The present work seeks to fully investigate, describe and characterize the distinct flow regimes existing within a mixing vessel at various rotational speeds. This investigation is computational in nature and simulates the flow within a baffled tank containing a Rushton turbine of the standard configuration. For a Re based on impeller diameter and blade rotational speed (Re â ¡ Ï ND2/μ) the following flow regimes were identified and investigated in detail: Reverse/reciprocating flows at very low Re (<10); stalled flows at low Re (â 10); laminar pumping flow for higher Re and transitional pumping flow (10 squared < Re <10 to the 4th). For the three Re numbers 1, 10 and 28, it was found that for the higher Re number (28), the flow exhibited the familiar outward pumping action associated with radial impellers under turbulent flow conditions. However, as the Re number decreases, the net radial flow during one impeller revolution was reduced and for the lowest Re number a reciprocating motion with negligible net pumping was observed. In order to elucidate the physical mechanism responsible for the observed flow pattern at low Re, the forces acting on a fluid element in the radial direction were analyzed. Based on this analysis, a simplified quasi-analytic model of the flow was developed that gives a satisfactory qualitative, as well as quantitative representation of the flow at very low Re. Investigation of the transitional flow regime (Re â 3000) includes a compilation and characterization of ensemble and turbulent quantities such as the Reynolds stress components, dissipation length η and time scales Ï , as well a detailed investigation of the near-impeller flow and trailing vortex. Calculation and compilation of all terms in the turbulent kinetic energy transport equation was performed (including generation and the illusive turbulent pressure work). Specifically, the most important transport mechanism was turbulent convection/diffusion from the impeller disk-plane/trailing vortex region. Mean flow transport of turbulent kinetic energy was primarily towards the impeller disk-plane and radially outward from the trailing vortex region. The turbulent pressure work was found to partially counteract turbulent convection. Turbulent dissipation followed by turbulent viscous work were found to be the least important mechanism responsible for turbulent transport with both terms being maximized within the vortex region and at the disk-plane down-stream from the vortices. / Ph. D.

Continuous processing in the pharmaceutical and fine chemical industries, particularly in micro/milli-scale reactors, has been a topic of interest in literature in recent years due to the advantages offered over batch reactions. One such advantage is the enhanced transport properties of operating at smaller scales, although the quantification of the transport phenomena is not straightforward when wall and entrance effects cannot be neglected. In the first study presented, various micro-mixer geometries and scales were considered to increase the mixing efficiency in liquid-liquid systems of diverse interfacial tensions for fast reactions. The conditions were varied over different flow regimes; including slug flow, parallel flow, and drop flow. A mass-transfer-limited test reaction was used to evaluate the overall volumetric mass transfer coefficients (Korga) as a function of the average rate of energy dissipation (ε) for each mixer design. The onset of drop flow occurred at a lower ε for the LL-Triangle mixer when compared with the Sickle or LL-Rhombus mixers for low interfacial-tension systems (i.e., n-butanol-water). In the drop flow regime for energy dissipation rates of around 20 to 500 W/kg, Korga values ranged from approximatively 0.14 to 0.35 s-1 and 0.004 to 0.015 s-1 for the relatively low and high interfacial-tension (i.e., toluene-water) systems, respectively. The second investigation explored the heat transfer properties of a FlowPlate® system by Ehrfeld Mikrotechnik BTS. First, in a non-reactive system with rectangular serpentine channels (d_h<1mm, 400<Re<2000), a Gnielinski-type model was fit to the internal Nusselt number. Using a silver-based thermal paste between the reactor and heat transfer fluid plates proved to reduce the external resistance to heat transfer by ~70%, yielding overall heat transfer coefficients of ~2200 [W/(m^2 K)]. Secondly, a Grignard reaction was highlighted as a test reaction to compare different reactors’ localized heat transfer characteristics (i.e., hotspot formation) with various micro-mixer geometries, materials, injection ports, and channel scales. Lastly, a case study of four reactions utilized the fourth Damköhler number to determine a maximum channel diameter that would remove sufficient heat to avoid hotspot formation. Each of these studies provides insight to aid in the proper selection of a reactor for a given set of physical properties and reaction kinetics/enthalpies.

