Orientadores: Vivaldo Silveira Junior, Javier Telis Romero / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia de Alimentos / Made available in DSpace on 2018-08-06T15:00:42Z (GMT). No. of bitstreams: 1 Gratao_AnaCarolinaAmaral_D.pdf: 2034155 bytes, checksum: 7a7cc4a961cab6b38ae3dc5ee5f3f9d8 (MD5) Previous issue date: 2006 / Doutorado / Engenharia de Alimentos / Doutor em Engenharia de Alimentos

Orientador: Marcelo Martins dos Santos / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-18T21:33:13Z (GMT). No. of bitstreams: 1 Dias_GilberlandioJesus_D.pdf: 729241 bytes, checksum: 697941f5eb00690299a087d1432b35cf (MD5) Previous issue date: 2011 / Resumo: Neste trabalho estudamos o escoamento de fluidos viscosos não Newtonianos, modelados pelo sistema estacionário incompressível de Navier-Stokes obedecendo a uma Lei de Potência, em domínios com canais infinitos. Tratamos basicamente de dois tipos de domínios: domínios com canais cuja seção transversal é limitada e domínios com canais possuindo seção transversal ilimitada. Tanto para domínios com seção transversal limitada quanto para domínios com seção transversal ilimitada, estudamos o problema proposto por Ladyzhenskaya e Solonnikov [Zap. Nauchn. Sem. Leningrad Otdel. Mat. Inst. Steklov (LOMI), 96(1980)117-160 (English Transl.: J. Soviet Math., 21, 1983, 728-761)]. Findamos nosso trabalho fazendo um estudo sobre estimativas em espaços de Sobolev com peso para soluções do sistema de Stokes com Lei de Potência / Abstract: In this work we study the flow of the viscous non-Newtonian fluids, modeled by the steady incompressible Navier-Stokes system obeying a power-law, in domains with infinite channels. We deal basically two types of domains: domains with channels whose cross section is limited and domains with channels having unlimited cross section. For both domains with limited cross section and for domains with unbounded cross section, we study the problem proposed by Ladyzhenskaya and Solonnikov [Zap. Nauchno. Sem Leningrad Otdel. Mat. Inst. Steklov (Lomi), 96 (1980) 117-160 (Portugu¿es Transl.: J. Soviet Math., 21, 1983, 728-761)]. We finished our work making a study of estimates in Sobolev weight spaces for solutions of the Stokes power-law system / Doutorado / Matematica / Doutor em Matemática

Some non-newtonian fluids exhibit nonmonotonous dependence of the shear stress on shear rate. This nonmonoticity leads to flow instabilities which result in formation of banded flow, namely in shear banding and vorticity banding. An important role is played here by so called stress diffusion which uniquely determines size of bands in the flow. If the classical kinetic approach is employed and the spatial inhomogeneity of the flow is taken into the account, then stress diffusion can be obtained in the fluid model, however this approach has difficulties with identifying heat transfer within the continuum. In this thesis, we present alternative approach how to introduce stress diffusion to fluid models. We employ thermodynamical framework proposed by Rajagopal and Srinivasa (2000), this approach guaranties thermodynamical consistency of resulting model and also the interplay between stress diffusion and heat transfer can be easily established. Furthermore, we extend this framework such that wider range of viscoelastic models can be obtained, in particular we derive Johnson-Segalman model. Powered by TCPDF (www.tcpdf.org)

