Thesis (M.S.)--University of Missouri-Columbia, 2007. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on October 23, 2007) Includes bibliographical references.

<p>The refilling and rewetting of a directly heated horizontal channel has been studied experimentally. The quenching characteristics and rewetting rates were obtained under different well-defined initial and boundary conditions. The parametric effects of initial wall temperature, inlet water flow rate and inlet water subcooling as well as effects of residual power input, tube insulation and dissolved air and ions in the inlet water were investigated.</p> <p>The results show that, in horizontal channels, the transverse gravity forces significantly affect the hydraulic, and consequently thermal, behaviour of the system. The heat transfer mechanisms were found to vary during transients, both axially and circumferentially. This results in large differences in the pre-quench characteristics with regard to the bottom and top of the channel.</p> <p>A simple physical model which can account for most of the observed characterisitcs was developed. The model consists of an inclined rewetting front and an entrained "liquid tongue" extending downstream from the rewetting front. The model was also supported by photographic studies.</p> <p>The propagation of the rewetting front appears to be largely controlled by hydrodynamic mechanisms. It was found that surface quenching can occur at very different wall temperatures along the tube. Thus, there is no well defined rewetting temperature. This is contrary to the predictions of the generally accepted conduction controlled rewetting model.</p> <p>Since hydrodynamic mechanisms dominate the thermohydraulic processes in the present flow situation, a simplified two-fluid model was used to analyze the processes. The wall temperature was obtained after the hydraulic equations of the liquid phase were solved. The wall was assumed to be in stable film boiling before quenching.</p> <p>A quench model based on a critical water level, (hʟ)crit' determined the transition of heat transfer mode from film boiling to transition boiling and subsequent quenching of the surface. (hʟ)crit was obtained using a model based on initiation of a Kelvin-Helmholtz type instability at the vapor film-liquid interface.</p> <p>The initiation of the interfacial instability is believed to be the governing mechanism that leads to surface rewetting. When the instability starts, local regions of enhanced heat transfer are assumed to form on the heater surface. This provides the necessary conditions for surface rewet. However, if the surface is highly conductive and has a high thermal capacity, these rewet spots may not grow and surface rewet may not occur. Therefore, the sufficient conditions would require that the rewet spots could grow or spread on the heating surface. For thin-walled tubes, because of low thermal capacity, rewet spots may spread once they are formed. Hence, interfacial instability is postulated to be both necessary and sufficient to quench thin-walled systems of the type studied.</p> <p>The simplified two-fluid model, together with the quench model were found to be quite successful in predicting the rewetting rates and details of the quenching characteristics for the refilling and rewetting experiments.</p> / Doctor of Philosophy (PhD)

<p>The role of nuclear energy systems while produce fissile materials has become an important and essential part of scenarios for the future development of nuclear energy. Definitive analyses and nucleonic comparisons of these breeder systems have been impeded by the lack of a rigorous and consistent methodology for describing fissile fuel production and fertile fuel utilization. The research reported here therefore addresses itself to this problem and is based on a synthesis of three concepts: (1) the lumped parameter formulation of reactor physics, (2) the establishment of symbiotic relationships between breeders and converters and (3) the use of material stockpile inventories.</p> <p>In the lumped parameter synergetic analysis the temporal variation of stockpile inventories and net electrical output of a selected system are established. The system is taken to consist of a general breeder reactor coupled to a fission converter reactor and fuel reprocessing-fabrication plant. By including the converter and processing plant and examining the temporal and nuclear behaviour of the entire system, various types of nuclear breeders can be analysed and subjected to a comparative analysis in a consistent manner. The use of lumped parameters, based on the integration of detailed space and energy dependent effects into single-valued parameters, has facilitated survey calculations and analysis of the conceptual systems defined herein. The temporal variation of the stockpile inventory is used to describe fissile fuel production and fertile fuel utilization since information, such as minimum inventory requirements and material replacement times, is provided. This approach eliminates the ambiguities involved in a single figure of merit description, such as, for example, the doubling time, and includes pre-steady-state effects and reprocessing lags and losses. To assess the net electrical production of the system, the consumption of electricity by the reactors and the processing plant is explicitly included.</p> <p>The synergetics of fast-fission, symbiotic fusion, hybrid fusion and spallation breeders are then investigated. In these analyses, the fissile and fertile inventories and power output are calculated over the system lifetime for a specific breeder power. The effects on the system inventories of varying breeder thermal power are also examined. Since the mathematical-physical formulations are specified in terms of lumped parameters, the results of changing these on the system can be easily dealt with. Four fissile fuel breeding systems are then compared using current economic data.</p> <p>On the basis of this study, it is evident that there exists no single breeder system which consistently outperforms the others in all aspects. The fast-fission breeder, while not a good fissile fuel producer, has the best power generating efficiency and, due to its relatively low capital costs, can produce electricity at the lowest cost. The symbiotic fusion breeder system has the shortest fissile fuel replacement time and requires less initial fuel investment but it produces electricity at the highest cost. For combined fissile fuel production and electrical generation, the hybrid fusion breeder excells and it is also a good conserver of fertile fuel. The spallation breeder outranks all others in fissile fuel production.</p> <p>While no single breeder was found to be superior in a general sense, the synergetics method of analysis has been shown to be effective in several specific respects. The temporal variations of the stockpile inventories and net power derived here have a physically reasonable basis and are mathematically tractable. The pre-steady-state effects can be described with great accuracy by two functions determined by the fuel management scheme. Processing lags and losses are also explicitly incorporated. The flexibility and usefulness of the developed methodology are enhanced by the fact that any material stockpile inventory in the system can be calculated. Essential to this procedure is the inclusion at the outset of all system components in a synergetic analysis.</p> / Doctor of Philosophy (PhD)

