The present study investigates experimentally the laminar mixing and heat transfer of a range of helical ribbon and anchor impellers for both Newtonian and inelastic non-Newtonian fluids. The work also correlates the experimental data empirically in the form of dimensionless groups. In order to estimate the relative importance and the effect of all the geometrical parameters on the mixing power and heat transfer, data from the published literature sources will be utilized and combined with the results from this study. Thus, reliable empirical correlations will be obtained which are applicable over the widest range of operating conditions. The study also investigates the ablity of the various impellers to level out temerature distributions. The measurement of these temperature gradients and the impeller power requirements gives a measure of the mixing efficiency of the impeller used.

Orientador: Geraldo de Freitas Maciel / Banca: André Luiz Seixlack / Banca: Luís Miguel Chagas da Costa Gil / Resumo: Os escoamentos na superfície livre que se processam sobre forte declividade podem desenvolver instabilidades ao cabo de tempo finito. Tais instabilidades aparecem sob formas de ondas tipo "hydraulic jumps" bem espaçados e são denominadas Roll Waves. Estas ondas, longas e periódicas, podem ser contínuas ou descontínuas; contínuas em problema Shallow Water viscoso e descontínuas para o caso não viscoso. Tal fenômeno pode ser observado tanto em escoamentos naturais como em canais artificiais e vertedouros de barragens. Tratando-se de escoamento de Fluidos não newtonianos, tal fenômeno pode ser visto facilmente em lavas torrenciais, avalanchas ou "debris flows". Nesta dissertação foram analisados matematicamente e numericamente o comportamento e as condições de existência para a formação de Roll Waves em escoamentos laminares e turbulentos. Em escoamentos turbulentos toma-se como referência os trabalhos realizados por Maciel (2001) numa reologia Binghamiana. Para escoamentos laminares, cita-se o trabalho de Mei (1994) em uma reologia tipo Power Law. No plano numérico, para escoamentos turbulentos, foram utilizadas rotinas do MATLAB® versão 6.5 e, para escoamentos laminares, rotinas em FORTRAN 90; onde pôde-se analisar e comparar resultados para diversas reologias. O foco desta dissertação foi tratar o problema Roll Waves como uma instabilidade na vizinhança do regime uniforme para Fluidos não newtonianos, em regimes turbulentos e laminares. A reologia tratada e representativa de diversos escoamentos na natureza foi a de Herschel Bulkley. A partir desta dissertação deixa-se, como perspectiva futura, um estudo mais aprofundado sob formação de ondas em fluidos hiperconcentrados tipo Herschel Bulkley com abordagem experimental a fim de validar resultados apontados nesta pesquisa. / Abstract: Flows that happen over strong slope with free surface can develop instabilities after some finite time. Such wave shaped instabilities appear in the flow and are of the type "hydraulic jumps" well spaced and they are called Roll Waves. Those waves are long and periodic, continuous or discontinuous, continuous in viscous Shallow Water problems, and discontinuous for the inviscid case. Roll Waves are uncommon in natural flows, but they are common in man made channels and dams spillway. For flows of non Newtonian fluids such phenomenon can be seen easily in lava torrent, avalanche and debris flow. In this work it were mathematically and numerically analyzed the behavior and the existence conditions for the generation of Roll Waves within laminar and turbulent flows. For turbulent flows it is taken as reference the works done by Maciel (2001) dealing with a Bingham rheology. For laminar flows the reference is the work done by Mei (1994) using a Power Law rheology. Numerically, for turbulent flows it were used MATLAB® 6.5 procedures and for laminar flows FORTRAN 90 procedures were developed. Using these reference procedures it was obtained compared and analyzed results for several rheologies. This work left as future perspective a deeper study about the generation of waves in hipper concentrated fluids such as Herschel Bulkley fluid, with an experimental approach aiming to validate results produced. The focus of this work was to treat the so called Roll Waves problem as an instability in the vicinity of the uniform flow regime for non Newtonian fluids under laminar and turbulent flow regimes. The Herschel Bulkley rheology that was treated in this work is representative of several flows that happen in nature. / Mestre

