Thesis (MSc (Mathematical Sciences. Applied Mathematics))--University of Stellenbosch, 2007. / The understanding and quantitative description of fluid flowthrough porousmedia, is a science which has been going on for many years and investigated in a variety of disciplines. Studies in this field have primarily been based on models, which can either be described as empirical or theoretical. Part of the current study is to understand fluid flow in porous media through studying three recent theoretical pore-scale models based on the concept of a Representative Unit Cell (RUC), to represent a porous medium. Amongst other assumptions, these models assumed plane Poiseuille flow throughout each pore section of a rectangular RUC. The main objective of this study is to numerically verify this assumption using Computational Fluid Dynamics (CFD) software, FLUENT version 6.2.16. Attention is also paid to comparison between these models with the experimental data, obtained during the model tests of airflow through a timber stack end, undertaken in a wind tunnel. The laminar and intermediate airflow through a timber stack end is simulated using the commercial software FLUENT, and the results are validated against the theoretical pore-scale models and experimental data. Two turbulence models which are, the Standard k − e and Reynolds-Stress models are used in these computations, the aimbeing to determine howwell they are able to reproduce the experimental data. The numerical results are in good agreement with one of the theoretical models presented and the experimental data.

Dissertation submitted in fulfilment of the requirements for the Masters Degree in Technology: Chemical Engineering in the Department of Chemical Engineering of Cape Peninsula University ofTechnology, 2005 / The emulsion used for this study is a new thermodynamically unstable multi-component waterin- oil (w/o) explosive type with an internal phase ratio of approximately 94%, i.e. far beyond the close packing limit of spherical droplets of 74%. Economic considerations and the ongoing need for continuous drilling, loading and blasting in the mining industry, has made long-distance pipeline transportation of these emulsion explosive systems a viable economic option. Presently, rheological characterization of emulsion explosives is well documented (Bampfield & Cooper, 1988, Utracki, 1980). However, very little or none has been done for this system, pertaining to the use of rheometry for prediction of pumping characteristics of these systems in long-distance pipeline transport. This Master's dissertation is devoted to develop rheological methods of testing, characterization and correlation in order to develop a basis for predicting the pumping characteristics of highly concentrated w/o emulsion explosives from rheometry. The literature and theory pertinent to the pipeline flow of high internal phase ratio emulsion explosives are presented, as well as the fundamentals of both concentric cylinder rheometry and pipe viscometry. The most relevant is the work of Bampfield and Cooper (1988), Utracki (1980) and Pal (1990). Two experimental test facilities were used for data collection. Pipeline experiments were done using an experimental test facility at African Explosives Limited (AEL), and rheometry was conducted at the Rheology Laboratory of the Cape Peninsula University of Technology Flow Process Research Centre. The AEL experimental test facility consisted of a four-stage Orbit progressive cavity pump, two fluid reservoirs, (a mixing tank and a discharge reservoir), five 45m HOPE (high density polyethylene) pipes of internal diameters of 35.9 mm, 48.1 mm, 55.9 mm, 65.9 mm and 77.6 mm pipes. The test work was done over a wide range of laminar flow rates ranging from 3 kg.min-I to 53 kg.min-I . Rheometry was done using a PaarPhysica MCR300 rheometer, and only standard rotational tests (i.e. flow curve) at 30 °c in controlled rate mode were done. Rheological characterisation was done using three rheological models, i.e. the Herschel-Bulkley, the Power Law and the Simplified Cross models. The coefficients obtained from these models were then used to predict pumping characteristics. The performances of these models were then evaluated by comparing the pipeline flow prediction to the actual pipeline data obtained from pipeline test experiments. It was found that the flow behaviour depicted by this explosive emulsion system was strongly non-Newtonian, and was characterized by two distinct regions of deformation behaviour, a lower Newtonian region of deformation behaviour in the shear rate region lower than 0.001 S-I and a strong shear thinning region in the shear rate range greater than 0.001 S-l. For all the models used for this study, it was evident that rheometry predicts the pumping characteristics of this high internal phase ratio emulsion reasonably well, irrespective of the choice of the model used for the predictions. It was also seen that the major difference between these models was in the lower shear rate domain. However, the Simplified Cross model was preferred over the other two models, since its parameter (the zero shear viscosity denoted by 110) can in general be correlated to the structure of the emulsion systems (i.e. mean droplet size, bulk modulus, etc.). Thus, structural changes induced by shearing (either inside the pump or when flowing inside a pipe) can be detected from changes in the value of the 110. The above statement implies that Tlo can be used as a quality control measure. Different pumping speeds were found to cause different degrees of shear-induced structural changes which were manifested by two opposing processes. These two opposing processes were the simultaneous coalescence and flocculation of droplets encountered at low rates of shear, and the simultaneous refinement and deflocculation of droplets encountered at high rates of shear. These two droplet phenomena were associated with a decrease or an increase in viscous effects, leading to both lower and higher viscous stresses and pumping pressures during pump start-up respectively.

