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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.

El entendimiento de los fenómenos de transferencia de calor y de masa en medios porosos implica el estudio de modelos de transporte de fluidos en la fracción vacía del medio; este hecho es de fundamental importancia en muchos sistemas de Ingeniería Química, tal como en procesos de extracción o en reactores catalíticos. Los estudios de flujo realizados hasta ahora (teóricos y experimentales) usualmente tratan al medio poroso como un medio efectivo y homogéneo, y toman como válidas las propiedades medias del fluido. Este tipo de aproximación no tiene en cuenta la complejidad del flujo a través del espacio vacío del medio poroso, reduciendo la descripción del problema a promedios macroscópicos y propiedades efectivas. Sin embargo, estos detalles de los procesos locales de flujo pueden llegar a ser factores importantes que influencien el comportamiento de un proceso físico determinado que ocurre dentro del sistema, y son cruciales para entender el mecanismo detallado de, por ejemplo, fenómenos como la dispersión de calor, la dispersión de masa o el transporte entre interfaces.La Dinámica de Fluidos Computacional (CFD) como herramienta de modelado numérico permite obtener una visión mas aproximada y realista de los fenómenos de flujo de fluidos y los mecanismos de transferencia de calor y masa en lechos empacados, a través de la resolución de las ecuaciones de Navier - Stokes acopladas con los balances de materia y energía y con un modelo de turbulencia si es necesario. De esta forma, esta herramienta permite obtener los valores medios y/o fluctuantes de variables como la velocidad del fluido, la temperatura o la concentración de una especie en cualquier punto de la geometría del lecho empacado.El objetivo de este proyecto es el de utilizar programas comerciales de simulación CFD para resolver el flujo de fluidos y la transferencia de calor y de masa en modelos bi/tri dimensionales de lechos empacados, desarrollando una estrategia de modelado aplicable al diseño de equipos para procesos de extracción o de reacción catalítica. Como referencia se tomaran procesos de tecnología supercrítica debido a la complejidad de los fenómenos de transporte involucrados en estas condiciones, así como a la disponibilidad de datos experimentales obtenidos previamente en nuestro grupo de investigación. Estos datos experimentales se utilizan como herramienta de validación de los modelos numéricos generados, y de las estrategias de simulación adoptadas y realizadas durante el desarrollo de este proyecto. / An understanding of the heat and mass transfer phenomena in a porous media implies the study of the fluid transport model within the void space; this fact is of fundamental importance to many chemical engineering systems such as packed bed extraction or catalytic reaction equipment. Experimental and theoretical studies of flow through such systems often treat the porous medium as an effectively homogeneous system and concentrate on the bulk properties of the flow. Such an approach neglects completely the complexities of the flow within the void space of the porous medium, reducing the description of the problem to macroscopic average or effective quantities. The details of this local flow process may, however, be the most important factor influencing the behavior of a given physical process occurring within the system, and are crucial to understanding the detailed mechanisms of, for example, heat and mass dispersion and interface transport.Computational Fluid Dynamics as a simulation tool allows obtaining a more approached view of the fluid flow and heat and mass transfer mechanisms in fixed bed equipment, through the resolution of 3D Reynolds averaged transport equations, together with a turbulence model when needed. In this way, this tool permit to obtain mean and fluctuating flow and temperature values in any point of the bed. The goal of this project is to use commercial available CFD codes for solving fluid flow and heat and mass transfer phenomena in two and three dimensional models of packed beds, developing a modeling strategy applicable to the design of packed bed chemical reaction and extraction equipment. Supercritical extraction and supercritical catalytic reaction processes will be taken as reference processes due to the complexity of the transport phenomena involved within this processes, and to the availability of experimental data in this field, obtained in the supercritical fluids research group of this university. The experimental data priory obtained by our research group will be used as validation data for the numerical models and strategies dopted and followed during the developing of the project.