Made available in DSpace on 2014-06-11T19:23:39Z (GMT). No. of bitstreams: 0 Previous issue date: 2007-12-07Bitstream added on 2014-06-13T19:50:38Z : No. of bitstreams: 1 vieira_as_me_ilha.pdf: 1217264 bytes, checksum: cb21063aba699b564242c2fc4b3c3ed4 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Os escoamentos na superfície livre que se processam sobre forte declividade podem desenvolver instabilidades ao cabo de tempo finito. Tais instabilidades aparecem sob formas de ondas tipo “hydraulic jumps” bem espaçados e são denominadas Roll Waves. Estas ondas, longas e periódicas, podem ser contínuas ou descontínuas; contínuas em problema Shallow Water viscoso e descontínuas para o caso não viscoso. Tal fenômeno pode ser observado tanto em escoamentos naturais como em canais artificiais e vertedouros de barragens. Tratando-se de escoamento de Fluidos não newtonianos, tal fenômeno pode ser visto facilmente em lavas torrenciais, avalanchas ou “debris flows”. Nesta dissertação foram analisados matematicamente e numericamente o comportamento e as condições de existência para a formação de Roll Waves em escoamentos laminares e turbulentos. Em escoamentos turbulentos toma-se como referência os trabalhos realizados por Maciel (2001) numa reologia Binghamiana. Para escoamentos laminares, cita-se o trabalho de Mei (1994) em uma reologia tipo Power Law. No plano numérico, para escoamentos turbulentos, foram utilizadas rotinas do MATLAB® versão 6.5 e, para escoamentos laminares, rotinas em FORTRAN 90; onde pôde-se analisar e comparar resultados para diversas reologias. O foco desta dissertação foi tratar o problema Roll Waves como uma instabilidade na vizinhança do regime uniforme para Fluidos não newtonianos, em regimes turbulentos e laminares. A reologia tratada e representativa de diversos escoamentos na natureza foi a de Herschel Bulkley. A partir desta dissertação deixa-se, como perspectiva futura, um estudo mais aprofundado sob formação de ondas em fluidos hiperconcentrados tipo Herschel Bulkley com abordagem experimental a fim de validar resultados apontados nesta pesquisa. / Flows that happen over strong slope with free surface can develop instabilities after some finite time. Such wave shaped instabilities appear in the flow and are of the type “hydraulic jumps” well spaced and they are called Roll Waves. Those waves are long and periodic, continuous or discontinuous, continuous in viscous Shallow Water problems, and discontinuous for the inviscid case. Roll Waves are uncommon in natural flows, but they are common in man made channels and dams spillway. For flows of non Newtonian fluids such phenomenon can be seen easily in lava torrent, avalanche and debris flow. In this work it were mathematically and numerically analyzed the behavior and the existence conditions for the generation of Roll Waves within laminar and turbulent flows. For turbulent flows it is taken as reference the works done by Maciel (2001) dealing with a Bingham rheology. For laminar flows the reference is the work done by Mei (1994) using a Power Law rheology. Numerically, for turbulent flows it were used MATLAB® 6.5 procedures and for laminar flows FORTRAN 90 procedures were developed. Using these reference procedures it was obtained compared and analyzed results for several rheologies. This work left as future perspective a deeper study about the generation of waves in hipper concentrated fluids such as Herschel Bulkley fluid, with an experimental approach aiming to validate results produced. The focus of this work was to treat the so called Roll Waves problem as an instability in the vicinity of the uniform flow regime for non Newtonian fluids under laminar and turbulent flow regimes. The Herschel Bulkley rheology that was treated in this work is representative of several flows that happen in nature.

