Dissertations / Theses on the topic 'Rushton Turbine'

Mixing efficiency in stirred tanks is an important consideration in the design of many industrial processes. Computational fluid dynamics (CFD) techniques have been employed in the present work to study the hydrodynamics in a tank stirred by a Rushton turbine. The effect of the impeller clearance on the velocity field and mixing has been investigated. It has been shown that at a low impeller clearance, the Rushton turbine generates a flow field that evolves from the typical two loops to a single loop flow pattern similar to that of an axial impeller. This single loop flow pattern resulted in an increase in axial flow and a decrease in mixing time at a constant power number. It has been found that a draft tube can be used with a single Rushton turbine, at a low clearance to aid axial flow and mixing, and this resulted in 50% reduction in mixing time. There was a good comparison between laser Doppler velocimetry (LDV) experimental and CFD simulation flow fields, both of which showed that the draft tube improved mixing in the tank by suppressing secondary circulation loops.

The present study investigates the influence of the fluid properties on the mixing and aeration process of a Rushton turbine stirred tanks. Once the Rushton turbine agitated reactor is designed and developed following common standards, the effects of the viscosity, density, and surface tension on the bubbling process are evaluated. The size of single gas bubbles issued from a submerged nozzle is estimated at constant gas flow rate varying the orifice diameter, gas phase injected, and the liquid medium. Four orifice diameters are used: 0.6 mm, 1.0 mm, 2.0 mm, and 5.0 mm in diameter. As liquid medium, glycerine aqueous solutions at three different glycerine volume concentrations (20%, 40% and 60%), salt aqueous solution (300 g/L of salt) and surfactant solutions using Tween 20 at 0.01 mM and 0.1 mM concentrations, are employed for the experiments. Instead, air and argon are used to analyse the influence of the gas properties on the bubble size. Subsequently, the evaluations of the bubble frequency, the time rising, gas hold up and power consumption are performed considering all the investigated solutions. The mentioned experiments are carried out at three different impeller speed: 0, 185 and 315 RPM. It has been found that the fluid properties have an important role on the bubble size which largely influence the gas frequency, the time rising, and the gas hold up. Finally, the objective is to study qualitatively the shape of the gaseous cavities in relation with the agitator speed and the gas phase flow rate in order to understand in which flow regime the different gas cavities are present. The experiments are carried out using water as liquid medium and air for the gas phase. Two different cases are investigated. In the first case, the impeller speed was varied from 150 RPM to 600 RPM, maintaining constant the gas flow rate at 0.5 L/min. In the second case, the impeller speed has been kept constant at 500RPM and the gas flow rate varied from 0.5 L/min to 1.5 L/min.

L'hydrodynamique 3D générée par une turbine de Rushton est analysée expérimentalement à l'aide de la technique de mesure P. I. V. . Une technique de moyenne de phase est mise en œuvre pour extraire les mouvements moyen, turbulent et organisé lié au passage périodique des pales de l'agitateur. Les résultats sont tout d'abord validés par rapport aux nombreuses données de la bibliographie. La technique de décomposition triple est utilisée pour quantifier les échanges d'énergie cinétique entre les trois mouvements ; les termes présents dans les équations de bilan d'énergie cinétique des trois mouvements sont calculés et le taux de dissipation visqueux de l'énergie cinétique turbulente est estimé. Une définition objective des tourbillons est mise en place pour localiser les vortex traînants et leur trajectoire dans la cuve : les interactions entre ces structures et les mouvements moyen et turbulent sont quantifiées. Nous terminons par la caractérisation des structures de la turbulence en termes d'échelles (Kolmogorov, Taylor, macro-échelle) et d'anisotropie<br>The 3D hydrodynamic generated by a Rushton turbine is analyzed by P. I. V. Technique. Phase average acquisition is performed in order measure mean velocity field, turbulent motion and organized flow induced by the impeller blade (trailing vortices). Results are compared firstly to previous works. Triple decomposition method enables to quantify kinetic energy exchanges between the three motions. Moreover, one can calculate the terms that constitute the kinetic energy balance of the three motions: in particular, the viscous dissipation rate of turbulent kinetic energy is estimated. An objective definition of vortex is used to locate the trailing vortices and their trajectories through the tank: interactions between organized structure and mean and turbulent flows are outlook. Finally, the structure of turbulence is defined in terms of length-scales (Kolmogorov, Taylor, macro scale) and anisotropy

