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RELAP-7 Progress Report: A Mathematical Model for 1-D Compressible, Single-Phase Flow Through a Branching Junction

In the literature, the abundance of pipe network junction models, as well as inclusion of dissipative losses between connected pipes with loss coefficients, has been treated using the incompressible flow assumption of constant density. This approach is fundamentally, physically wrong for compressible flow with density change. This report introduces a mathematical modeling approach for general junctions in piping network systems for which the transient flows are compressible and single-phase. The junction could be as simple as a 1-pipe input and 1-pipe output with differing pipe cross-sectional areas for which a dissipative loss is necessary, or it could include an active component, between an inlet pipe and an outlet pipe, such as a pump or turbine. In this report, discussion will be limited to the former. A more general branching junction connecting an arbitrary number of pipes with transient, 1-D compressible single-phase flows is also presented. These models will be developed in a manner consistent with the use of a general equation of state like, for example, the recent Spline-Based Table Look-up method [1] for incorporating the IAPWS-95 formulation [2] to give accurate and efficient calculations for properties for water and steam with RELAP-7 [3].

42 ENGINEERING↗

Validation of RELAP-7 for Forced Convective and Natural Circulation Reactor Flows

New reactor designs such as small modular reactors and newly proposed passive safety systems rely on natural circulation two-phase flow cooling of the reactor core under accident conditions. Without a pump to drive the flow, the circulation rate is a strong function of void fraction. Under these conditions where the flow rate, pressure drop, and heat transfer are all closely coupled through the mixture density, the accurate prediction of void fraction is pivotal. Furthermore, while these passive systems boast a more reliable cooling option, the sensitivity of the system to two-phase flow instabilities is more likely than in forced convective cooling and can result in dangerous density wave or flow excursion conditions. Improvement of one-dimensional system codes and further development of three-dimensional code capability are all important efforts in addressing these issues. The proposed work is a critical step towards providing confidence through validation of the capability of thermal-hydraulic tools to meet the emerging challenges in reactor simulation. Historically, system analysis codes develop a stiffness over time due to fine-tuning of adjustable code parameters that result in a reluctance or inability to adopt improved models. Therefore, a rigorous effort should be invested in preparation for RELAP-7 to identify required modeling improvements of constitutive relations and validation of the code applicability to the wide range of possible reactor flow conditions. Part of this validation involves the uncertainty quantification which is a critical step in the Code Scaling, Applicability, and Uncertainty (CSAU) methodology and Best-Estimate Plus Uncertainty (BEPU) licensing method. BEPU allows recovery of safety margins and potentially optimizing plant performance, resulting in economic benefit for the reactor operators. Beginning with the collection of past experimental data covering prototypic LWR conditions, this document reviews three critical datasets available for the validation of system codes. The experimental methods, procedures, facilities, instrumentation, and supplementary information are consolidated to aid the validation efforts of this work and future projects. These three datasets (824 conditions) are chosen due to their wide acceptance and demonstrated application for code validation. Two experimental datasets from the Nuclear Power Engineering Corporation (NUPEC) span prototypic conditions of Boiling Water Reactors (BWR) and Pressurized Water Reactors (PWR). These datasets are labeled as the BFBT (BWR Full-size Fine-mesh Bundle Test) and the PSBT (PWR Subchannel and Bundle Test) datasets respectively. The third dataset is taken in an internally heated annulus that is scaled based on a BWR subassembly and includes two-phase flows important to post-blowdown analysis. Together, the datasets consider the full range of pressure and mass flux expected in LWR forced convective flows from steady-state to long term cooling conditions. Recognizing the deficiency of available data under low-pressure, low-flow, a new natural circulation dataset consisting of 107 conditions is obtained. With system pressures ranging between 145 and 950 kPa, natural circulation is driven by a heat flux up to 275 kW/m2 in a 3 m long heated region of the annulus test section which is followed by a 2 m long unheated region before entering a condenser. Stable natural circulation flow rates in this facility were measured to be between 182 and 590 kg/m2-s. Pressure and temperature are measured at ten locations in the facility. In addition, measurements of void fraction, interfacial area concentration, and gas velocity are obtained at five axial locations in the annulus test section. The RELAP5-3D code demonstrates good accuracy for void fraction predictions in BFBT and PSBT benchmarks, but shows relatively large discrepancy in the annulus experiments at lower pressures. In two-phase natural circulation, large oscillations are observed in many system parameters during the simulation of 19 experiment cases which were conducted at low pressures, and the model shows good predictive performance with the remaining 88 experiment cases. However, some discrepancies in void fraction and temperature predictions are found which may require improved constitutive modeling under these low-pressure, low-flow condition. The quantified uncertainty in void fraction predictions in three forced convection benchmarks due to uncertainties in boundary conditions and geometries are relatively small, except for a few cases in the annulus experiment. The output uncertainty of the natural circulation model is quantified by considering the measurement error in boundary conditions, and it is shown that the output uncertainty ranges are relatively small for the range of conditions considered. Through this work, a clear pathway is provided for validation of RELAP7 once the code is available.

