Thesis (Ph. D.)--University of Wisconsin--Madison, 1959. / Typescript. Abstracted in Dissertation abstracts, v. 20 (1959) no. 2, p. 614-615. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 166-171).

Thesis (Ph. D.)--University of Texas at Austin, 2004. / Supervisor: Graham F. Carey. Vita. Includes bibliographical references.

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)

Made available in DSpace on 2015-07-13T12:10:21Z (GMT). No. of bitstreams: 0 Previous issue date: 2013-07-31. Added 1 bitstream(s) on 2015-07-13T12:25:21Z : No. of bitstreams: 1 000836682.pdf: 2242597 bytes, checksum: 64204d0074211d1723d7ad5c6f876572 (MD5) / 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 / 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

Thesis (MTech (Chemical Engineering))--Cape Technikon, 2004 / When designing the open channels to transport the homogenous non-Newtonian slurries, the effect of channel shape is one of the parameters that should be checked and very little research has been conducted to address this matter. Open channels are commonly applied in the mining industry where mine tailings have to be transported to the disposal dams at high concentrations to save water consumption. This thesis addresses the effect of the cross-sectional shape of the channel with emphasis on laminar and transitional flow of non-Newtonian fluids. The literature review on the flow of Newtonian and non-Newtonian fluids has been presented. The most relevant one to this topic is the work done by Straub et al (1958) for Newtonian fluids and the analytical work presented by Kozicki and Tiu (1967) for non-Newtonian fluids. Authors like Coussot (1994) and Haldenwang (2003) referred to their work but did not comprehensively verified it experimentally. Three flume shapes were designed to investigate this problem namely, rectangular, semi circular, and trapezoidal flume shape. The test rig consisted of a 10 m long by 300mm wide tilting flume that can be partitioned into two sections to form a 150 mm wide channel. All three flume shapes were tested in both the 150 mm and 300 mm wide flumes. This flume is linked to the in-line tube viscometer with three tube diameters namely, 13 mm; 28 mm; and 80 mm. The experimental investigation covered a wide range of flow rates (0.1-45l/s), and flume slopes (1-5 degrees). The fluids tested were kaolin suspension (5.4 - 9% v/v), CMC solution (1 - 4% m/m), and bentonite suspension (4.6 and 6.2% mlm). The models found in the literature were evaluated with the large database compiled from the test results to predict the laminar and transitional flow of these fluids with the aim of checking the effect of the cross-sectional shape of these channels selected in these flow regimes. For all the flume shapes and non-Newtonian fluids selected in this thesis it was found that in predicting the laminar flow, the effect of shape is adequately accounted for by the use of hydraulic radius. In predicting the transitional flow, it was found that the effect of shape does not have to be included.

Thesis (MTech(Civil Engineering))--Cape Peninsula University of Technology, 2006. / The performance of a centrifugal pump is altered for slurry or viscous materials (Stepanoff, 1969) and this needs to be accounted for. Usually, the suitable selection and evaluation of centrifugal pumps is based only on water pump performance curves supplied by the pump manufacturer (Wilson, Addie, Sellgren & Clift, 1997). In 1984 Walker and Goulas conducted a number of pump performance tests with kaolin clay slurries and coal slurries on a Warman 4/3 AH horizontal slurry pump and a Hazleton 3-inch B CTL horizontal pump (Walker and Goulas, 1984). Walker and Goulas have analysed the test data and correlated the performance derating both at the best efficiency flow rate (BEP) and at 10% of the best efficiency flow rate (0.1 BEP) to the modified pump Reynolds number (NRep). They have noticed that the head and the efficiency reduction ratio decreased for the pump Reynolds number less then 10⁶. Furthermore, Walker and Goulas obtained a reasonably good agreement (± 5%) between pump test data for non-Newtonian materials and pump performance prediction using the Hydraulics Institute chart. Sery and Slatter (2002) have investigated pump deration for non-Newtonian yield pseudoplastic materials. The NRep was calculated using the Bingham plastic viscosity (µp). Results have shown good agreement with regard to head and efficiency reduction ratios in comparison with previous work. However, Sery and Slatter's pump performance correlation using the HI chart did not reach the same conclusion. Error margin of ± 20% and ± 10% were found for head and efficiency respectively. This study is an attempt to reconcile the differences between Walker and Goulas (1984) and Sery and Slatter (2002) and extend the evaluation of these derating methods to pseudoplastic materials. The test work was conducted in the Flow Process Research Centre laboratory of the Cape Peninsula University of Technology using two centrifugal pumps; a Warman 6/4 and a GrW 4/3. The materials used were water, CMC solution bentonite and kaolin suspension at different concentrations (7% and 9% by weight for bentonite; 5%, 6% and 7% by weight for CMC; 17%, 19% and 21% by volume for kaolin).

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