L'étude a porté sur le fonctionnement de contacteurs gaz-liquide alimentés en gaz par une ou deux turbines autoaspirantes. Les mobiles étudiés sont la turbine Rushton et la turbine à pales inclinées à pompage bas. Dans la première partie de ce travail, le cas d'une seule turbine autoaspirante a été étudié. Les paramètres de l'hydrodynamique globale et locale, ainsi que le transfert de matière ont été déterminés pour chacun des mobiles et pour différentes configurations géométriques. Ce travail a permis de mettre en évidence les différents régimes existants pour la turbine Rushton autoaspirante et de les comparer au cas d'une turbine Rushton alimentée par un distributeur de gaz. La modélisation et la simulation d'un réacteur équipé d'une seule turbine autoaspirante Rushton ont également été faites. La comparaison des deux types de mobiles, Rushton et à pales inclinées montre que cette dernière est très intéressante comme mobile autoaspirant et présente des performances similaire à celles de la turbine Rushton , jusqu'à 3,5 kW/m3. La deuxième partie de cette thèse a porté sur l'association de deux turbines, dont au moins une est autoaspirante. Nous avons d'abord montré l'existence de la double autoaspiration. Puis nous avons étudié différentes associations de mobiles (turbine Rushton, turbines à pales inclinées à pompage haut et bas), autoaspirante ou pas, et identifié les paramètres géométriques (position des mobiles les uns par rapport aux autres et par rapport au bas du réacteur) qui peuvent influencer les performances du réacteur (rétention gazeuse globale, débit gazeux autoaspiré et le transfert de matière). L'association de deux turbines Rushton a ainsi été montrée comme la plus performante. Enfin, la comparaison avec un réacteur monoétagé permet de noter les avantages du multi-étagé autoaspirant qui permet d'atteindre des taux de rétention gazeuse nettement supérieur et des valeurs du coefficient volumique de transfert de matière kLa jusqu'à trois fois plus grand.

La structure des ecoulements d'eau generes par une turbine de rushton dans une cuve agitee munie de 4 chicanes verticales est etudiee dans 3 unites d'agitation realisees en similitude geometrique (50, 70 et 200 litres). Les vitesses moyenne et fluctuante ainsi que les structures fines de la turbulence sont mesurees par anemometrie et anemometrie doppler a laser. Les deux methodes sont comparees. Les profils de la vitesse moyenne adimensionnelle et de la moyenne quadratique des fluctuations de vitesse adimensionnelle sont pratiquement independantes de la taille de l'unite et du nombre de reynolds rapporte a l'agitateur. La structure fine de la turbulence (spectre de frequence, macroechelles, puissance dissipee) est independante de la taille de l'unite et du nombre de reynolds

Understanding the flow in stirred vessels can be useful for a wide number of industrial applications, like in mining, chemical and pharmaceutical processes. Remodeling and redesigning these processes may have a significant impact on the overall design characteristics, affecting directly product quality and maintenance costs. In most cases the flow around the rotating impeller blades interacting with stationary baffles can cause rapid changes of the flow characteristics, which lead to high levels of turbulence and higher shear rates. The flow is anisotropic and inhomogeneous over the entire volume. A better understanding and a detailed documentation of the turbulent flow field is needed in order to design stirred tanks that can meet the required operation conditions. This thesis describes efforts for accurate estimation of the velocity distribution and the turbulent characteristics (vorticity, turbulent kinetic energy, dissipation rate) in a cylindrical vessel agitated by a Rushton turbine (a disk with six flat blades) and in a tank typical of flotation cells. Results from simulations using FLUENT (a commercial CFD package) are compared with Time Resolved Digital Particle Image Velocimetry (DPIV) for baseline configurations in order to validate and verify the fidelity of the computations. Different turbulence models are used in this study in order to determine the most appropriate for the prediction of turbulent properties. Subsequently a parametric analysis of the flow characteristics as a function of the clearance height of the impeller from the vessel floor is performed for the Rushton tank as well as the flotation cell. Results are presented for both configurations along planes normal or parallel to the impeller axis, displaying velocity vector fields and contour plots of vorticity turbulent dissipation and others. Special attention is focused in the neighborhood of the impeller region and the radial jet generated there. This flow in this neighborhood involves even larger gradients and dissipation levels in tanks equipped with stators. The present results present useful information for the design of the stirring tanks and flotation cells, and provide some guidance on the use of the present tool in generating numerical solutions for such complex flow fields.<br>Master of Science