[pt] O deslocamento de um líquido por outro em espaços anulares é comumente encontrado na indústria do petróleo, e a maioria deles envolve materiais não newtonianos. O espaço anular muitas vezes apresenta irregularidades causadas pela erosão, onde quantidades consideráveis de fluido de perfuração podem ser deixadas para trás durante o processo de deslocamento, comprometendo a qualidade da operação de cimentação. Motivados por esse processo industrial, testes de deslocamento entre líquidos a vazão constante foram realizados em espaços anulares cuja parede externa possui, em uma determinada posição axial, um aumento repentino de diâmetro seguido de uma diminuição repentina de diâmetro mais a jusante. O objetivo dos experimentos era determinar a eficiência do deslocamento em função da vazão, reologia dos fluidos e geometria da cavidade. Os resultados revelaram forte influência desses parâmetros na eficiência de deslocamento. Ao mesmo tempo, um estudo numérico foi desenvolvido. Simulações numéricas das equações de Navier-Stokes em geometria axissimétrica para fluidos incompressíveis foram acopladas ao método Level-Set para captura da interface. Fluidos com viscosidade constante e o modelo newtoniano generalizado com função viscosidade de Carreau-Yasuda foram utilizados. Isso permitiu simular deslocamentos entre dois fluidos newtonianos e entre um fluido newtoniano e outro não-newtoniano. Este foi utilizado tanto como fluido deslocador quanto como deslocado. Foram realizadas simulações para várias razões de diâmetros, viscosidades, tempos de relaxação, e números de capilaridade e de Reynolds. Identificamos quando a aproximação do espaço anular por duas placas paralelas pode ser aplicada e calculamos como a forma da interface depende dos parâmetros investigados. / [en] The displacement of a fluid caused by another one, inside annular spaces, is commonly found in the oil industry and most of these rearrangements involve non-Newtonian materials. The annular space often shows irregularities caused by erosion, in which considerable amounts of drilling fluid can be left behind during the displacement process, compromising the cementing operation efficiency. Motivated by that industrial process, fluid-fluid displacement tests at constant flow rate were performed in annular spaces in which their exterior walls displayed - in a determined axial position - an abrupt expansion followed by an abrupt contraction. The purpose of the tests were to determine the displacement efficiency as a function of flow rate, rheological properties and geometric cavity. The results revealed a strong influence of these parameters on the displacement efficiency. At the same time, a numerical research was developed. Numerical simulations of the Navier-Stokes equations in axisymmetric geometry for incompressible fluids were coupled to the Level-Set method to capture the interface. Fluids with constant viscosity and the generalized Newtonian model with viscosity function of Carreau-Yasuda were used. That allowed to simulate displacements between two Newtonian fluids and a Newtonian and a non-Newtonian fluid. This was used both as a displacer and as a displaced fluid. Simulations were performed for several diameters and viscosities ratios, relaxatation time, capilar and Reynolds numbers. We identified when the approximation of the annular space by two parallel plates can be applied and calculated how the shape of the interface depends on the investigated parameters.

We develop a viscoelastic version of the volume of fluid algorithm for tracking deformable interfaces. The code uses the piecewise linear interface calculation method to reconstruct the interface, the continuous surface force formulation to model interfacial tension forces and utilizes the semi-implicit Stokes solver (enabling computations at low Reynolds numbers). The algorithm is primarily designed to simulate the flow of superposed fluids and the drop in a flow problem in 2D shear flows of viscoelastic and/or Newtonian fluids. The code is validated against linear stability theory for the two-layer flow case and against experimental and other documented numerical investigations for the droplet-matrix case. / Ph. D.

