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Non-Newtonian fluids are of great scientific interest due to their range of physical properties, which arise from the characteristic shear stress-shear rate relation for each fluid. The applications of non-Newtonian fluids are widespread and occur in many industrial (e.g. lubricants, suspensions, paints, etc.) and environmental (e.g. mud, ice, blood, etc.) problems, often involving multiple fluids. In this study, the novel technique of Incompressible Smoothed Particle Hydrodynamics (ISPH) with shifting (Lind et al., J. Comput. Phys., 231(4):1499-1523, 2012), is extended beyond the state-of-the-art to model non-Newtonian and multi-phase flows. The method is used to investigate important problems of both environmental and industrial interest. The proposed methodology is based on a recent ISPH algorithm with shifting with the introduction of an appropriate stress formulation. The new method is validated both for Newtonian and non-Newtonian fluids, in closed-channel and free-surface flows. Applications in complex moulding flows are conducted and compared to previously published results. Validation includes comparison with other computational techniques such as weakly compressible SPH (WCSPH) and the Control Volume Finite Element method. Importantly, the proposed method offers improved pressure results over state-of-the-art WCSPH methods, while retaining accurate prediction of the flow patterns. Having validated the single-phase non-Newtonian ISPH algorithm, this develops a new extension to multi-phase flows. The method is applied to both Newtonian/Newtonian and Newtonian/non-Newtonian problems. Validations against a novel semi-analytical solution of a two-phase Poiseuille Newtonian/non-Newtonian flow, the Rayleigh-Taylor instability, and a submarine landslide are considered. It is shown that the proposed method can offer improvements in the description of interfaces and in the prediction of the flow fields of demanding multi-phase flows with both environmental and industrial application. Finally, the Lituya Bay landslide and tsunami is examined. The problem is approached initially on the real length-scales and compared with state-of-the-art computational techniques. Moreover, a detailed investigation is carried out aiming at the full reproduction of the experimental findings. With the introduction of a k-ε turbulence model, a simple saturation model and correct experimental initial conditions, significant improvements over the state-of-the-art are shown, managing an accurate representation of both the landslide as well as the wave run-up. The computational method proposed in this thesis is an entirely novel ISPH algorithm capable of modelling highly deforming non-Newtonian and multi-phase flows, and in many cases shows improved accuracy and experimental agreement compared with the current state-of-the-art WCSPH and ISPH methodologies. The variety of problems examined in this work show that the proposed method is robust and can be applied to a wide range of applications with potentially high societal and economical impact.

