Finally, we prove that weak solutions to the compressible Navier-Stokes equations with the Navier boundary condition stabilize to static equilibrium states under a fair condition. / First, we show that the most general class of weak solutions to one-dimensional full compressible Navier-Stokes equations do not exhibit vacuum states in a finite time provided that no vacuum is present initially with the minimum physical assumptions on the data. Moreover, two initially non interacting vacuum regions will never meet each other in the future. / Secondly, we construct the local classical solutions to the compressible Navier-Stokes equations for initial vacuum far fields. In this case, we describe the blow-up phenomena of two-dimensional compact support smooth spherically symmetric solutions. When the far field of the initial state is away from vacuum, we obtain the global classical solutions and show the large time blow-up behavior of the gradient of the density. / This thesis deals with some important problems of compressible Navier-Stokes equations, including the well-posedness of the Cauchy problem, the regularity of the weak solutions constructed by Lions and Feireisl, and the dynamics of vacuum states, etc.. / Luo, Zhen. / Adviser: Zhouping Xin. / Source: Dissertation Abstracts International, Volume: 72-04, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 152-161). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

The mechanisms responsible for overland transport of faecal pathogens, particularly Cryptosporidium oocysts, from animal sources to water bodies are not fully understood. Surface properties of microbes, such as electrostatic charge and hydrophobicity, are thought to contribute to their aggregation and attachment to solid surfaces. There is conflicting evidence that methods used to purify Cryptosporidium oocysts from faecal material may affect the oocyst surface, leading to biased conclusions from transport studies. By studying oocyst surface properties, aggregation and soil attachment, this thesis addressed whether oocyst purification methods influence overland transport studies, and whether oocysts are likely to be associated with particles during transport. When using the microbial adhesion to hydrocarbon (MATH) assay with octane, oocyst hydrophobicity was shown to be method and isolate dependent, with oocysts displaying moderate to high hydrophobicity in 0.01 M KNO3. There was no observed attachment, however, to the hydrophobic octyl-SepharoseTM bead ligands when using the same suspension solution. Oocyst age did not appear to influence their hydrophobicity. A small but statistically significant proportion of oocysts displayed a net negative surface charge as observed by their attachment to an anion exchange ligand (DEAE). There was no difference in hydrophobicity or surface charge observed between purified oocysts and oocysts that had been extracted without the use of harsh chemicals and solutions with dehydrating properties. Purified oocysts did not aggregate at pH values between 3.3 and 9.0, nor in solutions lower than 0.59 M in ionic strength at a pH 2.7 which is approaching the reported isoelectric point of oocysts. This finding suggests that oocysts may not form aggregates under general environmental conditions. The association of purified oocysts with soil particles was observed in settling columns. Attachment to soil particles was not conclusive since the settling of the soil particles may have entrained single oocysts. Nonetheless, approximately 27% of oocysts were estimated to be unbound to soil or associated with small soil particles. Hence models for oocyst overland transport should consider a significant fraction as single entities or associated with soil particles less than about 3 μm in size.

At head of cover title: Australian Road Research Board / Bibliography: leaves 108-114 / xi, 114 leaves : ill ; 25 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, 1971

Lorentz forces provide a unique method for the control and mixing of gas flows without the physical intrusion of objects into the flow. Lorentz forces arise when an electric current is passed through a volume in the presence of a magnetic field. The interaction between the electric current and the electric and magnetic fields produces a body force which affects the flow. These forces have been investigated experimentally by other researchers and show promise as a way to accelerate combustion in diffusion flames by increasing the mixing rate of fuel and oxidant streams. Theoretical and numerical models were developed to gain insight into this process. Alkali metal seeding raises the electrical conductivity of a flame by two to three orders of magnitude. This has two significant effects: the Lorentz force becomes stronger for the same applied electric current and magnetic field, and the alkali seed concentration becomes a dominant factor in determining electrical conductivity of seeded gases. This makes electrical conductivity much easier to predict, and so the Lorentz body force produced is easier to determine. A theoretical basis for numerical modeling of reactive flows with variable body forces has been developed. Many issues are important in simulating gas flows. Conservation of chemical species must be carefully maintained. Mass transport by gaseous diffusion, which limits combustion rates in a diffusion flame, must be appropriately modeled. Viscous action is also important, since it promotes mixing of the fuel and oxidant streams. Convective, conductive, and diffusive transport of energy must be carefully treated since energy transport directly affects the fluid flow. A numerical model of an incompressible gas flow affected by Lorentz forces was written and tested. Although assumptions made in the model, such as isothermal conditions and uniform density, are not found in diffusion flames, the numerical model predicts velocity vector patterns similar to those observed in actual Lorentz force tests on diffusion flames. A simulation code for compressible, reactive gas flows which include Lorentz forces has also been written. Several parts of the model have been validated, and the approach used appears likely to produce successful simulations. Further validation studies will be required, however, before complete modeling of the diffusion flame can proceed. / Graduation date: 1995

