# Browsing by Subject "Viscous flow"

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Item A parallelized Eulerian VIScous Vorticity Equation (VISVE) method in an inertial and non-inertial frame of reference(2021-05) Wu, Chunlin; Kinnas, Spyros A.; Liljestrand, Howard M.; Sepehrnoori, Kamy; Raja, Laxminarayan L.; Johnson, Blair A.Show more A parallelized VIScous Vorticity Equation (VISVE) method that solves the vorticity transport equation to simulate the incompressible viscous flow in both the inertial and non-inertial frame of reference is proposed in this dissertation. The local concentration of vorticity near the wall and the wake is fully exploited by the current method, which is designed to efficiently solve the flow past a body with irregular wall boundaries surrounded by a small and compact computational domain in general shapes. The method is also parallelized using both Open Multi-Processing (Open-MP) and Message Passing Interface (MPI) in a hybrid manner to boost the speed of computations. The present method is implemented in the case of flow past a 3-D hydrofoil with one periodic direction and flow past a 3-D wing in the inertial frame of reference. The method is also applied to oscillatory flow past a 2-D circular cylinder, uniform flow past a rotating 2-D circular cylinder, uniform flow past a rotating 3-D circular cylinder, and uniform flow past a rotating propeller in the non-inertial frame of reference. The current results, such as the velocity field, vorticity field, and body forces, exhibit a high level of agreement with those of established numerical and experimental benchmark tests, demonstrating the accuracy and robustness of this method.Show more Item An analysis of salt welding(2010-05) Wagner, Bryce Hedrick; Jackson, M. P. A.; Cloos, Mark; Hudec, Mike; Steel, Ron; Sen, Mrinal; Peel, FrankShow more Salt can be removed by viscous flow and dissolution to form a salt weld. A complete weld forms when salt is completely removed by these processes. Where salt removal is incomplete, a partial weld forms. Though welds are frequently mentioned in the literature, the details of weld formation and the properties of salt welds are poorly understood. In Chapter 1, I use analytical and numerical models to quantify the role of viscous flow during salt welding. Where salt flow is limited by boundary drag against the salt contacts, evacuation is slow and up to ~50 m of salt will be left behind in a partial weld. Where salt flow is laterally unrestricted, a vanishingly thin (<< 1 m) smear of salt will remain. I conclude that layer-parallel wall rock translation or dissolution must act to remove any remnant salt to create a complete weld. In Chapter 2, I characterize partial welds containing halite and anhydrite on reflection seismic data by treating welds as thin beds. Below the temporal resolution of reflection seismic data, typically ~25-50 m for modern surveys with peak frequencies of ~10-30 Hz, reflections from the upper and lower evaporite contacts converge and interfere to form a single composite reflection. Thus, partial and complete welds are typically indistinguishable using travel-time differences alone. I then use amplitude information from synthetics and seismic examples to estimate remnant evaporite thickness. In Chapter 3, I investigate fluid flow near and through salt welds. I conclude dissolution during boundary flow can remove up to a few meters of salt per million years. Though dissolution plays a volumetrically insignificant but important role in weld formation, as runaway dissolution can create pathways for focused cross-weld migration of subsurface fluids. I identify features that influence cross-weld migration of subsurface fluids and then develop an empirical relationship between weld geometry and the tendency seal or leak hydrocarbons. I find that in the Campos Basin, offshore Brazil, salt welds containing remnant evaporites thinner than ~50 m that are broader than ~25 km2 in area are likely to leak.Show more Item The effects of viscous crossflow on sharp front displacements in two-layered porous media(1979) Zapata, Vito Joseph; Lake, Larry W.Show more The effects of viscous crossflow may play an important role in the overall displacement of oil by water. This work seeks not only to determine when viscous crossflow is important but also to calculate its effects on vertical sweep efficiency. This thesis analyzes viscous crossflow by comparing the existing solutions of Dykstra-Parsons and Hearn to computer simulation results. The solution by Dykstra-Parsons, which assumes no vertical permeability, agreed well with the numerical solution. However, the Hearn solution, which assumes infinite vertical permeability, required modifications when it was applied to displacements with mobility ratios greater than one. The computer simulator was a two-phase, two-dimensional, finite