The parallel-competing iodide-iodate reaction scheme has been used to study micromixing phenomena in baffled and unbaffled vessel of 0.29 m diameter (T) agitated by a Rushton turbine (D=1/3T) under turbulent conditions in a semi-batch mode. Firstly it was confirmed that by using successive injections, this reaction scheme is very efficient for such a study. Using this technique for the rest of the programme of work the first experiments were undertaken in the “standard baffled geometry”. Four agitator speeds giving mean specific energy dissipation rates, T ε , from ~0.2 W/kg to ~1.2 W/kg were used. For a given speed, addition at five different static feed locations, one just above the liquid surface and four submerged, were investigated. The four sub-surface feeding positions were associated with different local specific energy dissipation rates, εT, ranging from less than T ε , very close to the top of the liquid, to much greater close to the impeller. The point closest to the impeller was chosen to be such that feeding was estimated to be at the point of (εT)max. For the maximum speed, the segregation index, Xs, as a measure of the amount of 'waste product', was ~20% with feed onto the top of the liquid (as preferred industrially because of its convenience) or if slightly submerged. This 'waste' was reduced to ~5% by feeding at (εT)max. The distribution of εT was estimated from numerical solutions of the incorporation model combined with relationships arising from turbulence concept. A comparison was also made with results reported in the literature using the same reaction for two new devices developed for improved micromixing. By feeding at the carefully chosen position close to the impeller, the results with the Rushton turbine were as good as or better than with the special devices even at the comparatively low T ε of ~1.2 W/kg. It was estimated that the ratio of T T ε /ε (=φ) gave a maximum circumferentially averaged value of φ of ~90. The iodide-iodate technique was then used to ascertain the effectiveness of micromixing in a standard baffled reactor when feeding with pipes rotating with the impeller and discharging continuously into the region of (εT)max. The results when compared with those obtained using the fixed pipe at the equivalent position showed a significant intensification. Overall, a seven-fold reduction in ‘waste product’ was found between the most convenient fixed feed pipe position above the liquid surface and the rotating pipes, even at the modest T ε of ∼1.0 W/kg. This study is the first to use feeding continuously into the region of (εT)max. Thus an angular resolved (εT)max could be estimated from the incorporation model compared to a circumferentially averaged (εT)max obtained with a fixed pipe. The former was ∼3.0 times the latter, in close agreement with recent PIV based measurements. Finally the same geometry but without baffles was studied. The power number Po was measured and found to be Po=0.8, much less than Po=4.3 for the baffled tank. Visual decolourisation to give the macromixing time θm revealed evidence of a poor mixing region corresponding to the forced vortex region. The poor mixing in this region was confirmed by micromixing experiments. At the same T ε of 0.18 W/kg in the two cases, the values of segregation index, Xs, were found to be from ∼50% to 40% less than those III obtained with the baffled configuration except in the region close to the impeller where similar Xs values were found. These results are considered surprising, the unbaffled vessel proving much more effective for micromixing then expected. However, these improvements are limited by the very low maximum specific power input of 0.18 W/kg achievable with this configuration. Using the same micromixing model, all local (εT) values were > T ε . Clearly, this result is wrong. It is postulated that the swirling vortex flow past the fixed feed tube may give rise to a high very localised εT value. Clearly, further experimental and modelling work is required to gain a better understanding of the flow structure and micromixing in unbaffled vessels.

