Inherent safety is claimed for gas-cooled pebble bed reactors, such as the South African Pebble Bed Modular Reactor (PBMR), as a result of its design characteristics, materials used, fuel type and physics involved. Therefore, a proper understanding of the mechanisms of heat transfer, fluid flow and pressure drop through a packed bed of spheres is of utmost importance in the design of a high temperature Pebble Bed Reactor (PBR). In this study, correlations describing the effective thermal conductivity through packed pebble beds are examined. The effective thermal conductivity is a term defined as representative of the overall radial heat transfer through such a packed bed of spheres, and is a summation of various components of the overall heat transfer. This phenomenon is of importance because it forms an intricate part of the self-acting decay heat removal chain, which is directly related to the PBR safety case. In this study standard correlations generally employed by the thermal fluid design community for PBRs are investigated, giving particular attention to the applicability of the correlations when simulating the effective thermal conductivity in the near-wall region. Seven distinct components of heat transfer are examined namely: conduction through the solid, conduction through the contact area between spheres, conduction through the gas phase, radiation between solid surfaces, conduction between pebble and wall, conduction through the gas phase in the wall region, and radiation between the pebble and wall surface. The effective thermal conductivity models are typically a function of porosity in order to account for the pebble bed packing structure. However, it is demonstrated in this study that porosity alone is insufficient to quantify the porous structure in a randomly packed bed. A new Multi-sphere Unit Cell Model is therefore developed, which accounts more accurately for the porous structure, especially in the near-wall region. Conclusions on the applicability of the model are derived by comparing the simulation results with measurements obtained from various experimental test facilities. This includes the PBMRs High Temperature Test Unit (HTTU) situated on the campus of the North-West University in Potchefstroom in South Africa. The Multi-sphere Unit Cell Model proves to encapsulate the impact of the packing structure in a more fundamental way and can therefore serve as the basis for further refinement of models to simulate the effective thermal conductivity. / Thesis (PhD (Nuclear Engineering))--North-West University, Potchefstroom Campus, 2010

Inherent safety is claimed for gas-cooled pebble bed reactors, such as the South African Pebble Bed Modular Reactor (PBMR), as a result of its design characteristics, materials used, fuel type and physics involved. Therefore, a proper understanding of the mechanisms of heat transfer, fluid flow and pressure drop through a packed bed of spheres is of utmost importance in the design of a high temperature Pebble Bed Reactor (PBR). In this study, correlations describing the effective thermal conductivity through packed pebble beds are examined. The effective thermal conductivity is a term defined as representative of the overall radial heat transfer through such a packed bed of spheres, and is a summation of various components of the overall heat transfer. This phenomenon is of importance because it forms an intricate part of the self-acting decay heat removal chain, which is directly related to the PBR safety case. In this study standard correlations generally employed by the thermal fluid design community for PBRs are investigated, giving particular attention to the applicability of the correlations when simulating the effective thermal conductivity in the near-wall region. Seven distinct components of heat transfer are examined namely: conduction through the solid, conduction through the contact area between spheres, conduction through the gas phase, radiation between solid surfaces, conduction between pebble and wall, conduction through the gas phase in the wall region, and radiation between the pebble and wall surface. The effective thermal conductivity models are typically a function of porosity in order to account for the pebble bed packing structure. However, it is demonstrated in this study that porosity alone is insufficient to quantify the porous structure in a randomly packed bed. A new Multi-sphere Unit Cell Model is therefore developed, which accounts more accurately for the porous structure, especially in the near-wall region. Conclusions on the applicability of the model are derived by comparing the simulation results with measurements obtained from various experimental test facilities. This includes the PBMRs High Temperature Test Unit (HTTU) situated on the campus of the North-West University in Potchefstroom in South Africa. The Multi-sphere Unit Cell Model proves to encapsulate the impact of the packing structure in a more fundamental way and can therefore serve as the basis for further refinement of models to simulate the effective thermal conductivity. / Thesis (PhD (Nuclear Engineering))--North-West University, Potchefstroom Campus, 2010