42 ENGINEERING↗

RAVEN as Control Logic and Probabilistic Risk Assessment Driver for RELAP-7

The Next Generation of System Analysis Code (NGSAC) [1] aims to model and simulate the Nuclear Power Plant (NPP) thermo-hydraulic behavior with high level of accuracy. In this respect, Idaho National Laboratory (INL) is developing a NGSAC (known as RELAP-7) which will allow to model NPP responses for a set of accident scenarios (e.g., loss of off-site power).

99 GENERAL AND MISCELLANEOUS↗

Coupling of Pronghorn and RELAP-7 for a Pebble Bed Reactor

High temperature gas cooled reactors (HTGR) are a candidate for timely Gen-IV reactor technology deployment because of high technology readiness and walk-away safety. Among HTGRs, pebble bed reactors (PBRs) have attractive features such as low excess reactivity and online refueling. Pebble bed reactors pose unique challenges to analysts and reactor designers such as continuous burnup distribution depending on pebble motion and recirculation, radiative heat transfer across a variety of gas-filled gaps, and long design basis transients such as pressurized and depressurized loss of forced circulation. Modeling and simulation is essential for both the PBR’s safety case and design process. In order to verify and validate the new generation codes the Nuclear Energy Agency (NEA) Data bank provide a set of benchmarks data together with solutions calculated by the participants using the state of the art codes of that time. An important milestone to test the new PBR simulation codes is the OECD NEA PBMR-400 benchmark which includes thermal hydraulic and neutron kinetic standalone exercises as well as coupled exercises and transients scenarios. In this work, the reactor multiphysics code MAMMOTH and the thermal hydraulics code Pronghorn, both developed by the Idaho National Laboratory (INL) within the multiphysics object-oriented simulation environment (MOOSE), have been used to solve Phase 1 exercises 1 and 2 of the PBMR-400 benchmark. The steady state results are in agreement with the other participants’ solutions demonstrating the adequacy of MAMMOTH and Pronghorn for simulating PBRs.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Validation of Thermohydraulic Simulations using RELAP for Critical Dual Purpose Canisters

Simulations using the RELAP5-3D systems analysis code and STAR-CCM+, a high-fidelity CFD code, were performed on a model of a real-scale MPC-32 dual purpose canister undergoing a criticality event. These simulations were performed to provide code-to-code verification of the natural convection capabilities in RELAP5. The STAR-CCM+ simulations revealed various natural convection flow patterns that aided in the cooling of fission heat produced in the fuel rods in the canister. Negligible spatial temperature variations were observed across the canister in the STAR-CCM+ results, supporting the use of RELAP5 in predicting the sub-cooled regime. The surface-averaged rod temperature predicted by RELAP5 compared well with STAR-CCM+, verifying the predictive capability of RELAP5 for sub-cooled conditions.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Hot Zero and Full Power Validation of PHISICS RELAP-5 Coupling

