Characterization of heterogeneous soil hydraulic parameters of deep vadose zones is often difficult and expensive, making it necessary to rely on other sources of information. Pedotransfer functions (PTFs) based on soil texture data constitute a simple alternative to inverse hydraulic parameter estimation, but their accuracy is often modest. Inverse modeling entails a compromise between detailed description of subsurface heterogeneity and the need to restrict the number of parameters. We propose two methods of parameterizing vadose zone hydraulic properties using a combination of k-means clustering of kriged soil texture data, PTFs, and model inversion. One approach entails homogeneous and the other heterogeneous clusters. Clusters may include subdomains of the computational grid that need not be contiguous in space. The first approach homogenizes within-cluster variability into initial hydraulic parameter estimates that are subsequently optimized by inversion. The second approach maintains heterogeneity through multiplication of each spatially varying initial hydraulic parameter by a scale factor, estimated a posteriori through inversion. This allows preserving heterogeneity without introducing a large number of adjustable parameters. We use each approach to simulate a 95 day infiltration experiment in unsaturated layered sediments at a semiarid site near Phoenix, Arizona, over an area of 50 x 50 m(2) down to a depth of 14.5 m. Results show that both clustering approaches improve simulated moisture contents considerably in comparison to those based solely on PTF estimates. Our calibrated models are validated against data from a subsequent 295 day infiltration experiment at the site.

Slag, by itself, shows very little hydraulic activity. However, hydration is greatly accelerated by incorporation of the slag with Portland cement. This phenomenon is due to the activating role of calcium hydroxide released from the hydration of Portland cement. This study was aimed at finding other activators that will increase hydration in both synthetic and commercial slags. The effects of chemical composition and the aggregation state of the slag on the hydration process were also investigated. For the synthetic slags, the aggregation state was altered by different quenching techniques. The chemical composition was varied by synthesizing a series of slags. The degree of hydration was studied by developing a thermogravimetric analysis technique and the glass content was determined using microscopy. Minerals were determined using powder x-ray diffraction analysis.

A novel configuration of vertical downflow constructed wetland was used to treat up to 75 m3 per day of sugar beet processing wastewaters. The 403 m2, two-stage pilot system included planted and unplanted cells of a variety of sand depths (0.15 - 0.4 m) and sand particle size distributions (d10 = 0.07 - 1.2 mm). The hydraulic regime of each bed was also manipulated. Typical beet processing wastewaters contained 235 mg BOD l-1, 45 mg NH4-N l-1, 0.03 mg PO4-P l-1, 16 mg TSS l-1, at pH 8.2 and 29 °C. Overall performance of the pilot system, with respect to BOD, NH4-N, and TSS removal, was similar to, or better than, comparable two-stage vertical flow wetland systems. In vertical flow systems, influent BOD concentrations >600 mg l-1 were coincident with reduced rates of nitrification. Mean BOD removal rate in the pilot system was 38.8 g BOD m-2 d-1, with a mean loading rate of 40.4 g BOD m-2 d-1. The first-order reaction rate for BOD removal was calculated to be 0.369 m d-1 over the whole system. High rates of oxygen transfer and efficient removal of organic solids were seen as the most important factors enhancing BOD removal. Mean NH4-N removal rate in the pilot system was 5.6 g NH4-N m-2 d-1, with a mean loading rate of 7.3 g NH4-N m-2 d-1. The temperature corrected first-order reaction rate for NH4-N removal was calculated to be 0.23 m d-1 over the whole system. Nitrification accounted for between 85% and 99% of TKN removal. Evidence is presented which supports the hypothesis that cycles of assimilation/adsorption and release of NH4-N may play an important role in nitrification mechanisms in vertical flow constructed wetlands. In bed 1, removal of BOD and NH4-N were at their most efficient in the vegetated cell with the deepest (0.21 m), coarsest (d10 = 1.2 mm) sand layer. TSS removal was highest in an unvegetated cell with shallower (0.15 m), finer (d10 = 0.56 mm) sand. In bed 2, removal of BOD, NH4-N, and TSS were all at there most efficient in the vegetated cell with the deepest (0.4 m), coarsest (d10 = 0.1 mm) sand layer. Low influent phosphate concentrations may have limited nitrification rates in the pilot system. The surface area available for biofilm attachment, and media depth, both provided good models of NH4-N removal, whilst cell surface area was more important in solids removal. Media hydraulic conductivity at the beginning of the dosing cycle was five times higher in vegetated cells than in unvegetated cells. After 12 hours of dosing, media particle size distribution became the dominant factor determining media hydraulic conductivity. High influent BOD concentration was more closely associated with cell logging than hydraulic loading, TSS concentration, or BOD or TSS loading. Growth of one provenance of Phragmites australis was limited by phosphate availability. However, populations of nitrifying bacteria were highest in samples of media and roots taken from plots containing this provenance. No correlation was demonstrated between nitrifying bacteria population and root biomass. Water stress caused by high media hydraulic conductivity and inadequate influent distribution resulted in sub-optimal conditions for reed growth in bed 1. The study concludes with details of the proposed design of a full scale system designed to treat up to 1000 m3 d-1 of beet processing effluents.

