The F_N method, originated by C. E. Siewert, is developed for a bare, axially infinite critical cylinder. The full-range completeness and orthogonality properties of the singular eigenfunctions are used to derive an expression for the emerging angular flux, which is represented by a power series. The resulting equations are reduced to matrix form and computer solved. Examples of the results of this method for different parameters are presented. Comparisons with other models are made. A fourth order approximation was found to be sufficient to achieve up to four digit agreement with benchmark values. / Master of Science

This work has been aimed at developing a mechanistic, transient, 3-D numerical model to predict the behavior of an evaporating thin liquid film on a non-uniformly heated cylindrical rod with simultaneous parallel and cross flow of vapor. Interest in this problem has been motivated by the fact that the liquid film on a full-length boiling water reactor fuel rod may experience significant axial and azimuthal heat flux gradients and cross flow due to variations in the thermal-hydraulic conditions in surrounding subchannels caused by proximity to inserted control blade tip and/or the top of part-length fuel rods. Such heat flux gradients coupled with localized cross flow may cause the liquid film on the fuel rod surface to rupture, thereby forming a dry hot spot. These localized dryout phenomena can not be accurately predicted by traditional subchannel analysis methods in conjunction with empirical dryout correlations. To this end, a numerical model based on the Level Contour Reconstruction Method was developed. The Standard k- turbulence model is included. A cylindrical coordinate system has been used to enhance the resolution of the Level Contour Reconstruction Model. Satisfactory agreement has been achieved between the model predictions and experimental data. A model of this type is necessary to supplement current state-of-the-art BWR core thermal-hydraulic design methods based on subchannel analysis techniques coupled with empirical dry out correlations. In essence, such a model would provide the core designer with a "magnifying glass" by which the behavior of the liquid film at specific locations within the core (specific axial node on specific location within a specific bundle in the subchannel analysis model) can be closely examined. A tool of this type would allow the designer to examine the effectiveness of possible design changes and/or modified control strategies to prevent conditions leading to localized film instability and possible fuel failure.