This paper provides a review of current and upcoming innovations in development, validation, and uncertainty quantification of nuclear reactor multi-physics simulation methods. Multi-physics modelling and simulations (M&S) provide more accurate and realistic predictions of the nuclear reactors behavior including local safety parameters. Multi-physics M&S tools can be subdivided in two groups: traditional multi-physics M&S on assembly/channel spatial scale (currently used in industry and regulation), and novel high-fidelity multi-physics M&S on pin (sub-pin)/sub-channel spatial scale. The current trends in reactor design and safety analysis are towards further development, verification, and validation of multi-physics multi-scale M&S combined with uncertainty quantification and propagation. Approaches currently applied for validation of the traditional multi-physics M&S are summarized and illustrated using established Nuclear Energy Agency/Organization for Economic Cooperation and Development (NEA/OECD) multi-physics benchmarks. Novel high-fidelity multi-physics M&S allow for insights crucial to resolve industry challenge and high impact problems previously impossible with the traditional tools. Challenges in validation of novel multi-physics M&S are discussed along with the needs for developing validation benchmarks based on experimental data. Due to their complexity, the novel multi-physics codes are still computationally expensive for routine applications. This fact motivates the use of high-fidelity novel models and codes to inform the low-fidelity traditional models and codes, leading to improved traditional multi-physics M&S. The uncertainty quantification and propagation across different scales (multi-scale) and multi-physics phenomena are demonstrated using the OECD/NEA Light Water Reactor Uncertainty Analysis in Modelling benchmark framework. Finally, the increasing role of data science and analytics techniques in development and validation of multi-physics M&S is summarized.

The Pennsylvania State University (PSU) under the sponsorship of the US Nuclear Regulatory Commission (NRC) has prepared, organized, conducted, and summarized the Organisation for Economic Co-operation and Development/US Nuclear Regulatory Commission (OECD/NRC) benchmark based on the Nuclear Power Engineering Corporation (NUPEC) pressurized water reactor (PWR) subchannel and bundle tests (PSBTs). The international benchmark activities have been conducted in cooperation with the Nuclear Energy Agency (NEA) of OECD and the Japan Nuclear Energy Safety Organization (JNES), Japan. The OECD/NRC PSBT benchmark was organized to provide a test bed for assessing the capabilities of various thermal-hydraulic subchannel, system, and computational fluid dynamics (CFDs) codes. The benchmark was designed to systematically assess and compare the participants’ numerical models for prediction of detailed subchannel void distribution and department from nucleate boiling (DNB), under steady-state and transient conditions, to full-scale experimental data. This paper provides an overview of the objectives of the benchmark along with a definition of the benchmark phases and exercises. The NUPEC PWR PSBT facility and the specific methods used in the void distribution measurements are discussed followed by a summary of comparative analyses of submitted final results for the exercises of the two benchmark phases.

This paper introduces a framework for model selection that includes parameter estimation, uncertainty propagation, and quantified validation. The framework is applied to single-phase turbulent friction modeling in CTF, which is a thermal-hydraulic code for nuclear engineering applications. The friction model is chosen because it is well understood and easy to separate from other physics, which allows focus to be on the model selection framework instead of on the particulars of the chosen model. Two different empirical models are compared: the McAdams Correlation and the Simplified McAdams Correlation. The parameter estimation is performed by calibrating each of the friction models to experimental data using the Delayed Rejection Adaptive Metropolis algorithm, which is a Markov Chain Monte Carlo method. State point uncertainties are also considered, which are determined based on measurement errors from the experiment. The input parameter distributions are propagated through CTF using a statistical method with $\mathit{2000}$ samples. A variety of validation metrics is used to quantify which empirical model is more accurate. It is shown that model form uncertainty can be quantified using validation once all other sources of uncertainty—numerical, sampling, experimental, and parameter—have been quantitatively addressed. When multiple models are available, the one that has the smallest model form error can be selected. Though the framework is applied to a simple example here, the same process can quantify the model form uncertainty of more complicated physics, multiple models, and simulation tools in other fields. Therefore, this work is a demonstration of best practices for future assessments of model form uncertainty.

Best Estimate Plus Uncertainty (BEPU) approaches for nuclear reactor applications have been extensively developed in recent years. The challenge for BEPU approaches is to achieve multi-physics modeling with an acceptable computational cost while preserving a reasonable fidelity of the physics modeled. In this work, we present the core multi-physics computational framework developed for the efficient computation of uncertainties in Light Water Reactor (LWR) simulations. The subchannel thermal-hydraulic code CTF and the nodal expansion neutronic code PARCS are coupled for the multi-physics modeling (CTF-PARCS). The computational framework is discussed in detail from the Polaris lattice calculations up to the CTF-PARCS coupling approaches. Sampler is used to perturb the multi-group microscopic cross-sections, fission yields and manufacturing parameters, while Dakota is used to sample the CTF input parameters and the boundary conditions. Python scripts were developed to automatize and modularize both pre- and post-processing. The current state of the framework allows the consistent perturbation of inputs across neutronics and thermal-hydraulics modeling. Improvements to the standard thermal-hydraulics modeling for such coupling approaches have been implemented in CTF to allow the usage of 3D burnup distribution, calculation of the radial power and the burnup profile, and the usage of Santamarina effective Doppler temperature. The uncertainty quantification approach allows the treatment of both scalar and functional quantities and can estimate correlation between the multi-physics outputs of interest and up to the originally perturbed microscopic cross-sections and yields. The computational framework is applied to three exercises of the LWR Uncertainty Analysis in Modeling Phase III benchmark. The exercises cover steady-state, depletion and transient calculations. The results show that the maximum fuel centerline temperature across all exercises is $2474\mathrm{K}$ with $1.7\%$ uncertainty and that the most correlated inputs are the ²³⁸U inelastic and elastic cross-sections above 1 MeV.