Developing discontinuous Galerkin methods for the resolution of the incompressible Navier-Stokes equations

Informe de investigación elaborado a partir de una estancia en el Laboratorio de Diseño Computacional en Aeroespacial en el Massachusetts Institute of Technology (MIT), Estados Unidos, entre noviembre de 2006 y agosto de 2007. La aerodinámica es una rama de la dinámica de fluidos referida al estudio de los movimientos de los líquidos o gases, cuya meta principal es predecir las fuerzas aerodinámicas en un avión o cualquier tipo de vehículo, incluyendo los automóviles. Las ecuaciones de Navier-Stokes representan un estado dinámico del equilibrio de las fuerzas que actúan en cualquier región dada del fluido. Son uno de los sistemas de ecuaciones más útiles porque describen la física de una gran cantidad de fenómenos como corrientes del océano, flujos alrededor de una superficie de sustentación, etc. En el contexto de una tesis doctoral, se está estudiando un flujo viscoso e incompresible, solucionando las ecuaciones de Navier- Stokes incompresibles de una manera eficiente. Durante la estancia en el MIT, se ha utilizado un método de Galerkin discontinuo para solucionar las ecuaciones de Navier-Stokes incompresibles usando, o bien un parámetro de penalti para asegurar la continuidad de los flujos entre elementos, o bien un método de Galerkin discontinuo compacto. Ambos métodos han dado buenos resultados y varios ejemplos numéricos se han simulado para validar el buen comportamiento de los métodos desarrollados. También se han estudiado elementos particulares, los elementos de Raviart y Thomas, que se podrían utilizar en una formulación mixta para obtener un algoritmo eficiente para solucionar problemas numéricos complejos.

Experiments in a rotating Hele-Shaw cell

We introduce a modification to Hele-Shaw flows consisting of a rotating cell. A viscous fluid (oil) is injected at the rotation axis of the cell, which is open to air. The morphological instability of the oil-air interface is thus driven by centrifugal force and is controlled by the density (not viscosity) difference. We derive the linear dispersion relation and verify the maximum growth rate selection of initial patterns within experimental uncertainty. The nonlinear growth regime is studied in the case of vanishing injection rate. Several characteristic lengths are studied to quantify the patterns obtained. Experimental data exhibit good collapse for two characteristic lengths, namely, the radius of gyration and the radial finger length, which in the nonlinear regime appear to grow linearly in time.

Characterization of residential chimney conditions for flue gas flow measurements

A literature survey and a theoretical study were performed to characterize residential chimney conditions for flue gas flow measurements. The focus is on Pitot-static probes to give sufficient basis for the development and calibration of a velocity pressure averaging probe suitable for the continuous dynamic (i.e. non steady state) measurement of the low flow velocities present in residential chimneys. The flow conditions do not meet the requirements set in ISO 10780 and ISO 3966 for Pitot-static probe measurements, and the methods and their uncertainties are not valid. The flow velocities in residential chimneys from a heating boiler under normal operating condi-tions are shown to be so low that they in some conditions result in voiding the assumptions of non-viscous fluid justifying the use of the quadratic Bernoulli equation. A non-linear Reynolds number dependent calibration coefficient that is correcting for the viscous effects is needed to avoid significant measurement errors. The wide range of flow velocity during normal boiler operation also results in the flow type changing from laminar, across the laminar to turbulent transition region, to fully turbulent flow, resulting in significant changes of the velocity profile during dynamic measurements. In addition, the short duct lengths (and changes of flow direction and duct shape) used in practice are shown to result in that the measurements are done in the hydrodynamic entrance region where the flow velocity profiles most likely are neither symmetrical nor fully developed. A measurement method insensitive to velocity profile changes is thus needed, if the flow velocity profile cannot otherwise be determined or predicted with reasonable accuracy for the whole measurement range. Because of particulate matter and condensing fluids in the flue gas it is beneficial if the probe can be constructed so that it can easily be taken out for cleaning, and equipped with a locking mechanism to always ensure the same alignment in the duct without affecting the calibration. The literature implies that there may be a significant time lag in the measurements of low flow rates due to viscous effects in the internal impact pressure passages of Pitot probes, and the significance in the discussed application should be studied experimentally. The measured differential pressures from Pitot-static probes in residential chimney flows are so low that the calibration and given uncertainties of commercially available pressure transducers are not adequate. The pressure transducers should be calibrated specifically for the application, preferably in combination with the probe, and the significance of all different error sources should be investigated carefully. Care should be taken also with the temperature measurement, e.g. with averaging of several sensors, as significant temperature gradients may be present in flue gas ducts.

