Newtonian theory was applied, in this analysis, to the elliptic cone segment at angles of attack and sideslip. Closed form expressions for the aerodynamic coefficients and static stability derivatives were obtained. Expressions for the full and half conic bodies were given and approximate expressions were given for the half cone case. The circular cone results were obtained as a special case of the general results. Comparisons of the theoretical calculations with experimental results at hypersonic speeds were made of the aerodynamic coefficients and static derivatives for several conic segments. Generally, good agreement was observed for specified ranges of fineness ratios and angles of attack. / Master of Science

In this study we investigate the propagation of uncertainties in the input forces through a mechanical system. The system of interest was a wheel loader, but the methodology developed can be applied to any multibody systems. The modeling technique implemented focused on efficiently modeling stochastic systems for which the equations of motion are not available. The analysis targeted the reaction forces in joints of interest. The modeling approach developed in this thesis builds a foundation for determining the uncertainties in a Caterpillar 980G II wheel loader. The study begins with constructing a simple multibody deterministic system. This simple mechanism is modeled using differential algebraic equations in Matlab. Next, the model is compared with the CAD model constructed in ProMechanica. The stochastic model of the simple mechanism is then developed using a Monte Carlo approach and a Linear/Quadratic transformation method. The Collocation Method was developed for the simple case study for both Matlab and ProMechanica models. Thus, after the Collocation Method was validated on the simple case study, the method was applied to the full 980G II wheel loader in the CAD model in ProMechanica. This study developed and implemented an efficient computational method to propagate computational method to propagate uncertainties through "black-box" models of mechanical systems. The method was also proved to be reliable and easier to implement than traditional methods. / Master of Science

Yes / An idealised model of core-out in water assisted injection moulding (WAIM) is set up to isolate the effect of cooling by the water on the deposited layer thickness. Based on simulations, this is investigated for a specific case as a function of Pearson number and power law index. It is found that cooling significantly reduces the layer thickness to the extent that a change in the flow regime ahead of the bubble, from bypass to recirculating flow, is possible. For shear thinning melts with high temperature coefficient of viscosity, the simulations show very low layer thickness, which may indicate unfavourable conditions for WAIM. Although in the real moulding situation, other effects will be superimposed on those found here, the results provide new insights into the fundamentals of WAIM. Investigation of other effects characterised by Fourier and Reynolds numbers will be reported subsequently. Some early process measurement results from an experimental WAIM mould are presented. Reductions in residual wall thickness are observed as the water injection set pressure is increased and the duration of water bubble penetration through the melt is determined experimentally. The formation of voids within the residual wall is noted and observed to reduce in severity with increasing water injection pressure. The presence of such voids can be detected by the signature from an infrared temperatures sensor.

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

Thesis (PhD)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: See full text for abstract / AFRIKAANSE OPSOMMING: Sien volteks vir opsomming

