulation Environment). The initial development goal of the RELAP-7 approach focused primarily on the development of an implicit algorithm capable of strong (nonlinear) coupling of the dependent hydrodynamic variables contained in the 1-D/2-D flow models with the various 0-D system reactor components that compose various boiling water reactor (BWR) and pressurized water reactor nuclear power plants (NPPs). During Fiscal Year (FY) 2015, the RELAP-7 code has been further improved with expanded capability to support boiling water reactor (BWR) and pressurized water reactor NPPs analysis. The accumulator model has been developed. The code has also been coupled with other MOOSE-based applications such as neutronics code RattleSnake and fuel performance code BISON to perform multiphysics analysis. A major design requirement for the implicit algorithm in RELAP-7 is that it is capable of second-order discretization accuracy in both space and time, which eliminates the traditional first-order approximation errors. The second-order temporal is achieved by a second-order backward temporal difference, and the one-dimensional second-order accurate spatial discretization is achieved with the Galerkin approximation of Lagrange finite elements. During FY-2015, we have done numerical verification work to verify that the RELAP-7 code indeed achieves 2nd-order accuracy in both time and space for single phase models at the system level.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2014

RELAP-7 User's Guide

The document contains a user's guide on how to run the RELAP-7 code. The RELAP-7 code is the next generation nuclear reactor system safety analysis code being developed at the Idaho National Laboratory. RELAP-7 will become the main reactor systems simulation toolkit for the LWRS (Light Water Reactor Sustainability) program’s RISMC (Risk Informed Safety Margin Characterization) effort and the next generation tool in the RELAP reactor safety/systems analysis application series. RELAP-7 is written with object oriented programming language C++. A number of example problems and their associated input files are presented in this document to guide users to run the RELAP-7 code starting with simple pipe problems to problems with increasing complexity.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2016

RELAP-7 Theory Manual

This document summarizes the physical models and mathematical formulations used in the RELAP-7 code. In summary, the MOOSE based RELAP-7 code development is an ongoing effort. The MOOSE framework enables rapid development of the RELAP-7 code. The developmental efforts and results demonstrate that the RELAP-7 project is on a path to success. This theory manual documents the main features implemented into the RELAP-7 code. Because the code is an ongoing development effort, this RELAP-7 Theory Manual will evolve with periodic updates to keep it current with the state of the development, implementation, and model additions/revisions.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

DOE OSTI2016

RELAP-7 Pressurizer Component Development Updates

RELAP-7 is a nuclear systems safety analysis code being developed at the Idaho National Laboratory (INL). RELAP-7 development began in 2011 to support the Risk Informed Safety Margins Characterization (RISMC) Pathway of the Light Water Reactor Sustainability (LWRS) program. The overall design goal of RELAP-7 is to take advantage of the previous thirty years of advancements in computer architecture, software design, numerical methods, and physical models in order to provide capabilities needed for the RISMC methodology and to support nuclear power safety analysis. The code is being developed based on Idaho National Laboratory’s modern scientific software development framework – MOOSE (the Multi-Physics Object-Oriented Simulation Environment). The initial development goal of the RELAP-7 approach focused primarily on the development of an implicit algorithm capable of strong (nonlinear) coupling of the dependent hydrodynamic variables contained in the 1-D/2-D flow models with the various 0-D system reactor components that compose various boiling water reactor (BWR) and pressurized water reactor nuclear power plants (NPPs). As part of the efforts to expand the capability for PWR simulation, an equilibrium single-region pressurizer model has been implemented in RELAP-7. The pressurizer component can simulate pressure and water level change through insurge, spray, and heating processes. Two simple tests – one for insurge process and another for outsurge process – have been reported to demonstrate and verify the functions of the pressurizer model. The typical single-phase PWR system model presented in the first RELAP-7 milestone report has been updated, as part of system level test for the new pressurizer model. The updated PWR system model with the pressurizer component can be used for more realistic transient simulations. The addition of the equilibrium single-region pressurizer model represents the first step of developing a suite of pressurizer models with different levels of fidelities. Non-equilibrium two-region two-zone model and non-equilibrium five-region three zone model will be implemented in the near future. Cross comparison and validation will be pursued when higher fidelity pressurizer models are completed.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2016

RELAP-7 Software Verification and Validation Plan - Requirements Traceability Matrix (RTM) Part 2: Code Assessment Strategy, Procedure, and RTM Update

This document addresses two subjects involved with the RELAP-7 Software Verification and Validation Plan (SVVP): (i) the principles and plan to assure the independence of RELAP-7 assessment through the code development process, and (ii) the work performed to establish the RELAP-7 assessment plan, i.e., the assessment strategy, literature review, and identification of RELAP-7 requirements. Then, the Requirements Traceability Matrices (RTMs) proposed in previous document (INL-EXT-15-36684) are updated. These RTMs provide an efficient way to evaluate the RELAP-7 development status as well as the maturity of RELAP-7 assessment through the development process.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

