Publications

In 2010, the U.S. Department of Energy created its first Energy Innovation Hub, which focuses on improving Light Water Reactors (LWRs) through Modeling and Simulation. This hub, named the Consortium for the Advanced Simulation of LWRs (CASL), attempts to characterize and understand LWR behavior under normal operating conditions and use any gained insights to improve their efficiency. In collaboration with North Carolina State University (NCSU), CASL has worked extensively on the thermal-hydraulic subchannel code Coolant Boiling in Rod Arrays—Three Field (COBRA-TF). The NCSU/CASL version of COBRA-TF has been rebranded as CTF. This document focuses on code verification test problems that ensure CTF converges to the correct answer for the intended application. The suite of code verification tests are mapped to the underlying conservation equations of CTF, and significant gaps are addressed. Convergence behavior and numerical errors are quantified for each of the tests. Tests that converge at the correct rate to the corresponding analytic solution are incorporated into the CTF automated regression suite. A new verification utility is created for this purpose, which enables code verification by generalizing the process. For problems that do not behave correctly, the results are reported but the problem is not included in the regression suite. In addition to verification studies, this document also quantifies the existing tests of constitutive models. A few existing gaps are addressed by adding new unit tests.

Abstract not provided.

Wilks’ non-parametric method for setting tolerance limits using order statistics has recently become popular in the nuclear industry. The method allows analysts to predict a desired tolerance limit with some confidence that the estimate is conservative. The method is popular because it is simple and fits well into established regulatory frameworks. A critical analysis of the underlying statistics is presented in this work, including a derivation, analytical and statistical verification, and a broad discussion. Possible impacts of the underlying assumptions for application to computational tools are discussed. An in-depth discussion of the order statistic rank used in Wilks’ formula is provided, including when it might be necessary to use a higher rank estimate.

The traditional scientific process has been revolutionized by the advent of computational modeling, but the nuclear industry generally uses “legacy codes,” which were developed early in the evolution of computers. One example of a legacy code, the thermal hydraulic subchannel code CTF, is modernized in this work through the development of a novel residual-based version, CTF-R. Unlike its predecessor, CTF-R is not limited by the strict computational limitations of the early 1980's, and can therefore be designed such that it is inherently flexible and easy to use. A case study is examined to demonstrate how the flexibility of the code can be used to improve simulation results. In this example, the coupling between the solid and liquid fields is examined. Traditionally, this coupling is modeled explicitly, which imposes numerical stability limits on the time step size. These limits are derived and it is shown that they are removed when the coupling is made implicit. Further, the development of CTF-R will enable future improvements in next generation reactor modeling, numerical methods, and coupling to other codes. Through the further development of CTF-R and other residual-based codes, state-of-the-art simulation is possible.

Abstract not provided.

Abstract not provided.

In modern scientific analyses, physical experiments are often supplemented with computational modeling and simulation. This is especially true in the nuclear power industry, where experiments are prohibitively expensive, or impossible, due to extreme scales, high temperatures, high pressures, and the presence of radiation. To qualify these computational tools, it is necessary to perform software quality assurance, verification, validation, and uncertainty quantification. As part of this broad process, the uncertainty of empirically derived models must be quantified. In this work, three commonly used thermal hydraulic models are calibrated to experimental data. The empirical equations are used to determine single phase friction factor in smooth tubes, single phase heat transfer coefficient for forced convection, and the transfer of mass between two phases. Bayesian calibration methods are used to estimate the posterior distribution of the parameters given the experimental data. In cases where it is appropriate, mixed-effects hierarchical calibration methods are utilized. The analyses presented in this work result in justified and reproducible joint parameter distributions which can be used in future uncertainty analysis of nuclear thermal hydraulic codes. When using these joint distributions, uncertainty in the output will be lower than traditional methods of determining parameter uncertainty. The lower uncertainties are more representative of the state of knowledge for the phenomena analyzed in this work.

In modern scientific analyses, physical experiments are often supplemented with computational modeling and simulation. This is especially true in the nuclear power industry, where experiments are prohibitively expensive, or impossible, due to extreme scales, high temperatures, high pressures, and the presence of radiation. To qualify these computational tools, it is necessary to perform software quality assurance, verification, validation, and uncertainty quantification. As part of this broad process, the uncertainty of empirically derived models must be quantified. In this work, three commonly used thermal hydraulic models are calibrated to experimental data. The empirical equations are used to determine single phase friction factor in smooth tubes, single phase heat transfer coefficient for forced convection, and the transfer of mass between two phases. Bayesian calibration methods are used to estimate the posterior distribution of the parameters given the experimental data. In cases where it is appropriate, mixed-effects hierarchical calibration methods are utilized. The analyses presented in this work result in justified and reproducible joint parameter distributions which can be used in future uncertainty analysis of nuclear thermal hydraulic codes. When using these joint distributions, uncertainty in the output will be lower than traditional methods of determining parameter uncertainty. The lower uncertainties are more representative of the state of knowledge for the phenomena analyzed in this work.