PHISICS is a reactor analysis toolkit developed in the last 3 years at the Idaho National Laboratory that has been also coupled with the thermo-hydraulic plant simulator RELAP5-3D. PHISICS is aimed to provide an optimal trade off between needed computational resources and accuracy in the range of 10~100 cores. In fact this range has been identified as the next 5 to 10 years average computational capability available to nuclear engineer designing and optimizing nuclear reactor cores. Different publication has been already presented [1] showing test of the single modules composing the PHISICS package. Lately the Idaho National Laboratory had the opportunity to access to plant data for the first cycle of a PWR including Hot Zero Power (HZP) and Hot Full Power (HFP). This data provided the opportunity to validate the transport solver, the interpolation capability for mixed macro and micro cross section and the criticality search option of the PHISICS package. In the following we will firstly recall briefly the structure of the different PHISICS modules and then we will illustrate the modeling process and some preliminary results.

97 MATHEMATICS AND COMPUTING↗

Risk Analysis Virtual ENvironment

RAVEN has 3 major functionalities: 1. Provides a Graphical User Interface for the pre- and post-processing of the RELAP-7 input and output. 2. Provides the capability to model nuclear power plants control logic for the RELAP-7 code and dynamic control of the accident scenario evolution. This capability is based on a software structure that realizes a direct connection between the RELAP-7 solver engine (MOOSE) and a python environment where the variables describing the plant status are accessible in a scripting environment. RAVEN support the generation of the probabilistic scenario control by supplying a wide range of probability and cumulative distribution functions and their inverse functions. 3. Provides a general environment to perform probability risk analysis for RELAP-7, RELAP-5 and any generic MOOSE based applications. The probabilistic analysis is performed by sampling the input space of the coupled code parameters and it is enhanced by using modern artificial intelligence algorithms that accelerate the identification of the areas of major risk (in the input parameter space). This environment also provides a graphical visualization capability to analyze the outcomes. Among other approaches, the classical Monte Carlo and Latin Hypercube sampling algorithms are available. For the acceleration of the convergence of the sampling methodologies, Support Vector Machines, Bayesian regression, and collocation stochastic polynomials chaos are implemented. The same methodologies here described could be used to solve optimization and uncertainties propagation problems using the RAVEN framework.

Rabiti, Cristian↗

THE APPLICATION OF MAMMOTH FOR A DETAILED TIGHTLY COUPLED FUEL PIN SIMULATION WITH A STATION BLACKOUT

Accurate calculation of desired quantities to predict fuel behavior requires the solution of interlinked equations representing different physics. Traditional fuels performance codes often rely on internal empirical models for the pin power density and a simplified boundary condition on the cladding edge. These simplifications are performed because of the difficulty of coupling applications or codes on differing domains and mapping the required data. To demonstrate an approach closer to first principles, the neutronics application Rattlesnake and the thermal hydraulics application RELAP-7 were coupled to the fuels performance application BISON under the master application MAMMOTH. A single fuel pin was modeled based on the dimensions of a Westinghouse 17x17 fuel rod. The simulation consisted of a depletion period of 1343 days, roughly equal to three full operating cycles, followed by a station blackout (SBO) event. The fuel rod was depleted for 1343 days for a near constant total power loading of 65.81 kW. After 1343 days the fission power was reduced to zero (simulating a reactor shut-down). Decay heat calculations provided the time-varying energy source after this time. For this problem, Rattlesnake, BISON, and RELAP-7 are coupled under MAMMOTH in a split operator approach. Each system solves its physics on a separate mesh and, for RELAP-7 and BISON, on only a subset of the full problem domain. Rattlesnake solves the neutronics over the whole domain that includes the fuel, cladding, gaps, water, and top and bottom rod holders. Here BISON is applied to the fuel and cladding with a 2D axi-symmetric domain, and RELAP-7 is applied to the flow of the circular outer water channel with a set of 1D flow equations. The mesh on the Rattlesnake side can either be 3D (for low order transport) or 2D (for diffusion). BISON has a matching ring structure mesh for the fuel so both the power density and local burn up are copied accurately from Rattlesnake. At each depletion time step, Rattlesnake calculates a power density, fission density rate, burn-up distribution and fast flux based on the current water density and fuel temperature. These are then mapped to the BISON mesh for a fuels performance solve. BISON calculates the fuel temperature and cladding surface temperature based upon the current power density and bulk fluid temperature. RELAP-7 then calculates the fluid temperature, water density fraction and water phase velocity based upon the cladding surface temperature. The fuel temperature and the fluid density are then passed back to Rattlesnake for another neutronics calculation. Six Picard or fixed-point style iterations are preformed in this manner to obtain consistent tightly coupled and stable results. For this paper a set of results from the detailed calculation are provided for both during depletion and the SBO event. We demonstrate that a detailed calculation closer to first principles can be done under MAMMOTH between different applications on differing domains.

