Theoretical and numerical studies of slip flows

Tese de doutoramento em Ciência e Engenharia de Polímeros e CompósitosThis thesis presents an intensive study on slip flows of Newtonian and Non-Newtonian fluids carried out both analytically and numerically. Industrial applications of these flows are found in classical industries such as in polymer processing (for instance in extrusion) and in more modern applications as in lab-on-chip devices. Analytical solutions for flows under slip, are presented for both Newtonian, inelastic Newtonian and Non-Newtonian flows. These analytical solutions were missing in the literature and are helpful for both theoretical analysis and computer code validation. Slip boundary conditions were implemented in a computational fluid dynamics code, based on the finite volume method framework. New techniques for their implementation were devised, allowing to obtain convergence for reasonable Weissenberg numbers, using an appropriate iterative procedure to couple velocity, pressure and stress. The numerical code was then used to simulate benchmark problems, such as the 4:1 contraction, 1:4 expansion and slip-stick flows under slip, usually found in polymer processing.. The theoretical study of development length for Newtonian and viscoelastic fluids was performed for a channel flow under slip. New correlations for predicting the development length in micro and macro channels were devised. Other part of these thesis was dedicated to the theoretical study of electro-osmotic flows of complex fluids, for which analytical solutions for simple flows under the influence of the linear and nonlinear Navier slip boundary conditions were devised.Nesta tese é apresentado um estudo intensivo de escoamentos com escorregamento, envolvendo fluidos newtonianos e não-newtonianos. Este tipo de escoamentos pode ser encontrado na indústria, por exemplo no processo de extrusão e ainda em aplicações mais modernas, tais como aparelhos baseados no conceito “lab-on-chip”. São apresentadas soluções analíticas com escorregamento para fluidos newtonianos, e diversos fluidos não-newtonianos, tanto inelásticos como viscoelásticos. Estas soluções analíticas não existiam na literatura e são úteis tanto em termos teóricos assim como para a validação de códigos numéricos. As condições de fronteira de escorregamento foram implementadas num código numérico de mecânica dos fluidos computacional baseado no métodos dos volumes finitos. Foram desenvolvidas novas técnicas para a implementação destas condições de fronteira, permitindo obter convergência para valores razoáveis do número de Weissenberg, usando um processo iterativo para acoplar os campos de velocidades, pressões e tensões. Este código numérico foi depois usado para simular problemas de referência, tais como os escoamentos numa contracção súbita 4:1, numa expansão 1:4 e o escoamento “slip-stick”, sob a influência do escorregamento na parede. Estas geometrias são frequentemente utilizadas em processamento de polímeros, o que substancia a utilidade prática destas simulações. Foi feito um estudo numérico e teórico para descobrir o comprimento de desenvolvimento do escoamento num canal simples com escorregamento na parede, de fluidos newtonianos e viscoelásticos. Foram ainda propostas novas correlações para prever esse comprimento. Outra parte do trabalho foi dedicada ao estudo de electro-osmose, onde novas soluções analíticas para escoamentos simples sob a influência do modelo de escorregamento linear de Navier, são apresentadas.Fundação para a Ciência e a Tecnologia (FCT) - SFRH/BD/37586/2007Fundo Social Europeu Europeu (FSE) - Human Potential Operational Programm

Comparison of different numerical methods for the solution of the time-fractional reaction-diffusion equation with variable diffusion coefficient

In this work we perform a comparison of two different numerical schemes for the solution of the time-fractional diffusion equation with variable diffusion coefficient and a nonlinear source term. The two methods are the implicit numerical scheme presented in [M.L. Morgado, M. Rebelo, Numerical approximation of distributed order reaction- diffusion equations, Journal of Computational and Applied Mathematics 275 (2015) 216-227] that is adapted to our type of equation, and a colocation method where Chebyshev polynomials are used to reduce the fractional differential equation to a system of ordinary differential equationsCOMPETE, FEDER and Fundação para a Ciência e a Tecnologia (the Portuguese Foundation for Science and Technology (FCT)) through Strategic Projects - LA 25 – 2013-2014, PTDC/EME- MFE/113988/2009 and EXPL/CTM-POL/1299/2013. M. Rebelo acknowledge financial funding by the Portuguese Foundation for Science and Technology through the project PEstOE/MAT/UI0297/2013 (Centro de Matemática e Aplicacões