Thesis (PhD)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: Different generalized Newtonian fluids (where the normal stresses were neglected) were considered in this study. Analytical expressions were derived for time independent, fully developed velocity profiles of Herschel-Bulkley fluids (including the simplifications thereof: Newtonian, power law and Bingham plastic fluids) and Casson fluids through open channel sections. Both flow through cylindrical pipes (Hagen-Poiseuille flow) and parallel plates (plane Poiseuille flow) were brought under consideration. Equations were derived for the wall shear stresses in terms of the average channel velocities. These expressions for plane Poiseuille flow were then utilized in the modelling of flow through homogeneous, isotropic porous media. Flow through parallel plates was extended and a possibility of a moving lower wall (plane Couette-Poiseuille flow) was included for Herschel-Bulkley fluids (and the simplifications thereof). The velocity of the wall was assumed to be opposite to the pressure gradient (thus in the streamwise direction) yielding three different possible flow scenarios. These equations were again revisited in the study on flow over porous structures. Averaging of the microscopic momentum transport equation was carried out by means of volume averaging over an REV (Representative Elementary Volume). Flow through parallel plates enclosing a homogeneous porous medium (assumed homogeneous up to the external boundary) was studied at the hand of Brinkman’s equation. It was as- sumed (also for non-Newtonian fluids) that the term dominating outside the external boundary layer area is directly proportional to the superficial velocity that is, since only the viscous flow regime was considered, referred to as the ‘Darcy’ velocity if the diffusive Brinkman term is completely neglected. For a shear thinning or shear thickening fluid, the excess superficial velocity term was included in the proportionality coefficient that is constant for a particular fluid traversing a particular porous medium subjected to a specific pressure gradient. For such fluids only the inverse functions could be solved. If the ‘Darcy’ velocity is not reached within the considered domain, Gauss’s hypergeo- metric function had to be utilized. For Newtonian and Bingham plastic fluids, direct solutions were obtained. The effect of the constant yield stress was embedded in the proportionality coefficient. For linear flow, the proportionality coefficient consists of both a Darcy and a Forch- heimer term applicable to the viscous and inertial flow regimes respectively. Secondary averaging for different types of porous media was accomplished by using an RUC (Representative Unit Cell) to estimate average interstitial properties. Only homoge- neous, isotropic media were considered. Expressions for the apparent permeability as well as the passability in the Forchheimer regime (also sometimes referred to as the non-Darcian permeability) were derived for the various fluid types. Finally fluid flow in a domain consisting of an open channel adjacent to an infinite porous domain is considered. The analytically derived velocity profiles for both plane Couette- Poiseuille flow and the Brinkman equation were matched by assuming continuity in the shear stress at the porosity jump between the two domains. An in-house code was developed to simulate such a composite domain numerically. The difference between the analytically assumed constant apparent permeability in a macro- scopic boundary layer region as opposed to a dependency of the varying superficial velocity was discussed. This code included the possibility to alter the construction of the domain and to simulate axisymmetrical flow in a cylinder. / AFRIKAANSE OPSOMMING: Verskeie veralgemeende Newtoniese vloeistowwe (waarvan die normaalspannings ignoreer- baar is) word in hierdie studie beskou. Analitiese uitdrukkings vir tyd-onafhanklike, ten volle ontwikkelde snelheidsprofiele vir Herschel-Bulkley vloeistowwe (wat die vereen- voudigde weergawes daarvan insluit: Newtoniese, magswet- en Bingham-plastiek vloei- stowwe), sowel as Casson vloeistowwe, is afgelei vir vloei deur ‘n oop kanaal. Beide vloei deur silindriese pype (Hagen-Poiseuille vloei) en parallelle plate (vlak-Poiseuille vloei) is oorweeg. Vergelykings vir die skuifspannings op ‘n wand in terme van die gemiddelde snelhede is afgelei. Hierdie uitdrukking wat vir vlak-Poiseuille vloei verkry is, is in die modellering van vloei deur homogene, isotropiese poreuse media ook gebruik. Vloei deur parallelle plate is uitgebrei en die moontlikheid van ‘n bewegende onderste wand (vlak-Couette-Poiseuille vloei) is ondersoek vir Herschel-Bulkley vloeistowwe (en die vereenvoudigings daarvan). Dit word aangeneem dat die snelheid van die wand in die teenoorgestelde rigting as die drukgradiënt georiënteer is (dus in die stroomgewyse rigting) wat dan tot drie verskillende moontlike vloeigevalle lei. Hierdie vergelykings is weer in die studie van vloei oor poreuse strukture gebruik. Die gemiddelde van die mikroskopiese momentum transportvergelyking is bereken oor die volume van ‘n REV (“Representative Elementary Volume”). Vloei deur parallelle plate wat ‘n homogene poreuse medium omsluit (waar die medium homogeen aanvaar word tot by die eksterne grens) is bestudeer aan die hand van Brinkman se vergelyking. Daar is aanvaar (ook vir nie-Newtoniese vloeistowwe) dat die dominante term buite die eksterne grenslaaggebied direk eweredig is aan die oppervlaksnelheid en, aangesien slegs vloei in die viskeuse gebied oorweeg word, daarna verwys word as die “Darcy”- snelheid, indien die diffusiewe Brinkman-term heeltemal weglaatbaar is. Vir ‘n span-ningsverdunnende of -verdikkende vloeistof, word die oortollige oppervlaksnelheidsterm ingesluit by die proporsionaliteitskoëffisiënt wat konstant is vir ‘n spesifieke vloeistof wat deur ‘n sekere poreuse medium, onderhewig aan ‘n spesifieke drukgradiënt, vloei. Vir sulke vloeistowwe kon slegs die inverse funksies opgelos word. As die “Darcy”- snelheid nie binne die betrokke gebied bereik word nie, is daar van Gauss se hipergeometriese funksie gebruik gemaak. Vir Newtoniese en Bingham-plastiek vloeistowwe is egter direkte oplossings verkry. Die effek van die konstante toegeespanning is ingebed in die proporsionaliteitskoëffisiënt. Vir lineêre vloei bestaan die proporsionaliteitskoëffisiënt uit beide ‘n Darcy- en ‘n Forch- heimer-term wat van toepassing is in die viskeuse- en traagheidsvloeigebiede onder- skeidelik. Sekondˆere gemiddeldes vir verskillende tipes poreuse media is verkry; deur gebruik te maak van ‘n RUC (“Representative Unit Cell”) kan interstisiële gemiddelde eienskappe geskat word. Slegs homogene, isotrope media is in oorweging gebring. Uit- drukkings vir die o¨enskynlike deurlaatbaarheid sowel as die deurdringbaarheid in die Forchheimer-gebied (ook soms na verwys as die nie-Darcy deurlaatbaarheid) is afgelei vir die verskillende vloeistoftipes. Ten slotte is vloeistofvloei in ‘n gebied wat bestaan uit ‘n oop kanaal aangrensend aan ‘n oneindige poreuse domein ondersoek. Die analities-afgeleide snelheidsprofiele vir beide vlak-Couette-Poiseuille vloei en die Brinkman-vergelyking is gekoppel deur ‘n kontinu¨ıteit in die skuifspanning by die poreuse-sprong tussen die twee gebiede te aanvaar. ‘n Interne numeriese kode is ontwikkel om so ‘n saamgestelde domein numeries te simuleer. Die verskil tussen die analities konstant-aanvaarde deurlaatbaarheid in ‘n makroskopiese grenslaagstreek, eerder as ‘n afhanklikheid met die veranderende opper- vlaksnelheid, is bespreek. Hierdie kode sluit ook die moontlikheid in om die domein te herkonstrueer, asook om die simulasie van aksiaal-simmetriese vloei in ‘n silinder te ondersoek.