RELAP-7 Software Verification and Validation Plan: Requirements Traceability Matrix (RTM) Update and Code Verification Strategy

This document describes the recent progress of the RELAP-7 Software Verification and Validation Plan (SVVP). The RELAP-7 RTM has been updated by adding the validation requirement items, rearranging the requirement items, and introducing the classifier to better describe the RELAP-7 V&V status at a specified point in time. Also, from the perspective of nuclear system code validation, six items from the list of LWR safety-relevant phenomena were identified as validation data gaps. Lastly, motivated by the needs revealed from the previous RELAP-7 IV&V activities, the independent verification plan for RELAP-7 has been established. The verification method, procedure, and verification test coverage suite discussed in this document will be applied to the future work for the RELAP-7 independent verification.

42 ENGINEERING↗

DOE OSTI2016

IMPLEMENTATION AND VALIDATION OF A FULLY IMPLICIT ACCUMULATOR MODEL IN RELAP-7

This paper presents the implementation and validation of an accumulator model in RELAP-7 under the framework of preconditioned Jacobian free Newton Krylov (JFNK) method, based on the similar model used in RELAP5. RELAP-7 is a new nuclear reactor system safety analysis code being developed at the Idaho National Laboratory (INL). RELAP-7 is a fully implicit system code. The JFNK and preconditioning methods used in RELAP-7 is briefly discussed. The slightly modified accumulator model is summarized for completeness. The implemented model was validated with LOFT L3-1 test and benchmarked with RELAP5 results. RELAP-7 and RELAP5 had almost identical results for the accumulator gas pressure and water level, although there were some minor difference in other parameters such as accumulator gas temperature and tank wall temperature. One advantage of the JFNK method is its easiness to maintain and modify models due to fully separation of numerical methods from physical models. It would be straightforward to extend the current RELAP-7 accumulator model to simulate the advanced accumulator design.

Accumulator↗

DOE OSTI2017

Preliminary Study on the Suitability of a Second-Order Reconstructed Discontinuous Galerkin Method for RELAP-7 Thermal-Hydraulic Modeling

This document presents a preliminary study on the suitability of a second-order reconstructed discontinuous Galerkin (rDG) method for RELAP-7 thermal-hydraulic modeling. The document begins with a brief description of the governing equations for compressible, two-phase vapor and liquid flow, with a presentation of the seven-equation formulation details. A comparative study between the second-order rDG method and the RELAP-7's finite element method (FEM) with a entropy viscosity method (EVM) based numerical stabilization scheme (namely FEM-EVM) over a series of benchmark test problems is demonstrated. The intent for this suite of test problems is to provide baseline comparison data that demonstrate the performance of 1) the rDG solution and 2) the RELAP-7's FEM-EVM solution (with RELAP-7 code version dated August 15, 2017), on problems from single- to specific, limited two-phase flows. For all the test problems in this document, the rDG solutions were obtained with a second-order, two-step, explicit strong stability preserving Runge-Kutta time integration method. The computational results clearly indicate that the performance of the rDG method is superior to that of the RELAP-7's FEM-EVM method in all the test problems presented. Therefore, as far as the test problems in this document are considered, the second-order rDG method is recommended as an improved solution method option for RELAP-7.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

Implementation and validation of a fully implicit accumulator model in RELAP-7

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2015

RELAP-7 Progress Report. FY-2015 Optimization Activities Summary

This report summarily documents the optimization activities on RELAP-7 for FY-2015. It includes the migration from the analytical stiffened gas equation of state for both the vapor and liquid phases to accurate and efficient property evaluations for both equilibrium and metastable (nonequilibrium) states using the Spline-Based Table Look-up (SBTL) method with the IAPWS-95 properties for steam and water. It also includes the initiation of realistic closure models based, where appropriate, on the U.S. Nuclear Regulatory Commission’s TRACE code. It also describes an improved entropy viscosity numerical stabilization method for the nonequilibrium two-phase flow model of RELAP-7. For ease of presentation to the reader, the nonequilibrium two-phase flow model used in RELAP-7 is briefly presented, though for detailed explanation the reader is referred to RELAP-7 Theory Manual [R.A. Berry, J.W. Peterson, H. Zhang, R.C. Martineau, H. Zhao, L. Zou, D. Andrs, “RELAP-7 Theory Manual,” Idaho National Laboratory INL/EXT-14-31366(rev. 1), February 2014].