Made available in DSpace on 2015-05-14T12:13:59Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 577037 bytes, checksum: e0d8387a050d8e101f0d3cc14dc19dd9 (MD5) Previous issue date: 2011-04-25 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The equations of motion are obtained in the framework of Newtonian cosmology using only the Newtonian dynamics and Newtonian gravity. It is shown that these equations are in close correspondence with the ones obtained in the framework of general relativity, with the scale factor satisfying the same equation in both theories, when the pressure is neglected. The characteristics of the expansion for a universe dominated by radiation, matter or vacuum are obtained. The Newtonian gravity is formulated in geometrical language. In this scenario, it is shown that for homogeneous and isotropic universes, the equation for the geodesic deviation in Newtonian cosmology is exactly the same as the geodesic equation in Einstein cosmology. We discuss possible consequences of the assumption of a Yukawa correction to the New- tonian gravitational interaction. It is shown that this correction does not introduce any modi cation in the cosmological equations. We present and discuss a result obtained concerning the growth of density perturbations in Newtonian cosmological models with creation of matter, in the case in which the pressure is neglected. Some addition comments are done for a system in which the pressure is considered. We also investigate some aspects of quantum Newtonian cosmology and construct a wave function for a universe with continuous matter creation, in the framework of non-relativistic quantum mechanics. / As equações de movimento são obtidas na cosmologia Newtoniana, com o uso da dinâmica Newtoniana e da teoria da gravitação de Newton. Mostra-se que estas equações são equiva- lentes às da relatividade geral, com o fator de escala obedecendo a mesma equação em ambas as teorias, quando a pressão é desprezível. Discute-se as características da expansão para universos dominados por radiação, matéria ou vácuo. A gravitação Newtoniana é formulada na linguagem geométrica. Neste cenário, mostra-se que para universos homogêneos e isotrópicos, a equação para o desvio geodésico na cosmologia Newtoniana é exatamente a mesma que é obtida na teoria de Einstein. Discutimos as possíveis consequências de admitirmos a correção de Yukawa à intera- ção gravitacional Newtoniana. Mostra-se que esta correção não introduz modi cações nas equações cosmológicas. Apresentamos e discutimos um resultado sobre a evolução de perturbações em modelos cosmológicos Newtonianos, com criação de matéria, no caso em que a pressão é desprezível. Comentários adicionais são feitos para um sistema no qual a pressão é considerada. Investigamos, também, alguns aspectos da cosmologia Newtoniana quântica e construí- mos uma função de onda para um universo com criação contínua de matéria, no contexto da mecânica quântica não-relativística.

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This thesis is concerned with a theoretical and experimental study of the hydrodynamics and heat transfer characteristics of viscous fluids flowing in tubes under laminar conditions. Particular attention has been given to the effects of the rheological properties and their variation with temperature. A review of problems of this type showed that in spite of the many potential applications of the results in a wide range of industries the subject had not been well developed and further work is justified in order to fill some of the gaps in our knowledge. The early part of the thesis considers the justification of the work in this way and sets down the scope and objectives. A computer progracune was then developed to allow the governing equations of the problem to be solved numerically to give the velocity and temperature profiles and pressure drop for both heating and cooling conditions. The results were also presented in the form of Nusselt numbers as a function of the Graetz numberp since this form is useful for engineering design purposes. The validity of the predictions were then checked by a programme of experimental work. Temperature and velocity profiles have been measured in order to provide a more severe test of the theory than could be imposed by the measurement of overall heat transfer rates. A combined thermocouple probe/Pitot tube was developed to allow simultaneous measurements of velocity and temperature to be made. A Newtonian oil and two non-Newtonian Carbopol solutions were studied. This is the first time that velocity and temperature profiles have been measured for non-Newtonian fluids in this type of situation. The results of the work heve shown that (a) the velocity and temperature profiles and pressure drops are greatly affected by the temperature dependence of the rheological properties and since real viscous fluids are normally very temperature-sensitive it is important that this effect is properly taken into account. (b) the engineering design correlations commonly used for the prediction of heat transfer coefficients can be seriously in error, especially for cooling conditions and when non-Nevitonian fluids are being considered. (c) a mathematical model can be developed which accurately describes all the phenomena and gives predictions which are very close to those observed experimentally. An important objective was to develop more accurate engineering design correlations for non-isothermal pressure drop and heat transfer rates. / University of Bradford