difference model written by Dr. R. C. MacDonald. The simulator was modified in certain areas, such as the solution technique, injection scheme, and the coordinate system, as well as other areas in order to handle our particular objectives. Perhaps the most significant result presented in this thesis is that the infinite vertical permeability analytic solution may be attained without excessively large vertical permeabilities, if the length-to-thickness ratio is large. A correlation presented in this thesis in graphical form indicates when a reservoir may be described assuming no crossflow or when it may be described assuming infinite vertical permeability. Finally, modifications are made to the Hearn analytic solution which makes the solution more general and allows it to correctly handle sharp front displacements where the mobility ratio is greater than one.Show more Item Geometry and dynamics of fluid-fluid interfaces(2007-12) Thrasher, Matthew Evan, 1981-; Swinney, H. L., 1939-Show more We observed the evolution of unstable fluid interfaces in experiments on viscous fingering, pinch-off, and bouncing jets. If we can first identify classes of universal behavior, then we can begin building a unified framework to understand nonlinear processes. We performed the first experimental test of the harmonic moments of viscous fingering patterns, grown by injecting air into a thin layer of silicone oil, which was confined between two closely spaced plates, called a Hele-Shaw cell. We observed that the predicted decay of the moments was accurate within our measurement uncertainty, which confirmed the predicted conservation of the moments for zero surface tension. With greater forcing, the air bubble will undergo a secondary tip-splitting instability, where the fingers of air fork into two or more fingers. We discovered two selection rules for the changing base width and the nearly invariant opening angle of fjords, which are the regions of oil between the fingers of air. We then compared our experiments on viscous fingering with diffusion-limited aggregation (DLA), a model of un-stable growth. We calculated that DLA and viscous fingering have the same spectrum of singularities [called f([alpha])] within measurement uncertainty. Since the spectrum is a global encapsulation of the growth dynamics and scaling properties, we say that the two processes are in the same scaling universality class. All of these results for viscous fingering are expected to apply to other physical systems which approximate Laplacian growth, a model of an interface where its growth rate is determined by the local gradient of a field [phi] obeying Laplace's equation [gradient² phi] = 0. Next we present preliminary work on the experimental test of two predictions for flows in Hele-Shaw cells: 1) soliton-like behavior of two viscous domains and 2) self-similar, universal pinch-off of an inviscid bubble in a viscous liquid. Finally, we report our observations and analysis of a liquid stream with constant viscosity (i.e. Newtonian) which rebounds from the free surface of a moving bath. The stream bounces on a thin layer of lubricating air which is replenished by the relative motion of the jet and the bath.Show more Item Imaging particle migration with electrical impedance tomography: an investigation into the behavior and modeling of suspension flows(2004) Norman, Jay Thomas; Bonnecaze, R. T. (Roger T.)Show more Neutrally buoyant particles in low Reynolds number, pressure-driven suspension flows migrate from regions of high to low shear, and this migration is a strong function of the local concentration. When the particle density differs from that of the suspending fluid, buoyancy forces also affect particle migration. It is the ratio between the buoyancy and viscous forces, as quantified by a dimensionless buoyancy number, which determines the phase distribution of the suspension once the flow is fully developed. Although several experiments have verified shear-induced particle migration in neutrally buoyant suspensions, there is little data for particle migration when buoyancy effects are important. An accurate and efficient electrical impedance tomography (EIT) imaging technique is developed to non-invasively measure the distribution of positively and negatively buoyant particles in low Reynolds number pressure-driven flow in a pipe. vii Additionally, a bimodal suspension of heavy particles in a low Reynolds number pressure-driven pipe flow is investigated. The effects for a range of buoyancy numbers were probed by varying the flow rate. In all of the experiments, a significant fraction of the particle phase is observed to migrate towards the top or bottom of the pipe, depending on the relative density of the particles. The amount of migration away from the center of the pipe increases with increasing magnitude of the