Packed beds find extensive application in a wide variety of industries to cany out a large number of diverse processes. The main objective of the present work is to develop models to predict the arrangement of particles and based on them, to determine and evaluate the structural characteristics of packed beds. These problems have received only a limited attention in the literature. As a first attempt, spheres of uniform size are considered. Beds of aspect ratio up to 2 (referred to as low aspect ratio beds) are analyzed by application of principles of analytical geometry. Expressions are derived for the location of particles and for the structural characteristics of the beds, both of which show periodicity. This leads to the concept of a unit cell which is the repetitive section of the bed whose characteristics are the same as those of the complete bed. The beds fall into three distinct groups — those with aspect ratio between 1 and l√3⁄2, between 1√3⁄2 and 2, and with aspect ratio 2. Equations are distinct for each group. The aspect ratio shows marked influence on the structural characteristics of the beds. Agreement of the predictions on the overall void fraction with the available experimental data is excellent. Radial void fraction profiles are estimated by defining a concentric cylindrical channel (CCC) of an arbitrary thickness and with the cylindrical surface through the radial position of interest located at the middle of the CCC, and by accounting for the solid volumes of all the segments (in this CCC) of spheres with centers lying within a distance of a particle radius on either side of the cylindrical surface. The curved boundaries of the sphere segments are rigorously accounted for. The results show that the entire bed is filled with variations in the void fraction, starting from a value of unity at the wall and zero (or close to zero) towards the axis of the bed. Monte Carlo model for the simulation of high aspect ratio beds has not proved successful even with any of a wide variety of distribution functions for the coordinates of the sphere dropping point. With uniform distribution, the only distribution used in all the reports so far, and with normal distribution, there is not even a qualitative agreement with the reported data on void fraction variations. Distributions with asymmetric density functions such as exponential, Weibull, gamma and beta, show considerable improvement; beta distribution being the best. However even the best results with beta distribution show satisfactory agreement with the experimental data only up to about 2dp from the wall. Simulations with the cluster growth model, modified to account for the confining nature of the wall, lead to more satisfactory results. The proposed algorithm consists of building up the cluster, sphere by sphere, by calculating all possible interior and wall sites for placing an incoming sphere in a stable and non-overlapping position on the current cluster. A preference parameter is defined to place the new sphere at locations along the cross section of the column at which the experimental void fraction profiles show prominent minima, that is, locations around which the bed has relatively high solid volume. Void fraction profiles in beds of various aspect ratios simulated by this model show good agreement with the corresponding experimental data. The structural characteristics of the high aspect ratio beds thus simulated are evaluated. The number of spheres per unit length, Ni is correlated with the aspect ratio. It becomes proportional to the square of the aspect ratio, with the proportionality constant being close to 0.9, for aspect ratios greater than about 10. This follows since in these beds the overall void fraction becomes constant at 0.4. Majority of the spheres have contacts (with neighboring spheres) between 4 and 7, with the lower and upper limits for the coordination number being 2 and 9. The radial profile of the average coordination number (averaged over the height of the bed at the given radial position) shows small oscillations about a mean value of about 6 over almost the entire bed cross section starting from a distance of about ldp from the wall. At a distance of 0.5dp from the wall the predominant number of contacts is four while the mean value is about 4.3. The overall coordination number (averaged over the entire bed) shows inverse dependence on the aspect ratio. For random packings, that is, as the aspect ratio becomes infinity, the overall coordination number tends to six which corresponds to regular cubic arrangement. Cumulative number fraction, CNf is a global measure of the arrangement of spheres in beds of high aspect ratio. Its radial variation shows four distinct regions whose locations are independent of the aspect ratio The CNf values in each region are correlated with aspect ratio The correlations combined with that of NL lead to a very useful and effective model for predicting void fraction profiles in a bed of any specified aspect ratio The validity of the predictive model is demonstrated

Master of Science / Department of Mechanical and Nuclear Engineering / Hitesh Bindra / Storing excess thermal energy in a storage media that can later be extracted during peak-load times is one of the better economical options for nuclear power in future. Thermal energy storage integration with light water-cooled and advanced nuclear power plants is analyzed to assess technical feasibility of different storage media options. Various choices are considered in this study; molten salts, synthetic heat transfer fluids, and packed beds of solid rocks or ceramics. In-depth quantitative assessment of these integration possibilities are then analyzed using exergy analysis and energy density models. The exergy efficiency of thermal energy storage systems is quantified based on second law thermodynamics. The packed bed of solid rocks is identified as one of the only options which can be integrated with upcoming small modular reactors. Directly storing thermal energy from saturated steam into packed bed of rocks is a very complex physical process due to phase transformation, two phase flow in irregular geometries and percolating irregular condensate flow. In order to examine the integrated physical aspects of this process, the energy transport during direct steam injection and condensation in the dry cold randomly packed bed of spherical alumina particles was experimentally and theoretically studied. This experimental setup ensures controlled condensation process without introducing significant changes in the thermal state or material characteristics of heat sink. Steam fronts at different flow rates were introduced in a cylindrical packed bed and thermal response of the media was observed. The governing heat transfer modes in the media are completely dependent upon the rate of steam injection into the system. A distinct differentiation between the effects of heat conduction and advection in the bed were observed with slower steam injection rates. A phenomenological semi-analytical model is developed for predicting quantitative thermal behavior of the packed bed and understanding physics. The semi-analytical model results are compared with the experimental data for the validation purposes. The steam condensation process in packed beds is very stable under all circumstances and there is no effect of flow fluctuations on thermal stratification in packed beds. With these experimental and analytical studies, it can be concluded that packed beds have potential for thermal storage applications with steam as heat transfer fluid. The stable stratification and condensation process in packed beds led to design of a novel passive safety heat removal system for advanced boiling water reactors.

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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

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