The present study investigates experimentally the laminar mixing and heat transfer of a range of helical ribbon and anchor impellers for both Newtonian and inelastic non-Newtonian fluids. The work also correlates the experimental data empirically in the form of dimensionless groups. In order to estimate the relative importance and the effect of all the geometrical parameters on the mixing power and heat transfer, data from the published literature sources will be utilized and combined with the results from this study. Thus, reliable empirical correlations will be obtained which are applicable over the widest range of operating conditions. The study also investigates the ablity of the various impellers to level out temerature distributions. The measurement of these temperature gradients and the impeller power requirements gives a measure of the mixing efficiency of the impeller used. / Science Research Council

<p dir="ltr">Machine learning and deep learning techniques now provide innovative tools for addressing problems in biological, engineering, and physical systems. Physics-informed neural networks (PINNs) are a type of neural network that incorporate physical laws described by partial differential equations (PDEs) into their supervised learning tasks. This dissertation aims to enhance PINNs with improved training techniques and loss functions to tackle the complex physics of viscoelastic flow and rheology more effectively. The focus areas of the dissertation are listed as follows: i) Assigning relative weights to loss terms in training physics-informed neural networks (PINNs) is complex. We propose a solution using numerical integration via backward Euler discretization to leverage statistical properties of data for determining loss weights. Our study focuses on two and three-dimensional Navier-Stokes equations, using spatio-temporal velocity and pressure data to ascertain kinematic viscosity. We examine two-dimensional flow past a cylinder and three-dimensional flow within an aneurysm. Our method, tested for sensitivity and robustness against various factors, converges faster and more accurately than traditional PINNs, especially for three-dimensional Navier-Stokes equations. We validated our approach with experimental data, using the velocity field from PIV channel flow measurements to generate a reference pressure field and determine water viscosity at room temperature. Results showed strong performance with experimental datasets. Our proposed method is a promising solution for ’stiff’ PDEs and scenarios requiring numerous constraints where traditional PINNs struggle. ii) Machine learning algorithms are valuable for fluid mechanics, but high data costs limit their practicality. To address this, we present viscoelasticNet, a Physics-Informed Neural Network (PINN) framework that selects the appropriate viscoelastic constitutive model and learns the stress field from a given velocity flow field. We incorporate three non-linear viscoelastic models: Oldroyd-B, Giesekus, and Linear PTT. Our framework uses neural networks to represent velocity, pressure, and stress fields and employs the backward Euler method to construct PINNs for the viscoelastic model. The approach is multistage: first, it solves for stress, then uses stress and velocity fields to solve for pressure. ViscoelasticNet effectively learned the parameters of the viscoelastic constitutive model on noisy and sparse datasets. Applied to a two-dimensional stenosis geometry and cross-slot flow, our framework accurately learned constitutive equation parameters, though it struggled with peak stress at cross-slot corners. We suggest addressing this by exploring smaller domains. ViscoelasticNet can extend to other rheological models like FENE-P and extended Pom-Pom and learn entire equations, not just parameters. Future research could explore more complex geometries and three-dimensional cases. Complementing Particle Image Velocimetry (PIV), our method can determine pressure and stress fields once the constitutive equation is learned, allowing the modeling of future fluid applications. iii) Physics-Informed Neural Networks (PINNs) are widely used for solving inverse and forward problems in various scientific and engineering fields. However, most PINNs frameworks operate within the Eulerian domain, where physical quantities are described at fixed points in space. We explore coupling Eulerian and Lagrangian domains using PINNs. By tracking particles in the Lagrangian domain, we aim to learn the velocity field in the Eulerian domain. We begin with a sensitivity analysis, focusing on the time-step size of particle data and the number of particles. Initial tests with external flow past a cylinder show that smaller time-step sizes yield better results, while the number of particles has little effect on accuracy. We then extend our analysis to a real-world scenario: the interior of an airplane cabin. Here, we successfully reconstruct the velocity field by tracking passive particles. Our findings suggest that this coupled Eulerian-Lagrangian PINNs framework is a promising tool for enhancing traditional experimental techniques like particle tracking. It can be extended to learn additional flow properties, such as the pressure field for three-dimensional internal flows, and infer viscosity from passive particle tracking, providing deeper insights into complex fluids and their constitutive models. iv) Time-fractional differential equations are widely used across various fields but often present computational and stability challenges, especially in inverse problems. Leveraging Physics-Informed Neural Networks (PINNs) offers a promising solution for these issues. PINNs efficiently compute fractional time derivatives using finite differences and handle other derivatives via automatic differentiation. This study addresses two inverse problems: (1) anomalous diffusion and (2) fractional viscoelasticity. Our approach defines residual loss scaled with the standard deviation of observed data, using numerically generated and experimental datasets to learn fractional coefficients and calibrate parameters for the fractional Maxwell model. Our framework demonstrated robust performance for anomalous diffusion, maintaining less than 10% relative error in predicting the generalized diffusion coefficient and the fractional derivative order, even with 25% Gaussian noise added to the dataset. This highlights the framework’s resilience and accuracy in noisy conditions. We also validated our approach by predicting relaxation moduli for pig tissue samples, achieving relative errors below 10% compared to literature values. This underscores the efficacy of our fractional model with fewer parameters. Our method can be extended to model non-linear fractional viscoelasticity, incorporate experimental data for anomalous diffusion, and apply it to three-dimensional scenarios, broadening its practical applications.</p>