36 MATERIALS SCIENCE↗

The application of MAMMOTH for a detailed tightly coupled fuel pin simulation with a station blackout

The accurate calculation of desired quantities to predict fuel behavior in a nuclear reactor requires the solution of inter linked equations representing different physics phenomena. Traditional fuels performance codes often rely on internal empirical models for the pin power density and a simplified boundary condition on the cladding outer surface. These simplifications are performed because of the difficulty of coupling applications or codes on differing domains and mapping the required data. In this work the MAMMOTH application is employed in the demonstration of an approach that more consistent with first principles, in a simulation that couples the neutronics application Rattlesnake, the thermal fluids application RELAP-7 and the fuels performance application BISON. A single fuel pin was modeled based on the dimensions of a fuel rod from a Westinghouse 17*17 optimized PWR fuel assembly. The simulation consisted of a depletion period of 1343 days, representing three full operating cycles, followed by a station blackout (SBO) event. The fuel rod was depleted with a total pin power of 65.81 kW. After 1343 days the fission power was reduced to zero (simulating a reactor shutdown). Decay heat calculations provided the time-varying energy source after this time. For this problem, Rattlesnake, BISON, and RELAP-7 are coupled under MAMMOTH in a tightly coupled approach. Each system solves its physics on a separate mesh and, for RELAP-7 and BISON, on only a subset of the full problem domain. Rattlesnake solves the neutronics over the whole domain, which includes the fuel, cladding, gaps, water, and top and bottom rod holders. Here BISON is applied to the fuel and cladding with a 2-D axisymmetric domain, and RELAP-7 is applied to the flow of the circular outer water channel with a set of 1-D flow equations. For this work, the mesh on the Rattlesnake side is either be 3-D (for low order PN transport or diffusion) or 2-D axisymmetric (for diffusion). BISON has a matching ring structure mesh for the fuel so both the power density and local burnup are transferred accurately from Rattlesnake. At each depletion time step, Rattlesnake calculates a power density, fission density rate, burnup distribution and fast flux based on the current water density and fuel temperature. These are then mapped to the BISON mesh to perform a fuels performance solution. BISON calculates the fuel temperature and cladding surface temperature based upon the current power density and bulk fluid temperature. RELAP-7 then calculates the fluid temperature, water density fraction and water phase velocity based upon the cladding surface temperature. The fuel temperature and the fluid density are then passed back to Rattlesnake for another neutronics calculation. For this paper, sets of results from the detailed calculation are provided for both depletion and the SBO event. We demonstrate that a detailed simulation akin to first principles can be achieved using MAMMOTH and the various MOOSE application on differing domains. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

