This paper presents a review of the literature describing the packing structure and effective thermal conductivity of randomly packed beds consisting of mono-sized particles. In this study particular ...attention was given to the packing structure (porosity, coordination number, and contact angles) and heat transfer by solid conduction, gas conduction, contact area, surface roughness, as well as thermal radiation. New methods to analyse the models were developed giving new insights into the shortcomings of the correlations to predict and define the packing structure, as well as to simulate the effective thermal conductivity in the near-wall region. This information is of particular importance in the design and operation of high temperature packed bed nuclear reactors.
This study evaluates the psychometric properties of the Xhosa and Afrikaans version, the European Organization for Research and Treatment of Cancer (EORTC) of the Quality of Life Questionnaire ...Cervical Cancer Module (QLQ‐CX24). Translated Xhosa and Afrikaans versions, EORTC QLQ‐CX24 and the core questionnaire (the EORTC QLQ‐C30) were completed by 66 Xhosa and 142 Afrikaans speaking women newly diagnosed with cervical cancer. Construct reliability and validity of the EORTC QLQ‐CX24 questionnaire were assessed via factor analysis, multi‐trait scaling analyses and known group comparisons. The mean age was similar in the groups with a mean age of the Xhosa group (52 year) and Afrikaans group (49.2 year) (P = 0.25). The study groups had a high unemployment rate of, respectively, 52% (Xhosa) and 51% (Afrikaans) (P = 0.35). The Xhosa group had a statistically significant higher incidence of advanced stage (III and IV) disease (P = 0.006). Scale reliability was confirmed by Cronbach's α coefficients for internal consistency, which ranged from 0.73 to 0.81 (Xhosa) and 0.73 to 0.76 (Afrikaans). Clinical validity of both language versions was demonstrated by the ability to discriminate among different stages of cervical cancer. The translated Xhosa and Afrikaans versions of the EORTC QLQ‐CX24 were found to be reliable and valid measure of quality of life of women with cervical cancer.
► A new model to predict the effective thermal conductivity in a packed pebble bed. ► Specifically accounts for the porous structure. ► Enables improved prediction in the near-wall and wall regions. ...► Conduction component compares well with experimental data. ► Radiation component compares well for temperatures up to 1200°C.
This paper presents a new approach to the calculation of the effective thermal conductivity in packed pebble bed reactors, namely the Multi-sphere Unit Cell model. The model specifically accounts for the porous structure, which is characterised using the radial variation in porosity, coordination number and contact angles between adjacent spheres. It also accounts for solid and gas thermal conduction, contact area, surface roughness as well as the thermal radiation for pebble temperatures up to 1200°C. This more rigorous approach to characterising the porous structure enables improved prediction of the effective thermal conductivity in the near-wall and wall regions, resulting in better prediction of the temperatures at the reflector interface. Results obtained with the Multi-sphere Unit Cell model are compared with existing correlations and experimental data including those from the SANA-I experimental test facility.
•Vertical line-based approach to calculate angular, radial and regional porosities.•Methodology validated against analytical and published results.•Determine angular variation in porosity for ...cylindrical planes and wedges.•Determine radial variation in porosity for radial planes and wedges.•3D variation in porosity of angularly, radially and axially defined regions.
This paper proposes a vertical line-based methodology for the calculation of the porosity of packed beds of spheres. The results for the overall porosity, angular variation in porosity and tangentially averaged radial variation in porosity obtained through the use of this methodology are compared with the results of pre-existing methodologies and found to be in very good agreement, validating the vertical line-based methodology. Building upon this; the angular wedge porosities and angular plane porosities; the radial variation in porosity at different angular planes and the tangentially averaged porosities; and the regional porosities and grid porosities were evaluated for seven packed beds with different sized diameter aspect ratios. From the evaluation of the porosity results for specific points throughout these packed beds, it was found that the vertical line-based methodology has the capability to provide a detailed analysis of the porosity of a packed bed. It is shown that dividing a packed bed into sections, based on axial height, radial range and angular range, can be employed in the calculation of the 3D variation in porosity throughout a packed bed.
The effective thermal conductivity is an important parameter that is representative of the overall heat transfer in a packed bed of spheres. It includes the effects of conduction through the solid ...material and contact areas between spheres, conduction through the stagnant gas phase as well as thermal radiation between the surfaces of the spheres. An accurate prediction of the effective thermal conductivity is necessary for the design and analysis of packed pebble bed gas-cooled and solid fuel molten salt-cooled generation IV reactors, especially when considering the safety case. This includes the near-wall region where the packing structure is altered significantly. The well-known ZBS correlation is widely applied to predict the effective thermal conductivity and it is often implicitly assumed that it is equally applicable in the near-wall region. This paper presents an analysis of the validity of the ZBS correlation in this regard. In addition to this, an up-to-date review of methods used to predict the effective thermal conductivity is presented and methods that specifically account for the near-wall region are identified. It is noted that the contributions of the various heat transfer mechanisms are not yet fully understood and therefore the ability to separate the different mechanisms can be useful for understanding the characteristics in the near-wall region.
•Evaluation of the modelling approaches of selected Rocky and STAR-CCM+DEM models.•Effect of different parameters for DEM based packing models investigated.•Discrepancies in the published results ...identified and addressed.•Correlations for the prediction of the axial variation in porosity.•Piece-wise constant distribution of the regional average porosity.
