The work reported in this thesis falls into three distinct, though intimately related parts. Part I is concerned with the production of a variable temperature two-phase flow test facility for studying single and two-phase flows around arbitrary two-dimensional bodies. It includes the initial design study required to define an operational envelope for the facility, and the design and constructional features of its main components and ancilliary systems. The design of a two-phase flow vapour ventilation experiment is described, together with the operating procedure for the facility. Part II reports single and two-phase experiments with a two-dimensional circular cylinder, the two-phase flows being generated by inducing natural cavitation. The cavitation inception flow regime was found to be strongly influenced by viscous effects. Three forms of incipient cavitation were observed, two attached or very close to the cylinder surface, and one of a detached nature, occurring well downstream in the wake of the cylindrical test body. These inception modes have been related to the fully wetted viscous flow around the cylinder in the Reynolds number range 10⁵ <R_d<10⁶. The development of cavitation from these three aforementioned incipient states was investigated. Viscous effects were found to influence both the limited and developed cavitation flow regimes. For development of cavitation at Reynolds numbers corresponding broadly to the supercritical range for fully wetted flow, a critical cavitation number was found at which the apparent free stream lines of the flow changed from a concave to a convex disposition. For the experimental configuration used, this critical cavitation number was independent of Reynolds number, for Reynolds numbers above the critical value. With development of cavitation at Reynolds numbers corresponding broadly to the subcritical range for fully wetted flow, no such gross changes in flow pattern were observed, the displacement of the apparent free streamlines of the flow between the limited and fully developed cavitating states being minimal. Part III contains recommendations for modifications to the experimental facility and suggestions for further studies arising from the results reported herein.

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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.

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.

Thesis (Ph. D.)--University of Adelaide, Dept of Mechanical Engineering, 1987. / One microfilm reel (16 mm.) in pocket. Includes bibliographical references (leaves 194-201).

Thesis (Ph.D.) -- McMaster University, 1999. / Includes bibliographical references (leaves 222-229). Also available via World Wide Web.

Thesis (Ph. D.)--Ohio University, 2001. / Title from PDF t.p.

Thesis (Ph.D.)--University of Tulsa, 1974. / Bibliography: leaves 89-91.

Thesis (Ph.D.)--University of Tulsa, 1984. / Bibliography: leaves 73-75.

Thesis (Ph.D.)--University of Tulsa, 1990. / Bibliography: leaves 88-89.