Orientador: Geraldo de Freitas Maciel / Resumo: No contexto de Desastres "Naturais", as corridas de lama têm sido objeto de estudo devido ao seu poder erosivo e, muitas vezes, destrutivo, acarretando perdas materiais vultosas e ceifando vidas. Nestes escoamentos, quando em condições favoráveis de vazão, inclinação e reologia do fluido, podem surgir instabilidades que se propagam em forma de trem de ondas na superfície, denominadas roll waves. A literatura acerca do assunto trata, geralmente, dos critérios de geração, estabilidade, e determinação das características principais do fenômeno, como amplitude, comprimento e celeridade de onda. Nesta dissertação buscou-se estudar a tensão de cisalhamento no fundo na presença de roll waves, em duas vertentes: a primeira apresenta as roll waves em água limpa, baseando-se no trabalho clássico de Dressler (1949); a segunda, dando continuidade aos trabalhos do Grupo de Pesquisa de Reologia de Materiais Viscosos e Viscoplástcos (Grupo RMVP), focou no estudo de roll waves desenvolvendo-se em fluidos do tipo Herschel-Bulkley, em duas situações - canal de fundo impermeável e fundo com condição de permeabilidade, grande contribuição desta dissertação. Os modelos matemáticos foram desenvolvidos com base nas equações de águas rasas, cuja implementação numérica permitiu confrontar resultados experimentais e numéricos, que apresentaram boa aderência. Para o modelo com condição de permeabilidade no fundo, verificou-se a influência do fator de porosidade nas características das roll waves (ampli... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: Mudflows have been the focus of studies because of their erosive ability and often destructive power, causing material losses and taking away lives. Under favorable conditions of discharge, slope, disturbance, and rheology, these flows can develop a specific type of instability that is propagated downstream as shock waves, called roll waves. Most of the roll waves literature provides information on generation criteria, stability, and information of amplitudes, wavelengths, and celerity. This works brings a study of bottom shear stress in pulsating flows (roll waves) in 2 parts. In the first part, we present roll waves in clean water, based on Dressler’s work. In the second part, we continue the works of research team about roll waves developing in Herschel-Bulkley fluid under 2 conditions: impermeable bottom and porous bed. The mathematical models developed were based on shallow water equations. The results of these models were compared to Fluent and experimental results, showing a good agreement. For the mathematical model with porous bed condition, we evaluated the effect of porosity factor in properties of roll waves, and we observed that the amplitude of the roll wave usually increases, whereas the length and the celerity decrease with the presence of this factor. Finally, considering an impermeable bottom, the bottom shear stress presented an increase of 12% to 27%, depending on nature (laminar-turbulent) and dynamics (Froude number) of flow. Taking in account a porous b... (Complete abstract click electronic access below) / Mestre

Master of Science / Department of Mechanical and Nuclear Engineering / B. Terry Beck / The objective of this project was to first evaluate the feasibility of developing a viscous damping device that used a Non-Newtonian Shear Thickening Fluid (STF) and incorporating it as a door latch into an existing commercial dryer unit. The device would keep the door closed during sudden large magnitude impact loads while still allowing the door to open normally when force is applied gradually at the door handle. The first phase of the project involved performing background research on the subject and performing preliminary analysis in order to determine if the concept was feasible enough to be worth constructing a physical prototype. This preliminary analysis consisted of a literature review of existing damping mechanisms and shear thickening fluids, rheometer testing of shear thickening suspensions to obtain viscosity data, and performing numerical simulations to determine if a damper that fit the size requirements could produce enough resistance force. The focus for the second phase of the project was to demonstrate a proof of concept in the form of a working model prototype. This prototype did not need be of identical shape and proportions as the finalized design, but would be developed to facilitate experimental testing and evaluation of performance under the desired operating conditions. It was also necessary to design and construct the test setup for the dynamic testing of the dryer door opening so that the opening displacement as well as the force applied to the door could be recorded as a function of time. The final phase of the project consisted of improving upon the original prototype in order to prove the validity of a viscous latch beyond the proof of concept phase in a form closer to what is desired for the commercial product. This required reducing the physical size of the new prototype latch so as to fit within the space available in a particular dryer, incorporate a one-way ratcheting device into the latch to allow unrestricted closing of the door, and increase the operational temperature range of the damper.