<p>A numerical approach was taken to optimize in-core fuel management in CANDU reactors at equilibrium refuelling. A computer program called, OPTEX was written to obtain an optimum distribution of fuelling rates and initial fuel enrichment.</p> <p>In an on-power refuelled reactor such as CANDU, depletion effects are quite localized and the global power shape results from the distribution of fuelling rates and fixed absorbers in the core. An important group of fixed absorbers, called adjuster rods, can be replaced (and modified) a number of times during the life of the reactor. The optimization process in OPTEX can be applied to the adjuster grading and the fuel management problems simultaneously, yielding the desired reactivity worth for the adjusters as well as a nominal power distribution which satisfies the design limits on the fuel.</p> <p>The OPTEX approach consists in linearizing the system characteristics about points in the feasible domain of the state variables, and then using mathematical programing techniques to direct the search towards an improved state. The originality of the approach is that variational techniques, found in Generalized Perturbation Theory (GPT) or in sensitivity theory, are used to define the true gradients of the system characteristics.</p> <p>The computational advantages of this approach were illustrated with two applications of the code. Using a new correlation to properly account for the effects of enrichment and axial fuelling schemes on the channel power peaking, fresh fuel enrichment was optimized in a 850 MWe CANDU reactor using Lightly Enriched Uranium (LEU) fuel. The optimum uniform enrichment was of the order of 0.91%, but was found to be sensitive to the axial fuelling schemes used. In all cases, a significant reduction of 25-30% in fuelling costs was observed.</p> <p>The second problem dealt with adjuster grading in an existing 600 MW reactor. Starting with a current (nonuniform) distribution of adjuster weights, a new distribution of weights was found along with an optimized burnup distribution to yield a 3% reduction in fuelling costs while preserving the global adjuster reactivity worth.</p> <p>A number of other applications were identified. In particular, it was shown how, by introducing a time-dependent GPT, the UPTEX approach could be extended to deal with the optimization of the initial core and other fuelling transients.</p> / Doctor of Philosophy (PhD)

<p>A major concern in the design of control systems for nuclear power reactors is where and how many controllers and detectors are to be deployed in the reactor to satisfy design criteria. In order to answer this concern, we have developed an analytical method in which emphasis is placed on the linear regulator theory and the least square estimation theory.</p> <p>This work has four areas: realization of the measure of the optimality of the controller locations in terms of feedback gain in spatial control; calculation of the static set-points to compensate the excess reactivity of the reference state evaluation of dynamic range of controllers for regulating neutron fluxes; and estimation of additional responses counteracting burnup/fuelling induced random external disturbance.</p> <p>The deviations of neutron, iodine and xenon distributions from the reference states were expanded with the referenced λ-modes. The order of amplitude vector space was reduced by assumption of the dominant mode concept. Performance indices were formed with reduced state vectors and separated control functions. Pontryagin's maximum principle was applied to deterministic components and the square-root filtering to stochastic components.</p> <p>Problems were finally narrowed to solve a series of the algebraic matrix Lyapunov and Riccati equations whose solutions imply a linear transformation of adjoints to state vectors.</p> <p>A computer code ODZCR was developed for designing CANDU zone control systems using the above theories. Analysis of the existing 600 MWe CANDU zone control compartments in terms of their locations and numbers led to the following conclusions. The effective region for both spatial and bulk control was very limited and, hence, the current vertical compartments occupied the region most effectively: also the range of spatial control assigned to individual compartments was coincident with the spatial effective region found in the study.</p> <p>Alternatively we propose a horizontal zone control system that has comparable performance with better predictability.</p> / Doctor of Philosophy (PhD)