Call number: LD2668 .T4 1986 V57 / Master of Science / Biological and Agricultural Engineering

Master of Science / Department of Civil Engineering / David G. Chandler / Infiltration capacity influences the ability of a soil to absorb and transmit water through macropores and micropores of the soil structure. Infiltration is primarily influenced by the soil type, which is dependent on a number of factors including parent material, climate, biological activity, and topography. Spatial controls of land use, land cover, soil texture, slope position, slope gradient and slope aspect are a few of the variables influencing infiltration capacity within a uniform soil type. The goals of the thesis are to (1) quantify the spatial distribution of soil hydraulic properties at the surface of a hillslope using one measurement method - the automated mini-disk tension infiltrometer - and several analysis methods, (2) determine the dependence of depth on soil hydraulic properties using two measurement methods, and (3) compare the results of the investigation with information from the soil survey and soil investigations. First, automated mini-disk infiltrometers were used to determine soil hydraulic properties at ten sites along a hillslope in Konza Prairie Natural Research Area. Several analysis methods were used to extract hydraulic conductivity and sorptivity values from the infiltration data. Next, large intact soil cores were extracted from three selected sites at the same hillslope and analyzed at six depths using a large disk infiltrometer. Finally, the six segments of the large soil cores were analyzed using the same methods as the field measurements with the mini-disk infiltrometers. The results of the field investigation at the ten sites show a variability of soil hydraulic properties over an assumed homogeneous landscape. The values of hydraulic conductivity and sorptivity are dependent on the method of analysis. An empirically based approach produced more realistic values than a physically based approach. The results of the laboratory investigation of the three extracted soil cores also show a dependence of method of analysis and measurement. In addition, the results show a complex relationship among landscape position, depth, and soil structure. Finally, while soil surveys and soil descriptions can provide detailed information on soil properties, an infiltration investigation at a detailed spatial scale provides quantitative values for soil hydraulic properties.

