Orientador: Geraldo Maciel de Freitas / Co-orientador: Cláudio Kitano / Banca: Elaine Maria Cardoso / Banca: José Junji Ota / Resumo: Esta dissertação de mestrado faz uma abordagem do trabalho experimental desenvolvido no âmbito de pesquisa de escoamento de fluidos não-newtonianos em canais inclinados. Quando estes escoamentos são colocados em condições favoráveis de inclinação e vazão, pode-se constituir um domínio propício à propagação de instabilidades na superfície livre que, eventualmente, podem evoluir para um tipo específico de ondas, conhecidas na literatura como roll waves. Estas ondas, de comprimento e amplitude bem definidos, são especialmente afetadas pelas características do escoamento e do fluido. Em termos de fluido teste, foi confeccionado, caracterizado reologicamente e utilizado o gel de carbopol, de base polimérica e de propriedade não-newtonianas, com bom ajuste do modelo reológico de Herschel-Bulkley. Como existe na literatura uma grande lacuna no que diz respeito a medidas deste fenômeno tanto na natureza quanto em laboratório, buscou-se neste trabalho, projetar e construir um aparato experimental que fosse capaz de reproduzir as condições necessárias para a geração de roll waves, em condições controladas. Técnicas fotométricas e ultrassônicas foram utilizadas no experimento para aferir informações de altura de escoamento, após o fluido teste (gel de carbopol) ser perturbado, por um sistema específico projetado para este fim. O aparato experimental desenvolvido permite, doravante, simulações de roll waves em diversos cenários para fluidos de reologia diversa, constituindo assim, um suporte de grande valia ao entendimento e controle de roll waves presentes, por exemplo em corridas de lama / Abstract: This dissertation makes an approach to the experimental work carried out within the research of non-Newtonian fluids drained in inclined channels. When these flows are placed in favorable slope and flow, can be a suitable area to the spread of instability at the free surface which may eventually evolve into a specific type of waves, known in the literature as "roll waves". These waves of well- defined length and amplitude are especially affected by the flow characteristics and the fluid. In terms of fluid test was elaborated, rheologically characterized and used carbopol gel, polymer-based and non-Newtonian property, with good adjustment of the rheological model of Herschel-Bulkley. As there is a big gap in the literature regarding to both measures of this phenomenon in nature as in the laboratory, was sought in this work, the formation of an experimental apparatus that was able to reproduce the necessary conditions for the generation of roll waves in the laboratory, under those controlled conditions. Photometric and ultrasonic techniques were used in the experiment for measuring height information of the flow after the test fluid (carbopol gel) being disturbed by a specific system designed for this purpose. The experimental apparatus developed now enables simulations of roll waves in various scenarios for different fluid rheology, is thus an invaluable support to the understanding and control of this "roll waves" present in mud, for example / Mestre

M.Sc. / In this dissertation, a symmetry analysis of a third order non-linear partial differential equation which describes the filtration of a non-Newtonian liquid in porous media is performed. A review of the derivation of the partial differential equation is given which is based on the Darcy Law. The partial differential equation contains a parameter n and a function f. We derive the Lie Point Symmetries of the partial differential equation for all cases of n and f. These symmetries are used to find the invariant solutions of the partial differential equation. We find that there is only one conservation law for the partial differential equation with f and n arbitrary and we prove that there is no potential symmetry corresponding to this conservation law for any case of n and f.

The equation of motion for the flows of incompressible Newtonian fluids (Navier Stokes equations) under no-slip boundary conditions have been studied deeply from many perspectives. The questions of existence and uniqueness of both classical and weak solutions have received more than a fair share of attention. In this study the same problem for non-Newtonian fluids of second grade has been studied from the point of view of weak solutions and classical solutions for non-homogeneous boundary data, i.e., dynamical boundary conditions in regions with permeable boundaries. We consider the situation where a container is immersed in a larger fluid body and the boundary admits fluid particles moving across it in the direction of the normal. In this study we give alternative approaches through formulations of' dynamics at the boundary', the idea being that the normal component of velocity at the boundary is viewed as an unknown function which satisfies a differential equation intricately coupled to the flow in the region 'enclosed' by the boundary. We describe two mathematical models denoted by Problem PI and Problem P2. These models lead to dynamics at a permeable boundary, and a kinematical boundary condition for normal flow through the boundary. These conditions take into account the curvature of the boundary which enforces certain stresses. We then show with the help of the energy method that for fluids of second grade, the dynamics at the boundary and the boundary condition lead to conditional stability of the rest state for Problem P1 and Problem P2. We also prove uniqueness of classical solutions for the two models. The existence of a weak solution for this system of evolution equations is proved only for Problem P2 with the help of the Faedo-Galerkin method with a special basis. In this case the special basis is formed by eigenfunctions. The existence proof of at least one classical solution, local in time is established by means of a version of the Fixed-point Theorem of Bohnenblust and Karlin, and the Ascoli-Arzela Theorem. / Thesis (PhD (Applied Mathematics))--University of Pretoria, 2007. / Mathematics and Applied Mathematics / unrestricted