Continuous milli-scale and micro-scale structures such as FlowPlate® microreactors have emerged as a promising element of process intensification due to their inherently effective rates of mass and heat transfer. These microfluidic devices have proven to be a preferred solution in place of energy-intensive batch processes for certain pathways of fine chemical and pharmaceutical synthesis, most notably fast reactions taking place on the scale of milliseconds to seconds. Computational fluid dynamics (CFD) has become an increasingly valuable tool in the field of microreactor design and optimization for its ability to locally map complex fluid flow patterns and resolve microscopic scales of reactive mixing that are challenging to characterize experimentally. The primary objective of this research was thus to develop and validate a mathematical model for the simulation of chaotic flow and homogeneous mixing in continuous microreactors. The model needed to be versatile enough to handle transition between flow regimes within a given reactor as well as the coexistence of both chaotic and laminar flow patterns in the micromixing elements that comprise said reactors. This was successfully achieved through the implementation of a k-ω SST (shear-stress transport) turbulence model that accounts for the impact of small-scale temporal and spatial fluctuations generated in the micromixer geometries studied herein; be it a liquid-liquid mixer (LLM), a serpentine (SZ) or a tangential (TG) mixer. In a first CFD study, the computational predictions were validated based on excellent agreement with experimental pressure loss (R^2 > 0.997) and residence time distribution (RTD) data (R^2 > 0.97) in several LL microreactors at Reynolds numbers ranging from 210 to 2140. Furthermore, the local velocity distribution and streamlines were mapped across the 3D domain of these reactors and it was discovered, based on the emergence of advective recirculation zones and turbulent dispersion, that a drastic change in flow behaviour occurred in these mixing elements at a Reynolds number of about 640. The interspacing of LLM elements with straight microchannels proved to be a suitable approach to modulating pressure loss while concurrently maintaining the chaotic secondary flow patterns generated from the mixers. In a second CFD study, the impact of micromixer geometry on the local velocity fields and advective transport performance was investigated both from a macromixing and micromixing perspective. Like the LLM, the SZ and TG mixers conferred chaotic secondary flow patterns at characteristic Reynolds numbers between 500 and 1000. As such, it was concluded that it would be ideal to operate these mixers at water flow rates of at least 30 ml/min. Contour plots of the velocity magnitude coupled with the computation of RTD showed that the SZ virtually mimics a plug-flow profile over a volume of 77 mm3 or greater at 50 g/min. The RTD of the LLM and TG resembles that of a mixed flow pattern given that approximately 65-80% of their fluid volume is occupied by recirculation zones. As such, it required 65 LLMs in series (3105 mm3) and 80 TGs (1142 mm3) to approach the same pattern as 10 SZs (77 mm3) from a macromixing perspective. Micromixing time distributions (MTD) were also characterized by locally computing the decay time of small-scale segregation (t_SSS) as a function of flow rate, wherein higher flow rates generated lower characteristic mixing times. The TG and LLM conferred the broadest range of mixing times, spanning nearly four orders of magnitude in the range of [0.02 ms, 10 ms], whereas the SZ generated a much narrower MTD ranging between [0.024 ms, 0.69 ms]. Finally, the impact of geometry and flow conditions on reaction yield was assessed by characterizing the extent of a finite-rate reaction relative to an infinitely fast reaction taking place in parallel. The calculated yield for the competitive-parallel reaction scheme showed that the second Damköhler number (Dall) computed based on the mean tSSS provides useful information about whether the process will be limited by the intrinsic rate of reaction or by the rate of mass transfer, even though the reaction process is controlled by a combination of the RTD as well as loss of LSS and SSS. It was concluded that the change in MTD as a function of power dissipation should coincide with the reaction yield response, and that any deviation in that relationship is because of macroscopic blending of reactants in the entrance region.