The wall effect is known to present difficulties when attempting to predict the pressure drop over randomly packed beds. The Nuclear Safety Standard Commission, “Kerntechnischer Auss-chuss" (KTA), made considerable efforts to develop an equation which predicts the pressure drop over cylindrical randomly packed beds consisting of mono-sized spheres. The KTA was able to estimate a limiting line, which defines the region for which the wall effect is negligible, however the theoretical basis for this line is unclear. The goal of this investigation was to determine the validity of the KTA limiting line, using an explicit approach. Packed beds were generated using Discrete Element Modelling (DEM), and the flow through the beds simulated using Computational Fluid Dynamics (CFD). STAR-CCM+R was used for both DEM and CFD operations, and the methods developed for this explicit approach were validated with empirical data. The KTA correlation predictions for friction factors were com- pared with the CFD results, as well as the predictions from a few other correlations. The KTA correlation predictions for friction factors did not correspond well with the CFD results at low aspect ratios and low modified Reynolds numbers, due to the influence of the wall effect. The KTA limiting line was found to be valid, but not exact. A new limiting line for the KTA correlation was suggested, however the new limiting line improved little on the existing line and was the result of some major assumptions. In order to improve the determination of the position of the KTA limiting line further, criteria need to be established which determine how small the error in predicted friction factor must be before the KTA correlation can be accepted as accurate. / MIng (Nuclear Engineering), North-West University, Potchefstroom Campus, 2014

The wall effect is known to present difficulties when attempting to predict the pressure drop over randomly packed beds. The Nuclear Safety Standard Commission, “Kerntechnischer Auss-chuss" (KTA), made considerable efforts to develop an equation which predicts the pressure drop over cylindrical randomly packed beds consisting of mono-sized spheres. The KTA was able to estimate a limiting line, which defines the region for which the wall effect is negligible, however the theoretical basis for this line is unclear. The goal of this investigation was to determine the validity of the KTA limiting line, using an explicit approach. Packed beds were generated using Discrete Element Modelling (DEM), and the flow through the beds simulated using Computational Fluid Dynamics (CFD). STAR-CCM+R was used for both DEM and CFD operations, and the methods developed for this explicit approach were validated with empirical data. The KTA correlation predictions for friction factors were com- pared with the CFD results, as well as the predictions from a few other correlations. The KTA correlation predictions for friction factors did not correspond well with the CFD results at low aspect ratios and low modified Reynolds numbers, due to the influence of the wall effect. The KTA limiting line was found to be valid, but not exact. A new limiting line for the KTA correlation was suggested, however the new limiting line improved little on the existing line and was the result of some major assumptions. In order to improve the determination of the position of the KTA limiting line further, criteria need to be established which determine how small the error in predicted friction factor must be before the KTA correlation can be accepted as accurate. / MIng (Nuclear Engineering), North-West University, Potchefstroom Campus, 2014