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2014

An Update on Improvements to NiCE Support for RELAP-7

The Multiphysics Object-Oriented Simulation Environment (MOOSE) is a framework that facilitates the development of applications that rely on finite-element analysis to solve a coupled, nonlinear system of partial differential equations. RELAP-7 represents an update to the venerable RELAP-5 simulator that is built upon this framework and attempts to model the balance-of-plant concerns in a full nuclear plant. This report details the continued support and integration of RELAP-7 and the NEAMS Integrated Computational Environment (NiCE). RELAP-7 is fully supported by the NiCE due to on-going work to tightly integrate NiCE with the MOOSE framework, and subsequently the applications built upon it. NiCE development throughout the first quarter of FY15 has focused on improvements, bug fixes, and feature additions to existing MOOSE-based application support. Specifically, this report will focus on improvements to the NiCE MOOSE Model Builder, the MOOSE application job launcher, and the 3D Nuclear Plant Viewer. This report also includes a comprehensive tutorial that guides RELAP-7 users through the basic NiCE workflow: from input generation and 3D Plant modeling, to massively parallel job launch and post-simulation data visualization.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

RELAP-7 Closure Correlations

The RELAP-7 code is the next generation nuclear reactor system safety analysis code being developed at the Idaho National Laboratory (INL). The code is based on the INL’s modern scientific software development framework, MOOSE (Multi-Physics Object Oriented Simulation Environment). The overall design goal of RELAP-7 is to take advantage of the previous thirty years of advancements in computer architecture, software design, numerical integration methods, and physical models. The end result will be a reactor systems analysis capability that retains and improves upon RELAP5’s and TRACE’s capabilities and extends their analysis capabilities for all reactor system simulation scenarios. The RELAP-7 code utilizes the well-posed 7-equation two-phase flow model for compressible two-phase flow. Closure models used in the TRACE code has been reviewed and selected to reflect the progress made during the past decades and provide a basis for the colure correlations implemented in the RELAP-7 code. This document provides a summary on the closure correlations that are currently implemented in the RELAP-7 code. The closure correlations include sub-grid models that describe interactions between the fluids and the flow channel, and interactions between the two phases.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2016

Developing A Fully Implicit Compressible Flow Valve Model in RELAP-7 and Its Application in Short Term BWR Station Black-Out Analyses

This paper presents a set of dynamical models for SRV simulation and their implementation in the RELAP-7 code, which is a new reactor system analysis code being developed at INL. RELAP-7 is based on the MOOSE (the Multi-Physics Object-Oriented Simulation Environment) framework. The compressible flow SRV model covers three different sets of models: fully closed case, subsonic case, and choking case. The RELAP-7 is a fully implicit code and the preconditioned Jacobian-free Newton-Krylov (JFNK) method is used to solve the discretized nonlinear problem. The JFNK method generally needs a good preconditioning scheme to be effective and efficient. There are different ways to precondition the JFNK method. In RELAP-7, two main options are used to obtain the preconditioning matrix: (1) FDP (Finite Difference Preconditioning) option which uses the default finite differencing method provided in the PETSc package. PETSc is the numerical solver software developed by Argonne National Laboratory and used by MOOSE as the numerical solution engine; (2) SMP (Single Matrix Preconditioning) option which requires code developers to provide approximate analytical Jacobian inputs for the important diagonal and off-diagonal terms. Due to the strong discontinuity in the residual vector space when the compressible flow valve model switches from one set of model to another, FDP option cannot guarantee convergence. Instead, accurate analytical Jacobain terms are provided for the compressible flow valve model. With the SMP option selected, the compressible flow valve model can be solved efficiently under different cases. The developed compressible flow valve model has been used for SRV component simulation in several simplified BWR SBO (Station Black-Out) simulations with RELAP-7. This paper only presents cases for short-term SBO in which all the safety systems fail to start and function properly when SBO occurs. Consequently, only the SRVs automatically open and close periodically to control the primary system pressure and discharge the high temperature and high pressure steam into the suppression pool. Although simplified, this case is quite similar to what happened in Fukushima Daiichi Unit 1. Unit 1 had no RCIC system, while the isolation condenser system was believed to be non-functioning, or only available for a very short period of time during the accident. Therefore, the Unit 1 reactor core reached a fuel failure temperature only a few hours into the accident. Two short-term SBO cases will be compared: one with single SRV discharge line which represents all the SRV lines and another case with multi-group SRVs which represent each group of SRV line with different setting points.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2014

