A Semi-Analytical Partial n'th Collision Source (SAPNCS) method that is fully compatible with the standard three-dimensional SN has been developed. The method generates a matrix operator that calculates scattering source for particles that have suffered n collisions in a selected number of mesh cells. Adopting this scattering source as distributed source, the standard three-dimensional SN method then calculates the remaining contribution to the flux. The sum of uncollided and collided fluxes yields total flux. Several tests for photon transport calculation in x-y-z geometry have been fully conducted and the illustrative results demonstrating the capability of the method to mitigate and eliminate the observable ray effects are presented.

The angular dependence of the differential scattering cross section is typically represented as a truncated Legendre series expansion. If the scattering cross section is highly anisotropic, these expansions may result in negative regions in the -1 ≤ μ0 ≤ +1 interval, thus representing the cross section by negative values. These negative regions may cause negative components in the discrete ordinates scattering source, which are non-physical and which may adversely affect the iterative convergence of the exponential discontinuous spatial discretization scheme. Two methods are presented which produce a positive representation of the scattering cross section, and are designed to calculate a strictly positive scattering source. The first method constructs a scattering matrix from the exponential representation of the cross section derived from maximum entropy. Accuracy of these matrices is further improved by the application of SMART scattering theory. The second method adjusts the Legendre cross section moments with a constrained least squares algorithm. The adjustment is subject to constraints that the zeroth and first moment remain unchanged and that the resulting expansion is positive on all scattering angle cosines derived from a standard S N quadrature set. Extra moments from the maximum entropy representation of the cross section are also used to decrease the relative error of the modified moments. Numerical transport calculations using these two methods demonstrate consistent results with those using the standard truncated Legendre expansion of the cross section. The exponential discontinuous spatial scheme is shown to iteratively converged when these two methods are used. A comparison of these methods with results from multigroup and continuous energy Monte Carlo calculations are also shown to be consistent.

Critical calculations of unreflected cylinders filled with fissile solution were performed using the TWODANT code with the 118-isotope, 16-group Hansen-Roach neutron cross-section library. The benchmark experiments used were the France CRAC experiments. In these experiments unreflected 300mm and 800mm cylinders were used to contain the solution. The fissile solution was highly enriched (approximately 93%) uranyl nitrate solution of various concentrations. These concentrations varied from 21.4 g/l to 383 g/l in total uranium. The calculational results were compared to the experimental results and to calculations performed using the Monte-Carlo codes MCNP with a continuous-energy neutrons cross-section library and KENO V.a with a cross-section library based on the 16-group Hansen-Roach neutron cross-section set. The TWODANT and KENO V.a codes underestimated the calculated keff for most cases whereas MCNP in most cases showed a keff estimation much closer to unity. Dimension search performed using TWODANT show that the code is able to follow the trend in the measured critical height with a relatively constant bias of 8.96% of the measured height.

<p> We present a method to map the spectral and spatial distributions of radioactive sources using a small number of detectors. Locating and identifying radioactive materials is important for border monitoring, accounting for special nuclear material in processing facilities, and in clean-up operations. Most methods to analyze these problems make restrictive assumptions about the distribution of the source. In contrast, the source-mapping method presented here allows an arbitrary three-dimensional distribution in space and a flexible group and gamma peak distribution in energy. To apply the method, the system&rsquo;s geometry and materials must be known. A probabilistic Bayesian approach is used to solve the resulting inverse problem (<p style="font-variant: small-caps">IP</p>) since the system of equations is ill-posed. The probabilistic approach also provides estimates of the confidence in the final source map prediction. A set of adjoint flux, discrete ordinates solutions, obtained in this work by the Denovo code, are required to efficiently compute detector responses from a candidate source distribution. These adjoint fluxes are then used to form the linear model to map the state space to the response space. The test for the method is simultaneously locating a set of ¹³⁷Cs and ⁶⁰Co gamma sources in an empty room. This test problem is solved using synthetic measurements generated by a Monte Carlo (<p style="font-variant: small-caps">MCNP</p>) model and using experimental measurements that we collected for this purpose. With the synthetic data, the predicted source distributions identified the locations of the sources to within tens of centimeters, in a room with an approximately four-by-four meter floor plan. Most of the predicted source intensities were within a factor of ten of their true value. The chi-square value of the predicted source was within a factor of five from the expected value based on the number of measurements employed. With a favorable uniform initial guess, the predicted source map was nearly identical to the true distribution, and the source intensities agreed within the predicted uncertainty. Using experimental data, the mapping was more difficult due to laboratory limitations. However, by supplanting 14 flawed measurements (out of 69 total) with synthetic data, the proof-of-principle source mapping was nearly as accurate as the synthetic-only prediction. </p>

