Advanced Reactor Analysis

GOTHIC is a multi-dimensional, CFD-like tool that can be used for both system and containment analysis. It includes a flexible nodalization scheme (0-D to full 3D), a diverse equation set and models for fundamental physical phenomena, which makes the software applicable for a wide range of applications. The software has a graphical user interface (GUI) and post-processing capabilities, which allows for fast model creation and visualization of results. This allows for scoping studies or design concepts to be quickly investigated. It also includes aerosol modeling and fission product tracking capabilities.

GOTHIC includes many attributes and physical phenomena that are important for advanced reactor concepts currently being evaluated:

• Able to model complex geometries
• Models forced convection, natural circulation, buoyancy and thermal stratification
• Includes molecular and turbulent diffusion
• Several different turbulence models, including standard κ-ε
• Includes 2nd order accurate advection schemes
• Offers 2D conduction heat transfer in solids
• Component models for engineered safety equipment (e.g., pumps, valves, heat exchangers, etc.)
• Point neutron kinetics model
• Offers parallel processing to further decrease run time
• Nuclear QA program that complies with 10CFR50, Appendix B and applicable portions of ASME NQA-1

The GUI and QA aspects of this cannot be understated. Trying to incorporate these into existing tools after the fact will be expensive whereas they are already available in GOTHIC.

Moreover, it has been our experience that GOTHIC is able to provide results that were not realizable with other system or CFD tools. The system level tools do not provide the multi-dimensional effects that can be important while the CFD tools presented run time limitations and could not provide an integrated system response because they do not include models for plant equipment (e.g., pumps, valves, heat exchangers, etc.) or control system logic that GOTHIC offers.

Furthermore, GOTHIC's flexible nodalization allows for an integrated plant model (reactor vessel, coolant loops, containment, safety systems, etc.) to be created entirely in GOTHIC rather than needing multiple codes. This can be very valuable, particularly at the conceptual phase, because it streamlines the process to construct models and evaluate various design features when the entire system is represented in one model.

Therefore, GOTHIC provides high fidelity results in a computationally efficient manner, which is very beneficial for quickly assessing various design concepts. As a result, GOTHIC could be a valuable tool for your advanced reactor evaluations.

An example of the computational time for GOTHIC relative to CFD can be seen here.

GOTHIC has been benchmarked to ISP-43, which simulates a series of boron dilution transients. This paper was published as part of the International Congress on Advances in Nuclear Power Plants (ICAPP) in 2016. Relative to the CFD participants in the benchmark, GOTHIC was able to achieve similar (or better) results using far fewer cells and therefore provided a much more computationally efficient solution.

Similarly, we benchmarked GOTHIC using an impact experiment shown here. GOTHIC compared very well to the experimental data for wave dynamics and surface structure. This benchmark was done to support our qualification of GOTHIC for analyzing the response of spent fuel pools for seismic events.

Over the past several years we have added non-LWR fluid properties to GOTHIC, including sodium (Na), sodium-potassium (NaK), lead (Pb), lead-bismuth eutectic (LBE), heavy water (D2O), and a variety of molten salts (NaCl-MgCl2, LiF-BeF2, LiF-NaF-KF, NaF-ZrF4, KF-ZrF4 and NaBF4-NaF), with others in development. Additional details about the non-LWR capabilities can be seen in our paper from NURETH-18.

In addition to the general attributes for advanced reactors, specific attributes of GOTHIC for SFRs includes:

• Ability to model conduction within the fluid
• Aerosol and fission product tracking capabilities, which can be useful for aerosols in containment and from a sodium fire.

We recently completed a benchmark to the SHRT-17 and SHRT-45 loss of flow tests from EBR-II and the results were published in Nuclear Technology. We are currently extending the benchmark to include the BOP-301 and BOP-302R loss of heat sink tests from EBR-II and we are participating in the IAEA coordinated benchmark of the FFTF loss of flow test.

For MSRs with liquid fuel, a unique attribute of GOTHIC is the ability to track delayed neutron precursors and the decay heat released outside the core region. We have performed verification type testing and benchmarked to the molten salt reactor experiment (MSRE) at ORNL. The steady-state comparisons were presented at the ANS Winter Meeting and the comparisons to several transients will be published at the upcoming ICONE meeting. We also completed a pilot study for TerraPower's Molten Chloride Fast Reactor (MCFR). Coupling the existing point kinetics and radioactive isotope tracking capabilities in GOTHIC to support translational reactor physics is also being evaluated to support molten salt designs with liquid fuel.

