Due to the recent advancement in computer capability, numerical modelling starts to play an important role in making predictions and improving the understanding of physics in the studies of convective heat transfer to supercritical fluids. Many computational studies have been carried out in recent years to assess the ability of different turbulence models in reproducing the experimental data. The performance of these turbulence models varied significantly in predicting the heat transfer at supercritical pressures, especially for the phenomena of heat transfer deterioration (HTD). The results of these studies showed that the accuracy of different turbulence models was also dependent on the flow conditions. It is still necessary to test these turbulence models against newly available experimental data before the final conclusion can be drawn. In this work computational simulations on convective heat transfer of carbon dioxide (CO2) and water (H2O) at supercritical pressures flowing upward in vertical circular pipes have been carried out using the commercial code STAR-CCM+. Detailed comparisons are made between five turbulence models, including AKN low-Reynolds model by Abe et al. (AKN), Standard low-Reynolds k-ε model by Lien et al. (SLR), k-ω model by Wilcox (WI), SST k-ω model by Menter (SST), and the Reynolds Stress Transport (RST) model, against two independent experiments, i.e., water data by Watts (1980) and the recently published carbon dioxide data by Zahlan (2013). The performance of k-ε models with a two-layer approach, and that of k-ε models with wall-functions are also investigated. For the CO2 study, where wall temperatures in most cases are above the pseudo-critical temperature (Tpc), RST model is found both qualitatively and quantitatively better than other turbulence models in predicting the wall temperatures when HTD occurs. The RST model while superior, predicted HTD at higher heat fluxes as compared to experiments. The wall temperature trends predicted by SST and WI models are very similar to that predicted by RST, except that they start to predict HTD at even higher heat fluxes than RST, and the peak temperatures are overestimated significantly. Because RST and k-ω models (SST and WI) predict the HTD at higher heat fluxes as compared to experiments, often in literature they are overlooked. Rather CFD users should conduct sensitivity analyses on heat flux, and quite often as a result qualitatively excellent agreement can be observed in some of these models. The low-Reynolds turbulence models, i.e., SLR and AKN, tended to over-predict the wall temperature after the onset of first temperature peak, because the turbulence production predicted by these models failed to regenerate. The wall temperatures for these models did not show recovery after deterioration until the bulk temperature is close to Tpc, while experimentally recovery happened well upstream of this location. The k-ε models with two-layer approach, and the k-ε models with wall-functions both failed to predict the HTD in all cases. For the H2O study, where the wall temperatures in most cases are below the pseudo-critical temperature, the SLR model performed the best among all turbulence models in reproducing the experimental data. AKN model was also able to qualitatively predict the observed HTD, however, not as well as SLR. SST and RST models, on the other hand, under-predicted the buoyancy effect even at the lowest mass fluxes and hence did not adequately predict deterioration. In a few high-heat-flux cases with wall temperatures above Tpc, all the turbulence models show consistent response to that discussed in the CO2 study, i.e. RST model is quantitatively better than other turbulence models. Nevertheless, the wall temperature peaks predicted by RST model is very different from that observed experimentally, i.e. the measured peaks are much milder and more flattened than the predicted ones. All the turbulence models including RST overestimate the wall temperatures significantly when Tb<Tpc<Tw. The sensitivity studies of mesh parameters, user-defined fluid properties, turbulent Prandtl number, gravitational orientation, and various boundary conditions (e.g. heat flux, mass flux, pressure, and inlet temperature) have also been carried out, aiming to ensure the reliability of the obtained results, and to gain a deeper insight into the physics of heat transfer deterioration in supercritical fluids. Detailed mechanistic studies of HTD have been carried out for both the CO2 and H2O simulations using different turbulence models (RST, SST, and SLR) in various flow conditions. The radial distribution of fluid properties and turbulence at various axial locations provides direct evidence of the mechanisms involved near the locations of deterioration. The buoyancy effect is found to be responsible for the observed HTD in both experiments (i.e., when gravity forces are removed no deterioration is observed). The buoyancy force exerted on the near-wall low-density layer modifies the velocity profile (thus shear stress distribution) in a way that greatly reduces the near-wall turbulence production, resulting in the impairment of heat transfer. In the CO2 study where the wall temperature exceeds the Tpc in a very short distance from the inlet, the “entrance effect” is found to play a more important role in initially impairing the turbulence production. However, this effect is not observed in cases where wall temperature is below Tpc, which is attributed to the weaker density variation below Tpc. / Thesis / Master of Applied Science (MASc)