Dissertation submitted in fulfilment of requirements for the degree Master Technology: Chemical Engineering in the FACULTY OF ENGINEERING at the CAPE PENINSULA UNIVERSITY OF TECHNOLOGY, 2009 / The prediction of the energy losses when designing pipeline and pumping systems requires accurate loss coefficient data. But the loss coefficient data found in the open literature was not adequate for predicting the loss coefficient for Saunders straight-through diaphragm valves. As more accurate loss coefficient data to enable more efficient pipeline designs are scarce in the open literature, it is problematic to predict the head loss due to the pipeline fittings, and particularly for diaphragm valves. Most of the data given in the literature are for turbulent flow based on water. Due to water shortages mining operations are forced to increase their solids concentrations and to operate in laminar flow (Slatter, 2002). Consequently there is a need to determine loss coefficient data in laminar flow for valves used in these industries to ensure energy efficient designs (Pienaar et al., 2001; 2004) or if needed, to derive a new correlation to predict losses through Saunders diaphragm valves. However, a systematic study of various sizes of diaphragm valves of different manufacturers to ascertain, if the same loss coefficient can be applied, has never been done. Therefore a comparison will be made between the data produced in this work and the existing correlations. The objective of this research was to determine loss coefficient data in laminar, transitional and turbulent flow for the Saunders type straight-through diaphragm valves ranging from 40 mm to 100 mm in the fully open, 75 %, 50 % and 25 % open positions, using a range of Newtonian and non-Newtonian fluids. The test work was conducted on the valve test rig in the Flow Process Research Centre at the Cape Peninsula University of Technology. This work investigated only Newtonian and time independent homogeneous non-Newtonian fluids or slurries flowing through Saunders straight-through diaphragm valves in the turbulent, transitional and laminar regimes. Weir-type Saunders valves and time-dependent fluid behaviour were not investigated in this study. Preamble Non-Newtonian Loss Coefficients for Saunders Diaphragm Valves A Mume Kabwe The results for each test are presented in the form of valve loss coefficient (kvalve) against Reynolds number (Re). This thesis adds new loss coefficient data to the open literature, and a new correlation, which will be useful for designing pipelines in industries, as well as contributing to the academic debate in this discipline.

Thesis (MTech (Mechanical Engineering))--Peninsula Technikon, 1999 / Since 1996, a team at the Centre for Research in Applied Technology (CRATECH) at Peninsula Technikon, under NRF sponsorship and with industrial co-operation, has been involved in the simulation of Non-Newtonian flow behaviour in industrial processes, in particular, injection moulding of polymers. This study is an attempt to deal with some current issues of Non-Newtonian flow, in small areas, from the viewpoint of computational mechanics. It is concerned with the numerical simulation of Non-Newtonian fluid flows in mould cavities with re-entrant corners. The major complication that exists in this numerical simulation is the singularity of the stresses at the entry of the corner, which is responsible for nonintegrable stresses and the propagation of solution errors. First, the study focuses on the derivation of the equations of motion of the flow which leads to Navier- Stokes equations. Thereafter, the occurrence of singularities in the numerical solution of these equations is investigated. Singularities require special attention no matter what numerical method is used. In finite element analysis, local refinement around the singular point is often employed in order to improve the accuracy. However, the accuracy and the rate of convergence are not, in general, satisfactory. Incorporating the nature of singularity, obtained by an asymptotic analysis in the numerical solution, has proven to be a very effective way to improve the accuracy in the neighborhood of the singularity and, to speed up the rate of convergence. This idea has been successfully adopted in solving mainly fracture mechanics problems by a variety of methods: finite difference, finite elements, boundary and global elements, and spectral methods. In this thesis, the singular finite elements method (SFEM), similar in principle to the crack tip element used in fracture mechanics, is proposed to improve the solution accuracy in the vicinity of the singular point and to speed up the rate of convergence. This method requires minor modifications to standard finite element schemes. Unfortunately, this method could not be implemented in this study due to the difficulty in generating the mesh for the singular element. Only the standard finite element method with mesh refinement has been used. The results obtained are in accordance with what was expected.