Nova técnica para obtenção de fraturas com altíssima condutividade em poços de petróleo

Increase hydrocarbons production is the main goal of the oilwell industry worldwide. Hydraulic fracturing is often applied to achieve this goal due to a combination of attractive aspects including easiness and low operational costs associated with fast and highly economical response. Conventional fracturing usually involves high-flowing high-pressure pumping of a viscous fluid responsible for opening the fracture in the hydrocarbon producing rock. The thickness of the fracture should be enough to assure the penetration of the particles of a solid proppant into the rock. The proppant is driven into the target formation by a carrier fluid. After pumping, all fluids are filtered through the faces of the fracture and penetrate the rock. The proppant remains in the fracture holding it open and assuring high hydraulic conductivity. The present study proposes a different approach for hydraulic fracturing. Fractures with infinity conductivity are formed and used to further improve the production of highly permeable formations as well as to produce long fractures in naturally fractured formations. Naturally open fractures with infinite conductivity are usually encountered. They can be observed in rock outcrops and core plugs, or noticed by the total loss of circulation during drilling (even with low density fluids), image profiles, pumping tests (Mini-Frac and Mini Fall Off), and injection tests below fracturing pressure, whose flow is higher than expected for radial Darcian ones. Naturally occurring fractures are kept open by randomly shaped and placed supporting points, able to hold the faces of the fracture separate even under typical closing pressures. The approach presented herein generates infinite conductivity canal held open by artificially created parallel supporting areas positioned both horizontally and vertically. The size of these areas is designed to hold the permeable zones open supported by the impermeable areas. The England & Green equation was used to theoretically prove that the fracture can be held open by such artificially created set of horizontal parallel supporting areas. To assess the benefits of fractures characterized by infinite conductivity, an overall comparison with finite conductivity fractures was carried out using a series of parameters including fracture pressure loss and dimensionless conductivity as a function of flow production, FOI folds of increase, flow production and cumulative production as a function of time, and finally plots of net present value and productivity index

Simulação de fluxo de fluidos em meios porosos desordenados uma análise de efeito de escala na estimativa da permeabilidade e do coeficiente de arrasto

The present study provides a methodology that gives a predictive character the computer simulations based on detailed models of the geometry of a porous medium. We using the software FLUENT to investigate the flow of a viscous Newtonian fluid through a random fractal medium which simplifies a two-dimensional disordered porous medium representing a petroleum reservoir. This fractal model is formed by obstacles of various sizes, whose size distribution function follows a power law where exponent is defined as the fractal dimension of fractionation Dff of the model characterizing the process of fragmentation these obstacles. They are randomly disposed in a rectangular channel. The modeling process incorporates modern concepts, scaling laws, to analyze the influence of heterogeneity found in the fields of the porosity and of the permeability in such a way as to characterize the medium in terms of their fractal properties. This procedure allows numerically analyze the measurements of permeability k and the drag coefficient Cd proposed relationships, like power law, for these properties on various modeling schemes. The purpose of this research is to study the variability provided by these heterogeneities where the velocity field and other details of viscous fluid dynamics are obtained by solving numerically the continuity and Navier-Stokes equations at pore level and observe how the fractal dimension of fractionation of the model can affect their hydrodynamic properties. This study were considered two classes of models, models with constant porosity, MPC, and models with varying porosity, MPV. The results have allowed us to find numerical relationship between the permeability, drag coefficient and the fractal dimension of fractionation of the medium. Based on these numerical results we have proposed scaling relations and algebraic expressions involving the relevant parameters of the phenomenon. In this study analytical equations were determined for Dff depending on the geometrical parameters of the models. We also found a relation between the permeability and the drag coefficient which is inversely proportional to one another. As for the difference in behavior it is most striking in the classes of models MPV. That is, the fact that the porosity vary in these models is an additional factor that plays a significant role in flow analysis. Finally, the results proved satisfactory and consistent, which demonstrates the effectiveness of the referred methodology for all applications analyzed in this study.

