Intrusive and Non-intrusive Reduced Order Modeling for Flow Analysis of Typical Rod Bundle Geometries in Liquid Metal Cooled Reactors

Nuclear energy is regarded as a low-carbon energy source that can help mitigate global warming and ensure energy supply security. The Generation IV nuclear reactors were proposed to improve the sustainability, safety, and economics of nuclear energy. Among the alternative Generation IV designs, liquid metal cooled fast reactors (LMFRs) are considered the most promising due to their superior neutronic and thermal-hydraulic performance.

Thermal-hydraulic analysis plays a crucial role in reactor design, ensuring safe and efficient operation. Numerical simulations are widely used to investigate these complex phenomena. Recently, Computational Fluid Dynamics (CFD) has increasingly been used to model detailed fluid dynamics and heat transfer in nuclear systems. However, high-fidelity CFD simulations are still computationally expensive and time-consuming, which limits their application to many-query simulations, e.g., uncertainty quantification, sensitivity analysis, and optimization.

Reduced order modeling (ROM) is an emerging data-driven framework that aims to reduce computational cost while maintaining acceptable accuracy. Given a set of known high-fidelity solutions (i.e., snapshots), a reduced system is constructed based on the most dominant features extracted from the snapshots. ... mehrThen, ROMs are employed to approximate the system response for unknown input parameters. In many applications, ROM acceleration is in the order of 1000 or more, making them attractive for parametric studies and real-time simulations.

The framework for constructing ROMs is not unique. They can be generally categorized into intrusive and non-intrusive methods. Intrusive ROMs require access to and modification of the high-fidelity partial differential equations. In contrast, non-intrusive ROMs are purely data-driven and treated as "black boxes" to approximate the relationship between parameters and system responses.

Through reviewing the existing literature, both intrusive and non-intrusive ROM techniques have been successfully applied to various physical problems. However, their applications in nuclear engineering are still limited.

Additionally, most existing ROMs are developed as \emph{global ROMs}, i.e., built on the whole computational domain. That is feasible for small to medium-scale problems. However, for large-scale geometries, preparing CFD solutions for ROM training is computationally prohibitive. To tackle this challenge, domain decomposition methods are integrated. That leads to the so-called \emph{local ROMs}, as opposed to \emph{global ROMs}.

The local methodology consists of several steps. Firstly, the computational domain is divided into smaller subdomains based on its geometrical features. The ROMs can be built for each part and then coupled to reconstruct the global solution. Given the widespread presence of repetitive structures, it can build domains larger than the training geometries. Therefore, the approach can significantly reduce the computational cost for generating snapshots for large scale models.

In short, this dissertation focuses on the development and application of both intrusive and non-intrusive ROMs for fluid dynamics in LMFRs. The applications aim to demonstrate the capabilities of ROMs for large models relevant to nuclear engineering scenarios. The \emph{POD-Galerkin} ROM is selected as an intrusive method, while the \emph{POD with interpolation (PODI)} ROM is employed as a non-intrusive method. Both techniques are explained in detail. The influence of ROM settings on model performance is structurally investigated. For local ROMs, PODI is selected to build subdomain-level ROMs, and a Dirichlet-Neumann coupling strategy is adopted to assemble those partitions to form the global system.

This research demonstrates the capabilities of ROMs for thermal-hydraulic analysis of LMFRs. POD-Galerkin ROMs can accurately predict the flow fields based on a few snapshots. PODI techniques can reach satisfactory accuracy with appropriate model configurations. The implementation of local ROMs shows that iterative schemes can couple multiple local subproblems. It is feasible to approximate a domain that is larger than the one used to generate snapshots.

The outcomes of this study provide valuable insights into the numerical analysis for nuclear reactor systems. ROM has great potential to enhance the efficiency and effectiveness of thermal-hydraulic simulations, advancing nuclear reactor design and safety quantification. Additionally, the local ROM framework demonstrates a promising direction. That denotes training ROMs in small domains while applying them to large-scale problems.