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LSENS, a general chemical kinetics and sensitivity analysis code for homogeneous gas-phase reactions. 2: Code description and usage

LSENS, the Lewis General Chemical Kinetics Analysis Code, has been developed for solving complex, homogeneous, gas-phase chemical kinetics problems and contains sensitivity analysis for a variety of problems, including nonisothermal situations. This report is part 2 of a series of three reference publications that describe LSENS, provide a detailed guide to its usage, and present many example problems. Part 2 describes the code, how to modify it, and its usage, including preparation of the problem data file required to execute LSENS. Code usage is illustrated by several example problems, which further explain preparation of the problem data file and show how to obtain desired accuracy in the computed results. LSENS is a flexible, convenient, accurate, and efficient solver for chemical reaction problems such as static system; steady, one-dimensional, inviscid flow; reaction behind incident shock wave, including boundary layer correction; and perfectly stirred (highly backmixed) reactor. In addition, the chemical equilibrium state can be computed for the following assigned states: temperature and pressure, enthalpy and pressure, temperature and volume, and internal energy and volume. For static problems the code computes the sensitivity coefficients of the dependent variables and their temporal derivatives with respect to the initial values of the dependent variables and/or the three rate coefficient parameters of the chemical reactions. Part 1 (NASA RP-1328) derives the governing equations describes the numerical solution procedures for the types of problems that can be solved by lSENS. Part 3 (NASA RP-1330) explains the kinetics and kinetics-plus-sensitivity-analysis problems supplied with LSENS and presents sample results.

Radhakrishnan, Krishnan↗

Uncertainty Quantification and Sensitivity Analysis of Nuclear Construction Cost Reduction Pathways

High construction costs have plagued recent nuclear projects and they hamper the widespread deployment of nuclear technology. The Nuclear Cost Reduction Tool is a plant economic framework that quantifies the impact that various plant design and construction attributes have on construction costs and cost overruns and shows the positive effects of learning over a series of deployments. However, a downside of the current model is that all model outputs and capabilities are deterministic. To provide a more comprehensive view, this study evaluated the impact of model parameter uncertainty through a sensitivity analysis applied to 18 model parameters. This approach quantified the impact of model uncertainty on the output variables of Net Overnight Capital Cost (Net OCC), Construction Duration (CD), and Levelized Cost of Electricity (LCOE). Monte Carlo analysis revealed uncertainty distributions for these variables, showing that absolute uncertainty decreases over a series of deployments. A local sensitivity analysis showed that even small parameter perturbations (5%) can have a significant impact on project execution, highlighting areas that could reduce costs by billions across an order book of plants. The results of this study have improved the understanding of the model and identified the most impactful model parameters and construction attributes.

Levelized Cost of Electricity↗

Design sensitivity analysis and optimization tool (DSO) for sizing design applications

The DSO tool, a structural design software system that provides the designer with a graphics-based menu-driven design environment to perform easy design optimization for general applications, is presented. Three design stages, preprocessing, design sensitivity analysis, and postprocessing, are implemented in the DSO to allow the designer to carry out the design process systematically. A framework, including data base, user interface, foundation class, and remote module, has been designed and implemented to facilitate software development for the DSO. A number of dedicated commercial software/packages have been integrated in the DSO to support the design procedures. Instead of parameterizing an FEM, design parameters are defined on a geometric model associated with physical quantities, and the continuum design sensitivity analysis theory is implemented to compute design sensitivity coefficients using postprocessing data from the analysis codes. A tracked vehicle road wheel is given as a sizing design application to demonstrate the DSO's easy and convenient design optimization process.

Chang, Kuang-Hua↗

Uncertainty and sensitivity analysis of fission gas behavior in engineering-scale fuel modeling

The role of uncertainties in fission gas behavior calculations as part of engineering-scale nuclear fuel modeling is investigated using the BISON fuel performance code and a recently implemented physics-based model for the coupled fission gas release and swelling. Through the integration of BISON with the DAKOTA software, a sensitivity analysis of the results to selected model parameters is carried out based on UO2 single-pellet simulations covering different power regimes. The parameters are varied within ranges representative of the relative uncertainties and consistent with the information from the open literature. The study leads to an initial quantitative assessment of the uncertainty in fission gas behavior modeling with the parameter characterization presently available. Also, the relative importance of the single parameters is evaluated. Moreover, a sensitivity analysis is carried out based on simulations of a fuel rod irradiation experiment, pointing out a significant impact of the considered uncertainties on the calculated fission gas release and cladding diametral strain. The results of the study indicate that the commonly accepted deviation between calculated and measured fission gas release by a factor of 2 approximately corresponds to the inherent modeling uncertainty at high fission gas release. Nevertheless, higher deviations may be expected for values around 10% and lower. Implications are discussed in terms of directions of research for the improved modeling of fission gas behavior for engineering purposes.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Uncertainty and Sensitivity Analysis of Reactivity Insertion Accidents using BISON Fuel Performance Code