<p> This study focused on developing a better understanding of granular dynamics in pebble bed reactor cores through experimental work and computer simulations. The work completed includes analysis of pebble motion data from three scaled experiments based on the annular core of the Pebble Bed Fluoride Salt-Cooled High- Temperature Reactor (PB-FHR). The experiments are accompanied by the development of a new discrete element simulation code, GRECO, which is designed to offer a simple user interface and simplified two-dimensional system that can be used for iterative purposes in the preliminary phases of core design. The results of this study are focused on the PB-FHR, but can easily be extended for gas-cooled reactor designs.</p><p> Experimental results are presented for three Pebble Recirculation Experiments (PREX). PREX 2 and 3.0 are conventional gravity-dominated granular systems based on the annular PB-FHR core design for a 900 MWth commercial prototype plant and a 16 MWth test reactor, respectively. Detailed results are presented for the pebble velocity field, mixing at the radial zone interfaces, and pebble residence times. A new Monte Carlo algorithm was developed to study the residence time distributions of pebbles in different radial zones. These dry experiments demonstrated the basic viability of radial pebble zoning in cores with diverging geometry before pebbles reach the active core.</p><p> Results are also presented from PREX 3.1, a scaled facility that uses simulant materials to evaluate the impact of coupled fluid drag forces on the granular dynamics in the PB-FHR core. PREX 3.1 was used to collect first of a kind pebble motion data in a multidimensional porous media flow field. Pebble motion data were collected for a range of axial and cross fluid flow configurations where the drag forces range from half the buoyancy force up to ten times greater than the buoyancy force. Detailed analysis is presented for the pebble velocity field, mixing behavior, and residence time distributions for each fluid flow configuration.</p><p> The axial flow configurations in PREX 3.1 showed small changes in pebble motion compared to a reference case with no fluid flow and showed similar overall behavior to PREX 3.0. This suggests that dry experiments can be used for core designs with uniform one-dimensional coolant flow early in the design process at greatly reduced cost. Significant differences in pebble residence times were observed in the cross fluid flow configurations, but these were not accompanied by an overall horizontal diffusion bias. Radial zones showed only a small shift in position due to mixing in the diverging region and remained stable in the active core. The results from this study support the overall viability of the annular PB-FHR core by demonstrating consistent granular flow behavior in the presence of complex reflector geometries and multidimensional fluid flow fields.</p><p> GRECO simulations were performed for each of the experiments in this study in order to develop a preliminary validation basis and to understand for which applications the code can provide useful analysis. Overall, the GRECO simulation results showed excellent agreement with the gravity-dominated PREX experiments. Local velocity errors were found to be generally within 10-15% of the experimental data. Average radial zone interface positions were predicted within two pebble diameters. GRECO simulations over predicted the amount of mixing around the average radial zone interface position and therefore can be treated as a conservative upper bound when used in neutronics analysis. Residence time distributions from the GRECO velocity data based on the Monte Carlo algorithm closely matched those derived from the experiment velocity statistics. GRECO simulation results for PREX 3.1 with coupled drag forces showed larger errors compared to the experimental data, particularly in the cases with cross fluid flow. The large discrepancies suggest that GRECO results in systems with coupled fluid drag forces cannot be used with high confidence at this point and future development work on coupled pebble and fluid dynamics with multidimensional fluid flow fields is required.</p>