M.Ing. / The aim of this research was to investigate the use of stream processing on the graphics processing unit (GPU) and to apply it into the hydraulic modelling of a water distribution system. The stream processing model was programmed and compared to the programming on the conventional, sequential programming platform, namely the CPU. The use of the GPU as a parallel processor has been widely adopted in many different non-graphic applications and the benefits of implementing parallel processing in these fields have been significant. They have the capacity to perform from billions to trillions of floating-point operations per second using programmable shader programs. These great advances seen in the GPU architecture have been driven by the gaming industry and a demand for better gaming experiences. The computational performance of the GPU is much greater than the computational capability of CPU processors. Hydraulic modelling of water distribution systems has become vital to the construction of new water distribution systems. This is because water distribution networks are very complex and are nonlinear in nature. Further, modelling is able to prevent and anticipate problems in a system without physically building the system. The hydraulic model that was used was the Gradient Method, which is the hydraulic model used in the EPANET software package. The Gradient Method produces a linear system which is both positive-definite and symmetric. The Cholesky method is currently being used in the EPANET algorithm in order to solve the linear equations produced by the Gradient Method. Thus, a linear solution method had to be selected for the use in both parallel processing on the GPU and as a hydraulic network solver. The Conjugate Gradient algorithm was selected as an ideal algorithm as it works well with the hydraulic solver and could be converted into a parallel algorithm on the GPU. The Conjugate Gradient Method is one of the best-known iterative techniques used in the solution of sparse symmetric positive definite linear systems. The Conjugate Gradient Method was constructed both in the sequential programming model and the stream processing model, using the CPU and the GPU respectively on two different computer systems. The Cholesky method was also programmed in the sequential programming model for both of the computer systems. A comparison was made between the Cholesky and the Conjugate Gradient Methods in order to evaluate the two methods relative to each other. The findings in this study have shown that stream processing on the GPU can be used in the parallel GPU architecture in order to perform general-purpose algorithms. The results further affirmed that iterative linear solution methods should only be used for large linear systems.

This thesis describes an investigation into the effect of fluid and flow parameters on cavitation dynamics and cavitation erosion. A rotating disc test apparatus was developed fo: dow-type cavitation studies. A vibratory test device was also developed to study the role of cathodic and anodic potentials applied to cavitating bodies. Some major results are given below. Erosion "peaksat about 50°C in water, but under certain conditions material degradation caused by increased corrosion rate cancels out thermodynamic effects at higher temperatures. An erosion peak is also observed as a function of static pressure. Damage increases with velocity until cavitation is fully developed, at which stage the influence of velocity becomes negligible. The changes in erosion zone geometry and mass loss caused by temperature, velocity and pressure variations may be correlated with the effect these parameters have on the cavitation pressure profile. Efforts are described to develop a system for measuring this profile in the rotating disc device. Water quality including dissolved ions, as well as solid and gas impurities, influences both cavitation inception and the amount of cavitation damage caused. The synergism between cavitation erosion and corrosion causes high damage rates in corrosive, cavitating liquids. Solid impurities at medium concentrations may enhance or retard cavitation damage substantially, depending on the physical properties of the solid. Below the saturation level, increasing concentration of dissolved air in water results in a slight decrease in damage, but damage can be almost completely eliminated by the release of air bubbles into the cavitation region. Another important result is that the gas developed by the application of external potentials to a cavitating body provides protection against cavitation erosion through a gas cushioning mechanism. Cathodic protection of cavitating bodies will thus serve to decrease damage rates even in the case of corrosion-resistant materials like stainless / GR 2016