Cette thèse propose une étude expérimentale de la turbulence au sein d'un réacteur agité standard muni d'une turbine Rushton, fonctionnant en régime monophasique. L'anémométrie laser à deux volumes de mesure a été développée, sur la base d'un velocimètre bi-composante, pour permettre la mesure directe des variances des gradients des fluctuations de vitesse dont est composé le taux moyen local de dissipation d'énergie cinétique de turbulence epsilon. La technique est validée, avec moins de 5% d'écart, dans le cadre d'une turbulence de grille ou epsilon est connu. La comptabilité de la résolution spatiale obtenue avec les échelles de l'écoulement autorise l'utilisation de cette technique dans les mélangeurs. Après avoir identifié et extrait la contribution périodique due au passage des pales, les mesures d’epsilon montrent que : _ plus de 60% de l'énergie mécanique injectée sur l'arbre de la turbine est dissipée dans la région des chicanes et dans les couches limites de paroi. _ la turbulence peut être considérée comme localement isotrope dans l'ensemble du réacteur. _ en comparaison avec les résultats expérimentaux, le calcul d’epsilon par : epsilon = A((q²)³/²)/L donne des valeurs bien supérieures à proximité de l'agitateur et du même ordre de grandeur dans les zones de recirculation. Une étude des échelles de la turbulence a été conduite dans l'ensemble du réacteur. Ceci a amené à la modification de l'hypothèse de Taylor, en tenant compte notamment de la vitesse de convection des structures cohérentes mesurée dans le refoulement de la turbine, à partir des corrélations spatio-temporelles des fluctuations de vitesse. Enfin, le jet généré par le mobile a été modélisé à partir des équations de la dynamique. Une viscosité dynamique a été introduite et un bon accord a été trouvé entre les mesures expérimentales et les profils analytiques trouvés.

A theoretical study on the hydrodynamics of mixing processes in stirred tanks is described. The primary objective of this study is to investigate flow field and power consumption generated by the six blades Rushton turbine impeller in baffled, flat-bottom cylindrical tank both at laminar and turbulent flow regime both qualitatively and quantitatively. Experimental techniques are expensive and time consuming in characterizing mixing processes. For these reasons, computational fluid dynamics (CFD) has been considered as an alternative method. In this study, the velocity field and power requirement are obtained using FASTEST, which is a CFD package. It employs a fully conservative second order finite volume method for the solution of Navier-Stokes equations. The inherently time-dependent geometry of stirred vessel is simulated by a multiple frame of reference approach. The flow field obtained numerically agrees well with those published experimental measurements. It is shown that Rushton turbine impeller creates predominantly radial jet flow pattern and produces two main recirculation flows one above and the other below the impeller plane. Throughout the tank impeller plane dimensionless radial velocity is not affected significantly by the increasing impeller speed and almost decreases linearly with increase in radial distance. Effect of the baffling on the radial and tangential velocities is also investigated. It is seen that tangential velocity is larger than radial velocity at the same radial position in unbaffled system. An overall impeller performance characteristic like power number is also found to be in agreement with the published experimental data. Also power number is mainly affected by the baffle length and increase with increase in baffle length. It is concluded that multiple frame of reference approach is suitable for the prediction of flow pattern and power number in stirred tank.

Stirred vessels are used in a wide variety of process industries such as fine chemicals, pharmaceuticals, polymers and foods. In order to design efficient mixing vessels, a deep understanding of the blending processes is required. In cases where the fluid is not completely transparent, traditional optical laser based techniques are ineffective. One of the most promising techniques to study opaque systems is based on the detection of a tracer that emits gamma rays. Positron Emission Particle Tracking (PEPT) has been developed at the University of Birmingham and has been used in a wide range of applications including stirred tanks. However, for agitated vessels, any attempt of validation of the PEPT technique versus other techniques cannot be found. Hence, this work aims to validate and explore the potential of Lagrangian data in a well known mixing system such as a standard baffled vessel stirred by a Rushton turbine. As part of the validation, comparison with Eulerian PIV/LDA data has been also undertaken and some underestimation of the high velocities in the system was found in the impeller region. By using a selective interpolation algorithm of the tracer locations, this problem was greatly reduced although a perfect match with optical technique is not feasible. As further contribution to Lagrangian studies of mixing processes, Computational Fluid Dynamics (CFD) simulations have been undertaken to give both Eulerian and Lagrangian velocities and particle paths. However, it has been shown that traditional approaches to Lagrangian numerical simulation are unable to produce good trajectories that can be compared to experimental data. A novel three-step approach was suggested and implemented in order to achieve good paths, which then have been compared to the experimental trajectories. Qualitative and quantitative analysis of experimental Lagrangian data showed that the trajectories are erratic and follow random paths; furthermore, frequency analysis applied to portions of trajectories does not reveal any dominant low frequency in the system. Finally, circulation studies were undertaken in order to characterise mixing processes. This focused on tracking the tracer every time it leaves and returns a control volume proving the value of analysing time and return length distributions, since it was possible to compare the circulation times achieved in PEPT with published work. The trajectography approach used in this work is the first attempt at using trajectories from PEPT as a tool to characterise mixing performance rather than only using the data to find Eulerian velocities and vector plots.