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Submitted by Izabel Franco (izabel-franco@ufscar.br) on 2016-10-05T19:18:20Z No. of bitstreams: 1 TeseCEMac.pdf: 12049463 bytes, checksum: acd65707762e60b912f35a2d267ad5b7 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-10-20T13:40:54Z (GMT) No. of bitstreams: 1 TeseCEMac.pdf: 12049463 bytes, checksum: acd65707762e60b912f35a2d267ad5b7 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-10-20T13:41:14Z (GMT) No. of bitstreams: 1 TeseCEMac.pdf: 12049463 bytes, checksum: acd65707762e60b912f35a2d267ad5b7 (MD5) / Made available in DSpace on 2016-10-20T13:41:32Z (GMT). No. of bitstreams: 1 TeseCEMac.pdf: 12049463 bytes, checksum: acd65707762e60b912f35a2d267ad5b7 (MD5) Previous issue date: 2016-04-26 / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Due to the high capacity of oxygen transfer and versatility, pneumatic reactors have been constantly used in bioprocesses. However, aiming to expand the use of these bioreactors in the industry, as well as increase the understanding of the complex phenomena that occur in these devices, this thesis aimed to evaluate the hydrodynamic, oxygen transfer and shear conditions in three models of pneumatic reactors (bubble column, concentric-tube airlift and split-cylinder airlift) in the scales of 5 and 10 L, using as liquid phase four Newtonian fluids and eight non-Newtonian fluids, and five specific air flow rate (air of 1 to 5 vvm). Related to the hydrodynamic were studied the global gas hold-up (g), the gas hold-ups in the riser (R) and in the downcomer (D), liquid circulation time (tC), superficial liquid velocity in the riser (ULR) and in the downcomer (ULD), and the percentage energy losses in the riser (%ER+%EFR), in the downcomer (%ED+%EFD), and in the bottom (%EB) of airlift reactors. The values of g, R, D, ULR and ULD showed increasing behaviour with increase of air and decreasing behaviour with the kinematic liquid viscosity (L) and the rheologic properties (K e n), and observed the opposite for tC. The higher values of g, R, D and tC were obtained for concentric-tube airlift reactor (ACC) and scale of 10 L. With exception of ULR of Newtonian fluids, the others liquid velocity tests resulted in higher values for split-cylinder airlift reactors (ASC) and scale of 10 L. This result was attributed to the greater driving force (R-D) to liquid circulation obtained in the ASC reactors and the higher energy losses in the riser and in the downcomer observed in the ACC reactors. In the bottom of the airlift reactors, the higher values of %EB were obtained to the ASC reactor. To evaluate the mass transfer were studied, the average bubble diameter (Db), the volumetric oxygen transfer coefficient (kLa) and the terms that compose the kLa, the convective mass transfer coefficient (kL) and the specific interfacial area of mass transfer (aL). With the increase of air, L, K and n, the air bubbles were predominantly coalescent in water, presenting distorted shape, and non-coalescent with spherical/elliptical shape in the other solutions. It was observed a similar behavior between the kLa and aL parameters, which were directly proportional to the air and inversely proportional to the L, K and n. In water, the aL values were lower than glycerol solutions due to the higher Db values observed in this liquid. For the kL, it was observed a decreasing behaviour with the increase of the air in the most solutions. The magnitude of kL values was due mainly the oxygen difusivity in the liquid, and the higher values were observed to the water, following by the non-Newtonian solutions. In general, the higher values of the mass transfer parameters were obtained in the ACC reactor and in the scale of 10 L. The proposed method to the estimate the average shear rate velocity based on Kolmogorov’s theory of isotropic turbulence showed results consistent with the literature relative to the behavior and magnitude of this variable, as well as the results obtained by the analysis of the morphological changes of Streptomyces clavuligerus in two models of airlift reactors and two aeration conditions. Were proposed correlations to predict all evaluated parameters. Were obtained in all cases a good fit with the experimental data, with deviations between the calculated and experimental values below 20%. / Devido à alta capacidade de transferência de oxigênio e versatilidade, reatores pneumáticos têm sido constantemente utilizados em bioprocessos. Entretanto, visando ampliar a utilização destes reatores na indústria, assim como aumentar a compreensão dos fenômenos complexos que ocorrem nestes dispositivos, na presente tese teve-se como objetivo avaliar as condições hidrodinâmicas, de transferência de oxigênio e de cisalhamento em três modelos de reatores pneumáticos (coluna de bolhas, airlift de cilindros concêntricos e airlift split-cylinder) nas escalas de 5 e 10 L, utilizando como fase líquida quatro fluidos newtonianos e oito fluidos nãonewtonianos e cinco vazões específicas de ar (ar de 1 a 5vvm). Em termos hidrodinâmicos foram estudadas as retenções gasosas global (g), no riser (R) e no downcomer (D), tempo de circulação do líquido (tC), velocidade superficial do líquido no riser (ULR) e no downcomer (ULD) e as perdas percentuais de energia no riser, no downcomer e na base (%EB) de reatores airlift. Os valores de g, R, D, ULR e ULD apresentaram comportamento crescente com o aumento de ar e decrescente com a viscosidade cinemática do líquido (L) e propriedades reológicas (K e n), sendo observado o oposto para tC. Os maiores valores de g, R, D e tC foram obtidos em reator airlift de cilindros concêntricos (ACC) e escala de 10 L. Com exceção de ULR de fluidos newtonianos, os demais testes de velocidade do líquido resultaram em maiores valores nos reatores airlift split-cylinder (ASC) e escala de 10 L. Tal resultado foi atribuído a maior força motriz (R-D) para circulação do líquido obtida em ASC e às maiores perdas de energia no riser e no downcomer observadas em reatores ACC. Na base dos reatores, os maiores valores de %EB foram obtidos para reator ASC. Para avaliação da transferência de massa foram estudados o diâmetro da bolha (Db), o coeficiente volumétrico de transferência de oxigênio (kLa) e os termos que o compõe, coeficiente convectivo de transferência de massa (kL) e área interfacial específica de transferência de massa (aL). Bolhas de ar, com o aumento de ar, L, K e n foram predominantemente coalescentes em água, apresentando formato distorcido e nãocoalescentes com formato esférico/elíptico nas demais soluções. Observou-se um comportamento análogo entre kLa e aL, com relação direta à ar e inversa à L, K e n. Em água, os valores de aL foram inferiores às soluções de glicerol em virtude do maior Db observado neste líquido. Para kL, observou-se um comportamento decrescente com o aumento de ar na maioria das soluções. A magnitude dos valores de kL obedeceu principalmente a difusividade do oxigênio no líquido, sendo os maiores valores observados para água, seguido das soluções não-newtonianas. De maneira geral, os maiores valores dos parâmetros de transferência de massa foram obtidos em reator ACC de 10 L. O método proposto para estimativa da taxa de cisalhamento com base na teoria de turbulência isotrópica de Kolmogorov apresentou resultados condizentes com a literatura em termos de comportamento e magnitude desta variável, assim como com os resultados obtidos pela análise das alterações morfológicas de Streptomyces clavuligerus em dois modelos de reatores airlift e duas condições de aeração. Para todos os parâmetros avaliados foram propostas correlações para sua predição, sendo obtidos em todos os casos bons ajustes aos dados experimentais com desvios inferiores à 20%. Palavras-chave: reatores pneumáticos, retenção gasosa, kLa, diâmetro da bolha, velocidade

