Browsing by Subject "Multiphase flow"

Now showing 1 - 3 of 3
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    Numerical and Theoretical Studies of Air Entrainment and Bubble Acoustics under Breaking Waves
    (2021-12) Gao, Qiang
    Bubbles and breaking waves play a critical role in many physical processes. However, bubble formation mechanism, trajectories, and their acoustic signatures are still poorly understood due to the complex process of breaking waves. To study the bubble transport dynamics and their formation mechanism, a technique for Lagrangian tracking of bubbles and detecting their time-evolution behaviors is developed. Five possible behaviors are considered: formation, extinction, continuity, binary fragmentation, and binary coalescence. The technique is based on establishing a network of mappings between bubbles identified at adjacent time instants. The accuracies for continuity, binary fragmentation, and binary coalescence are estimated to be 99.5%, 90%, and 95%, respectively. The algorithm is proved to be accurate and robust by extensive validations using the breaking wave cases. Bubble entrainment mechanism and bubble trajectory are investigated. Air filaments and cavities in plunging breaking waves, generically cylinders, produce bubbles through an interface instability. A generalized dispersion relation is obtained that spans the Rayleigh–Taylor and Plateau–Rayleigh instabilities as cylinder radius varies. The analysis provides insight into the role of surface tension in the formation of bubbles from filaments and cavities. Small filaments break up into bubbles through a Plateau–Rayleigh instability driven through the action of surface tension. Large air cavities produce bubbles through a Rayleigh–Taylor instability driven by gravity and moderated by surface tension, which has a stabilizing effect. Surface tension, interface curvature, and gravity are all important for cases between these two extremes. Bubble trajectories and their interaction with breaking wave flow fields are also studied here. A simulation framework for bubbly flow and the sound radiated by breaking waves is presented. It consists of a two-phase flow solver, an algorithm to track bubbles and bubble creation rates, and a module to compute the sound generated by newly-formed bubbles. The sounds from breaking, third-order Stokes waves of 0.25m wavelength and two slopes are calculated. The results show encouraging agreement with existing laboratory observations and identify the importance of air cylinder breakup in bubble creation.
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    Stress-driven melt segregation and reactive melt in ltration in partially molten rocks deformed in torsion with applications to melt extraction from Earth's mantle.
    (2010-10) King, Daniel S. H.
    Melt extraction from Earth's upper mantle requires transport of magma from regions of partial melting at depth to the Earth's surface. During its ascent, melt interacts chemically and mechanically with the rock matrix. Melt reduces the viscosity of the partially molten rock compared to that of a melt-free rock. This weakening is a potential mechanism of strain localization that could have significant geodynamical implications. Magma interacts chemically with mineral phases during its ascent, dissolving phases in which it is undersaturated and precipitating phases in which it is oversaturated. Such melt-rock reaction can be a driving force for melt migration. Water and other volatiles also partition into the melt from minerals and are then expelled to Earth's oceans or atmosphere. This process leaves behind stronger dehydrated rocks, and it could be the mechanism by which the oceanic lithosphere (mechanical boundary layer) is formed. The work presented here is an experimental investigation of several mechanisms that influence the distribution of melt within a viscously deformable partially molten rock. Three mechanisms are considered, either alone or in various combinations. (1) An applied shear stress causes melt to align and segregate into melt-rich bands with a consistent geometrical relationship to the shear geometry. In Chapter 2, we investigate possible means of scaling the bands that form in experimental samples to Earth's mantle and explore the evolution of melt-rich bands at high shear strain. (2) Interfacial tension driven flow acts to homogenize the distribution of melt within a partially molten sample. In Chapter 3, we investigate the evolution of melt distribution during static annealing of a sample containing melt-rich bands. We compare the experimental results with models of interfacial tension driven flow to determine which mechanisms control the rate of melt redistribution. (3) A melt source that is undersaturated in some component, when coupled with a sink that is rich in that component, will infiltrate into the sink through reactive flow. This reactive flow can develop into an instability in which fingers of high melt fraction propagate into the sink. In Chapter 4 we investigate this process both under static conditions and in combination with stress-driven melt segregation.
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    Topics in Viscous Potential Flow of Two-Phase Systems
    (2010-02) Padrino Inciarte, Juan Carlos
    Two-phase flows are ubiquitous, from natural and domestic environments to industrial settings. However, due to their complexity, modeling these fluid systems remains a challenge from both the perspective of fundamental questions on the dynamics of an individual, smooth interface, and the perspective of integral analyses, which involve averaging of the conservation laws over large domains, thereby missing local details of the flow. In this work, we consider a set of five problems concerning the linear and non-linear dynamics of an interface or free surface and the study of cavitation inception. Analyses are carried out by assuming the fluid motion to be irrotational, that is, with zero vorticity, and the fluids to be viscous, although results from rotational analyses are presented for the purpose of comparison. The problems considered here are the following: First, we analyze the non-linear deformation and break-up of a bubble or drop immersed in a uniaxial extensional flow of an incompressible viscous fluid. The method of viscous potential flow, in which the flow field is irrotational and viscosity enters through the balance of normal stresses at the interface, is used in the analysis. The governing equations are solved numerically to track the motion of the interface by coupling a boundary element method with a time-integration routine. When break-up occurs, the break-up time computed here is compared with results obtained elsewhere from numerical simulations of the Navier–Stokes equations, which thus keeps vorticity in the analysis, for several combinations of the relevant dimensionless parameters of the problem. For the bubble, for Weber numbers 3 [less than or equal] We [less than or equal] 6, predictions from viscous potential flow shows good agreement with the results from the Navier–Stokes equations for the bubble break-up time, whereas for larger We, the former underpredicts the results given by the latter. Including viscosity increases the break-up time with respect to the inviscid case. For the drop, as expected, increasing the viscous effects of the irrotational motion produces large, elongated drops that take longer to break up in comparison with results for inviscid fluids. In the second problem, we compute the force acting on a spherical bubble of variable radius moving within a liquid with an outer spherical boundary. Viscous potential flow and the dissipation method, which is another purely irrotational approach stemming from the mechanical energy equation, are both systematically implemented. This exposes the role of the choice of the outer boundary condition for the stress on the drag, an issue not explained in the literature known to us. By means of the well-known “cell-model” analysis, the results for the drag are then applied to the case of a swarm of rising bubbles having a certain void fraction. Computations from the dissipation method for the drag coefficient and rise velocity for a bubble swarm agree with numerical solutions; evaluation against experimental data for high Reynolds and low Weber numbers shows that all the models considered, including those given in the literature, overpredict the bubble swarm rise velocity. In the next two problems, we apply the analysis of viscous potential flow and the dissipation method to study the linear dynamics of waves of “small” amplitude acting either on a plane or on a spherical interface separating a liquid from a dynamically inactive fluid. It is shown that the viscous irrational theories exhibit the features of the wave dynamics by comparing with the exact solution. The range of parameters for which good agreement with the exact solution exists is presented. The general trend shows that for long waves the dissipation method results in the best approximation, whereas for short waves, even for very viscous liquids, viscous potential flow demonstrates better agreement. Finally, the problem of cavitation inception for the flow of a viscous liquid past a stationary sphere is studied by means of the theory of stress-induced cavitation. The flow field for a single phase needed in the analysis is found from three different methods, namely, the numerical solution of the Navier–Stokes equations, the irrotational motion of a viscous fluid, and, in the limit of no inertia, the Stokes flow formulation. The new predictions are then compared with those obtained from the classical pressure criterion. The main finding is that at a fixed cavitation number more viscous liquids are at greater risk to cavitation.