Supercritical fluids exhibit distinctive thermophysical properties and heat transfer characteristics that offer potential for improving the efficiency and safety of power generation systems. However, accurately modeling and predicting the heat transfer behavior of supercritical fluids, especially in the deteriorated heat transfer (DHT) regime, where the heat transfer coefficient is significantly reduced due to buoyancy and variations in properties, poses challenges and uncertainties. Therefore, the objective of this thesis is to enhance the understanding of the thermal-hydraulic characteristics of supercritical fluids, specifically water and carbon dioxide, across various heat transfer conditions and geometries.

In Chapter 2, the potential utilization of supercritical fluids in various engineering applications, including Generation IV nuclear reactors, waste heat recovery, and concentrated solar power, is presented. The chapter provides a concise introduction to the supercritical properties of fluids, highlighting supercritical carbon dioxide as an illustrative example. Furthermore, a comprehensive and succinct overview of the fundamental components of the majority of supercritical Nusselt number correlations is undertaken. The different forms of dimensionless variables relevant to supercritical Nusselt number correlations, such as Reynolds numbers, Prandtl numbers, Grashof number, Buoyancy parameter, and correction factors, are systematically classified and introduced.

In Chapter 3, a comprehensive model for supercritical Nusselt number correlations was developed using a preliminary Spearman's rank correlation analysis and empirical modeling for various combinations of dimensionless variables. The dataset, which was validated using Bae's experimental dataset for upward supercritical carbon dioxide flow in a 6.32 mm diameter channel at 8.12 MPa, was post-processed to include 33 commonly used dimensionless variables and 1,149,016 dimensionless groups. Through the Spearman's rank correlation analysis, 7,408 dimensionless groups exhibiting a strong positive monotonic relationship with the Nusselt number were identified. These dimensionless groups were then empirically correlated and compared to the Spearman's rank correlation coefficients. The results of this study reveal one correlation that exhibits a minimum root mean square percentage error (RMSPE) of 0.595% and no outliers exceeding ±5%.

In Chapter 4, a new approach is proposed to accurately replicate the Joule heating heat flux profile using Joule's Law, the resistivity equation, Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) functions, and a resistivity-temperature correlation. Through this approach, it is discovered that by employing PCHIP-modeled Joule heating profiles, the predicted wall temperature in both the Normal Heat Transfer (NHT) and DHT regimes aligns closely with experimental observations in terms of both trend and magnitude. Conversely, when using conventional constant heat flux profiles, the upstream and downstream wall temperatures are found to be overestimated and underestimated, respectively. Additionally, the theoretical analysis of the relationship between the maximum heat flux percentage deviation (MHFPD) and experimental conditions is conducted. An equation is derived to estimate the MHFPD based on the difference in wall temperature and the electrical resistivity of the material. This equation provides a valuable tool for predicting the MHFPD in practical applications.

In Chapter 5, tubes with variable cross-sectional geometries are investigated to mitigate DHT of Supercritical Water (SCW) upward flow. Specifically, three types of variable cross-sectional geometries, namely converging channels, diverging channels, and periodic geometries, are modeled and analyzed. The results indicated that the convergent channels effectively suppress and delay the occurrence of DHT downstream, whereas the divergent channels exhibit opposite effects by promoting DHT. On the other hand, the periodic geometries, characterized by alternating convergent and divergent sections, successfully suppress DHT with minimal impact on pressure drop. Based on an analysis of the velocity and turbulent kinetic energy (TKE) contours, it is concluded that the cross-sectional velocity profile is flattened due to buoyancy-induced flow laminarization (DHT). However, the convergent section of the flow reverses this laminarization effect through the nozzle acceleration. Therefore, mitigation of the laminarization effect can be achieved without the need for additional vortex generation.

This thesis contributes to the existing knowledge gap by providing a systematic review of supercritical fluid heat transfer literature, a comprehensive methodology to find the best form of Nusselt number correlation, a theoretical methodology to model Joule heating effect for CFD validation, and a numerical investigation on mitigating DHT regime with variable cross-sectional geometries. The implications, limitations and future research directions of the studies are discussed and suggested for potential applications in power generation systems using supercritical fluids.