buoyancy number. The bimodal suspension displayed an adverse density gradient for low buoyancy numbers. A scaling analysis is introduced to predict the formation of an unstable particle distribution. Furthermore, observations of the phase distribution at several positions downstream of the inlet indicate that suspension flows of buoyant particles become fully developed earlier than that observed for neutrally buoyant particles, with higher buoyancy numbers becoming fully developed more rapidly. A scaling for the prediction of the fully developed length is presented that matches experimental observations reasonably well. The experimental observations of the particle distributions were favorably compared to the predictions of an isotropic suspension balance model.Show more Item A mixed spectral and finite volume method for compressible viscous flows(1993) Minyard, Tommy Keith, 1968-; Kallinderis, Y. (Yannis)Show more The thesis presents a mixed spectral/finite volume method for compressible viscous flows. The method is evaluated for accuracy and robustness via test cases for various Mach numbers. The domain is divided into a viscous region and an inviscid region. The viscous region uses the full Navier-Stokes equations, while the inviscid region employs the Euler equations. A high order Chebyshev collocation spectral method is developed for the viscous region to resolve boundary layers. This method avoids the dense grids needed by finite-volume methods to resolve the viscous areas. A finite-volume method based on a Lax-Wendroff type scheme is employed for the inviscid region. A special interface formulation is developed for coupling the spectral with the finite-volume method. Comparisons with analytic results as well as convergence histories are presentedShow more Item On the motion of flexible strings and filaments in inertial and viscous regimes(2007-12) Lin, Bisen, 1976-; Ravi-Chandar, K.Show more Study of the dynamics of strings and filaments has broad applications, for instance, macroscopic coil motion in petroleum engineering and microscopic one-armed swimmers in biological science. In this work, we study the motions of flexible strings and thin filaments in two different regimes, inertial and viscous, theoretically and experimentally. Quantitative experiments on the whirling string show that steady motion exists only when the string whirls at its natural frequencies and that whirling motions for other frequencies exhibit rich dynamics. Furthermore, three kinds of response have been observed experimentally for the planar excitation: planar steady oscillation; two-dimensional (2D) to three-dimensional (3D) transient response; 3D steady whirling motion. These phenomena repeat as the driving frequency is increased. The forced response of a string subjected to planar excitation is analyzed through a perturbation technique and multiple time scale method. The steady-state whirling motion of linear elastic filaments under self-weight with rotary excitation at one end and free at the other has been examined; specifically, the effect of bending stiffness has been investigated both theoretically and experimentally. The theoretical predictions have been compared with the experimental results for thin filaments with different bending stiffness to demonstrate the effect of bending stiffness directly. The dynamic response of thin filaments under planar excitation has also been studied experimentally. The two-dimensional dynamics of an Euler elastica in low-Reynolds number regime has been studied. Tension effects have been shown to be either comparable to or dominant over the bending contributions for the microscopic one-armed swimmers. Hence one may change the tension in situ through the externally or internally generated forces, thus changing the effective bending stiffness, and as a consequence controlling the swimming velocity and the propulsion efficiency. Finally, the low-Reynolds-number dynamics of a micro-string has been studied, in order to understand the physics underpinning eukaryotic sperm flagellar swimming. Both linear analysis of small-amplitude swimming and fully numerical simulations show that time-reversal symmetry is broken, which leads to the propulsion. Numerical studies have been performed for different boundary conditions and different forcing levels. Comparison with previous bending model illustrated that, for the same equivalent bending stiffness, the micro-string has higher propulsion efficiency with similar swimming velocity. Excellent agreement between the simulation predictions and the experimentally observed flagellar wave-forms has been obtained. With this theoretical model, observations of swimming characteristics of the sperm of different species are reconciled into a single scaling relationship, characterized by the so-called \string sperm number". Our results imply that