RELAP-7 Numerical Stabilization: Entropy Viscosity Method

The RELAP-7 code is the next generation nuclear reactor system safety analysis code being developed at the Idaho National Laboratory (INL). The code is based on the INL's modern scientific software development framework, MOOSE (Multi-Physics Object Oriented Simulation Environment). The overall design goal of RELAP-7 is to take advantage of the previous thirty years of advancements in computer architecture, software design, numerical integration methods, and physical models. The end result will be a reactor systems analysis capability that retains and improves upon RELAP5's capability and extends the analysis capability for all reactor system simulation scenarios. RELAP-7 utilizes a single phase and a novel seven-equation two-phase flow models as described in the RELAP-7 Theory Manual (INL/EXT-14-31366). The basic equation systems are hyperbolic, which generally require some type of stabilization (or artificial viscosity) to capture nonlinear discontinuities and to suppress advection-caused oscillations. This report documents one of the available options for this stabilization in RELAP-7 -- a new and novel approach known as the entropy viscosity method. Because the code is an ongoing development effort in which the physical sub models, numerics, and coding are evolving, so too must the specific details of the entropy viscosity stabilization method. Here the fundamentals of the method in their current state are presented.

42 ENGINEERING↗

DOE OSTI2014

Methodology for the Incorporation of Passive Component Aging Modeling into the RAVEN/ RELAP-7 Environment

Passive system, structure and components (SSCs) will degrade over their operation life and this degradation may cause to reduction in the safety margins of a nuclear power plant. In traditional probabilistic risk assessment (PRA) using the event-tree/fault-tree methodology, passive SSC failure rates are generally based on generic plant failure data and the true state of a specific plant is not reflected realistically. To address aging effects of passive SSCs in the traditional PRA methodology [1] does consider physics based models that account for the operating conditions in the plant, however, [1] does not include effects of surveillance/inspection. This paper represents an overall methodology for the incorporation of aging modeling of passive components into the RAVEN/RELAP-7 environment which provides a framework for performing dynamic PRA. Dynamic PRA allows consideration of both epistemic and aleatory uncertainties (including those associated with maintenance activities) in a consistent phenomenological and probabilistic framework and is often needed when there is complex process/hardware/software/firmware/ human interaction [2]. Dynamic PRA has gained attention recently due to difficulties in the traditional PRA modeling of aging effects of passive components using physics based models and also in the modeling of digital instrumentation and control systems. RAVEN (Reactor Analysis and Virtual control Environment) [3] is a software package under development at the Idaho National Laboratory (INL) as an online control logic driver and post-processing tool. It is coupled to the plant transient code RELAP-7 (Reactor Excursion and Leak Analysis Program) also currently under development at INL [3], as well as RELAP 5 [4]. The overall methodology aims to: • Address multiple aging mechanisms involving large number of components in a computational feasible manner where sequencing of events is conditioned on the physical conditions predicted in a simulation environment such as RELAP-7. • Identify the risk-significant passive components, their failure modes and anticipated rates of degradation • Incorporate surveillance and maintenance activities and their effects into the plant state and into component aging progress. • Asses aging affects in a dynamic simulation environment 1. C. L. SMITH, V. N. SHAH, T. KAO, G. APOSTOLAKIS, “Incorporating Ageing Effects into Probabilistic Risk Assessment –A Feasibility Study Utilizing Reliability Physics Models,” NUREG/CR-5632, USNRC, (2001). 2. T. ALDEMIR, “A Survey of Dynamic Methodologies for Probabilistic Safety Assessment of Nuclear Power Plants, Annals of Nuclear Energy, 52, 113-124, (2013). 3. C. RABITI, A. ALFONSI, J. COGLIATI, D. MANDELLI and R. KINOSHITA “Reactor Analysis and Virtual Control Environment (RAVEN) FY12 Report,” INL/EXT-12-27351, (2012). 4. D. ANDERS et.al, "RELAP-7 Level 2 Milestone Report: Demonstration of a Steady State Single Phase PWR Simulation with RELAP-7," INL/EXT-12-25924, (2012).

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2014

RELAP-7 Software Verification and Validation Plan

This INL plan comprehensively describes the software for RELAP-7 and documents the software, interface, and software design requirements for the application. The plan also describes the testing-based software verification and validation (SV&V) process—a set of specially designed software models used to test RELAP-7. The RELAP-7 (Reactor Excursion and Leak Analysis Program) code is a nuclear reactor system safety analysis code being developed at Idaho National Laboratory (INL). The code is based on the INL’s modern scientific software development framework – MOOSE (Multi-Physics Object-Oriented Simulation Environment). The overall design goal of RELAP-7 is to take advantage of the previous thirty years of advancements in computer architecture, software design, numerical integration methods, and physical models. The end result will be a reactor systems analysis capability that retains and improves upon RELAP5’s capability and extends the analysis capability for all reactor system simulation scenarios.

97 MATHEMATICS AND COMPUTING↗