A distributed order viscoelastic model for small deformations

In this work we discuss the connection between classical, fractional and dis- tributed order viscoelastic Maxwell models, presenting the basic theory supporting these constitutive equations, and establishing some background on the admissibility of the dis- tributed order Maxwell model. We derive the storage and loss modulus functions for the distributed order viscoelastic model and perform a fitting to experimental data. The fitting results are compared with the Maxwell and Fractional Maxwell models.L.L. Ferr´as would also like to thank FCT for financial support through projects UIDB/ 00013/2020 and UIDP/00013/2020. M.L. Morgado aknowledges funding by FCT through project UID/Multi/04621/2019 of CEMAT/IST-ID, Center for Computational and Stochastic Mathematics, Instituto Su perior T´ecnico, University of Lisbon. This work was partially supported by the Funda¸c˜ao para a Ciˆencia e a Tecnologia (Por tuguese Foundation for Science and Technology) through the project UIDB/00297/2020 (Centro de Matem´atica e Aplica¸c˜oes). The authors also acknowledge financial support from COST Action CA15225, a network supported by COST (European Cooperation in Science and Technology)

Stable and convergent finite difference schemes on nonuniformtime meshes for distributed-order diffusion equations

In this work, stable and convergent numerical schemes on nonuniform time meshes are proposed, for the solution of distributed-order diffusion equations. The stability and convergence of the numerical methods are proven, and a set of numerical results illustrate that the use of particular nonuniform time meshes provides more accurate results than the use of a uniform mesh, in the case of nonsmooth solutions.The authors acknowledge the support of the Center for Mathematics and Applications (CMA)—FCT-NOVA, Center for Computational and Stochastic Mathematics, Instituto Superior Técnico, and CMAT—Centre of Mathematics—University of Minho. The first author acknowledges Fundação para a Ciência e Tecnologia (Portuguese Foundation for Science and Technology) within Projects UIDB/04621/2020 and UIDP/04621/2020. The second author acknowledges the Fundação para a Ciência e a Tecnologia through Project UIDB/00297/2020 (Centro de Matemática e Aplicações). The third author acknowledges the funding by Fundação para a Ciência e Tecnologia through Projects UIDB/00013/2020 and UIDP/00013/202

A primer on CFD-DEM for polymer-filled suspensions

This work reports on an evaluation of the computational fluid dynamics–discrete element method (CFD-DEM) numerical approach to study the behavior of polymer-filled suspensions in a parallel-plate rheometer. For this purpose, an open-source CFD-DEM solver is used to model the behavior of such suspensions considering different particle volume fractions and different types of fluid rheology. We first validate the numerical approach for the single-phase flow of the continuum phase (fluid phase) by comparing the fluid’s azimuthal velocity and shear stress components obtained from the open-source solver against the analytical expressions given in cylindrical coordinates. In addition, we compare the numerical torque given by the numerical procedure with analytical expressions obtained for Newtonian and power law fluids. For both cases, there is a remarkable agreement between the numerical and analytical results. Subsequently, we investigated the effects of the particle volume fraction on the rheology of the suspension. The numerical results agree well with the experimentally measured ones and show a yield stress phenomenon with the increase of the particle volume fraction.This research was funded by FEDER through the COMPETE 2020 Programme and National Funds through FCT (Portuguese Foundation for Science and Technology) under projects UID-B/05256/2020, UID-P/05256/2020, UIDB/ 00013/2020, UIDP/00013/2020, UIDB/00532/ 2020, PTDC/EMS-ENE/3362/2014–POCI-01-0145-FEDER-016665

High-order methods for systems of fractional ordinary differential equations and their application to time-fractional diffusion equations

