No description available.

No description available.

This thesis is focused attention on one-dimensional models for fast transient flows in a kinematic non-equilibrium. Besides the thermodynamic non-equilibrium, there is another type of non-equilibrium: the kinematic non-equilibrium, or drift between the phases. Such flow models include bubbly gas/liquid flows which are characterized by strong coupling between the phases, due to the rapid interphase transfers of mass, momentum and energy. As a consequence the assumptions that the phase pressures and the phase temperatures are equal at any cross-section appear consistent with experimental observations. The set of equations includes a momentum equation which has the form of a relaxation law of the drift velocity. This equation is based on a simplified version of the so-called Voinov - Berne equation for the momentum of the gas in a bubbly flow. The ability of the model to predict steady state critical flows is tested first. This is done by means of an analysis of the sensitivity to variations of the main parameters, and also by comparing the results with two sets of original experimental data on air-water critical flows. Finally, the model is tested in transient conditions, modelling the water hammer phenomena.

The slotted plate flow meter has been widely tested as an obstruction flow meter during the past several years. It has been tested for both single-phase flows as well as for two-phase flows. Previous studies have revealed that the slotted plate flow meter is always better in performance and accuracy than the standard orifice plate flow meter. This study is primarily based on how a slotted plate responds to horizontal two-phase flow with air and water being used as the working fluids. The plates under consideration are those with beta ratios of 0.43 and 0.467. Experiments have been performed with six different configurations of the slotted plate test sections. The performances of the slotted plate flow meters will be compared to that of a standard orifice plate flow meter and then with a venturi. The effects of varying the upstream quality of the two-phase flow on the differential pressure and the coefficient of discharge of the slotted plates, the standard orifice plate and the venturi will be evaluated. Response characteristics at low differential pressures will be investigated. Tests for repeatability will be performed by studying the effects of the gas Reynolds number and the upstream quality on the differential pressure. The differential pressures across the slotted plates, the standard orifice plate and the venturi will be compared. Reproducibility will be evaluated by comparing the data obtained from all six different configurations. One of the main objectives of this study is to arrive at the best suitable procedure for accurately measuring the flow rate of two-phase flow using the slotted plate flow meter.

In previous studies the slotted orifice plate has demonstrated superior performance characteristics to those of the standard orifice plate. In this study, these comparisons are investigated further. The response characteristics of the slotted orifice plate to the standard orifice plate and V-Cone for two-phase flows of water and air at various qualities, flow rates, and pressures are shown visually. The effect of oil as it flows through a slotted orifice plate and standard orifice plate are visually documented. The effect of manufacturing accuracy on the slotted orifice plates is investigated as to the effect on the coefficient of discharge, percent change in pressure, and Reynolds number. The slotted orifice plate mixes two-phase flow better than the standard orifice plate and V-Cone. There is a manufacturing effect on the slotted orifice plates; the larger the area of the slots, the larger the discharge coefficient.

The present work focuses on the study of two-phase flow behavior called “Intermittent Buoyancy Induced Flow” (IBIF) resulting from the loss of coolant circulation in a CANDU nuclear reactor core. The main objectives are to study steam bubble formation and migration through the pressure tube and into the feeder tubes and headers, and to study the effect of pressure tube sagging on the two-phase flow behavior during IBIF. Experiments are conducted using air and water flow at atmospheric pressure to qualitatively examine the IBIF phenomena. The test showed oscillating periodic behavior in the void fraction as the air vents. In addition to this, a mathematical model based on a simplified momentum balance for the liquid and gas phases was formulated. The model was further solved and compared to the experimental data. The model predictions showed a reasonable agreement within the investigated range of void fractions.

The present work focuses on the study of two-phase flow behavior called “Intermittent Buoyancy Induced Flow” (IBIF) resulting from the loss of coolant circulation in a CANDU nuclear reactor core. The main objectives are to study steam bubble formation and migration through the pressure tube and into the feeder tubes and headers, and to study the effect of pressure tube sagging on the two-phase flow behavior during IBIF. Experiments are conducted using air and water flow at atmospheric pressure to qualitatively examine the IBIF phenomena. The test showed oscillating periodic behavior in the void fraction as the air vents. In addition to this, a mathematical model based on a simplified momentum balance for the liquid and gas phases was formulated. The model was further solved and compared to the experimental data. The model predictions showed a reasonable agreement within the investigated range of void fractions.