[pt] Doenças cardiovasculares são responsáveis por um elevado número de óbitos em seres humanos. Muitas dessas patologias são dependentes do ciclo cardíaco e estão localizadas na aorta, a maior e principal artéria do nosso corpo. O conhecimento dos padrões de escoamento e distribuições de tensões nas paredes da aorta podem auxiliar no diagnóstico e prevenção de algumas dessas doenças. Dessa forma, estudou-se numericamente o escoamento do sangue, durante o ciclo cardíaco, em um modelo 3D da aorta de um paciente específico, após a implantação de TAVI (Transcatheter Aortic Valve Implantation). O ciclo cardíaco é formado por dois períodos chamados de sístole e diástole. Durante a sístole, sangue é bombeado do coração para a aorta, apresentado altos valores de vazão, resultando em escoamento turbulento. Por outro lado, na diástole, com o fechamento da válvula aórtica, o sangue escoa com baixas velocidades em regime laminar. Até hoje, cientistas enfrentam um desafio na modelagem da turbulência, pois não existe uma única modelagem que forneça previsibilidade para todas as situações envolvendo o regime turbulento, com esforço computacional razoável. Para seleção do modelo de turbulência mais adequado para análise do escoamento no interior da aorta, na presença da transição de regimes de escoamento durante o ciclo cardíaco, com um custo razoável, selecionou-se a metodologia baseada na Média de Reynolds. Diferentes modelos foram comparados com dados experimentais extraídos do mesmo modelo aórtico em escala real, porém em regime permanente, com vazão correspondente ao pico da sístole. Por fim, avaliou-se o impacto das condições de contorno e dos modelos de turbulência durante o ciclo cardíaco na distribuição e valores de tensões e grandezas turbulentas no endotélio vascular. Mostrou-se que a distribuição espacial das médias temporais de tensão foram qualitativamente e quantitativamente similares, para os dois ciclos cardíacos representativos de diferentes pacientes, porém com pequenas mudanças locais para cada caso. Em termos dos modelos de turbulência, observou-se que o modelo SAS (Scale Adaptive Simulation) foi capaz de representar a relaminarização do escoamento sanguíneo no período diastólico. / [en] Cardiovascular diseases are responsible for a high number of deaths in humans. Many of these pathologies are dependent on the cardiac cycle and are located in the aorta, the largest and main artery in our body. Knowledge of flow patterns and stress distributions in the walls of the aorta can help in the diagnosis and prevention of some of these diseases. Thus, the flow of blood during the cardiac cycle was numerically studied in a 3D model of the aorta of a specific patient, after TAVI (Transcatheter Aortic Valve Implantation) implantation. The cardiac cycle consists of two periods called systole and diastole. During the systole, blood is pumped from the heart to the aorta, presenting high flow rates, resulting in a turbulent flow. On the other hand, in diastole, with the closure of the aortic valve, the blood flows with low velocities in laminar regime. Until today, scientists face a challenge in turbulence modeling, as there is no single model that provides predictability for all situations involving the turbulent regime, with reasonable computational effort. In order to select the most suitable turbulence model for the analysis of the flow inside the aorta, in the presence of the transition of flow regimes during the cardiac cycle, with a reasonable cost, the methodology based on the Reynolds Average was selected. Different models were compared with experimental data extracted from the same real-scale aortic model, but a in steady state, with flow corresponding to the systolic peak. Finally, the impact of boundary conditions and turbulence models during the cardiac cycle on the distribution and values of stresses and turbulent quantities in the vascular endothelium were evaluated. It was shown that the spatial distribution of the temporal averages of tension was qualitatively and quantitatively similar, for the two cardiac cycles representative of different patients, but with small local changes for each case. In terms of turbulence models, it was observed that the SAS (Scale Adaptive Simulation) model was able to represent the relaminarization of blood flow in the diastolic period.

The laminar-turbulent transition in viscous fluid flows is one of the most intriguing problems in fluid dynamics today. In view of the enormous applications it has in a variety of fields such as aircraft design, turbomachinery, etc., scientists have now realized the importance of tackling this problem effectively. Three-dimensional flows are usually associated with pressure gradient, streamline curvature, streamline convergence / divergence etc., all acting simultaneously. Towards a better understanding of the transition process and modeling the transition zone, it is important to study the effect of each of these parameters on the transitional flow. The present work aims at studying experimentally the effect of lateral streamline convergence alone on the laminar-turbulent transition zone under constant stream-wise pressure. The experimental setup consists of a low turbulence wind tunnel with its test section modified to cause lateral streamline convergence under constant pressure. This is achieved by converging the side-walls and appropriately diverging the roof, thus maintaining a constant stream-wise pressure. The half angle of convergence is chosen as 100 , which is approximately the same as the half of the turbulent spot envelope in constant pressure two-dimensional flows. Experiments are carried out to analyze the development of the laminar and transitional boundary layers, intermittency distribution in the transition zone and the overall characteristics of an artificially induced turbulent spot. The laminar velocity profiles are found to be of the Blasius type for two-dimensional constant pressure flows. However, the converging streamlines are found to contribute to an increased thickness of the boundary layer as compared to the corresponding two-dimensional flow. The intermittency distribution in the transition zone is found to follow the universal intermittency distribution for two-dimensional constant pressure flow. A simple linear-combination model for two-dimensional flows is found to perform very well in predicting the measured velocity profiles in the transition zone. An artificially introduced turbulent spot is found to propagate along a conical envelope with an apex cone angle of 220 which is very nearly the value for a corresponding constant pressure two-dimensional flow. The spot shapes and celerities are also comparable to those in two-dimensional flow. In summary, the present study brings out many similarities between a constant pressure laterally converging flow and a constant pressure two-dimensional flow.