<p>A frequently important source of image degradation in diagnostic radiography series from the scattering of radiation within the object itself. The research presented in this dissertation is directed towards the elucidation of this source of radiographic image degradation.</p> <p>The physical context selected is the passage of collimated thermal neutrons through an object of radiographic interest while the mathematical context is that of neutron transport. The analytical and computational methods are selected to emphasize the macroscopic image degradation effects of object scattering. Accordingly, isotropic neutron scattering and thermal one-group neutron-nucleus macroscopic cross-sections are employed as characterizations of the relevant interaction physics. Calculations and experiments undertaken pertain primarily to homogeneous objects of plunar geometry.</p> <p>The conceptual basis of this dissertation is divided into two domains.</p> <p>First, the transport of a collimated neutron beam through an object is modelled in isolation to the image formation domain with the goal of estimating the extent of object scattering that occurs. This is accomplished initially for a one dimensional homogeneous infinite slab object using a one-group integral transport formulation based on the point source diffusion kernel. An original solution to this particular form of the integral neutron transport equation is developed featuring the exact specification of a build-up factor function based on the forward partial neutron current and admitting an arbitrary degree of multiple scattering.</p> <p>Additionally, an original extension to the double Pℯ method for solving the one-group integro-differential neutron transport equation is developed for calculating the two-dimensional transport of collimated neutrons through a rectangular object.</p> <p>The second approach involves calculating the distribution of object scattered neutrons on the image formation plane thereby quantifying the incurred image degradation. This is accomplished by incorporating both problem domains into a system transfer function framework, involving the calculation of scattering based spatially variant point and line spread functions which are applied in the response determination for a homogeneous knife-edged slab object. Applications to the location of edges and corners on blurred neutron radiographs are established. These should ultimately be useful in the accurate radiographic dimensioning of nuclear fuel pins.</p> <p>One significant result of these calculations is the quantitative evaluation of scattering based distortions that have previously been noted in neutron radiographic edge responses. The existence and relative magnitude of this phenomenon has been confirmed here using an analog Monte Carlo simulation. Experimental tests using the neutron radiography facility at the McMaster Nuclear Reactor have also been undertaken. Each of these confirmation techniques suggests that this scattering based edge distortion may possess merit as a neutron beam diagnostic indicator.</p> <p>In summary, image degradation attributable to object scattering has been quantitatively examined and clarified for thermal neutron radiography. Applications in the interpretation of radiographic responses are thereby enhanced.</p> / Doctor of Philosophy (PhD)

<p>Finite amplitude pressure waves were investigated in a horizontal air-water system to determine the multidimensional propagation characteristics. Five classes of waves were analysed in this system of which four occurred in the water phase. The duct used to investigate these waves was square, 9 cm on a side, and 5 m in length.</p> <p>Weak shock waves of finite length were used in the gas phase. Theory by Whitham accurately predicted the attenuation.</p> <p>Pressure wave propagation in the water was dominated in all cases by characteristics associated with a Klein-Gordon equation. This equation is derived assuming a free surface but is found to play a role even when the surface of the water has an applied pressure.</p> <p>Pressure waves in the water under a free surface were studied in the system. Amplitudes of this class of waves were found to be small and they travel quickly throughout the system.</p> <p>An impulsive applied pressure to the water at a vertical wall can generate two types of waves depending on the period of the pressure pulse. If it is longer than a cutoff period defined by the Klein-Gordon dispersion relation, amplitudes decay as tˉ½, where t is the time, and exponentially with distance. If the period is less than cutoff, pressure waves in the water can propagate down the duct under a free surface. Pressure amplitudes in the water at the vertical wall can be large due to additive effects from the applied surface pressure.</p> <p>The water region beneath the shock can act as a three dimensional waveguide. This phenomenon depends on the depth of the water. High pressure amplitudes can occur in the water relative to the shock. The frequency source needed to drive the waveguide is conjectured to be a Klein-Gordon wave packet which remains steady with the shock.</p> <p>If bubbles are present in the water so that the effective sound speed in the water is less than the speed of the shock, high amplitudes will exist in the water accompanying the shock since energy cannot quickly disperse away from the shock region.</p> / Doctor of Philosophy (PhD)