The paper deals with the evaluation of the distribution of the porosity of a model of the HTR-10 packed bed reactor which was generated using a Discrete Element Method (DEM) approach. The porosity of the packed bed was determined using semi-analytical methodologies. To evaluate the validity of the model, selected aspects of the DEM approach were first investigated. It was found that the appropriate packing method is to drop the spheres at a specified rate from the top of the packed bed domain. The preferable model for the contact force between the spheres was found to be the Hertz-Mindlin model. It was also established that the Young’s modulus of the spheres should be larger than 0.1 GPa. A value of less than 0.1 GPa has a marked negative effect on the porosity. The values for the porosity predicted by previously proposed correlations for the radial and axial variations in porosity were determined to be too small. From the analysis of the packed bed model, the overall porosity was found to be 0.382, whilst the average porosities of the pipe, conical and cylindrical sections were found to be 0.439, 0.378 and 0.381 respectively. Correlations are derived to describe the axial variation of the porosity in the pipe, conical and cylindrical regions. A piece-wise constant description of the distribution in the porosity is finally provided by dividing the packed bed into 34 regions and determining the average porosity of each region.
This paper describes the results of a study of the variation in the radial direction in the porosity of annular packed beds. A comparison is made between the predictions by a number of empirical ...correlations found in literature, the porosities obtained from physical experiments and the porosities obtained from the analysis of numerically generated packed beds. It is concluded that the numerical annular packed beds can be considered as acceptable representations of the actual annular packed beds. From the comparison between a number of exponential correlations proposed by various authors for the variation in the radial direction in the “averaged” porosity and the numerical results it is recommended that the correlation proposed by Hunt and Tien be used to describe the variation in the radial direction in the porosity. It is, however, also recommended that a further thorough study be conducted to develop a more detailed understanding of the porosity characteristics of annular packed beds.
•The radiation and conduction components of the effective thermal conductivity are separated.•Near-wall effects have a notable influence on the effective thermal conductivity.•Effective thermal ...conductivity is a function of the macro temperature gradient.•The effective thermal conductivity profile shows a characteristic trend.•The trend is a result of the interplay between conduction and radiation.
The effective thermal conductivity represents the overall heat transfer characteristics of a packed bed of spheres and must be considered in the analysis and design of pebble bed gas-cooled reactors. During depressurized loss of forced cooling conditions the dominant heat transfer mechanisms for the passive removal of decay heat are radiation and conduction. Predicting the value of the effective thermal conductivity is complex since it inter alia depends on the temperature level and temperature gradient through the bed, as well as the pebble packing structure. The effect of the altered packing structure in the wall region must therefore also be considered. Being able to separate the contributions of radiation and conduction allows a better understanding of the underlying phenomena and the characteristics of the resultant effective thermal conductivity. This paper introduces a purpose-designed test facility and accompanying methodology that combines physical measurements with Computational Fluid Dynamics (CFD) simulations to separate the contributions of radiation and conduction heat transfer, including the wall effects. Preliminary results obtained with the methodology offer important insights into the trends observed in the experimental results and provide a better understanding of the interplay between the underlying heat transfer phenomena.
•A short description of the newly built NWTCTF test facility is provided.•Experimental investigation of effective thermal conductivity in the near-wall region.•Effects of conduction and radiation ...heat transfer are included.•Results are presented for structured and randomly packed beds of graphite spheres.•Near-wall effects have a notable influence on the effective thermal conductivity.
The effective thermal conductivity is an important parameter that represents the overall heat transfer in packed beds, including packed pebble beds. Experimental test facilities have been used to determine the effective thermal conductivity of packed pebble beds; however, the experimental results are often case specific and do not account for wall effects in the near-wall region. Recently the Near-Wall Thermal Conductivity Test Facility (NWTCTF) was developed at the North-West University in Potchefstroom, South Africa to perform detailed investigations of the conduction and radiation heat transfer phenomena in the near-wall region of a packed bed of spheres. The experimental test facility was introduced in a previous paper and some results were presented. This paper provides a short description of the test facility and then presents extensive experimental results obtained for structured and randomly packed beds consisting of 60 mm diameter graphite spheres at temperatures of up to 800 °C, together with associated uncertainties. Results obtained demonstrate the effect of the near-wall region, the packing structure and the presence of the wall on the effective thermal conductivity.
•Different 1D/3D co-simulation implementation strategies within the CFD industry were identified.•Four different 1D/3D co-simulation strategies were explored to investigate the radiative- and ...convective heat transfer, and natural circulation phenomena occurring in a simplified water cooled RCCS facility.•The impact on simulation – stability, time and results were investigated.•The 1D/3D co-simulation methodologies were compared to a full 1D model consisting of the same specifications and setup.
1D/3D co-simulation is a promising approach for the modelling and simulation of complex systems. These systems are typically computationally intensive. By combining the desired features of a one-dimensional (1D) systems code and a three-dimensional (3D) Computational Fluid Dynamics (CFD) code, the required resources are optimized whilst still retaining an acceptable level of accuracy. Co-simulation has been applied in various domains and scenarios, often without a comprehensive study on the impact to simulation- stability, -time, and results. The purpose of this study is to explore the behaviour of some of the strategies by applying them to the simulation of the natural circulation occurring in a simplified Reactor Cavity Cooling System (RCCS). Four different co-simulation approaches were explored to investigate the radiative- and convective- heat transfer as well as the natural circulation phenomena occurring in a RCCS facility. Typically, in these four modelling approaches a 3D methodology was employed to model the radiation and convection heat transfer in the cavity between the heater wall and the outer wall of the riser. The 1D methodology was employed to model the remainder of the RCCS system. The 1D systems code, Flownex, and the 3D CFD code Ansys Fluent were used to perform the 1D/3D co-simulations. Each of the codes modelled a relevant part of the RCCS facility and the models were coupled by explicitly exchanging boundary conditions or relevant data between the 1D and 3D regions. The validity of the coupled 1D/3D approaches was investigated by comparing them with a full 1D simulation.