Bubble and cavitation effects phenomena can be encountered in two-phase gas-liquid systems in industry. In certain industries, particularly high-risk systems such as a nuclear reactor/plant, the detection of bubble dynamics, and the monitoring and measurement of their characteristics are necessary in controlling temperature. While in the petro-chemical engineering industry, such as oil transportation pipelines, the detection and monitoring of bubbles/cavitation phenomena are necessary to minimise surface erosion in fluid carrying components or downstream facilities. The high sensitivity of Acoustic Emission (AE) technology is feasible for the detection and monitoring of bubble phenomena in a two phase gas-liquid system and is practical for application within the industry. Underwater measurement of bubble oscillations has been widely studied using hydrophones and employing acoustic techniques in the audible range. However, the application of Acoustic Emission (AE) technology to monitor bubble size has hitherto not been attempted. This thesis presents an experimental investigation aimed at exploring AEs from gas bubble formation, motion and destruction. AE in this particular investigation covers the frequency range of between 100 kHz to 1000 kHz. The AE waveform analysis showed that the AE parameter from single bubble inception and burst events, i.e. AE amplitude, AE duration and AE energy, increased with the increase of bubble size and liquid viscosity. This finding significantly extends the potential use of AE technology for detecting the presence of bubbles in two-phase flow. It is concluded that bubble activity can be detected and monitored by AE technology both intrusively and non-intrusively. Furthermore, the bubble size can be determined by measurement of the AE and this forms the significant contribution of this thesis.

Incomplete data is a pervasive problem in health research, and as a result statistical methods enabling inference based on partial information play a critical role. This thesis explores estimation of regression coefficients and associated inferences when variables are incompletely observed. In the later chapters, we focus primarily on settings with incomplete covariate data which arise by design, as in studies with two-phase sampling schemes, as opposed to incomplete data which arise due to events beyond the control of the scientist. We consider the problem in which "inexpensive" auxiliary information can be used to inform the selection of individuals for collection of data on the "expensive" covariate. In particular, we explore how parameter estimation relates to the choice of sampling scheme. Efficient sampling designs are defined by choosing the optimal sampling criteria within a particular class of selection models under a two-phase framework. We compare the efficiency of these optimal designs to simple random sampling and balanced sampling designs under a variety of frameworks for inference. As a prelude to the work on two-phase designs, we first review and study issues related to incomplete data arising due to chance. In Chapter 2, we discuss several models by which missing data can arise, with an emphasis on issues in clinical trials. The likelihood function is used as a basis for discussing different missing data mechanisms for incomplete responses in short-term and longitudinal studies, as well as for missing covariates. We briefly discuss common ad hoc strategies for dealing with incomplete data, such as complete-case analyses and naive methods of imputation, and we review more broadly appropriate approaches for dealing with incomplete data in terms of asymptotic and empirical frequency properties. These methods include the EM algorithm, multiple imputation, and inverse probability weighted estimating equations. Simulation studies are reported which demonstrate how to implement these procedures and examine performance empirically. We further explore the asymptotic bias of these estimators when the nature of the missing data mechanism is misspecified. We consider specific types of model misspecification in methods designed to account for the missingness and compare the limiting values of the resulting estimators. In Chapter 3, we focus on methods for two-phase studies in which covariates are incomplete by design. In the second phase of the two-phase study, subject to correct specification of key models, optimal sub-sampling probabilities can be chosen to minimise the asymptotic variance of the resulting estimator. These optimal phase-II sampling designs are derived and the empirical and asymptotic relative efficiencies resulting from these designs are compared to those from simple random sampling and balanced sampling designs. We further examine the effect on efficiency of utilising external pilot data to estimate parameters needed for derivation of optimal designs, and we explore the sensitivity of these optimal sampling designs to misspecification of preliminary parameter estimates and to the misspecification of the covariate model at the design stage. Designs which are optimal for analyses based on inverse probability weighted estimating equations are shown to result in efficiency gains for several different methods of analysis and are shown to be relatively robust to misspecification of the parameters or models used to derive the optimal designs. Furthermore, these optimal designs for inverse probability weighted estimating equations are shown to be well behaved when necessary design parameters are estimated using relatively small external pilot studies. We also consider efficient two-phase designs explicitly in the context of studies involving clustered and longitudinal responses. Model-based methods are discussed for estimation and inference. Asymptotic results are used to derive optimal sampling designs and the relative efficiencies of these optimal designs are again compared with simple random sampling and balanced sampling designs. In this more complex setting, balanced sampling designs are demonstrated to be inefficient and it is not obvious when balanced sampling will offer greater efficiency than a simple random sampling design. We explore the relative efficiency of phase-II sampling designs based on increasing amounts of information in the longitudinal responses and show that the balanced design may become less efficient when more data is available at the design stage. In contrast, the optimal design is able to exploit additional information to increase efficiency whenever more data is available at phase-I. In Chapter 4, we consider an innovative adaptive two-phase design which breaks the phase-II sampling into a phase-IIa sample obtained by a balanced or proportional sampling strategy, and a phase-IIb sample collected according to an optimal sampling design based on the data in phases I and IIa. This approach exploits the previously established robustness of optimal inverse probability weighted designs to overcome the difficulties associated with the fact that derivations of optimal designs require a priori knowledge of parameters. The efficiency of this hybrid design is compared to those of the proportional and balanced sampling designs, and to the efficiency of the true optimal design, in a variety of settings. The efficiency gains of this adaptive two-phase design are particularly apparent in the setting involving clustered response data, and it is natural to consider this approach in settings with complex models for which it is difficult to even speculate on suitable parameter values at the design stage.