Thesis submitted in fulfilment of the requirements for the degree Master of Technology: Civil Engineering in the Faculty of Engineering at the CAPE PENINSULA UNIVERSITY OF TECHNOLOGY 2014 / The current problems of orifice, nozzle and Venturi flow meters are that they are limited to turbulent flow and the permanent pressure drop produced in the pipeline. To improve these inadequacies, converging-diverging (C-D) tubes were manufactured, consisting of symmetrical converging and diverging cones, where the throat is the annular section between the two cones, with various angles and diameter ratios to improve the permanent pressure loss and flow measurement range. The objective of this study was firstly to evaluate the permanent pressure loss, secondly to determine the discharge coefficient values for various C-D tubes and compare them with the existing differential pressure flow meter using Newtonian and non-Newtonian fluids, and finally to assess the performance of these differential pressure flow meters. The tests were conducted on the multipurpose test rig in the slurry laboratory at the Cape Peninsula University of Technology. Newtonian and non-Newtonian fluids were used to conduct experiments in five different C-D tube flow meters with diameter ratios (β) of 0.5, 0.6 and 0.7, and with angles of the wall to the axis of the tube (θ) of 15°, 30° and 45°. The results for each test are presented firstly in the form of static pressure at different flow rates. It was observed that the permanent pressure loss decreases with the flow rate and the length of the C-D tube. Secondly, the results are presented in terms of discharge coefficient versus Reynolds number. It was found that the Cd values at 15° drop earlier than at 30° and 45°; when viscous forces become predominant, the Cd increases with increasing beta ratio. The Cd was found to be independent of the Reynolds number for Re>2000 and also a function of angle and beta ratio. Preamble Performance of a symmetrical converging-diverging tube differential pressure flow meter Finally, the error analyses of discharge coefficients were assessed to determine the performance criteria. The standard variation was found to increase when the Reynolds number decreases. The average discharge coefficient values and their uncertainties were determined to select the most promising C-D tube geometry. An average Cd of 0.96, with an uncertainty of ±0.5 % for a range of Reynolds numbers greater than 2,000 was found. The comparison between C-D tubes 0.6(15-15) and classical Venturi flow meters reveals that C-D 0.6(15-15) performs well in turbulent range and shows only a slight inaccuracy in laminar. This thesis provides a simple geometrical differential pressure flow meter with a constant Cd value over a Reynolds number range of 2000 to 150 000.

Ice sheets, such as the Greenland Ice Sheet or Antarctic Ice Sheet, have a fundamental impact on landscape formation, the global climate system, and on sea level rise. The slow, creeping flow of ice can be represented by a non-linear version of the Stokes equations, which treat ice as a non-Newtonian, viscous fluid. Large spatial domains combined with long time spans and complexities such as a non-linear rheology, make ice sheet simulations computationally challenging. The topic of this thesis is the efficiency and error control of large simulations, both in the sense of mathematical modelling and numerical algorithms. In the first part of the thesis, approximative models based on perturbation expansions are studied. Due to a thick boundary layer near the ice surface, some classical assumptions are inaccurate and the higher order model called the Second Order Shallow Ice Approximation (SOSIA) yields large errors. In the second part of the thesis, the Ice Sheet Coupled Approximation Level (ISCAL) method is developed and implemented into the finite element ice sheet model Elmer/Ice. The ISCAL method combines the Shallow Ice Approximation (SIA) and Shelfy Stream Approximation (SSA) with the full Stokes model, such that the Stokes equations are only solved in areas where both the SIA and SSA is inaccurate. Where and when the SIA and SSA is applicable is decided automatically and dynamically based on estimates of the modeling error. The ISCAL method provides a significant speed-up compared to the Stokes model. The third contribution of this thesis is the introduction of Radial Basis Function (RBF) methods in glaciology. Advantages of RBF methods in comparison to finite element methods or finite difference methods are demonstrated. / eSSENCE