<p>The propagation of weak shock waves through a horizontal stratified two-phase system has been investigated both theoretically and experimentally to demonstrate the various facets of its interaction with the phases, fuel bundles and flow network branches. Two types of shock tubes are used: a lucite shock tube is utilized in monitoring the mechanism at the interface of the phases by high speed photography and the other one is an aluminum shock tube of 101.6 mm inner diameter with flow network branches is used in investigating the shock wave behaviour inside a pressure tube during blow-down and loss of coolant accidents.</p> <p>This dissertation can be divided in to three broad categories. First, the inclusion of the interfacial roughness factor in the analysis of the shock wave propagation through a two-phase system inside a pressure tube weakens the strength of the shock waves, because of the energy loss due to frictional resistance at the interface. The interface is subjected to a combined effect of the waves propagating both in the gas and liquid phases of the system. High speed photography of the interface is considered to estimate the parameters pertaining to the generation of the ripples at the interface and the coupling of this parameter to a quasi-steady energy balance for the system can provide the values of the magnitude of the overpressures in the system.</p> <p>Secondly, the interaction of weak shock waves with three different types of fuel bundles used in CANDU reactors is presented. Depending on the percentage of the flow area available, different fuel bundles produce different magnitudes of the overpressure. For the transmitted waves, the choking is markedly observed even for moderate range of the shock waves. Presence of liquid phase enhances the strengths of overpressure for the reflected and transmitted waves. Inside the fuel bundles, the shock waves cause unusual vibrational effects which may be detrimental to the life of the fuel elements.</p> <p>Around the network, the two-phase propagation velocity is observed to be same as the gas phase propagation velocity is observed as the gas phase propagation velocity. Though tap and distilled water exhibit variations in the maximum overpressures, the time averaged magnitude under these two systems agree very well everywhere in the network branches. The vertical pressure profiles in the tap water has dispersive and high oscillatory nature whereas in the distilled water the rise in overpressure is dispersive, but smooth in nature. In distilled water, the pre-pulses moving under a free surface travel at the speed of sound in water and for those in tap water, this velocity is influenced by the presence of air bubbles in the tube walls.</p> / Doctor of Philosophy (PhD)

<p>Reflux condensation in vertical inverted U-tube steam generators forms an important heat removal mechanism for nuclear reactors in certain accidents. Reflux condensation phenomena in single vertical tubes were studied for two well defined boundary conditions to develop an improved understanding of the mechanisms governing heat removal and liquid holdup. A correspondence between an imposed boundary condition and its resulting flow regime has been made where total reflux condensation occurs for an imposed drop across the tube and fill and dump cycling occurs for an imposed steam flow rate at the tube inlet.</p> <p>Total reflux condensation is characterized by a flow pattern made by a single-phase region oscillating over a two-phase region. This flow region can be maintained indefinitely while the average single-phase and two-phase region lengths remain constant. It is also characterized by the complete condensation of the injected steam with all the condensate flowing back to the tube inlet.</p> <p>Fill and dump cycling is characterized by a cyclical operation where, during one cycle, the length of the single-phase region increases at the expense of the two-phase region until a point where the system becomes unstable and the single-phase region is ejected from the top of the tube. All the injected steam is condensed and contrary to total reflux condensation, not all the condensate flows back to the tube inlet. Instead, part of the condensate is carried over the condensation length to form the single-phase region. This flow regime could be qualified as dynamic as opposed to quasi-static for total reflux condensation.</p> <p>Experimental measurements were made in three single vertical tubes with a cooling jacket. These data show fill and dump cycling to be more efficient than total reflux condensation in condensing steam and to allow the condensate not to be trapped in the tube as in total reflux condensation. In addition, the experimental data suggest that total reflux condensation could be well the limiting flow regime for fill and dump cycling as the cycle period becomes very long and consequently it could define conservative lower bounds for the values of total heat removal.</p> <p>An analysis of counter-current film-wise condensation was conducted to model total reflux condensation, central to this model is an extended Nusselt's model of film-wise condensation, a linearized stability analysis of the condensate film flow and the use of three concepts: critical layer, maximum mechanical energy and transfer and film instability. The agreement between the experimental data and the prediction of total heat removal (via condensation rates) and liquid holdup is satisfactory. Both the present model and the experimental data show that flooding occurs at the tube inlet and plays a key role in defining the heat removal and the distribution of condensate in the tube. In particular, it is shown that for a given inlet cooling water temperature, the flooding flow rates, in terms of the Kutateladze variable, are nearly independent of the tube size and system pressure. In general, for a given tube size and system pressure, the inlet cooling water temperature has a notable influence on the value of the flooding flow rates, except for the smaller tube size, and it does not affect the amount of condensate holdup in the tube.</p> <p>The results of the present work could be used in small-break LOCA analyses were the present model could estimate the heat removal capabilities of steam generators and the amount of coolant (condensate holdup) trapped in the steam-generator tubes that would be available for core cooling.</p> / Doctor of Philosophy (PhD)

<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)