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Stellar structure is investigated within the framework of scalar-tensor gravity. Novel perturbative analytical results are obtained for constant-density stars and for Newtonian polytropes in the quadratic model with coupling function A(Φ) = exp(αΦ+1/2βΦ^2). They are compared to full numerical calculations, and possible applications to main-sequence stars, white dwarfs, and the Chandrasekhar mass are indicated. It is found that Buchdahl's theorem is violated in Brans-Dicke theory for stars with exponentially-decaying density profiles. However, the mass-to-radius ratio M/R tends to the constant-density value in a certain limit. It is observed that for β < 0, there exists a maximum value of η = P0/ρo for constant-density stars, where P0 and ρ0 are the central pressure and density, respectively. It is conjectured that if such a maximum value also exists for other equations of state, and is less than the constant-density maximum value, then knowledge of P/ρ in the centre of a star can be used to constrain β. / Thesis / Master of Science (MSc)

Yes / A novel Euler-Lagrangian (EL) computational uid dynamics (CFD) nite volume-based model to simulate the gas mixing of sludge for anaerobic digestion is developed and described. Fluid motion is driven by momentum transfer from bubbles to liquid. Model validation is undertaken by assessing the ow eld in a labscale model with particle image velocimetry (PIV). Conclusions are drawn about the upscaling and applicability of the model to full-scale problems, and recommendations are given for optimum application.

Yes / For the first time, an Euler-Lagrange model for Computational Fluid Dynamics (CFD) is used to model a full-scale gas-mixed anaerobic digester. The design and operation parameters of a digester from a wastewater treatment works are modelled, and mixing is assessed through a novel, multi-facetted approach consisting of the simultaneous analysis of (i) velocity, shear rate and viscosity flow patterns, (ii) domain characterization following the average shear rate value, and (iii) concentration of a non-diffusive scalar tracer. The influence of sludge’s non-Newtonian behaviour on flow patterns and its consequential impact on mixing quality were discussed for the first time. Recommendations to enhance mixing effectiveness are given: (i) a lower gas mixing input power can be used in the digester modelled within this work without a significant change in mixing quality, and (ii) biogas injection should be periodically switched between different nozzle series placed at different distances from the centre. / The first author is funded via a University of Birmingham Postgraduate Teaching Assistantship award.

Yes / For the first time, a set of Lattice-Boltzmann two-way coupling pointwise Euler-Lagrange models is applied to gas mixing of sludge for anaerobic digestion. The set comprises a local model, a “first-neighbour” (viz., back-coupling occurs to the voxel where a particle sits, plus its first neighbours) and a “smoothing-kernel” (forward- and back-coupling occur through a smoothed-kernel averaging procedure). Laboratory-scale tests display grid-independence problems due to bubble diameter being larger than voxel size, thereby breaking the pointwise Euler-Lagrange assumption of negligible particle size. To tackle this problem and thereby have grid-independent results, a novel data-scaling approach to pointwise Euler-Lagrange grid independence evaluation, based on an application of the Buckingham π theorem, is proposed. Evaluation of laboratory-scale flow patterns and comparison to experimental data show only marginal differences in between the models, and between numerical modelling and experimental data. Pilot-scale simulations show that all the models produce grid-independent, coherent data if the Euler-Lagrange assumption of negligible (or at least, small) particle size is recovered. In both cases, a second-order convergence was achieved. A discussion follows on the opportunity of applying the proposed data-scaling approach rather than the smoothing-kernel model.

A basic experimental study of the aerodynamic breakup of a viscoelastic non-Newtonian liquid injected into a supersonic stream was conducted. All test runs were made either at a free stream Mach number of 2.4 and a total pressure of 4.1 atm or a Mach number of 4.0 and a total pressure of 10.9 atm. The air flow had a total temperature of 300 K, and the injectant was always at room temperature. The injectant used for the majority of the test runs was diethylmalonate thickened with polymethyl-methacrylate, which has the characteristics of being viscoelastic. A limited number of test runs were made with glycerin in order to make a comparison between the behavior of Newtonian and viscoelastic non-Newtonian fluids. Several areas concerning the disintegration of the viscoelastic non-Newtonian fluid were investigated, including the effects of free stream Mach number, injection velocity, jet diameter, twin in-line jets, injection angle, and injector shape. Spark Shadowgraphs of 1.2 microsecond duration and high speed movies were obtained to qualitatively appraise the breakup behavior. The breakup of the jet was found to be a function of free stream Mach number and jet diameter, injection angle, and frontal area. It also was observed that the breakup behavior of the viscoelastic non-Newtonian fluid is remarkably different from that of (Newtonian) glycerin. The time scales for breakup are substantially increased regarding the dissemination of the viscoelastic liquid as compared to the Newtonian glycerin. Furthermore, penetration of the viscoelastic non-Newtonian fluid was observed to be on the order of 50% less than that measured for glycerin at comparable injection conditions. / Master of Science