An Ocean Current Turbine (OCT) numerical simulation for creating, testing and tuning flight and power takeoff controllers, as well as for farm layout optimization is presented. This simulation utilizes a novel approach for analytically describing oceanic turbulence. This approach has been integrated into a previously developed turbine simulation that uses unsteady Blade Element Momentum theory. Using this, the dynamical response and power production of a single OCT operating in ambient turbulence is quantified. An approach for integrating wake effects into this single device numerical simulation is presented for predicting OCT performance within a farm. To accomplish this, far wake characteristics behind a turbine are numerically described using analytic expressions derived from wind turbine wake models. These expressions are tuned to match OCT wake characteristics calculated from CFD analyses and experimental data. Turbine wake is characterized in terms of increased turbulence intensities and decreased mean wake velocities. These parameters are calculated based on the performance of the upstream OCT and integrated into the environmental models used by downstream OCT. Simulation results are presented that quantify the effects of wakes on downstream turbine performance over a wide range of relative downstream and cross stream locations for both moored and bottom mounted turbine systems. This is done to enable the development and testing of flight and power takeoff controllers designed for maximizing energy production and reduce turbine loadings. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2016. / FAU Electronic Theses and Dissertations Collection

This thesis examines the elegant theory of polar and Legendre duality, and its potential use in convex geometry and geometric analysis. It derives a theorem of polar - Legendre duality for all convex bodies, which is captured in a commutative diagram. A geometric flow on a convex body induces a distortion on its polar dual. In general these distortions are not flows defined by local curvature, but in two dimensions they do have similarities to the inverse flows on the original convex bodies. These ideas can be extended to higher dimensions. Polar - Legendre duality can also be used to examine Mahler's Conjecture in convex geometry. The theory presents new insight on the resolved two-dimensional problem, and presents some ideas on new approaches to the still open three dimensional problem.

Indiana University-Purdue University Indianapolis (IUPUI) / We numerically investigate the underlying physics of two peculiar phenomena, which are axis-switching and saddle-back velocity profile, in both laminar and turbulent rectangular jets using lattice Boltzmann method (LBM). Previously developed computation protocols based on single-relaxation-time (SRT) and multiple-relaxation-time (MRT) lattice Boltzmann equations are utilized to perform direct numerical simulation (DNS) and large eddy simulation (LES) respectively. In the first study, we systematically study the axis-switching behavior in low aspect-ratio (AR), defined as the ratio of width over height, laminar rectangular jets with <italic>AR=1</italic> (square jet), 1.5, 2, 2.5, and 3. Focuses are on various flow properties on transverse planes downstream to investigate the correlation between the streamwise velocity and secondary flow. Three distinct regions of jet development are identified in all the five jets. The <italic>45&deg</italic> and <italic>90&deg</italic> axis-switching occur in characteristic decay (CD) region consecutively at the early and late stage. The half-width contour (HWC) reveals that <italic>45&deg</italic> axis-switching is mainly contributed by the corner effect, whereas the aspect-ratio (elliptic) feature affects the shape of the jet when <italic>45&deg</italic> axis-switching occurs. The close examinations of flow pattern and vorticity contour, as well as the correlation between streamwise velocity and vorticity, indicate that <italic>90&deg</italic> axis-switching results from boundary effect. Specific flow patterns for <italic>45&deg</italic> and <italic>90&deg</italic> axis-switching reveal the mechanism of the two types of axis-switching respectively. In the second study we develop an algorithm to generate a turbulent velocity field for the boundary condition at jet inlet. The turbulent velocity field satisfies incompressible continuity equation with prescribed energy spectrum in wave space. Application study of the turbulent velocity profile is on two turbulent jets with <italic>Re=25900</italic>. In the jets with <italic>AR=1.5</italic>, axis-switching phenomenon driven by the turbulent inlet velocity is more profound and in better agreement with experimental examination over the laminar counterpart. Characteristic jet development driven by both laminar and turbulent inlet velocity profile in square jet (<italic>AR=1</italic>) is also examined. Overall agreement of selected jet features is good, while quantitative match for the turbulence intensity profiles is yet to be obtained in future study. In the third study, we analyze the saddle-back velocity profile phenomenon in turbulent rectangular jets with AR ranging from 2 to 6 driven by the developed turbulent inlet velocity profiles with different turbulence intensity (<italic>I</italic>). Saddle-back velocity profile is observed in all jets. It has been noted that the saddle-back's peak velocities are resulted from the local minimum mixing intensity. Peak-center difference <italic>&Delta_pc</italic> and profound saddle-back (PSB) range are defined to quantify the saddle-back level and the effects of AR and <italic>I</italic> on saddle-back profile. It is found that saddle-back is more profound with larger AR or slimmer rectangular jets, while its relation with <italic>I</italic> is to be further determined.