An Extended Volume of Fluid Method and its Application to Single Bubbles Rising in a Viscoelastic Liquid

An extended volume of fluid method is developed for two-phase direct numerical simulations of systems with one viscoelastic and one Newtonian phase. A complete set of governing equations is derived by conditional volume-averaging of the local instantaneous bulk equations and interface jump conditions. The homogeneous mixture model is applied for the closure of the volume-averaged equations. An additional interfacial stress term arises in this volume-averaged formulation which requires special treatment in the finite-volume discretization on a general unstructured mesh. A novel numerical scheme is proposed for the second-order accurate finite-volume discretization of the interface stress term. We demonstrate that this scheme allows for a consistent treatment of the interface stress and the surface tension force in the pressure equation of the segregated solution approach. Because of the high Weissenberg number problem, an appropriate stabilization approach is applied to the constitutive equation of the viscoelastic phase to increase the robustness of the method at higher fluid elasticity. Direct numerical simulations of the transient motion of a bubble rising in a quiescent viscoelastic fluid are performed for the purpose of experimental code validation. The well-known jump discontinuity in the terminal bubble rise velocity when the bubble volume exceeds a critical value is captured by the method. The formulation of the interfacial stress together with the novel scheme for its discretization is found crucial for the quantitatively correct prediction of the jump discontinuity in the terminal bubble rise velocity

Stratospheric constituent measurements using UV solar occultation technique

The photochemistry of the stratospheric ozone layer was studied as the result of predictions that trace amounts of pollutants can significantly affect the layer. One of the key species in the determination of the effects of these pollutants is the OH radical. A balloon flight was made to determine whether data on atmospheric OH could be obtained from lower resolution solar spectra obtained from high altitude during sunset

Computational studies of viscoelastic multiphase flows

A finite element code based on the level set method is developed for performing two and three dimensional direct numerical simulations (DNS) of viscoelastic two-phase flow problems. The Oldroyd-B constitutive equation is used to model the viscoelastic liquid. The code is used to study transient and steady state shapes of Newtonian and viscoelastic drops in simple shear and buoyancy driven flows. The roles of the governing dimensionless parameters: Capillary number (Ca), Deborah Number (De) and the polymer concentration parameter c, in determining deformation of drops and bubbles, are also analyzed. The numerical code permits us to vary Ca, De and c independently, which is difficult to achieve experimentally. This capability is used to isolate the roles of these parameters on the nature of viscoelastic stress near the drop surface and their effect on drop deformation. Results for simple shear flows indicate that when the drop phase is Newtonian and the matrix phase viscoelastic, the viscoelastic stresses pull the ends of the drop near the tips of the major axis and near the tips of the minor axes they are tangential, and thus have the net effect of increasing drop deformation. Viscoelastic stresses have the opposite effect when the drop phase is viscoelastic and the matrix phase is Newtonian. Additionally, due to the extensional nature of viscoelastic stresses, drops sheared by viscoelastic fluids develop pointed ends, a phenomenon observed experimentally and popularly known as tip-streaming. For buoyancy driven bubbles rising in quiescent viscoelastic fluids, simulations show that the rise velocity oscillates before reaching a steady value. The shape of the bubble, the magnitude of velocity overshoot and the amount of damping depend mainly on c and the bubble radius. Simulations show that there is a critical bubble volume range in which there is a sharp increase in the terminal velocity with increasing bubble volume similar to the behavior observed in experiments. An explanation for this phenomenon is offered based on the transient oscillations and shape change. The structure of the wake of a bubble rising in a Newtonian fluid is strikingly different from that of a bubble rising in a viscoelastic fluid. In addition to the two recirculation zones at the equator of the bubble rising in a Newtonian fluid, two more recirculation zones exist in the wake of a bubble rising in viscoelastic fluids which influence the shape of a rising bubble. Also, the direction of motion of the fluid a short distance below the trailing edge of a bubble rising in a viscoelastic fluid is in the opposite direction to the direction of motion of the bubble. The wake is \u27negative\u27 in the sense that the direction of fluid velocity behind the bubble is the opposite of that for a Newtonian fluid