The development of Accident Tolerant Fuels (ATF) has expanded into a considerable research program in the wake of the events at the Japanese Fukushima Daiichi nuclear power plant in 2011. The ATF goal is to insert a test assembly into a commercial reactor by 2022. To support this, testing of the ATF design under off-normal conditions is needed to assess the 'enhanced accident tolerance' capability of the fuel rod design over standard UO{sub 2}-Zircaloy concepts. Transient testing capabilities are necessary for off-normal testing of events such as loss of coolant accidents (LOCA) and reactivity insertion accidents (RIA). A transient testing program has been developed to support the testing of ATF designs. The Transient Reactor Test (TREAT) facility has been chosen as the site to perform the transient testing of the ATF designs. TREAT is a versatile test facility capable of subjecting fuel specimens to various off-normal conditions. Historic TREAT experiments were performed in a variety of experimental test vehicles including static environment capsules, once-through flowing systems, and also recirculating flowing systems. The planned TREAT experiments will be operated under PWR conditions. Therefore, a static capsule vehicle is under development to handle required temperatures and pressures. The static capsule, termed the Static Environment Rodlet Transient Test Apparatus (SERTTA), will be used for irradiation tests in TREAT to subject ATF fuel rodlets to a range of power pulse conditions and environments. To aid in the design and analysis of future tests in TREAT, the fuel performance code BISON is being used. Fuel performance codes capable of accident modeling have been developed for some time and they have shown an ability to reproduce experimental results with some degree of adequacy, but they still require extensive verification and validation. Future experiments in TREAT will add to a limited database of past transient tests performed in transient reactors to support LWR systems. These tests can be used for future verification and validation of fuel performance codes. Understanding the impact of the uncertainty of influential parameters is critical for not only analyzing the results of the experiment but also for modeling and validation of codes. For example, uncertainties associated with the initial manufactured state of the sample, instrument measurements, material property models, and planned experiment conditions can provide important insight into model performance, experimental data, and play an important role in experimental design. The objective of this work is to perform an uncertainty and sensitivity analysis on a simplified RIA case of a standard UO{sub 2}-Zircaloy sample using expected nominal conditions in the SERTTA capsule in TREAT. The BISON fuel performance code is used in conjunction with DAKOTA (Design Analysis Kit for Optimization and Tera-scale Applications) to perform the uncertainty and sensitivity analysis. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Practical implementation of an accurate method for multilevel design sensitivity analysis

Solution techniques for handling large scale engineering optimization problems are reviewed. Potentials for practical applications as well as their limited capabilities are discussed. A new solution algorithm for design sensitivity is proposed. The algorithm is based upon the multilevel substructuring concept to be coupled with the adjoint method of sensitivity analysis. There are no approximations involved in the present algorithm except the usual approximations introduced due to the discretization of the finite element model. Results from the six- and thirty-bar planar truss problems show that the proposed multilevel scheme for sensitivity analysis is more effective (in terms of computer incore memory and the total CPU time) than a conventional (one level) scheme even on small problems. The new algorithm is expected to perform better for larger problems and its applications on the new generation of computer hardwares with 'parallel processing' capability is very promising.

Nguyen, Duc T.↗

An easily implemented static condensation method for structural sensitivity analysis

A black-box approach to static condensation for sensitivity analysis is presented with illustrative examples of a cube and a car structure. The sensitivity of the structural response with respect to joint stiffness parameter is calculated using the direct method, forward-difference, and central-difference schemes. The efficiency of the various methods for identifying joint stiffness parameters from measured static deflections of these structures is compared. The results indicate that the use of static condensation can reduce computation times significantly and the black-box approach is only slightly less efficient than the standard implementation of static condensation. The ease of implementation of the black-box approach recommends it for use with general-purpose finite element codes that do not have a built-in facility for static condensation.