Pressure tubes made of Zr-2.5%Nb alloy are used to contain fuels and coolant in CANDU nuclear power reactors. The pressure tube oxidizes during reactor operation and hydrogen ingress through the oxide grown on the tube limits its lifetime. Little attention was paid to the intermediate tube manufacturing processes in enhancing the oxidation resistance. In addition, the oxide grown on the tube experiences various thermal cycles depending on the reactor shutdown and startup cycles. To address these two aspects and to better understand the oxidation process of the Zr-2.5Nb tube, research was conducted in two parts: i) effects of tube fabrication on oxidation behavior, and ii) thermal cycling behaviors of oxides grown on a pressure tube. / In the first part, the optimum manufacturing process was pursued to improve the corrosion resistance of Zr-2.5Nb tubes. Experimental micro-tubes were fabricated with various manufacturing routes in the stages of billet preparation, hot extrusion and cold drawing. These were oxidized in air at 400oC and 500oC, and in an autoclave at 360oC lithiated water. Microstructure and texture of the tubes and oxides were characterized with X-ray diffraction, scanning electron microscope and optical microscope. Special emphasis was given to examinations of the metal/oxide interface structures. A correlation between the manufacturing process and oxidation resistance was investigated in terms of tube microstructure and the metal/oxide interface structure. As a result, it was consistently observed that uniform interface structures were formed on the tubes which had a fine distribution of secondary phases. These microstructures were found to be beneficial in enhancing the oxidation resistance as opposed to the tubes that had coarse and continuous beta-Zr phases. Based on these observations, a schematic model of the oxidation process was proposed with respect to the oxidation resistance under oxidizing temperatures of 360oC, 400oC and 500oC. / In the second part, the oxides grown on a standard Zr-2.5Nb pressure tube were analyzed by X-ray diffraction peak broadening and line shift. Crystallite size, t-ZrO2 fraction and residual stress of the zirconium oxides were investigated upon several thermal cycles at delta T range of 500oC - 750oC. The oxide residual stresses measured by the sin2 psi method were always compressive around 2 GPa. Different stress-states were noticed with the oxides grown on different sections of pressure tube. The compressive stress was released when the oxide was thermally cycled at the highest delta T of 750oC. Discussion was given to the effects of anisotropic nature of thermal expansion coefficients and crystallographic texture on the stress-state of Zr oxides. / L'alliage Zr-2.5%Nb est présentement utilisé pour fabriquer les tubes contenant les grappes à combustion dans les réacteurs nucléaires CANDU. L'oxydation de ces tubes durant l'usage normale dans le réacteur et la pénétration d'hydrogène à travers leurs couches d'oxyde protectrice détériore leur durée de vie. Jusqu'à présent personne n'a porté attention à l'effet des paramètres de fabrication intermédiaire à augmenter la résistance de ces tubes à l'oxydation. De plus, l'oxyde sur le tube est soumis au cyclage thermique durant la mise en marche et l'arrêt du réacteur nucléaire. Pour mieux comprendre l'effet des deux aspects mentionnés ci-dessus et l'oxydation des tubes de Zr-2.5Nb, la présente recherche fut entreprise en deux parties: i) l'étude des variables de fabrication sur l'oxydation, et ii) l'étude du cyclage thermique sur l'oxyde des tubes. / Dans la première partie les paramètres de fabrication optimale sont cernés pour améliorer la résistance à la corrosion des tubes de Zr-2.5Nb. Des micro-tubes expérimentales furent fabriquées en variant les paramètres de fabrication aux étapes de préparation de la billet, de l'extrusion à chaud et de l'étirage à froid. Subséquemment, ceux-ci furent oxydés dans l'aire à 400oC et 500oC et dans un autoclave contenant de l'eau à 360oC en présence d'ions de lithium. La microstructure et la texture des tubes et de leurs oxydes ont été caractérisées par la diffraction rayons-x, la microscopie à balayage électronique et par microscopie optique. Une attention particulière a été portée à la structure de l'interface métal/oxyde. La corrélation entre les variables de procédé et la résistance à la corrosion des tubes a été étudiée en fonction de la microstructure du tube et la structure de l'interface métal/oxyde. Une interface uniforme fut constamment observée sur des tubes ayant une phase secondaire finement distribuée. Par la présente recherche, cette microstructure améliore la résistance à l'oxydation versus une microstructure de beta-Zr grossière et continue. Basée sur les observation de cette recherche, une modèle schématique du processus d'oxydation a été proposée par rapport à la résistance d'oxydation aux températures de 360oC, 400oC et 500oC. / Dans la seconde partie, les oxydes d'un tube de Zr-2.5Nb standard ont été analysés en mesurant l'élargissement et le déplacement des pics de diffractométrie de rayons-x. La taille des cristaux, la fraction de t-ZrO2 et la contrainte résiduelle des oxydes de zirconium furent caractérisés en fonction de plusieurs cycles thermique ayant un delta T entre 500oC et 750oC. La contrainte résiduelle, mesuré par la technique sin2 psi, fut toujours d'ordre compressive et autour de 2 GPa. Différents états de contrainte ont été observés sur les oxydes à différentes sections des tubes. Après le cyclage thermique ayant le plus grand delta T de 750oC, l'état de stress compressif est relâché. Une discussion est présentée pour relier les effets de l'anisotropie des coefficients d'expansion thermique et la texture cristallographique sur l'état de stress dans les oxydes de Zr.

Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2006. / Source: Dissertation Abstracts International, Volume: 68-02, Section: B, page: 1279. Adviser: David N. Ruzic. Includes bibliographical references (leaves 145-155) Available on microfilm from Pro Quest Information and Learning.

Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2006. / Source: Dissertation Abstracts International, Volume: 68-02, Section: B, page: 1280. Adviser: George H. Miley. Includes bibliographical references (leaves 148-153) Available on microfilm from Pro Quest Information and Learning.

Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2007. / Source: Dissertation Abstracts International, Volume: 69-02, Section: B, page: 1301. Adviser: Brent J. Heuser. Includes bibliographical references (leaves 105-106) Available on microfilm from Pro Quest Information and Learning.

Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2007. / Source: Dissertation Abstracts International, Volume: 69-02, Section: B, page: 1302. Adviser: Rizwan Uddin. Includes bibliographical references. Available on microfilm from Pro Quest Information and Learning.