<p>A new method is presented for measuring local void-fraction and its distribution in gas-liquid two-phase flow. The method is based on reconstructing the physical distribution of steam and water (phase distribution) from the energy spectrum of fast neutrons scattered in the test section. The unique relationship between neutron energy and angle of single scatterings in the liquid phase is utilized to reconstruct the phase distribution.</p> <p>Monte Carlo simulations of scattering in the test sections have been used in developing the method. The validity of the Monte Carlo methodology for this purpose is discussed within the logic of the MORSE computer code employed in this work. The usage of the code is verified by simulating actual experiments during the course of the work.</p> <p>The neutron scattering problem is formulated into non-linear mappings of the phase distribution to the measured neutron spectrum via matrices. The phase distribution is reconstructed by solving the inverse problem posed by the mappings. The non-linearity is overcome by applying a series of successive-approximations to the mappings. The mathematical foundations of the inverse problem are discussed and its implementation in the form of a numerical algorithm is shown.</p> <p>The energy spectra of the scattered neutrons are measured for a few test sections, and the results are shown to compare favourably with those obtained from Monte Carlo simulations. The techniques used in the measurements are also discussed.</p> <p>The conclusion of this study is that the proposed new method can be applied successfully for measuring phase distributions of gas-liquid flows. The method in contrast to other radiation methods, requires only a single exposure of the test section to radiation. The inverse problem of reconstructing the phase distribution is solvable and the required neutron energy spectrum can be measured using available techniques. The only restriction is that the test section diameter has to be of order of one mean-free-path of the source neutrons in the scattering medium (about 100 mm in water for 14 MeV neutrons). This is necessary to reduce the contributions from neutron rescattering that complicate the reconstruction problem.</p> / Doctor of Philosophy (PhD)

<p>The search for an enhancement of nuclear energy suggests that breeding of fissile fuel from fertile materials as well as the rejuvenation of spent nuclear fuel is of major importance. With the development of linear accelerator breeders it is possible, in principle, to enrich depleted nuclear fuel and to reenrich spent thermal reactor fuel for continued burnup without reprocessing. The management of separated fissile isotope is thus largely avoided.</p> <p>The symbiotic nuclear reactor system analyzed here consists of a linear accelerator breeder and a conventional nuclear converter reactor capable of burning natural uranium fuel. With repeated breed-burn cycles the system nuclear fuel can be brought to fuel burnups of up to and exceeding 27 times the conventional system once-through fuel burnup.</p> <p>The analysis undertaken here shows considerable potential for uranium based fuel cycles relative to that for thorium fuel cycles for the case of low fuel burnup rejuvenation without reprocessing. Consequently uranium-plutonium fuel cycles are analyzed for schemes with periodic chemical fuel reprocessing as well as without reprocessing.</p> <p>This analysis involves the development of a detailed symbiotic system dynamic mass-energy conservation formulation, yielding results ranging from detailed system isotopic concentration histories to general system fuel mass flow and energy flow. A comparison is made between the major parameters of the symbiotic reactor system and its equivalent conventional system.</p> <p>Optimum symbiotic system characteristics are generally obtained for net accumulated fuel burnups below 9 times the conventional once-through fuel burnup. For the presently estimated fuel to capital-operational cost fraction a marginally favorable symbiotic system is only obtained with an energy self-sufficient breeder subsystem. For increased fuel cost fractions, however, the symbiotic system shows, highly improved system characteristics even for net power consuming breeder subsystems.</p> / Doctor of Philosophy (PhD)

<p>The neutron image unsharpness which generally limits radiographic resolution to a qualitative assessement has been studied in detail and found to exhibit unique features at object boundaries and material discontinuities. These radiographic features provide intrinsic criteria for accurate dimensional measurements and the determination of material boundaries.</p> <p>As a basis for our investigation, the analysis of the underlying radiation-conversion and transport phenomena of the neutron imaging process was undertaken. The resultant functional image characterizations were found to be dependent on the radiographed object geometry, object dimensions, and material composition. Two avenues for extracting quantitative details from radiographs have thereupon been identified. Firstly, the coordinates bounding an object or regions of material discontinuities were found to be obtainable by an adaptation of the experimental optical density data to the functional representation. Secondly, the optical density variations due to image unsharpness was found to possess functional inflections at object boundaries and material discontinuities.</p> <p>The applications of both methods to the determination of limits of internal material discontinuities and dimensions of objects have been investigated in some detail. Experimental tests of the inflection approach show excellent agreement with theory. A mathematical-theoretical characterization of the neutron imaging phenomenon has thus been established and developed into a practical tool for extracting dimensional information from a neutron radiographic image.</p> / Doctor of Philosophy (PhD)