Les transferts entre phases dans une cuve agitee mecaniquement sont mal connus et mal maitrises. C'est pourquoi nous avons choisi d'orienter notre travail vers la comprehension de l'hydrodynamique d'un reacteur en systeme diphasique. Pour ce faire nous avons etudie le mouvement d'un liquide en presence de gaz a l'aide de la technique de mesure de velocimetrie par image de particules piv, technique tres peu utilisee jusqu'a present dans le domaine de l'agitation. Cette nouvelle technique de mesure permet d'obtenir des champs de vitesses instantanees et moyennes. Nous l'appliquons dans ce travail a l'analyse experimentale du flux de liquide autour d'une turbine de rushton. Nous presentons dans un premier temps le principe et les techniques d'exploitation de la piv puis nous validons cette technique par la determination des echelles de turbulence et du taux de dissipation energetique generes par la turbine. Cette procedure experimentale est ensuite appliquee a l'etude des structures turbulentes que sont les tourbillons trainants. Pour ce faire, nous utilisons un systeme de synchronisation qui permet de faire des mesures a differents angles entre deux pales. Ainsi, nous caracterisons les tourbillons trainants turbulents en fonction de leur position par rapport aux pales, en terme d'energie cinetique et de cisaillement. Dans une derniere partie, nous etudions l'influence de la presence de gaz sur le flux de liquide en regime de dispersion complete et de chargement. L'exploitation de ces acquisitions nous permet de decrire simultanement les champs de vitesses et les cavites gazeuses qui se developpent a l'arriere des pales de la turbine. Les interactions entre ces cavites gazeuses et les tourbillons trainants sont ainsi demontrees. L'influence des differents types de cavites gazeuses sur l'efficacite du melange gaz-liquide est analysee.