External gear machines (EGMs) are used in a variety of industries ranging from fluid power machinery to fluid handling systems and fuel injection applications. Energy efficiency requirements and new trends in hydraulic technology necessitate the development of novel EGMs optimized for efficiency and reliability in all of these applications. A crucial piece in the novel EGM development process is a numerical model that can simulate the operation of EGM and predict its volumetric and hydro-mechanical performance.<div><br></div><div>The EGM simulation models developed in the past have focused mostly on the challenges related to the modeling of the theoretical behavior and elementary fluid dynamics, and determining appropriate modeling schemes. Key aspects related to the flow and geometry are either considered in a simplified manner or not considered at all. In particular, the current simulation models assume the fluid to be Newtonian and the leakage flows to be laminar. However, EGMs working in fluid handling applications operate with non-Newtonian fluids. Further, in fuel injection applications, due to low fluid viscosity and high operating speed, the internal leakage flows may not remain laminar.</div><div><br></div><div>With respect to the geometric aspects, the gears in EGMs are prone to manufacturing errors that are not accounted by any simulation model. In addition, there is no method available in the literature for accurately modeling the leakage flows through curve-constricted geometries in EGMs. Further, the goal of current simulation tools is related to the prediction of the volumetric performance of EGMs. However, an equally important characteristic, hydro-mechanical performance, is often ignored. Finally, the energy flow during EGM operation can result in the variation of the fluid temperature. Thus, the isothermal assumption of current simulation tools is another major limitation.</div><div><br></div><div>The work presented in this dissertation is focused on developing numerical methodologies for the modeling of EGMs that addresses all the aforementioned limitations of the current models. In this work, techniques for evaluating non-Newtonian internal flows in EGMs is developed to permit an accurate modelling of EGMs working with non-Newtonian fluids. For fuel injection EGMs, flow regime at the tooth tips of the gears is investigated and it is shown that the flow becomes turbulent for such EGMs. A methodology for modeling this turbulent flow is proposed and its impact on the performance of EGMs is described. To include gear manufacturing errors in the simulation model, numerical techniques are developed for modeling the effects of two common gear manufacturing errors: conicity and concentricity. These two errors are shown to have an opposite impact on the volumetric efficiency of the EGM. For the evaluation of flows through curve-constricted leakage paths in EGMs, a novel flow model is developed in this work that is applicable for a wide range of geometry and flow conditions. Modeling of the hydro-mechanical efficiency of EGMs is accomplished by developing methodologies for the evaluation of torque losses at key interfaces. Finally, to account for the thermal effects in EGMs, a thermal model is developed to predict the temperature distribution in the EGM and its impact on the EGM performance.</div><div><br></div><div><div>To validate the numerical methodologies developed in this work, several experiments are conducted on commercial gear pumps as well as on a custom apparatus designed and manufactured in the course of this research work. The results from the experiments are found to match those obtained from the simulations which indicates the validity of the methodologies developed in this work. </div><div><br></div><div>These numerical methodologies are based on the lumped parameter approach to allow the coupling with mechanical models for gear micromotion and permit fast computations so that the model can be used in optimization algorithms to develop energy efficient and reliable EGMs.</div><div><br></div><div>The methodologies described in the dissertation are useful for accurate analysis of a variety of EGMs working with different types of fluids and at wide range of operating conditions. This capability will be valuable for pump designers in developing novel better performing EGM designs optimized for various applications.</div><div><br></div></div>

O presente trabalho consiste em uma extensão do sistema FreeFlow-2D para simular escoamentos de fluidos não newtonianos bidimensionais com superfí cies livres, onde o fluido é descrito pelos modelos de Cross ou o modelo ``power-law\'\'. O método numérico empregado é o método GENSMAC. As equações governantes são aproximadas pelo método de diferenças finitas em uma malha deslocada e partículas marcadoras são utilizadas para a visualização do escoamento e localização da superfície livre. Resultados numéricos são apresentados. Em particular, a presente implementação é validada comparando-se a solução numérica com uma solução analítica / This work presents an extention of the Freeflow-2D system to non-Newtonian free surface flows. The governing equations are solved by the finite difference method on a staggered grid. Marker particles are used to describe the fluid providing the location and the visualization of the free surface. The methodology employed is based on the GENSMAC method. The fluid is modelled by the Cross and power-law models. Numerical examples are presented. The code is validated by making a comparison between analytical and numerical solutions

O presente trabalho consiste em uma extensão do sistema FreeFlow-2D para simular escoamentos de fluidos não newtonianos bidimensionais com superfí cies livres, onde o fluido é descrito pelos modelos de Cross ou o modelo ``power-law\'\'. O método numérico empregado é o método GENSMAC. As equações governantes são aproximadas pelo método de diferenças finitas em uma malha deslocada e partículas marcadoras são utilizadas para a visualização do escoamento e localização da superfície livre. Resultados numéricos são apresentados. Em particular, a presente implementação é validada comparando-se a solução numérica com uma solução analítica / This work presents an extention of the Freeflow-2D system to non-Newtonian free surface flows. The governing equations are solved by the finite difference method on a staggered grid. Marker particles are used to describe the fluid providing the location and the visualization of the free surface. The methodology employed is based on the GENSMAC method. The fluid is modelled by the Cross and power-law models. Numerical examples are presented. The code is validated by making a comparison between analytical and numerical solutions