tension plays a crucial role in flagellar elasticity and provides impetus for studying a different model underlying the physics of flagellar swimming. For example, it is possible to postulate alternate hypotheses for active force generation by the dynein motors; it also enables the formulation of a different role to the micro-filaments in general, one based on tension rather than one based on bending.Show more Item Parallel adaptive C¹ macro-elements for nonlinear thin film and non-Newtonian flow problems(2008-08) Stogner, Roy Hulen, 1979-; Carey, Graham F.Show more This research deals with several novel aspects of finite element formulations and methodology in parallel adaptive simulation of flow problems. Composite macroelement schemes are developed for problems of thin fluid layers with deforming free surfaces or decomposing material phases; experiments are also run on divergence-free formulations that can be derived from the same element classes. The constrained composite nature and C¹ continuity requirements of these elements raises new issues, especially with respect to adaptive refinement patterns and the treatment of hanging node constraints, which are more complex than encountered with standard element types. This work combines such complex elements with these applications and with parallel adaptive mesh refinement and coarsening (AMR/C) techniques for the first time. The use of adaptive macroelement spaces also requires appropriate programming interfaces and data structures to enable easy and efficient implementation in parallel software. The algorithms developed for this work are implemented using object-oriented designs described herein. One application class of interest concerns heated viscous thin fluid layers that have a deformable free surface. These problems occur in both normal scale laboratory and industrial applications and in micro-fluidics. Modeling this flow via depth averaging gives a nonlinear boundary value problem describing the transient evolution of the film thickness. The model is dominated by surface tension effects which are described by a combination of nonlinear second and fourth-order operators. This research work also includes studies using the divergence-free forms constructed from these elements for certain classes of non-Newtonian fluids such as the Powell-Eyring and Williamson shear-thinning viscosity models. In addition to the target problems we conduct verification studies in support of the simulation development. In the final application investigated, C¹ elements are used in conforming finite element approximations of the Cahn-Hilliard phase field model for moving interface and phase separation problems. The nonlinear Cahn-Hilliard equation combines anti-diffusive configurational free energy based terms with a fourth-order interfacial free energy based term. Numerical studies include both manufactured and physically significant problems, including parametric studies of directed pattern self-assembly in phase decomposition of thin films. The main new contributions include construction of C¹ and div-free macroelement classes suitable for AMR/C with nonconforming hanging node meshes; a posteriori error estimation for fourth-order problems using these and other element classes; use of projection operators to automate the correct treatment of constraints at hanging nodes and through AMR/C steps; design of supporting data structures and algorithms for implementation in a parallel object oriented framework; variational formulations, methodology and numerical experiments with nonlinear fourth-order flow and transport models; and parametric and Monte Carlo studies of directed phase decomposition.Show more Item Parallel hp adaptive finite element analysis for viscous incompressible flow problems(1995-08) Patra, Abani Kumar; Not availableShow more Item Physical controls on hydrate saturation distribution in the subsurface(2012-12) Behseresht, Javad; Bryant, Steven L; Mohanty, Kishore K; Hesse, Marc A; Prodanović, Maša; Sharma, Mukul MShow more Many Arctic gas hydrate reservoirs such as those of the Prudhoe Bay and Kuparuk River area on the Alaska North Slope (ANS) are believed originally to be natural gas accumulations converted to hydrate after being placed in the gas hydrate stability zone (GHSZ) in response to ancient climate cooling. A mechanistic model is proposed to predict/explain hydrate saturation distribution in “converted free gas” hydrate reservoirs in sub-permafrost formations in the Arctic. This 1-D model assumes that a gas column accumulates and subsequently is converted to hydrate. The processes considered are the volume change during hydrate formation and consequent fluid phase transport within the column, the descent of the base of gas hydrate stability zone through the column, and sedimentological variations with depth. Crucially, the latter