HYDRODYNAMICS OF SMALL BUBBLES IN NON-NEWTONIAN AQUEOUS SOLUTIONS OF XANTHAN GUM

Free motion of small air bubbles in the volume range of 1-1000 mm3 (microlitre) has been studied in a column with different concentrations of xanthan gum ranging from 520 to 2580 ppm (w∕w). Two high-speed cameras were used to capture the continuous movement of bubbles up to 2000 frames per second. The sizes as well as the rise velocities of bubbles were measured by means of an image analysis software connected to the cameras. A precise method has been developed to create bubbles with high accuracy and controlled specified volumes. One of the main objectives of this work was to investigate the presence of the often-reported discontinuity in the rise velocity versus volume of air bubbles in non-Newtonian fluids. No abrupt velocity change was observed in our studies for the bubble volume range from 1 to 100 microlitre, which has been reported to occur by some other researchers. A thorough rheological study on the working concentrations of xanthan gum has been performed to interpret the observations with the existing hypothesis in literature for velocity­ volume discontinuity. To be able to evaluate the results of the rise velocity for xanthan gum solutions in respect to the jump velocity, the same measurements were repeated using two different concentrations of CMC, namely, 0.4% and 0.6% w/w as a second non-Newtonian fluid

Bubble-Induced Entrainment at Viscoplastic-Newtonian Interfaces

The passage of single air bubbles through the horizontal interface between miscible viscoplastic and Newtonian fluids, considering various combinations of densities and viscosities for the fluid layers, is studied computationally. The primary focus is on the quantity of liquid transferred from the lower layer (Viscoplastic fluid) to the upper layer (Newtonian fluid) as a result of the bubble's ascent, a factor with significant implications for the turbidity of methane-emitting lakes and water bodies. The results show that at $Bo>1$ and moderate $Ar$, prolate-shaped bubbles crossing the interface undergo elongation in the direction of their poles. This elongation is further accentuated when the viscosity of upper layer is less than the plastic viscosity of the lower layer. The bubble is found to break up when leaving the lower layer, of a critical capillary number, $Ca_c \approx 5$. The results show a significant reduction in the volume of entrainment compared to the Newtonian counterpart. This suggests disturbances caused by the rising bubble at the interface dissipate over a smaller region. Four distinct entrainment regimes are identified, mainly indicating the height to which the entrained fluid can be transported away from the interface. In contrast to Newtonian fluids, the volume of entrainment increases by decreasing the viscosity of the upper layer. Interestingly, the heavy yield stress fluid that has been dragged up into the the light Newtonian fluid does not recede down by time

Numerical simulation of Newtonian/non-Newtonian multiphase flows : deformation and collision of droplets