Thesis (MTech (Chemical Engineering))--Cape Peninsula University of Technology, 2008. / Certain non-Newtonian fluids exhibit a yield stress which can be measured with a variety of instruments varying from very sophisticated rotary and tube viscometers to hand-held slump cones and cylinders of various sizes. Accurate yield stress measurement is significant for process design and disposal operations for thickenend tailings. The slump value was first related to the yield stress by Murata (1984). Later, that work was corrected by Christensen (1991) for an error in the mathematical analysis. Slump, based on a circular cylindrical geometry was first investigated by Chandler (1986). These concepts led to the study by Pashias et al., (1996) that formed the basis for the current research. The Flow Process Research Centre (FPRC) at the Cape Peninsula University of Technology developed a slump meter designed to lift the cone or cylinder vertically at controlled lifting speeds. In addition the simple hand-held cylinder which is an adaptation of slump cones which were originally developed by the concrete industry to determine the flowability of fresh concrete was also used. The vane technique was used as a control. Cones and cylinders made of stainless steel and PVC were fitted to the slump meter. The yield stresses of four non-Newtonian fluids at different concentrations were tested in four different configurations at different lift speeds to ascertain whether the measuring position, lift speed, slip, geometry, wall surface material, and stability has an effect on the value of yield stress measured. The effect of different predictive models was also ascertained.The cylinder, lump and cone models relating slump to yield stress was used in the dimensional analysis of the results. The objective of this work was to determine if the slump tests (cone, cylinder and the hand-held cylinder) would generate yield stress values comparable to those found using the vane technique. It was establised that there was no significant effect of lift speed, stability, geometry and wall surface material on the value of yield stress. The effect of measuring position on the value of yield stress calculated gave a difference of 25%. Using dimensional analysis, the lump model (Hallbom, 2005) more accurately predicts the material yield stress when using the hand-held cylinder as well as all the cone results (due to its specific geometry), and cylinder configurations, thus affirming the work of Clayton et al., 2003. It is concluded that, although the materials and concentrations tested induced errors within 40%, the hand-held cylinder shows promise as a reliable, quick and simple way of measuring the yield stress.

Thesis (MTech (Chemical Engineering))--Cape Peninsula University of Technology, 2009. / This study investigated water-in-oil (WIG) super-concentrated emulsions used as pumpable explosives. The aqueous phase of the emulsions is a supersaturated nitrate salt solution (at room temperature), with a volume fraction usually greater than 0.8. Aqueous phase droplets are deformed by packing and contact with neighbouring droplets. Compounds of this kind are thermodynamically unstable and their instability is related to the coarsening of emulsions (droplet coalescence) and phase transition (crystallisation) in the dispersed phase. However, it was demonstrated that the dominating mechanism is slow crystallisation inside the supercooled droplets. The main goal of this thesis therefore concerned a phenomenological study of the dependence of type and concentration of surfactant, as well as the ageing processes, on the rheological properties of these emulsions. The bulk rheological measurements were carried out using a rotational dynamic rheometer MCR 300 (Paar Physica). Samples of different types of surfactant (Pibsa-MEA, Pibsa-UREA, Pibsa-IMIDE, SMO and SMO/Pibsa-MEA) and different concentrations of surfactants were studied. The results of the measurements include the flow and viscoelastic properties of the materials. The rheological parameters have been correlated with the kinetics of structural changes during ageing as a function of emulsion formulation content. The emulsions under study were non-Newtonian liquids. It was demonstrated that different surfactant types yield different interfacial properties. In fact, both the interfacial tension and the interfacial elastic modulus were found to decrease according to the sequence MEA-UREAMEAlSMG- IMIDE-SMG. It was established that the surfactant type and surfactant concentration affected the bulk rheological properties of explosive emulsions. Indeed, both the elastic modulus and the yield stress as function of surfactant type decreased in the following order: MEA-IMIDE-UREA-MEAlSMG, whereas they also decreased as the surfactant concentration increased. However the sensitivity of the rheological parameters to the type or concentration of surfactant was found to decrease as the droplet size increased. Moreover, the changes in rheological parameters were more strongly expressed than any changes in interfacial tension. This last finding is considered as rather important. It seems reasonable to assume that it provides proof of an active role of a surfactant not only as a compound responsible for the interfacial tension, but also creating additional sources of elasticity.