enable disconnection of the gas column during hydrate formation, which leads to substantial variation in hydrate saturation distribution. One form of variation observed in Arctic hydrate reservoirs is that zones of very low hydrate saturations are interspersed abruptly between zones of large hydrate saturations. The model was applied on data from Mount Elbert well, a gas hydrate stratigraphic test well drilled in the Milne Point area of the ANS. The model is consistent with observations from the well log and interpretations of seismic anomalies in the area. The model also predicts that a considerable amount of fluid (of order one pore volume of gaseous and/or aqueous phases) must migrate within or into the gas column during hydrate formation. This work offers the first explanatory model of its kind that addresses "converted free gas reservoirs" from a new angle: the effect of volume change during hydrate formation combined with capillary entry pressure variation versus depth. Mechanisms by which the fluid movement, associated with the hydrate formation, could have occurred are also analyzed. As the base of the GHSZ descends through the sediment, hydrate forms within the GHSZ. The net volume reduction associated with hydrate formation creates a “sink” which drives flow of gaseous and aqueous phases to the hydrate formation zone. Flow driven by saturation gradients plays a key role in creating reservoirs of large hydrate saturations, as observed in Mount Elbert. Viscous-dominated pressure-driven flow of gaseous and aqueous phases cannot explain large hydrate saturations originated from large-saturation gas accumulations. The mode of hydrate formation for a wide range of rate of hydrate formation, rate of descent of the BGHSZ and host sediments characteristics are analyzed and characterized based on dimensionless groups. The proposed transport model is also consistent with field data from hydrate-bearing sand units in Mount Elbert well. Results show that not only the petrophysical properties of the host sediment but also the rate of hydrate formation and the rate of temperature cooling at the surface contribute greatly to the final hydrate saturation profiles.Show more Item Unsteady growth and relaxation of viscous fingers(2003) Moore, Mitchell George; Swinney, H. L., 1939-Show more Viscous fingering occurs when a less viscous fluid is driven into a more viscous fluid in a porous medium or a thin layer geometry known as a Hele-Shaw cell. The problem is studied because of its applications to filtration and oil extraction, because of its relationship to other moving interface problems, such as solidification and flame fronts, and because the mathematical idealization of the problem has a number of unusual properties. One set of our experiments was performed in rectangular Hele-Shaw channels where fingers travel down the long axis of the cell. These experiments revealed several phenomena that were not observed in previous experiments. At low flow rates, growing fingers exhibited width fluctuations that intermittently narrowed the finger as they evolved. The magnitude of these fluctuations was proportional to Ca−0.64, where Ca is the capillary number, which is proportional to the finger velocity. This relation held for all aspect ratios studied (60 < (channel width)/(channel thickness) < 500) up to the onset of tip instabilities in the fingers. At higher flow rates, finger pinch-off and reconnection events were observed. These events appear to be caused by an interaction between the actively growing finger and suppressed fingers at the back of the channel. Both the fluctuation and pinch-off phenomena were robust but not explained by current theory. Our other experiments were performed in a Hele-Shaw cell with radial symmetry. These fingers generate highly ramified patterns as the air enters the cell from a central point. We have examined the relaxation of the fine structure of these patterns due to surface tension by removing the forcing after a pattern was grown. This relaxation, unlike most coarsening processes, was not dynamically scale invariant. Rather, it exhibits two distinct dynamic length scales that grow as different powers of time: l1(t) ∼ t0.22, l2(t) ∼ t0.31. These lengths correspond respectively to the scale below which the pattern is smooth (non-ramified) and the distance between different fingers in the pattern. The measured exponents were in agreement with the results of recent numerical studies of diffusion-controlled coarsening of fractal clusters [Lipshtat et al. Phys. Rev. E 65, 050501 (2002)]. A consequence of the existence of two length scales is that the patterns at late times depended on the structural form at the onset of coarsening, providing information on the age of the fractal. We also present preliminary work on the fractal dimension of viscous fingering patterns.Show more