A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, South Africa, in fulfilment of the requirements for the degree of Doctor of Philosophy, 2013. / The aim of the thesis is to derive group invariant, exact, approximate analytical and numerical solutions for a two-dimensional laminar, non-Newtonian pre-existing hydraulic fracture propagating in impermeable and permeable elastic media. The fracture is driven by the injection of an incompressible, viscous non-Newtonian fluid of power law rheology in which the fluid viscosity depends on the magnitude of the shear rate and on the power law index n > 0. By the application of lubrication theory, a nonlinear diffusion equation relating the half-width of the fracture to the fluid pressure is obtained. When the interface is permeable the nonlinear diffusion equation has a leak-off velocity sink term. The half-width of the fracture and the net fluid pressure are linearly related through the PKN approximation. A condition, in the form of a first order partial differential equation for the leak-off velocity, is obtained for the nonlinear diffusion equation to have Lie point symmetries. The general form of the leak-off velocity is derived. Using the Lie point symmetries the problem is reduced to a boundary value problem for a second order ordinary differential equation. The leak-off velocity is further specified by assuming that it is proportional to the fracture half-width. Only fluid injection at the fracture entry is considered. This is the case of practical importance in industry. Two exact analytical solutions are derived. In the first solution there is no fluid injection at the fracture entry while in the second solution the fluid velocity averaged over the width of the fracture is constant along the length of the fracture. For other working conditions at the fracture entry the problem is solved numerically by transforming the boundary value problem to a pair of initial value problems. The numerical solution is matched to the asymptotic solution at the fracture tip. Since the fracture is thin the fluid velocity averaged over the width of the fracture is considered. For the two analytical solutions the ratio of the averaged fluid velocity to the velocity of the fracture tip varies linearly along the fracture. For other working conditions the variation is approximately linear. Using this observation approximate analytical solutions are derived for the fracture half-width. The approximate analytical solutions are compared with the numerical solutions and found to be accurate over a wide range of values of the power-law index n and leak-off parameter β. The conservation laws for the nonlinear diffusion equation are investigated. When there is fluid leak-off conservation laws of two kinds are found which depend in which component of the conserved vector the leak-off term is included. For a Newtonian fluid two conservation laws of each kind are found. For a non-Newtonian fluid the second conservation law does not exist. The behaviour of the solutions for shear thinning, Newtonian and shear thickening fluids are qualitatively similar. The characteristic time depends on the properties of the fluid which gives quantitative differences in the solution for shear thinning, Newtonian and shear thickening fluids.

A dissertation submitted to the Faculty of Science,University of the Witwatersrand, in fulfilment of the requirements for the degree of Master of Science. December 2016. / This research is concerned with the analysis of a two-dimensional Newtonian fluid-driven fracture in a permeable rock. The fluid flow in the fracture is laminar and the fracture is driven by the injection of a Newtonian fluid into it. Most of the problems in litera- ture involving fluid flow in permeable rock formation have been modeled with the use of Darcy's law. It is however known that Darcy's model breaks down for flows involv- ing high fluid velocity, such as the flow in a porous rock formation during hydraulic fracturing. The Forchheimer flow model is used to describe the non-Darcy fluid flow in the porous medium. The objective of this study is to investigate the problem of a fluid-driven fracture in a porous medium such that the flow in the porous medium is non-Darcy. Lubrication theory is applied to the system of partial di erential equations since the fracture that is considered is thin and its width slowly varies along its length. For this same reason, Perkins-Kern-Nordgren approximation is adopted. The theory of Lie group analysis of differential equations is used to solve the nonlinear coupled sys- tem of partial differential equations to obtain group invariant solutions for the fracture half-width, leak-o depth and length of the fracture. The strength of fluid leak-off at the fracture wall is classi ed into three forms, namely, weak, strong and moderate. A group invariant solution of the traveling wave form is obtained and an exact solution for the case in which there is weak fluid leak-off at the interface is found. A dimensionless parameter, F0, termed the Forchheimer number was obtained and investigated. Nu- merical results are obtained for both the case of Darcy and non-Darcy flow. Computer generated graphs are used to illustrate the analytical and numerical results. / MT2017

A research report submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, in partial fulfillment of the requirements for the degree of Master of Science in Engineering Johannesburg, 2017 / The development of methods which are better able to predict the effect of large scale emergent roughness elements on the flow characteristics requires a better understanding of the drag coefficient under conditions likely to occur in the field. A laboratory investigation was carried out with newly developed equipment to quantify the drag force on various shaped cylinders, as well as the drag on an individual cylinder surrounded by an array of cylinders. The relationship between the drag coefficient and cylinder Reynolds number for a single circular cylinder was found to be of similar form but larger in magnitude than the established relationship for an infinitely long cylinder; the relationship departs from the infinite cylinder relationship for low cylinder Reynolds numbers. Contrary to previous research, the results for the multiple cylinder investigation did not reveal a clear relationship between the cylinder density and drag coefficient. Equations were developed and verified with existing laboratory data. These should be improved and extended by further research for field use. / MT2017