<p>Heavy water moderated thermal nuclear fission reactors have a greater inherent neutron economy than light water or graphite moderated reactor designs. Consequently, such units, operating on a variety of fuel cycles, may play an ever-increasing role in meeting future global energy demands. This thesis explores, analytically, the operational advantages and challenges associated with the use of a low enriched uranium (LEU) fuel cycle in advanced reactors based on the CANDU heavy water moderated, pressure tube design concept. The flexibility afforded through the use of LEU fuel is applied to enhance the operational and safety characteristics of reactors utilizing this fuel cycle. An investigation of factors influencing coolant void reactivity is conducted. Design modifications are introduced to reduce the coolant void reactivity, while maintaining the continued capability of high power operation. An enrichment and element radius graded fuel bundle design is developed with a central graphite core, an inner ring of 14 fuel elements, and an outer ring of 21 fuel elements. Fuel and lattice design perturbations are investigated to examine the effect of lattice pitch variations, capability of radioisotope production, the use of burnable poisons, and light water coolant. Xenon override requirements with LEU fuel are addressed. The efficacy of using modified two group (M-2) neutron diffusion theory for LEU fuel management studies is investigated. A modelling strategy is developed for the simulation of reactivity devices and fuel lattice properties using the M-2 methodology with a fixed energy cut-off. Detailed fuel management studies are conducted to examine the operational intricacies of LEU fuelling. Improved checkerboard type fuelling strategies are developed. Finally, the CANDU - Spectral Shift Advanced Thermal Reactor (CANDU-SSATR) is introduced and characterized. This multi-spectrum high burnup advanced reactor design utilizing simplified fuel management strategies holds great promise for the future.</p> / Doctor of Philosophy (PhD)

<p>The ability to predict the flow patterns and flow pattern transitions in a two-phase flow process is useful for an accurate prediction of the pressure drop, heat and mass transfer rates, and also for the choice of appropriate two-phase flow design parameters for the system. During a loss of coolant accident (LOCA) in a nuclear reactor, two-phase flow may exist in the primary heat transport loop, and a knowledge of the flow patterns that are occurring at the various flow conditions is needed to accurately model the accident scenario.</p> <p>Horizontal gas-liquid two-phase flow patterns and flow pattern transitions have been investigated both theoretically and experimentally for a pipe of 5.08 cm i.d., annulus geometries of outer tube diameter 5.08 cm i.d. and inner-to-outer diameter ratios from 0.375 to 0.625, and for a 37-rod nuclear fuel type bundle flow system having an outer tube diameter of 10.16 cm i.d. and rods of diameter, 1.27 cm. The 28-rod bundle flow geometry was also studied theoretically. The flow conditions were at inlet pressures of about 1 to 2 bar and at near room temperature.</p> <p>In this study, the time averaged void fraction and pressure drop measurements were also successfully obtained. The instantaneous and time averaged void fraction measurements were achieved by the ring type capacitance transducers based on the differences in the dielectric constants of the liquid and gas phases. The various flow patterns occurring in the pipe, annulus and rod bundle flow systems were successfully characterized by direct visual observation through the transparent test sections and also from the signal waveforms of the instantaneous fluctuations in the void fraction, the pressure drop measurements and the ultrasonic transmission waveforms. Flow pattern transitions were determined from both the results of the measured void fraction and direct visual observation.</p> <p>The experimental results show that the flow pattern structures occurring in horizontal annulus and rod bundle geometries are similar to those observed for the pipe flow case, except the annulus flow system where we characterized two additional flow patterns, namely, "Annulus-Slug" and "Annulus-Plug". These flow patterns are similar to the Slug and Plug flow structures observed for the pipe geometry, but are restricted to the lower annulus channel gap below the annulus rod. These occur at the flow conditions that would otherwise lead to Stratified flow patterns for pipe flow cases.</p> <p>The results show that the flow pattern transitions for the annulus and rod bundle flow geometries are significantly different from those of the normal pipe flow. The flow pattern transitions for the annulus flow geometries were observed to be significantly influenced by different inner-to-outer diameter ratios, except the Stratified Smooth to Stratified Wavy transition. The Stratified to Intermittent and the Intermittent to Dispersed Bubble transitions occur at lower superficial liquid velocities, while the Intermittent to Annular transition occurs at higher superficial gas velocities for larger inner-to-outer diameter ratios. In the rod bundle geometries, the flow pattern transitions were observed to vary slightly with the particular angle of orientation of the bundle within the enclosing tubeshell. The various influences on the flow pattern transitions observed in the present study are mainly due to the differences in geometries and force distributions.</p> <p>From direct visual observation results, we also observed that interfacial waves in the rod bundle flow geometry were generated and dissipated at the rod bundle end plates. No significant effect of the rod bundle end plates on the other flow patterns was observed, except a slight effect on the regularity of these intermittent flow patterns, usually becoming more apparent at higher flow rates.</p> / Doctor of Philosophy (PhD)