SINGLE PHASE ANALYTICAL MODELS FOR TERRY TURBINE NOZZLE

All BWR RCIC (Reactor Core Isolation Cooling) systems and PWR AFW (Auxiliary Feed Water) systems use Terry turbine, which is composed of the wheel with turbine buckets and several groups of fixed nozzles and reversing chambers inside the turbine casing. The inlet steam is accelerated through the turbine nozzle and impacts on the wheel buckets, generating work to drive the RCIC pump. As part of the efforts to understand the unexpected “self-regulating” mode of the RCIC systems in Fukushima accidents and extend BWR RCIC and PWR AFW operational range and flexibility, mechanistic models for the Terry turbine, based on Sandia National Laboratories’ original work, has been developed and implemented in the RELAP-7 code to simulate the RCIC system. RELAP-7 is a new reactor system code currently under development with the funding support from U.S. Department of Energy. The RELAP-7 code is a fully implicit code and the preconditioned Jacobian-free Newton-Krylov (JFNK) method is used to solve the discretized nonlinear system. This paper presents a set of analytical models for simulating the flow through the Terry turbine nozzles when inlet fluid is pure steam. The implementation of the models into RELAP-7 will be briefly discussed. In the Sandia model, the turbine bucket inlet velocity is provided according to a reduced-order model, which was obtained from a large number of CFD simulations. In this work, we propose an alternative method, using an under-expanded jet model to obtain the velocity and thermodynamic conditions for the turbine bucket inlet. The models include both adiabatic expansion process inside the nozzle and free expansion process out of the nozzle to reach the ambient pressure. The combined models are able to predict the steam mass flow rate and supersonic velocity to the Terry turbine bucket entrance, which are the necessary input conditions for the Terry Turbine rotor model. The nozzle analytical models were validated with experimental data and benchmarked with CFD simulations. The analytical models generally agree well with the experimental data and CFD simulations. The analytical models are suitable for implementation into a reactor system analysis code or severe accident code as part of mechanistic and dynamical models to understand the RCIC behaviors. The cases with two-phase flow at the turbine inlet will be pursued in future work.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Thermal Hydraulics Safety Analyses of TRIGA Reactor Upon Fuel Reconfiguration

Safety analyses of the Training, Research, Isotope, General Atomics (TRIGA) reactor at Kansas State University(KSU) is performed using thermal hydraulic simulations based on changes to reactivity or the volumetric heat generation rate due to changes in the positioning of the enriched fuel elements in the reactor core. If the reactivity or neutronics parameters are known, then they can be used to simulate the thermal energy state of the material which is crucial to assess the safety of the nuclear fuel inside a nuclear reactor. Several thermal hydraulics models and codes have been developed in the past to assess reactor safety. RELAP (Reactor Excursion and Leak Analysis Program) is one such tool widely used throughout the world for safety analyses. Although RELAP is considered a reliable tool by regulators, vendors, and operators, it lacks the numerical fidelity provided by 3-D computational fluid dynamics (CFD) models. This work involves the critical task of assessing safety of a research reactor upon fuel reconfiguration based on models developed in RELAP and comparing them with a commercially available 3-D CFD program. The TRIGA Mark-II reactor, designed by General Atomics and located at Kansas State University, is a class of small pool type inherently safe research reactor licensed to operate at steady state power of up to 1.25 MW. It has a cylindrical core measuring 0.45 meters diametrically and 0.38 meters axially positioned in a tank measuring 1.98 meters diametrically and 6.25 meters axially. It has uranium zirconium hydride (UZrH) fuel rods housed in stainless steel cladding material arranged in five concentric rings (B,C,D,E and F rings, in that order, moving outwards from the center). TRIGA fuel is nominally 20% enriched, but the reactivity of the fuel can be changed by using burnable poisons (not used at KSU), or by varying the total weight percent of uranium in the UZrH fuel meat. The TRIGA reactor is designed to be an inherently safe reactor and is designed to be cooled by natural convection. Thus it is of paramount importance to avoid the film boiling regime; failing to do so will subject the fuel to severe conditions, possibly resulting in its failure due to fuel/clad interactions. A high DNBR ratio is a primary consideration in the reactor core design and thus any modification in the core should ensure that this criteria is always met. In order to fully utilize the capabilities of KSU TRIGA reactor facility, it should be operated at its full capacity, i.e. 1.25 MW, which requires increasing the fuel loading in some of the E- and F-ring elements from 8.5% U (nominal) to 12.0% U (nominal). Only four elements are to be switched to 12% loading, causing local power peaking in these elements. The degree of power peaking to be expected in these 12%-loaded fuel elements was calculated based on a detailed MCNP (Monte Carlo N-Particle code) model of the reactor core. Some preliminary results of the calculations are presented in this paper based on changes in peaking factors and power levels. To predict reactor thermal behavior, axial changes in the peaking factors obtained from MCNP models were used to calculate volumetric energy density functions for a single channel one dimensional RELAP model and a three dimensional COMSOL model of the TRIGA MARK-II reactor. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Risk-Informed Safety Margin Characterization Methods Development Work