GOTHIC already includes a library of over 50 different gases that can support high-temperature gas reactor (HTGR) designs. Other important attributes of GOTHIC for HTGRs includes:

• Steady and transient analysis including compressibility effects.
• Wall-to-Wall radiation heat transfer with plans to add participating media in the next release.
• Jet mixing.

A digital twin is a replica of a physical asset and generally consists of three primary elements:

1. A data warehouse the continuously collects sensor information from the physical asset.
2. Advanced modeling and simulation tools to fill in knowledge gaps (e.g., nonexistent data) for the physical asset and predict future response based on current state, including uncertainty assessments of available data and predictions.
3. Machine Learning and Artificial Intelligence algorithms that train on the data and to identify causal relationships to produce a surrogate (or reduced order model) that can then estimate the expected response of the physical asset based on the accumulated knowledge.

Once established, the digital twin can be used for:

1. Deviation Detection since the digital twin has an expected response for the physical asset and is continuously collecting new information from the physical asset, it can identify deviations between expected and as operating conditions.
2. Predictive Maintenance the expected response from the digital twin can be extended to provide an estimate of asset health and remaining lifetime. Such information can be used to determine when maintenance will be required, considering accumulation of actual operation, expected future evolutions, predicted performance degradation, and considering probability and significance of unexpected transients (such as design basis accident). Pre-emptively determining asset maintenance needs or determining the time until required asset maintenance can be lengthened based on as-operating conditions allows for O&M efforts to be dynamically prioritized on critical assets.

The Digital Twin is dynamic continuously collecting information from the physical asset and then updating (or retraining) the Machine Learning algorithms based on the new information. Therefore, scalability of deployed models is an important feature of transitioning trained models into production, where they can be used to guide decision making. To accommodate a large volume of sequential sensor data, models amenable to online updates such as recurrent neural networks (RNNs) and architectures based on the Transformer model are used.

Machine Learning (ML), and in particular deep learning, are rapidly growing in various engineering disciplines across a wide range of industries. Machine learning models as part of sophisticated software deployments are able to process enormous amounts of sensor data in real time to make intelligent decisions which are otherwise infeasible. This can enhance safety and economy for next-generation nuclear plants by enabling early detection of coming anomalies over a wide range of time scales.

Statistical validation of machine learning model output is an important step in the deployment process, necessary for ensuring that a given model is performing as designed and proving defensible results. As is standard practice in machine learning, some fraction of the available training data will be held out for cross-validation and testing purposes. Appropriate figures of merit are computed on both the held out data and training data, and compared to assess overfitting vs. underfitting of the training data.

To ensure unbiased learning, steps will be taken to a) quantify domain coverage of the potential input plant operational phase space and b) demonstrate methodology for ensuring efficient phase space coverage of inputs. This can be achieved through techniques like PCMQ. Also, a PRA framework can be leveraged to account for component failures and control actions, while the simulation tool predicts results from potential pathways.

Digital Twins can then be coupled with Virtual Reality or Augmented Reality environments to visualize results and improve effectiveness of the Digital Twin

Integrated Research Project (IRP) titled Development and Application of a Data-Driven Methodology for Validation of Risk-Informed Safety Margin Characterization Models, US Department of Energy (DOE) Nuclear Energy University Program (NEUP).

NAS is partnered with North Carolina State University investigating data driven modeling.

US Department of Energy (DOE) Advanced Research Projects Administration-Energy (ARPA-E) MEITNER Project: Development of a Nearly Autonomous Management and Control System (NAMAC).

NAS is partnered with North Carolina State University to develop a Nearly Autonomous Management And Control (NAMAC) system for nuclear plants. NAMAC will be used to diagnose the plant state, project the effects of actions and uncertainties into the future behavior and make prioritized recommendations to the operator for the best strategy to cope with any situation with respect to plant safety, performance, and cost. GOTHIC has been selected as the computational engine to satisfy the advanced Modeling and Simulation requirements of NAMAC. A primary near-team goal for NAMAC is to improve plant safety by reducing operator errors, and promoting dynamic and effective management of abnormal transient and accident scenarios. Longer term goals will be to reduce operating costs and minimize the plant risk profile by affecting the system design, allowing SSC reclassification and reducing the EPZ). NAS believes the NAMAC concept is vital to the nuclear industry and is proud to be at the forefront of developing and demonstrating this technology. Additional information is available from ARPA-E.