Gangadharan, S. N.↗

Fuel performance uncertainty quantification and sensitivity analysis in the presence of epistemic and aleatoric sources of uncertainties

Fuel performance modeling and simulation includes many uncertain parameters from models to boundary conditions, manufacturing parameters and material properties. These parameters exhibit large uncertainties and can have an epistemic or aleatoric nature, something that renders fuel performance code-to-code and code-to-measurements comparisons for complex phenomena such as the pellet cladding mechanical interaction (PCMI) very challenging. Additionally, PCMI and other complex phenomena found in fuel performance modeling and simulation induce strong discontinuities and non-linearities that can render difficult to extract meaningful conclusions form uncertainty quantification (UQ) and sensitivity analysis (SA) studies. In this work, we develop and apply a consistent treatment of epistemic and aleatoric uncertainties for both UQ and SA in fuel performance calculations and use historical benchmark-quality measurement data to demonstrate it. More specifically, the developed methodology is applied to the OECD/NEA Multi-physics Pellet Cladding Mechanical Interaction Validation benchmark. A cold ramp test leading to PCMI is modeled. Two measured quantities of interest are considered: the cladding axial elongation during the irradiations and the cladding outer diameter after the cold ramp. The fuel performance code used to perform the simulation is FAST. The developed methodology involves various steps including a Morris screening to decrease the number of uncertain inputs, a nested loop approach for propagating the epistemic and aleatoric sources of uncertainties, and a global SA using Sobol indices. The obtained results indicate that the fuel and cladding thermal conductivities as well as the cladding outer diameter uncertainties are the three inputs having the largest impact on the measured quantities. More importantly, it was found that the epistemic uncertainties can have a significant impact on the measured quantities and can affect the outcome of the global sensitivity analysis.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Screening sensitivity analysis of a PWR fuel assembly FEM structural model

Within the present project, computational methods to describe the static mechanical response of PWR fuel assemblies (FA) in the reactor core are developed. For this purpose a structural model of a PWR fuel assembly has been implemented with the Finite Element Method (FEM) using the ANSYS APDL Mechanical code. The purpose of the model is to investigate the long-term creep deformation of the fuel assemblies in the reactor core, commonly known as fuel assembly bow. FA bow is considered to be a complex process with a large number of influencing mechanisms and many only roughly known boundary conditions. Uncertainty and sensitivity analyses are a common way to investigate the predictive power and reliability of such complex models. Hence, as a first approach to understand the importance of the many model parameters, a qualitative sensitivity analysis of the model was conducted using the screening method proposed by Morris. In the first part of the paper, the FA structural model and its principal parameters are presented. The second part presents first the different simulation experiments used for the screening analyses. Based on the model description, relevant input parameters are then identified and a typical range of values is determined. The sensitivity analysis is performed in two subsequent steps. First, the model is screened for influential stiffness parameters with the objective of stiffening the FA structure. Second, the influence of the uncertain boundary conditions and material models on the FA creep deformation is tested. For the considered FA design it is concluded that the influence of the involved uncertainties is comparable to the influence of the parameters which can increase the stiffness. An integral approach accounting for these uncertainties is hence necessary to predict FA bow reliably in order to take additional measures for a further reduction of FA bow amplitudes. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Advanced Performance Metrics and their Application to the Sensitivity Analysis for Model Validation and Calibration

High-quality generator dynamic models are critical to reliable and accurate power systems studies and planning. With the availability of PMUs, measurement-based approach for model validation has gained significant prominence. In this approach, the quality of a model is analyzed by visually comparing measured generator response with the model-based simulated response for large system disturbances. This paper proposes a new set of performance metrics to assess the model validation results to facilitate automation of the model validation process. In the proposed methodology, first, the slow governor response and comparatively faster oscillatory response are separated, and then a separate set of performance metrics is calculated for each of these two components. These proposed metrics quantify the mismatch between the actual and model-based response in a comprehensive manner without missing any information enabling automation of the process. Furthermore, in this paper, we are also proposing that the sensitivity analysis for model calibration be performed with respect to the proposed metrics for the systematic identification of key parameters. In this work, results obtained using both simulated and real-world case-studies validate the effectiveness of the proposed performance metrics for model validation and their application to the sensitivity analysis for model calibration.