Title: Non-newtonian fluid flow simulation using lattice Boltzmann method Author: Bc. Pavel Kuriščák Department: Mathematical Institute, Charles University Supervisor: RNDr. Ing. Jaroslav Hron Ph.D. Supervisor's e-mail address: Jaroslav.Hron@mff.cuni.cz Abstract: The aim of this thesis is to find and estabilish a modification to the Lattice Boltzmann Method, allowing it to simulate non-newtonian behaviour of fluids. In the theoretical part of thesis, there is introduced a derivation, based on the work of [22], that is capable of arriving to macroscopical Navier-Stokes equa- tions completely a priori from the Boltzmann equation, utilizing the Hermite basis expansion. This derivation is afterwards applied to the method suggested by [11], that uses the changed equilibrium distribution to fine-tune the local fluid viscosity according to the non-newtonian model. In the last part of thesis, this method is implemented in the form of lattice kinetic scheme and tested on three sample problems. Keywords: Lattice Boltzmann Method, non-newtonian fluids, Hermite expansion, lattice kinetic scheme

Abstract A computer program has been written to simulate the conditions of the early uni- verse and to test a new idea in the mechanism of structure formation observed in our universe today. The model utilises Newtonian hydrodynamic equations includ- ing gravitational and electromagnetic forces in two spatial dimensions. It is proposed that augmenting gravitational forces with plasma forces will complement the prob- lematic Big Bang theory of structure formation which relies on gravity alone. Two sets of initial conditions are tested and the products of the simulation are analysed in a statistical way using power spectra and the two-point correlation function. Differ- ences in the initial conditions were not seen to produce significantly different results. The results show that the Hubble expansion term significantly reduces power in the gravity models but plasma forces can retain power better than similar gravitation- only models. Initial velocity perturbations significantly modify the power spectrum gradient in the higher modes. Some power spectra displayed a definite bend in gra- dient at a scale which is verified by galaxy survey observations. Plasma forces also appear to cluster matter on smaller scales more efficiently than gravity alone. Thus, this simulation lays a foundation for a more detailed and realistic model that may be compared with real matter distribution observations.