Submitted by Luciana Sebin (lusebin@ufscar.br) on 2016-09-30T12:00:09Z No. of bitstreams: 1 DissMMB.pdf: 2553777 bytes, checksum: 21e951a2087a84913403141b819234c7 (MD5)<br>Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-10-20T13:44:47Z (GMT) No. of bitstreams: 1 DissMMB.pdf: 2553777 bytes, checksum: 21e951a2087a84913403141b819234c7 (MD5)<br>Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-10-20T13:44:55Z (GMT) No. of bitstreams: 1 DissMMB.pdf: 2553777 bytes, checksum: 21e951a2087a84913403141b819234c7 (MD5)<br>Made available in DSpace on 2016-10-20T13:45:03Z (GMT). No. of bitstreams: 1 DissMMB.pdf: 2553777 bytes, checksum: 21e951a2087a84913403141b819234c7 (MD5) Previous issue date: 2016-02-26<br>Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)<br>The type and operational conditions of a bioreactor chosen during the production phase of a product of interest affect not only the morphology and growth of filamentous microorganisms but also the product itself. Still the most common process to produce bioproducts is submerged cultures in conventional stirred and aerated bioreactors, with impeller of type six flat-blade turbine, or Rushton turbine (RT), which promotes good mixing and suitable oxygen transfer, but its power consumption is high and it causes high shear rate to the broth creating a hostile environment to the microorganisms. Alternatively, an impeller of the type “Elephant Ear” (EE) is shown in the literature as a “low shear” impeller, more suitable for the cultivation of shear sensitive microorganisms. This impeller creates a mixed flow (axial and radial) of broth with down flow (EEDP) or up (EEUP) depending on its geometry. This study aimed to evaluate the best association of impellers for filamentous fungi cultures in a conventional bioreactor. Initially the volumetric coefficient of oxygen transfer (kLa) and the power consumption of seven different association of impellers were evaluated. The results obtained the factorial design methodology showed that the associations EEDP-EEUP, RT-EEDP, and EEDP-RT, showed the best results regarding the oxygen transfer and the power consumption, being up to 87% more efficient than the standard RT-RT association. Two of the better performing association and the traditional (RT-RT) were selected to be evaluated regarding the shearing, by using empirical equations and the size of the eddies, evaluated by the Kolmogorov microscale. The association that showed higher values on the Kolmogorov scale and least shearing was EEDPEEUP, with shearing up to 60% lower than the RT-RT association. In the last step the effects of shear on the morphology of the fungi Aspergillus niger was evaluated. Short-term cultures (4h) were cultivated so that the cellular growth would not harm the analysis. The results showed that on the culture that used the EEDP-EEUP association the morphological form of cell clumps predominated, while on the culture that used the RT-RT association the morphological form of branched hyphae predominated, suggesting that the RT-RT association causes more shearing and can cause irreversible damage to the fungal cells.<br>O crescimento celular e a morfologia de microrganismos filamentosos, bem como o produto de interesse são afetados pelo modelo de biorreator e pelas condições de operação adotadas durante a etapa de produção. O processo mais adotado industrialmente para produção de bioprodutos ainda são os cultivos submersos em biorreatores convencionais tipo tanque agitado e aerado, sendo o impelidor tipo turbina de seis pás planas ou turbina de Rushton (RT) o mais utilizado por promover boa mistura e adequada transferência de oxigênio, porém seu consumo de potência é alto além de impor alto cisalhamento ao caldo gerando um ambiente hostil ao microrganismo. Alternativamente, o impelidor tipo “orelha de Elefante” ou “Elephant ear” (EE) é apresentado na literatura como um impelidor de “baixo cisalhamento” mais adequado para o cultivo dos microrganismos sensíveis ao cisalhamento. Esse impelidor promove um escoamento misto (axial e radial) do caldo com escoamento para baixo (EEDP) ou para cima (EEUP) dependendo da sua geometria. O presente trabalho teve como objetivo avaliar as melhores associações de impelidores para cultivos de fungos filamentosos em biorreator convencional. Primeiramente sete diferentes associações foram avaliadas em relação ao coeficiente volumétrico de transferência de oxigênio (kLa) e consumo de energia. Os resultados obtidos utilizando a metodologia de planejamento experimental fatorial mostraram que as configurações EEDP-EEUP, RT-EEDP e EEDP-RT foram as que apresentaram melhores resultados em relação à transferência de oxigênio e consumo de potência, com eficiência até 87% superior à associação padrão RT-RT. Foram então selecionadas duas das associações de melhor desempenho e a tradicional (RT-RT) para serem avaliadas em relação ao cisalhamento, através de equações empíricas e em relação ao tamanho dos turbilhões, avaliado pela microescala de Kolmogorov. A associação que apresentou maiores valores para microescala de Kolmogorov e menor cisalhamento foi a EEDP-EEUP, com cisalhamento até 60% inferior que a observada quando utilizada a associação RT-RT. Na última etapa verificou-se os efeitos do cisalhamento na morfologia do fungo Aspergillus niger. Foram realizados cultivos de curta duração (4 h) para evitar que o crescimento celular prejudicasse a análise. Os resultados mostraram que no cultivo utilizando o sistema EEDP-EEUP predominou a forma morfológica de aglomerados celulares (clumps), enquanto que no cultivo com impelidores Rushton (RT-RT) predominou a forma morfológica de hifas ramificadas, sugerindo um cisalhamento mais intenso provocado por este sistema de agitação, que pode acarretar danos irreversíveis às células fúngicas.

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.<br>Ph. D.

The relationship between operating parameters, cell hydrodynamics, flotation response and scale-up of flotation rates has been explored using three geometrically similar Rushton turbine flotation cells with volumes of 2.25, 10 and 50dm³. Mean energy dissipation values measured using Laser Doppler Velocimetry (LDV) and a torque turntable method were in good agreement. As the cell volume was increased, the mean energy dissipation was proportional to N³D, rather than N³D² as may be expected based on dimensional analysis. Possible reasons for this difference are discussed. Aeration resulted in a slight increase in mean energy dissipation. Bubble diameters were measured using a University of Cape Town bubble size analyser to determine the frother concentration at which a constant bubble diameter was achieved for all operating conditions and cell volumes. The critical frother concentration required to achieve this was 20 ppm MIBC.