24 POWER TRANSMISSION AND DISTRIBUTION↗

PSA 2025 Presentation: "Modeling and Sensitivity Analysis of a Generation IV Pebble Bed Reactor Using MELCOR 2.2"

Accompanying the advancement of reactor technologies is the need for computational modeling and simulation to predict their behavior under normal operating conditions and accident scenarios. New Generation IV reactor designs which employ non-conventional fuel have a particular need for modeling the behavior and release of radionuclides and other material from the fuel. In this work, MELCOR version 2.2, a system-level safety and accident scenario code developed by Sandia National Laboratories, was used to model a 200-MWth pebble bed modular reactor and calculate the inventories of circulating and deposited graphite, metal dust, and elemental components released from the fuel elements. A base case modeling the reactor under standard operating conditions was calculated using MELCOR and the inventories were extrapolated to 30 years of operation time using a logarithmic regression fit. A sensitivity analysis was also performed in which several key parameters for the base case model were modified to explore the effect of these changes on the inventories calculated by MELCOR. A set of transient scenario simulations for a depressurized loss of forced cooling (DLOFC) accident were also performed. The results of the sensitivity analysis and transient simulations are reported and discussed in relation to the modeling techniques used for this study.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

Sensitivity Analysis of Successful Evacuee Proportion in Hypothetical Seismic Nuclear Emergency Situation

A magnitude 5.8 earthquake, which is the strongest earthquake ever detected in Korea, occurred in Gyeongju on 12 September, 2016. People were worried about not only the impact to their safety and quality of life as directly affected from the earthquake, but also the secondary impact from such a nuclear power plant (NPP) accident incurred by the earthquake. Public awareness is changing such that the risk of earthquakes is no longer a story of other countries. Even if the current situation in Korea is not regarded, it is important to assess the seismic hazard to an NPP and prepare for preventing the effects related with the earthquake impact. Developing a seismic evacuation model is necessary in a part of a level 3 probabilistic safety assessment (PSA) because it is one of the most affecting factors of public radiation exposure and health effects in an emergency phase. In a previous study, a sensitivity analysis of the evacuation speed in a hypothetical NPP accident by an earthquake has been carried out, and population doses resulting from various seismic evacuation scenarios associated with evacuation speed have been compared. In addition to the previous study, the proportion of evacuees who evacuate successfully with adequate speed has been considered and a sensitivity analysis has been performed in this study.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

VUSAT - A VERA-CS Uncertainty and Sensitivity Analysis Toolkit

VERA-CS (the Virtual Environment for Reactor Applications, Core Simulator) is a high-fidelity multiphysics core simulator under development by the Consortium for Advanced Simulation of Light Water Reactors (CASL). VERA-CS includes three main components: MPACT for reactor physics and neutron transport, COBRA-TF for thermal-hydraulics, and ORIGEN for isotopic depletion. VERA-CS has been applied to an array of problems including core physics analysis, and the modeling for all of the fuel cycles of Watts Bar Nuclear Unit 1 (WBN1). MPACT is a 3D pin-resolved reactor transport code developed by Oak Ridge National Laboratory (ORNL) and the University of Michigan. COBRA-TF (CTF) is a three-field two-phase flow subchannel analysis code developed by ORNL and North Carolina State University. CTF solves the mass, momentum, and energy equations for the liquid, vapor, and droplet phases for each subchannel in the core and captures the axial flow within each channel as well as cross-flow between channels. Direct coupling between neutronics (MPACT) and thermal-hydraulics (CTF) in VERA-CS provides temperature and density feedback. CTF includes a number of models important for LWR safety and design analysis including flow regime dependent two-phase wall heat transfer, inter-phase heat transfer and drag, droplet breakup, and quench-front tracking. ORIGEN is developed by ORNL and released through the SCALE package. ORIGEN is directly integrated in MPACT through its API to calculate the changes in nuclides for every depletable cross-section region. Uncertainties exist in safety calculations with computer codes for nuclear reactor modeling and simulation, and they come from code limitations, scaling inaccuracies embedded in the experimental data, and uncertainties associated with the state of the reactor at the initiation of the transient. Consequently, for applications of high fidelity calculations using VERA-CS, proper uncertainty quantification (UQ) and sensitivity analysis (SA) of the computing models of reactor neutronics and thermal-hydraulics are important to comprehensively understand the results. New methods in UQ and SA have to be developed in multi-physics calculations using VERA-CS. Toward this end, a software package called VUSAT which stands for VERA-CS Uncertainty and Sensitivity Analysis Toolkit has been developed to facilitate the applications of VERA-CS within the context of best estimate plus uncertainty (BEPU) analysis framework. In this work, the VUSAT application to analyze departure from nucleate boiling (DNB) is presented.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Adjoint-based sensitivity analysis for high-energy density radiative transfer using flux-limited diffusion

Uncertainty quantification and sensitivity analyses are a vital component for predictive modeling in the sciences and engineering. The adjoint approach to sensitivity analysis requires solving a primary system of equations and a mathematically related set of adjoint equations. The information contained in the equations can be combined to produce sensitivity information in a computationally efficient manner. Here in this work, sensitivity analyses are performed on systems described by flux-limited radiative diffusion using the adjoint approach. The sensitivities computed are shown to agree with standard perturbation theory and require significantly less computational time. The adjoint approach saves the computational cost of one forward solve per sensitivity, making the method attractive when multiple sensitivities are of interest.