This report summarizes the research activity developed during the Fiscal year 2014 within the Risk Informed Safety Margin and Characterization (RISMC) pathway within the Light Water Reactor Sustainability (LWRS) campaign. This research activity is complementary to the one presented in the INL/EXT-??? report which shows advances Probabilistic Risk Assessment Analysis using RAVEN and RELAP-7 in conjunction to novel flooding simulation tools. Here we present several analyses that prove the values of the RISMC approach in order to assess risk associated to nuclear power plants (NPPs). We focus on simulation based PRA which, in contrast to classical PRA, heavily employs system simulator codes. Firstly we compare, these two types of analyses, classical and RISMC, for a Boiling water reactor (BWR) station black out (SBO) initiating event. Secondly we present an extended BWR SBO analysis using RAVEN and RELAP-5 which address the comments and suggestions received about he original analysis presented in INL/EXT-???. This time we focus more on the stochastic analysis such probability of core damage and on the determination of the most risk-relevant factors. We also show some preliminary results regarding the comparison between RELAP5-3D and the new code RELAP-7 for a simplified Pressurized Water Reactors system. Lastly we present some conceptual ideas regarding the possibility to extended the RISMC capabilities from an off-line tool (i.e., as PRA analysis tool) to an online-tool. In this new configuration, RISMC capabilities can be used to assist and inform reactor operator during real accident scenarios.

97 MATHEMATICS AND COMPUTING↗

RAVEN: a GUI and an Artificial Intelligence Engine in a Dynamic PRA Framework

Increases in computational power and pressure for more accurate simulations and estimations of accident scenario consequences are driving the need for Dynamic Probabilistic Risk Assessment (PRA) [1] of very complex models. While more sophisticated algorithms and computational power address the back end of this challenge, the front end is still handled by engineers that need to extract meaningful information from the large amount of data and build these complex models. Compounding this problem is the difficulty in knowledge transfer and retention, and the increasing speed of software development. The above-described issues would have negatively impacted deployment of the new high fidelity plant simulator RELAP-7 (Reactor Excursion and Leak Analysis Program) at Idaho National Laboratory. Therefore, RAVEN that was initially focused to be the plant controller for RELAP-7 will help mitigate future RELAP-7 software engineering risks. In order to accomplish this task, Reactor Analysis and Virtual Control Environment (RAVEN) has been designed to provide an easy to use Graphical User Interface (GUI) for building plant models and to leverage artificial intelligence algorithms in order to reduce computational time, improve results, and help the user to identify the behavioral pattern of the Nuclear Power Plants (NPPs). In this paper we will present the GUI implementation and its current capability status. We will also introduce the support vector machine algorithms and show our evaluation of their potentiality in increasing the accuracy and reducing the computational costs of PRA analysis. In this evaluation we will refer to preliminary studies performed under the Risk Informed Safety Margins Characterization (RISMC) project of the Light Water Reactors Sustainability (LWRS) campaign [3]. RISMC simulation needs and algorithm testing are currently used as a guidance to prioritize RAVEN developments relevant to PRA.

97 MATHEMATICS AND COMPUTING↗

A flooding induced station blackout analysis for a pressurized water reactor using the RISMC toolkit

In this paper we evaluate the impact of a power uprate on a pressurized water reactor (PWR) for a tsunami-induced flooding test case. This analysis is performed using the RISMC toolkit: the RELAP-7 and RAVEN codes. RELAP-7 is the new generation of system analysis codes that is responsible for simulating the thermal-hydraulic dynamics of PWR and boiling water reactor systems. RAVEN has two capabilities: to act as a controller of the RELAP-7 simulation (e.g., component/system activation) and to perform statistical analyses. In our case, the simulation of the flooding is performed by using an advanced smooth particle hydrodynamics code called NEUTRINO. The obtained results allow the user to investigate and quantify the impact of timing and sequencing of events on system safety. The impact of power uprate is determined in terms of both core damage probability and safety margins.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