This thesis presents a simulation model of sliding process of friction, which combines Newtonian particle dynamics and finite element method to study friction mechanisms that bridging micro and macro scales. In the thesis, it first reviews the importance of studying pavement friction that is associated to safety of drivers, society economics and environmental impact. Then, the hybrid numerical methods of Newtonian particle dynamics and finite element method have been introduced, and the rules to bridge these two methods also have been discussed for solid material that assumes the forces and displacements are continuous at the interface of these two methods. The fundamental theories of friction mechanisms are built upon the surface roughness, adhesion and deformation at the contact between two surfaces. At last, the simulation model of sliding process is presented with the hybrid method, and its visualization and result analysis has been given. At the same time, this thesis also includes the procedures of establishing the simulation of the hybrid methods with C++ programming like the program framework, structure and the major pieces of the program. / Master of Science

This thesis is concerned with a theoretical and experimental study of the hydrodynamics and heat transfer characteristics of viscous fluids flowing in tubes under laminar conditions. Particular attention has been given to the effects of the rheological properties and their variation with temperature. A review of problems of this type showed that in spite of the many potential applications of the results in a wide range of industries the subject had not been well developed and further work is justified in order to fill some of the gaps in our knowledge. The early part of the thesis considers the justification of the work in this way and sets down the scope and objectives. A computer progracune was then developed to allow the governing equations of the problem to be solved numerically to give the velocity and temperature profiles and pressure drop for both heating and cooling conditions. The results were also presented in the form of Nusselt numbers as a function of the Graetz numberp since this form is useful for engineering design purposes. The validity of the predictions were then checked by a programme of experimental work. Temperature and velocity profiles have been measured in order to provide a more severe test of the theory than could be imposed by the measurement of overall heat transfer rates. A combined thermocouple probe/Pitot tube was developed to allow simultaneous measurements of velocity and temperature to be made. A Newtonian oil and two non-Newtonian Carbopol solutions were studied. This is the first time that velocity and temperature profiles have been measured for non-Newtonian fluids in this type of situation. The results of the work heve shown that (a) the velocity and temperature profiles and pressure drops are greatly affected by the temperature dependence of the rheological properties and since real viscous fluids are normally very temperature-sensitive it is important that this effect is properly taken into account. (b) the engineering design correlations commonly used for the prediction of heat transfer coefficients can be seriously in error, especially for cooling conditions and when non-Nevitonian fluids are being considered. (c) a mathematical model can be developed which accurately describes all the phenomena and gives predictions which are very close to those observed experimentally. An important objective was to develop more accurate engineering design correlations for non-isothermal pressure drop and heat transfer rates.

In this thesis, we review some basic properties of the Einstein-aether gravity. We derive the field equations from an action and study a subclass of this theory corresponding to the Einstein-Maxwell like theory. We also show that the G&ouml / del type metrics are also exact solutions of this theory. Furthermore, we determine the observational constraints on the dimensionless preferred parameters of this theory using the parametrized post- Newtonian formalism. We stress that none of calculations and discussions are original in this thesis.

The process of fluid injection into granular media is relevant to a wide number of applications such as enhanced oil recovery, grouting, and the construction of permeable reactive barriers. The response of the subsurface is dependent on multiple factors such as in-situ stresses, fluid properties, flow rate, and formation type. Based on these conditions a variety of response mechanisms can be initiated ranging from simple porous infiltration to hydraulic fracturing. Currently, the mechanics of fluid injection into competent rock are well understood and can be sufficiently modeled using linear elastic fracture mechanics. Because the grains in rock formations are individually cemented together, they exhibit cohesion and are able to support tensile stresses. The linear elastic method assumes tensile failure due to stress concentrations at the fracture tip. A fracture propagates when the stress intensity factor exceeds the material toughness (Detournay, 1988) However, understanding fluid injection in cohesionless granular media presents a much larger obstacle. Currently, no theoretical models have been developed to deal with granular media displacements due to fluid injection. Difficulty arises from the complexity of fluid rheology and composition used in engineering processes, the strong coupling between fluid flow and mechanical deformation, the non-linear response of subsurface media, and the multi-scale nature of the problem. The structure of this thesis is intended to first give the reader a basic background of some of the fundamental concepts for non-Newtonian fluid flow in granular media. Fluid properties as well as some interaction mechanisms are described in relation to the injection process. Next, the results from an experimental series of injection tests are presented with a discussion of the failure/flow processes taking place. We developed a novel technique which allows us to visualize the injection process by use of a transparent Hele-Shaw cell. Specifically, we will be using polyacrylamide solutions at a variety of concentrations to study non-Newtonian effects on the response within the Hele-Shaw cell. By performing tests at a range of solution concentrations and injection rates we are to be able to identify a transition from an infiltration dominated flow regime to a fracturing dominated regime.