42 ENGINEERING↗

Adaptive surrogate modeling by ANOVA and sparse polynomial dimensional decomposition for global sensitivity analysis in fluid simulation

The Polynomial Dimensional Decomposition (PDD) is employed in this work for the global sensitivity analysis and uncertainty quantification (UQ) of stochastic systems subject to a moderate to large number of input random variables. Due to the intimate connection between the PDD and the Analysis of Variance (ANOVA) approaches, PDD is able to provide a simpler and more direct evaluation of the Sobol' sensitivity indices, when compared to the Polynomial Chaos expansion (PC). Unfortunately, the number of PDD terms grows exponentially with respect to the size of the input random vector, which makes the computational cost of standard methods unaffordable for real engineering applications. In order to address the problem of the curse of dimensionality, this work proposes essentially variance-based adaptive strategies aiming to build a cheap meta-model (i.e. surrogate model) by employing the sparse PDD approach with its coefficients computed by regression. Three levels of adaptivity are carried out in this paper: 1) the truncated dimensionality for ANOVA component functions, 2) the active dimension technique especially for second- and higher-order parameter interactions, and 3) the stepwise regression approach designed to retain only the most influential polynomials in the PDD expansion. During this adaptive procedure featuring stepwise regressions, the surrogate model representation keeps containing few terms, so that the cost to resolve repeatedly the linear systems of the least-squares regression problem is negligible. The size of the finally obtained sparse PDD representation is much smaller than the one of the full expansion, since only significant terms are eventually retained. Consequently, a much smaller number of calls to the deterministic model is required to compute the final PDD coefficients.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Failure Bounding And Sensitivity Analysis Applied To Monte Carlo Entry, Descent, And Landing Simulations

In the study of entry, descent, and landing, Monte Carlo sampling methods are often employed to study the uncertainty in the designed trajectory. The large number of uncertain inputs and outputs, coupled with complicated non-linear models, can make interpretation of the results difficult. Three methods that provide statistical insights are applied to an entry, descent, and landing simulation. The advantages and disadvantages of each method are discussed in terms of the insights gained versus the computational cost. The first method investigated was failure domain bounding which aims to reduce the computational cost of assessing the failure probability. Next a variance-based sensitivity analysis was studied for the ability to identify which input variable uncertainty has the greatest impact on the uncertainty of an output. Finally, probabilistic sensitivity analysis is used to calculate certain sensitivities at a reduced computational cost. These methods produce valuable information that identifies critical mission parameters and needs for new technology, but generally at a significant computational cost.

Gaebler, John A.↗

Local and Global Sensitivity Analysis of a Reactive Transport Model Simulating Floodplain Redox Cycling

Reactive transport models (RTMs) are essential tools that simulate the coupling of advective, diffusive, and reactive processes in the subsurface, but their complexity makes them difficult to understand, develop and improve without accompanying statistical analyses. Although global sensitivity analysis (SA) can address these issues, the computational cost associated with most global SA techniques limits their use with RTMs. In this study, we apply distance-based generalized sensitivity analysis (DGSA), a novel and computationally efficient method of global SA, to a floodplain-scale RTM and compare DGSA results to those from local SA. Our test case focuses on the impact of 17 uncertain environmental parameters on spatially and temporally variable redox conditions within a floodplain aquifer. The input parameters considered include flow and diffusion rates, geochemical reaction rates, and the spatial distribution of sediment facies. Sensitivity was evaluated for three distinct components of the model response, encompassing both multidimensional and categorical output. Parameter rankings differ between local SA and DGSA, due to nonlinear effects of individual parameters and interaction effects between parameters. DGSA results show that fluid residence time, which is controlled by aquifer permeability, generally exerts a stronger control on redox conditions than do geochemical reaction rates. Sensitivity indices also demonstrate that sulfate reduction is key for establishing and maintaining reducing conditions throughout the aquifer. Furthermore, these results provide insights into the key drivers of heterogeneous redox processes within floodplain aquifers, as well as the main sources of uncertainty when modeling complex subsurface systems.

54 ENVIRONMENTAL SCIENCES↗