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This dissertation considers the effect of measuring randomly varying local hydraulic conductivities K(x) on one's ability to predict steady state flow within a bounded domain, driven by random source and boundary functions. That is, the work concerns the prediction of local hydraulic head h(x) and Darcy flux q(x) by means of their unbiased ensemble moments (h(x))(κ) and (q(x))(κ) conditioned on measurements of K(x). These predictors satisfy a deterministic flow equation in which (q(x))(κ) = -(κ)(x)∇(h(x))(κ) + r(κ)(x) where κ(x) is a relatively smooth unbiased estimate of K(x) and r(κ)(x) is a "residual flux." A compact integral expression is derived for r(κ)(x) which is rigorously valid for a broad class of K(x) fields, including fractals. It demonstrates that (q(x))(κ) is nonlocal and non-Darcian so that an effective hydraulic conductivity does not generally exist. It is shown analytically that under uniform mean flow the effective conductivity may be a scalar, a symmetric or a nonsymmetric tensor, or a set of directional scalars which do not form a tensor. For cases where r(κ)(x) can neither be expressed nor approximated by a local expression, a weak (integral) approximation (closure) is proposed, which appears to work well in media with pronounced heterogeneity and improves as the quantity and quality of K(x) measurements increase. The nonlocal deterministic flow equation can be solved numerically by standard methods; the theory here shows clearly how the scale of grid discretization should relate to the scale, quantity and quality of available data. After providing explicit approximations for the prediction error moments of head and flux, some practical methods are discussed to compute κ(x) from noisy measurements of K(x) and to calculate required second moments of the associated estimation errors when K(x) is log normal. Nonuniform mean flow is studied by conducting high resolution Monte Carlo simulations of two dimensional seepage to a point sink in statistically homogeneous and isotropic log normal K(x) fields. These reveal the existence of radial effective hydraulic conductivity which increases from the harmonic mean of K(x) near interior and boundary sources to geometric mean far from such sources for σ^2/Υ (the variance of ln K) at least as large as 4. They suggest the possibility of replacing r(κ)(x) by a local expression at distances of few conditional integral scales from the interior and boundary sources. Special attention is paid to the "art" of random field generation, and comparisons are made between four alternative methods with five different random number generators.

The two-dimensional, viscous flow around an elliptic cylinder undergoing prescribed unsteady motions is analyzed. The fluid is taken to be incompressible. Departing from the conventional vorticity-stream function approach, the Biot-Savart law of induced velocities is utilized to account for the contribution to the velocity field of the different vorticity fields comprising the flow. These include the internal vorticity due to the rotation of the body, the free vorticity in the fluid surrounding the body, and the bound vorticity distributed along the body contour. In order to apply the method, the body must be assumed to be replaced by fluid of the same density as the undisturbed surroundings. The replacement fluid must have a rigid motion exactly the same as the actual body motion. This can be achieved by placing suitable distributed vorticity fields within and on the surface of the body. The bound vorticity on the body surface is in the form of a vortex sheet, and its distribution is governed by a Fredholm integral equation of the second kind. The equation is derived in detail. It is solved numerically. The motion of the free vorticity in the flow field is governed by the Navier-Stokes equations written in terms of vorticity. The descretized vorticity transport equation is derived for a control volume and is solved numerically using an explicit method with a forward-difference for the time derivative, and a central-difference for the diffusive terms. An upwind method is used for convection terms. The results obtained using the present method are compared with a number of special cases available in the literature. Viscous flows around a circular cylinder rotating in any arbitrary fashion possess an exact solution, as presented in Chapter 2. Two cases of this flow are chosen for comparison. In the first case the circular cylinder is initially given an impulsive twist such that it rotates with a constant velocity about its axis. In the second case, the angular velocity of the circular cylinder increases with time exponentially. For a Reynolds number of 100, based on the cylinder radius and the internal vorticity, the exact solutions are compared with the numerical results. Viscous flow around an elliptic cylinder of .0996 aspect ratio rotating with a constant angular velocity is another special case, available in the literature, which is chosen for comparison. For this case the Reynolds number, based on the cylinder semi-major-axis and internal vorticity is 202. The agreement in all above-mentioned cases is excellent. Finally, viscous flow around an elliptic cylinder of .25 aspect ratio undergoing a combined translation and pitching oscillation is presented. A Reynolds number of 500, based on the semi-major-axis and body translational velocity, is chosen for this case. No similar case has been reported until now. This case, however, is only one of the many cases that can be handled by the present method.

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A theoretical model was developed to predict the air distribution pattern and thus to design perforated ventilation ducts equipped with a fan. The analysis of the air distribution pattern of such systems requires accurate measurement procedures. Several experimental methods were tested and compared. Accordingly, the piezometric flush taps and thermo-anemometer were selected to measure respectively the duct air pressure and the outlet air flow. / Based on the equations of energy and momentum conservation, a model was formulated to predict the air flow performance of perforated ventilation ducts and to evaluate the outlet discharge angle and the duct regain coefficients without evaluating frictional losses. The basic assumptions of the model were validated by experimentally proving the equivalence of the friction losses expressed in the 2 cited equations. When compared to experimental results measured from four wooden perforated ventilation ducts with aperture ratios of 0.5, 1.0, 1.5, and 2.0, the model predicted the outlet air flow along the full length of perforated duct operated under turbulent flow conditions with a maximum error of 9%. The regain coefficient and the energy correction factor were equal to one, and the value of the discharge coefficient remained constant at 0.65, along the full length of the perforated duct. The outlet air jet discharge angle varied along the entire duct length, and was not influenced by friction losses for turbulent flow. / Assuming a common effective outlet area, the model was extended to match the performance of the fan and the perforated duct and to determine their balance operating point.