Thesis (MTech (Mechanical Engineering))--Cape Peninsula University of Technology, 2016. / This dissertation presents how material properties (solids densities, particle size distributions, particle shapes and concentration) of gold tailings slurries are related to their rheological parameters, which are yield stress and viscosity. In this particular case Bingham yield stresses and Bingham plastic viscosities. Predictive models were developed from analysing data in a slurry database to predict the Bingham yield stresses and Bingham plastic viscosities from their material properties. The overall goal of this study was to develop a validated set of mathematical models to predict Bingham yield stresses and Bingham plastic viscosities from their material properties. The interaction of the non-Newtonian material properties is very complex at varying mass solids concentrations. The evaluation of these interactions in terms of constitutive equations is almost impossible and the relationship between material properties, mass solids concentration and rheology can only be modelled in a statistical manner. The validity of each model is checked to ensure that predictions and interpretations are unbiased and efficient. This is done by comparing the resulting models to experimental data generated from test work. An in-depth analysis was conducted to see the interrelationship between the material properties and how they affect the yield stress and viscosity values.

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, South Africa, in ful lment of the requirements for the degree of Masters of Science. May 27, 2015. / Abstract The unsteady three-dimensional ow of a thin slender rivulet of incompressible Newtonian uid down an inclined porous plane is investigated. The leak-o velocity is not speci ed in the model but is determined in the process of deriving the invariant solution. A second order nonlinear partial di erential equation in two spatial variables and time and containing the leak-o velocity is derived for the height of the thin slender rivulet. Using Lie group analysis it is found that the partial di erential equation can be reduced in two steps to an ordinary di erential equation provided the leak-o velocity satis es a rst order linear partial di erential equation in three variables. An exact analytical solution with a dry patch in the central region is derived for a special leak-o velocity. Two models are considered, one with the leak-o velocity proportional to the height of the rivulet and the other with leak-o velocity proportional to the cube of the height. Numerical solutions are obtained for the height of the rivulet using a shooting method which also determines the two-dimensional boundary of the rivulet on the inclined plane. The e ect of uid leak-o on the height and width of the rivulet is investigated numerically and compared in the two models. The conservation laws for the partial di erential equation with no uid leak-o are investigated. Two conserved vectors are derived, the elementary conserved vector and a new conserved vector. The Lie point symmetry of the partial di erential equation associated with each conserved vector is obtained. Each associated Lie point symmetry is used to perform a double reduction of the partial di erential equation, but the solutions obtained are not physically signi cant.

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The velocity fields around a circular cylinder in a crossflow of drag-reducing polymeric solutions and water were experimentally investigated using a laser-Doppler velocimeter. Measured boundary-layer velocity profiles indicated that the flow parameter controlling the drag on a bluff body in drag-reducing flows is the turbulence intensity rather than the Reynolds number. For turbulence intensity less than 0.7% polymer addition induced delayed separation. For turbulence intensity over 1% the opposite effect was true. Time-averaged velocity profiles of water did not show any significant difference between self-induced and forced oscillatory flows. Heat, mass and momentum transfer of Newtonian and power-law non-Newtonian fluids were theoretically investigated using an implicit finite-difference scheme. The results clearly· indicated that shear-dependent non-Newtonian viscosity controls the entire transport processes of the power-law fluids. For the major portion of the boundary layer, it was found that the more shear thinning the material exhibits, the lower the skin friction and the higher the heat transfer result. Accounting for the motion of the stagnation point provided an improved prediction of heat transfer for Newtonian fluid. / Doctor of Philosophy

In this scientific work, we use two effective methods : Lie groups theory and the finite element method, to explain why the transition from laminar flow to turbulence flow depends on the variation of the Reynolds number. We restrict ourselves to the case of incompressible viscous Newtonian fluid flows. Their governing equations, i.e. the continuity and Navier-Stokes equations are established and investigated. Their solutions are expressed explicitly thanks to Lie's theory. The stability theory, which leads to an eigenvalue problem is used together with the finite element method, showing a way to compute the critical Reynolds number, for which the transition to turbulence occurs. The stationary flow is also studied and a finite element method, the Newton method, is used to prove the stability of its convergence, which is guaranteed for small variations of the Reynolds number. / Mathematical Sciences / M.Sc. (Applied Mathematics)