The High Pressure Test Unit (HPTU) forms part of the Pebble Bed Modular Reactor (PBMR) Heat Transfer Test Facility (HTTF). One of the test sections that forms part of the HPTU is the Braiding Effect Test Section (BETS). This test section allows for the evaluation of the so–called ‘braiding effect’ that occurs in fluid flow through a packed pebble bed. The braiding effect implies an apparent enhancement of the fluid thermal conductivity due to turbulent mixing that occurs as the flow criss–crosses between the pebbles. The level of enhancement of the fluid thermal conductivity is evaluated from the thermal dispersion effect. The so–called thermal dispersion quantity r K is equivalent to an effective Peclet number eff Pe based on the inverse of the effective thermal conductivity eff k . This thesis describes the experiments carried out on three different BETS test sections with pseudo–homogeneous porosities of 0.36, 0.39 and 0.45, respectively. It also provides the values derived for the enhanced fluid thermal conductivity for the range of Reynolds numbers between 1,000 and 40,000. The study includes the following: * Compilation of a literature study and theoretical background. * An uncertainty analysis to estimate the impact of instrument uncertainties on the accuracy of the empirical data. * The use of a Computational Fluid Dynamics (CFD) model to simulate the heat transfer through the BETS packed pebble bed.* Application of the CFD model combined with a numerical search technique to extract the effective fluid thermal conductivity values from the measured results. * The assessment of the results of the experiments by comparing it with the results of other investigations found in the open literature. The primary outputs of the study are the effective fluid thermal conductivity values derived from the measured data on the HPTU plant. The primary variables that were measured are the temperatures at radial positions at different axial depths inside the bed and the total mass flow rate through the test section. The maximum and minimum standard uncertainties for the measured data are 10.80% and 0.06% respectively. The overall effective thermal conductivities that were calculated at the minimum and maximum Reynolds numbers were in the order of 1.166 W/mK and 38.015 W/mK respectively. A sensitivity study was conducted on the experimental data and the CFD data. A maximum uncertainty of 5.92 % was found in the calculated effective thermal conductivities. The results show that relatively high values of thermal dispersion quantities or effective Peclet numbers are obtained for the pseudo–homogeneous packed beds when compared to randomly packed beds. Therefore, the effective thermal conductivity is low and it can be concluded that the radial mixing in the structured packing is low relative to the mixing obtained in randomly packed beds. / Thesis (M.Ing. (Mechanical Engineering))--North-West University, Potchefstroom Campus, 2011.

The High Pressure Test Unit (HPTU) forms part of the Pebble Bed Modular Reactor (PBMR) Heat Transfer Test Facility (HTTF). One of the test sections that forms part of the HPTU is the Braiding Effect Test Section (BETS). This test section allows for the evaluation of the so–called ‘braiding effect’ that occurs in fluid flow through a packed pebble bed. The braiding effect implies an apparent enhancement of the fluid thermal conductivity due to turbulent mixing that occurs as the flow criss–crosses between the pebbles. The level of enhancement of the fluid thermal conductivity is evaluated from the thermal dispersion effect. The so–called thermal dispersion quantity r K is equivalent to an effective Peclet number eff Pe based on the inverse of the effective thermal conductivity eff k . This thesis describes the experiments carried out on three different BETS test sections with pseudo–homogeneous porosities of 0.36, 0.39 and 0.45, respectively. It also provides the values derived for the enhanced fluid thermal conductivity for the range of Reynolds numbers between 1,000 and 40,000. The study includes the following: * Compilation of a literature study and theoretical background. * An uncertainty analysis to estimate the impact of instrument uncertainties on the accuracy of the empirical data. * The use of a Computational Fluid Dynamics (CFD) model to simulate the heat transfer through the BETS packed pebble bed.* Application of the CFD model combined with a numerical search technique to extract the effective fluid thermal conductivity values from the measured results. * The assessment of the results of the experiments by comparing it with the results of other investigations found in the open literature. The primary outputs of the study are the effective fluid thermal conductivity values derived from the measured data on the HPTU plant. The primary variables that were measured are the temperatures at radial positions at different axial depths inside the bed and the total mass flow rate through the test section. The maximum and minimum standard uncertainties for the measured data are 10.80% and 0.06% respectively. The overall effective thermal conductivities that were calculated at the minimum and maximum Reynolds numbers were in the order of 1.166 W/mK and 38.015 W/mK respectively. A sensitivity study was conducted on the experimental data and the CFD data. A maximum uncertainty of 5.92 % was found in the calculated effective thermal conductivities. The results show that relatively high values of thermal dispersion quantities or effective Peclet numbers are obtained for the pseudo–homogeneous packed beds when compared to randomly packed beds. Therefore, the effective thermal conductivity is low and it can be concluded that the radial mixing in the structured packing is low relative to the mixing obtained in randomly packed beds. / Thesis (M.Ing. (Mechanical Engineering))--North-West University, Potchefstroom Campus, 2011.