The main focus of this work is to investigate experimentally the transition to turbulence of a yield stress shear thinning fluid in Hagen-Poiseuille flow. By combining direct high speed imaging of the flow structures with Laser Doppler Velocimetry (LDV), we provide a systematic description of the different flow regimes from laminar to fully turbulent. Each flow regime is characterized by measurements of the radial velocity, velocity fluctuations, and turbulence intensity profiles. In addition we estimate the autocorrelation, the probability distribution, and the structure functions in an attempt to further characterize transition. For all cases tested, our results indicate that transition occurs only when the Reynolds stresses of the flow equals or exceeds the yield stress of the fluid, i.e. the plug is broken before transition commences. Once in transition and when turbulent, the behavior of the yield stress fluid is somewhat similar to a (simpler) shear thinning fluid. We have also observed the shape of slugs during transition and find that their leading edges to be highly elongated and located off the central axis of the pipe, for the non-Newtonian fluids examined. Finally we present a new phenomenological approach for quantifying laminar-turbulent transition in pipe flow. This criterion is based on averaging a local Reynolds number to give ReG. Our localised parameter shows strong radial variations that are maximal at approximately the radial positions where puffs first appear during the first stages of turbulent transition. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

The continual advance in manufacturing processes has resulted in significantly more compact, high performance, devices. Consequently, heat extraction has become the limiting factor, and of primary concern. Therefore, a substantial amount of research has been done regarding high efficiency micro heat exchangers, employing novel working fluids. This dissertation numerically investigated the thermal behaviour of microchannel elements cooled by Newtonian and non-Newtonian fluids, with the objective of maximising thermal conductance subject to constraints. This was done, firstly, for a two-dimensional simple microchannel, and secondly, for a three-dimensional complex microchannel. A numerical model was used to solve the governing equations relating to the flow and temperature fields for both cases. The geometric configuration of each cooling channel was optimised for Newtonian and non-Newtonian fluids, at a fixed inlet velocity and heat transfer rate. In addition, the effect of porosity on thermal conductance was investigated. Geometric optimisation was employed to the simple and complex microchannels, whereby an optimal geometric ratio (height versus length) was found to maximise thermal conductance. Moreover, analysis indicated that the bifurcation point of the complex microchannel could be manipulated to achieve a higher thermal conductance. In both cases, it was found that the non-Newtonian fluid characteristics resulted in a significant variation in thermal conductance as inlet velocity was increased. The ii characteristics of a dilatant fluid greatly reduced thermal conductance on account of shear-thickening on the boundary surface. In contrast, a pseudoplastic fluid showed increased thermal conductance. A comparison of the simple and complex microchannel showed an improved thermal conductance resulting from greater flow access to the conductive area, achieved by the complex microchannel. Therefore, it could be concluded that a complex microchannel, in combination with a pseudoplastic working fluid, substantially increased the thermal conductance and efficiency, as opposed to a conventional methodology. / Dissertation (MEng)--University of Pretoria, 2012. / gm2014 / Mechanical and Aeronautical Engineering / unrestricted

This work uses high-speed video imaging to study the formation of filaments, during impact and rebounding of drops with polymer additives. We use PEO of different concentrations from 10 to 1000 ppm and study how drops rebound from various different surfaces: superhydrophilic, hydrophilic, hydrophobic, and superhydrophobic. Bouncing occurs for all surfaces at low impact velocities. We specifically focus on the phenomenon of the generation of polymer filaments, which are pulled out of the free surface of the drop during its rebounding from micro-pillared or rough substrates. We map the parameter regime, in terms of polymer concentration and impact Weber number, where the filaments are generated in the most repeatable manner. This occurs for regularly pillared surfaces and drops of 100 ppm PEO concentrations, where numerous separated filaments are observed. In contrast, for superhydrophobic coatings with random roughness the filaments tend to merge forming a branching structure. Impacts on inclined surfaces are used to deposit the filaments on top of the pillars for detailed study.

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