<p>In a pressurizer water nuclear power plant, the pressure of the primary heat transport system is maintained mainly through the operation of a pressurizer. Existing pressurizer models are not satisfactory in predicting pressurizer behaviour in response to operating or accidental transients. This is mainly due to lack of understanding on non-thermodynamic equilibrium and other local two-phase phenomenon in the pressurizer. The primary objectives of this work are to prepare necessary tools for a systematic study of the pressurizer and to investigate pressurizer phenomena under quasi-steady-states and to determine the effects of major pressurizer control parameters to the behaviour of the pressurizer.</p> <p>To achieve the first objective a rate form of equation of state is analytically derived. It is used as an analytical expression of pressurizer pressure response as well as to support and to guide the rest of the work. lDRIFF, a two-phase simulation code consisting of a lumped homogeneous model and a differentially formulated drift-flux model, is developed to accommodate any physical assumptions in pressurizer modelling. A laboratory scale pressurizer system, complete with a glass pressurizer tank, a simulated primary heat transport system and substantial monitoring facilities is also developed. Together, they provide analytical, numerical and empirical tools needed in a systematic study of pressurizer phenomena.</p> <p>To achieve the second objective, various quasi-steady-state conditions in the pressurizer are simulated experimentally and four distinct flow regimes are identified in the pressurizer. With the help of numerical extrapolation by using the IDRIFF code, the data are analyzed to produce, among other things, a correlation of average void fraction, a pressurizer flow-regime map with the transitions of flow-patterns semi-analytically modelled, and a general understanding of pressurizer behaviour under quasi-steady-states.</p> <p>In addition, the effects of changes in pressurizer heater, steam-bleed flow and pressurizer surge-line flow to the behaviour of the pressurizer are investigated. Perturbation transients, where the dynamic effect of the parameters can be isolated from other transient factors, are empirically and numerically simulated. The resulting overall pressurizer behaviour and observed local phenomena are analyzed in terms of their relation to quasi-steady-state behaviour, global and local pressure response, local phase distribution and pressurizer stability. Several flow and heat transfer mechanisms, such as the temperature of the steam being controlled by the liquid saturation pressure, are also summarized.</p> <p>It is believed that the preparation of research tools and the accumulation of information learnt during the course of the current endeavour has formed an essential basis for a further systematic study of nuclear power plant pressurizer and has brought the study one step closer to the goal of achieving a complete understanding of pressurizer phenomena.</p> / Doctor of Philosophy (PhD)