The complex nature of multiphase flows, particularly in the presence of non-Newtonian rheologies in the phases, limits the applicability of theoretical analysis of physical equations as well as setting up laboratory experiments. As a result, Computational Fluid Dynamics (CFD) techniques are essential tools to study these problems. Despite the advances in numerical simulation techniques in this field in the past decade, the applicability of these approaches are limited by challenges appearing in specific applications, and particular consideration must be taken into account for each of these problems. The present thesis aims at three-dimensional numerical solution of Newtonian/non-Newtonian multiphase flow problems in the context of finite-volume discretization approach with applications in different natural and industrial processes. This thesis is organized in five chapters. The first chapter aims at providing an introduction to the motivation behind this work. We also present some application of the context of this thesis in industrial processes, followed by a small introductory on the CTTC research group, objectives and the outline of the thesis. The core of this thesis lays within chapters two, three and four. In chapter 2, using a conservative level-set method, three-dimensional direct numerical simulation of binary droplets collision is performed. A novel lamella stabilization approach is introduced to numerically resolve the thin lamella film appeared during a broad range of collision regimes. This approach demonstrates to be numerically efficient and accurate compared with experimental data, with a significant save-up on computational costs in three-dimensional cases. The numerical tools introduced are validated and verified against different experimental results for a wide range of collision regimes where very good agreement is seen. Besides, for all the cases studied in this chapter, a detailed study of the energy budgets are provided. In chapter 3, the physics of a single droplet subjected to shear flow is studied in details, with a primary focus on the effect of viscosity on walls critical confinement ratio. First, we highly validate the ability of the numerical tools on capturing the correct physics of droplet deformation. This chapter continues by three-dimensional DNS study of subcritical (steady-state) and supercritical (breakup) deformations of the droplet for a wide range of walls confinement in different viscosity ratios. The results indicate the existence of two steady-state regions in a viscosity ratio-walls confinement ratio graph, which are separated by a breakup region. Overall, these achievements indicate a promising potential of the current approach for simulating droplet deformation and breakup, in applications of dispersion science and mixing processes. In chapter 4, with the help of experience gained in the previous chapters, a finite-volume based conservative level-set method is used to numerically solve the non-Newtonian multiphase flow problems. One set of governing equations is written for the whole domain where different rheological properties may appear. Main challenging areas of numerical simulation of multiphase non-Newtonian fluids, including tracking of the interface, mass conservation of the phases, small timestep problems encountered by non-Newtonian fluids, numerical instabilities regarding the high Weissenberg Number Problem (HWNP), instabilities encouraged by low solvent to polymer viscosity ratio in viscoelastic fluids and instabilities encountered by surface tensions are discussed and proper numerical treatments are provided in the proposed method. The numerical method is validated for different types of non-Newtonian fluids, e.g. shear-thinning, shear-thickening and viscoelastic fluids using structured and unstructured meshes, where the extracted results are compared against analytical, numerical and experimental data available in the literature.La naturaleza compleja de los flujos multifásicos, particularmente en presencia de reologías no newtonianas, limita la aplicabilidad del análisis teórico de ecuaciones físicas y también de los experimentos de laboratorio. Por lo tanto, las técnicas de dinámica de fluidos computacional (CFD) son esenciales para estudiar estos problemas. A pesar de los avances en las técnicas de simulación numérica en esta área durante la última década, la aplicabilidad de estos enfoques está limitada por los desafíos que aparecen en las aplicaciones específicas, y se debe considerar de forma particular cada uno de estos problemas. La presente tesis tiene como objetivo la solución numérica tridimensional de los problemas de flujo multifase newtoniano / no newtoniano en el contexto del enfoque de discretización de volúmenes finitos con aplicaciones en diferentes procesos naturales e industriales. Esta tesis está organizada en cinco capítulos. El primer capítulo proporciona una introducción y la motivación de este trabajo. También presentamos alguna aplicación de esta tesis en procesos industriales, seguida de una corta introducción al grupo de investigación del CTTC, los objetivos y el resumen de la tesis. En el capítulo 2, utilizando un método CLS, se realiza una simulación numérica directa (DNS) tridimensional de colisión de gotitas binarias. Se introduce un nuevo enfoque de estabilización de lamella para resolver numéricamente la capa delgada de fluido ("lamella") que aparece durante muchos regímenes de colisión. Este enfoque demuestra ser numéricamente eficiente y preciso en comparación con los datos experimentales, con una importante reducción de costos computacionales en casos tridimensionales. Las herramientas numéricas introducidas se validan y verifican con diferentes resultados experimentales para diferentes casos de colisión en los que se observa un muy buen acuerdo. Además, para todos los casos estudiados en este capítulo, se proporciona un estudio detallado de los balances de energía. En el capítulo 3, se estudia en detalle la física de una sola gota sometida a flujo de cizallamiento, con un enfoque principal en el efecto de la viscosidad en el confinamiento crítico de las paredes. Primero, validamos la capacidad de las herramientas numéricas para capturar la física correcta de la deformación de las gotitas. Este capítulo continúa con el estudio tridimensional DNS de las deformaciones subcríticas (estado estable) y supercríticas (ruptura) de la gota para un amplio rango de confinamiento de paredes en diferentes relaciones de viscosidad. Los resultados indican la existencia de dos regiones de estado estable en un gráfico de una relación de confinamiento de las paredes y la viscosidad, que están separados por una región de ruptura. En general, estos logros indican un potencial importante del enfoque actual para simular la deformación y ruptura de las gotitas, en aplicaciones de la ciencia de la dispersión y los procesos de mezcla. En el capítulo 4, con la ayuda de la experiencia adquirida en los capítulos anteriores, se utiliza un método CLS de volumen finito para resolver numéricamente los problemas de flujo multifase no newtonianos. Las principales áreas desafiantes de la simulación numérica de fluidos multifásicos no newtonianos incluso el seguimiento de la interfaz, la conservación de masa de las fases, los problemas de pequeños paso de tiempo encontrados por los fluidos no newtonianos, las inestabilidades numéricas relacionadas con el problema del alto número de Weissenberg (HWNP), inestabilidades fomentadas por una baja relación de viscosidad de disolvente a polímero en fluidos viscoelásticos y las inestabilidades encontradas por las tensiones superficiales son discutidos y se proporcionan tratamientos numéricos adecuados para el método propuesto. El método numérico se valida para diferentes tipos de fluidos no newtonianos, utilizando diluyentes de cizallamiento, espesamiento de cizallamiento y fluidos viscoelásticos utilizando mallas estructuradas y no estructuradas, donde los resultados extraídos se comparan con los datos analíticos, numéricos y experimentales disponibles en la literatura