Taking into account the regularity properties of the solutions of fractional differential equations, we develop a numerical method which is able to deal, with the same accuracy, with both smooth and nonsmooth solutions of systems of fractional ordinary differential equations of the Caputo-type. We provide the error analysis of the numerical method and we illustrate its feasibility and accuracy through some numerical examples. Finally, we solve the time-fractional diffusion equation using a combination of the method of lines and the newly developed hybrid method.L.L. Ferras would like to thank FCT - Fundacao para a Ciencia e a Tecnologia, I.P. (Portuguese Foundation for Science and Technology) for financial support through the scholarship SFRH/BPD/100353/2014 and Project UID-MAT-00013/2013. M.L. Morgado aknowledges the financial support of FCT, through the Project UID/Multi/04621/2019 of CEMAT/IST-ID, Center for Computational and Stochastic Mathematics, Instituto Superior Tecnico, University of Lisbon. This work was also partially supported by FCT through the Project UID/MAT/00297/2019 (Centro de Matematica e Aplicacoes)

Advanced polymer simulation and processing

[Excerpt] Polymer processing techniques are of paramount importance in the manufacture of polymer parts. The key focus is on producing parts with the desired quality, which usually refers to mechanical performance, dimensional conformity, and appearance. To maximize the overall efficiency of polymer processing techniques, advanced modeling codes are needed along with experimental setups to simulate and optimize the processes. [...]This research was funded by FEDER through the COMPETE 2020 Programme and National Funds through FCT-Portuguese Foundation for Science and Technology under the projects UIDB/05256/2020 and UIDP/05256/2020. It was also funded by FCT through CMAT (Centre of Mathematics of the University of Minho) through projects UIDB/00013/2020 and UIDP/00013/2020

Effect of polymer melt wall slip on the flow balance of profile extrusion dies

This work describes the implementation of the wall slip boundary condition in an in-house developed 3D numerical code based on the Finite Volume Method. For this purpose, several phenomenological models relating the velocity and the shear stress at the wall were implemented. This new feature is verified using a simple case study, by comparing the numerical results with those obtained through the corresponding analytical solution. Then, the potentialities of the new code are illustrated performing flow simulations of a polymer melt in a complex flow channel. The results obtained show that the slip at the wall influences the flow distribution at the die flow channel outlet. Therefore, and to assess the relevance of slippage in the optimal die geometry, the automatic optimization of a die flow channel, required for the production of a specific thermoplastic profile, is performed using both the no-slip and slip boundary conditions, together with two alternative optimization strategies. It is shown that slip favors the flow balance of the dies and also other issues of its performance.The authors gratefully acknowledge funding from Fundação para a Ciência e Tecnologia, FCT (COMPETE Program) under the projects FCOMP-01-0124 - FEDER-010190 (Ref. PTDC / EME - MFE/102729/2008) and FCOMP-01-0124-FEDER-015126 (Refª. FCT PTDC/EME-MFE/113988/2009), and FEDER, via FCT, under the PEst-C/CTM/LA0025/2011 (Strategic Project - LA 25 - 2011-2012)

On the effect of the wall slip boundary conditon

This work describes the implementation and assessment of the wall slip boundary condition in a 3D numerical modelling code, based on the finite volume method, that is being developed by the research team. Several phenomenological models relating the velocity and the shear stress at the wall were implemented. The capabilities of the new numerical code are illustrated with three case studies where the wall slip boundary conditions play an important role, namely the flow in a smooth contraction, the stick-slip phenomenon an the flow in a profile extrusion die. The results obtained are qualitatively in accordance with the theoretical expectations and evidence the importance of wall slip

Development of a machine learning model and a user interface to detect illegal swimming pools

Portuguese legislation states the compulsory reporting of the addition of amenities, such as swimming pools, to the Portuguese tax authority. The purpose is to update the property tax value, to be charged annually to the owner of each real estate. According to MarketWatch, this decade will bring a global rise to the number of swimming pools due to certain factors such as: cost reduction, increasing health consciousness, and others. The need for inspections to ensure that all new constructions are communicated to the competent authorities is therefore rapidly increasing and new solutions are needed to address this problem. Typically, supervision is done by sending human resources to the field, involving huge time and resource consumption, and preventing the catalogue from updating at a rate close to the speed of construction. Automation is rapidly becoming an absolute requirement to improve task efficiency and affordability. Recently, Deep Learn- ing algorithms have shown incredible performance results when used for object detection tasks. Based on the above, this work presents a study on the various existing object detec- tion algorithms and the implementation of a Deep Learning model capable of recognizing swimming pools from satellite images. To achieve the best results for this specific task, the RetinaNet algorithm was chosen. To provide a smooth user experience with the developed model, a simple graphical user interface was also created