Abnormal pressures have been measured in the deep boreholes at the Bruce site, southern Ontario, where a deep geologic repository for low and intermediate level radioactive waste disposal has been proposed. The pressure regime in the stratigraphic units exhibits either higher than hydrostatic pressure (over-pressured) or lower than hydrostatic pressure (under-pressured) are considered to be abnormal. At the Bruce site, the Ordovician sediments are under-pressured while the underlying Cambrian sandstone and the overlying Guelph carbonate are over-pressured. Hypotheses have been documented in literature to explain the phenomenon of abnormal pressures. These hypotheses include osmosis, glacial loading and deglaciation unloading, exhumation of overlying sediments, crustal flexure and the presence of an immiscible gas phase. Previous work on the Bruce site has shown that the under-pressures in the Ordovician limestone and shales could not be explained by glaciation and deglaciation or by saturated analyses. The presence of a gas phase in the Ordovician formations has been determined to be a reasonable cause of the under-pressure developed in the Ordovician shales and limestones at the Bruce site. Support for the presence of a gas phase includes solution concentrations of methane, concentrations of environmental isotopes related to methane and estimates of water and gas saturations from laboratory core analyses. The primary contribution of this thesis is the sensitivity analyses performed on the hydrogeologic parameters with respect to a one dimensional two-phase flow model. First, a one dimensional two-phase air and water flow model was adopted and reconstructed to simulate the long-term evolution of the groundwater regimes at the DGR site. Then the hydrogeologic parameters which impact the presence of under-pressure in the groundwater are investigated. Data required to quantify the properties of geologic media and groundwater are adopted directly from borehole testing and laboratory testing results. The permeable boundaries of the domain are assumed to be water saturated and pressure specified (using hydrostatic conditions in the Guelph Formation and hydrostatic with 120 m over-pressure condition in the Cambrian and Precambrian). Isothermal conditions were assumed, thus constant water density and viscosity values are estimated for the average total dissolved solids (TDS) concentration of the modelled stratigraphic column. A constant diffusion coefficient (a diffusivity of $0.25\times10^{-8}$ m$^2$/s) of air in water is assumed with a saturation-dependent tortuosity. The air generation rate is assumed to simulate the gas phase generated in the Ordovician formations. The numerical simulation of up to 4 million years provides a means to explore the behaviour of gas phase dissipation due to partitioning into the water phase and diffusive transport in the solute phase. Results confirmed that the presence of a gas phase would result in the under-pressure in water.