Simulação numérica de escoamentos de fluídos pelo método de elementos finitos baseado em volumes de controle com a técnica de passo fracionado

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Assessing the effectiveness of 30% sodium chloride aqueous solution for the preservation of fixed anatomical specimens: a 5-year follow-up study

Anatomical specimens used in human or veterinary anatomy laboratories are usually prepared with formaldehyde (a cancerous and teratogenic substance), glycerin (an expensive and viscous fluid), or ethanol (which is flammable). This research aimed to verify the viability of an aqueous 30% sodium chloride solution for preservation of anatomical specimens previously fixed with formaldehyde. Anatomical specimens of ruminant, carnivorous, equine, swine and birds were used. All were previously fixed with an aqueous 20% formaldehyde solution and held for 7days in a 10% aqueous solution of the same active ingredient. During the first phase of the experiment, small specimens of animal tissue previously fixed in formaldehyde were distributed in vials with different concentrations of formaldehyde, with or without 30% sodium chloride solution, a group containing only 30% sodium chloride, and a control group containing only water. During this phase, no contamination was observed in any specimen containing 30% sodium chloride solution, whether alone or in combination with different concentrations of formaldehyde. In the second phase of the experiment, the 30% sodium chloride solution, found to be optimal in the first phase of the experiment, was tested for its long-term preservation properties. For a period of 5years, the preserved specimens were evaluated three times a week for visual contamination, odors, and changes in color and texture. There was no visual contamination or decay found in any specimen. Furthermore, no strange odors, or changes in color or softness were noted. The 30% sodium chloride solution was determined to be effective in the preservation of anatomic specimens previously fixed in formaldehyde.

Experimental setup for measuring roll waves on laminar open channel flows

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Uso das ondas de Lamb e Scholte para caracterização de líquidos

Pós-graduação em Engenharia Elétrica - FEIS

On the radial expansion of tubular structures in a quark-gluon plasma

We study the radial expansion of cylindrical tubes in a hot QGP. These tubes are treated as perturbations in the energy density of the system which is formed in heavy ion collisions at RHIC and LHC. We start from the equations of relativistic hydrodynamics in two spatial dimensions and cylindrical symmetry and perform an expansion of these equations in a small parameter, conserving the nonlinearity of the hydrodynamical formalism. We consider both ideal and viscous fluids and the latter are studied with a relativistic Navier-Stokes equation. We use the equation of state of the MIT bag model. In the case of ideal fluids we obtain a breaking wave equation for the energy density fluctuation, which is then solved numerically. We also show that, under certain assumptions, perturbations in a relativistic viscous fluid are governed by the Burgers equation. We estimate the typical expansion time of the tubes. (C) 2012 Elsevier B.V. All rights reserved.

The geomorphology and morphometry of the banded terrain in Hellas basin, Mars

Hellas basin is a large impact basin situated in the southern highlands of Mars. The north-western part of the basin has the lowest elevation (-7.5 km) on the planet and contains a possibly unique terrain type, which we informally call “banded terrain”. The banded terrain is made up of smooth-looking banded deposits that display signs of viscous behavior and a paucity of superimposed impact craters. In this study, we use newly acquired high spatial resolution images from the High Resolution Imaging Science Experiment (HiRISE) in addition to existing datasets to characterize the geomorphology, the morphometry and the architecture of the banded terrain. The banded terrain is generally confined to the NW edge of the Alpheus Colles plateau. The individual bands are ~3–15 km-long, ~0.3 km-wide and are separated by narrow inter-band depressions, which are ~65 m-wide and ~10 m-deep. The bands display several morphologies that vary from linear to concentric forms. Morphometric analysis reveals that the slopes along a given linear or lobate band ranges from 0.5° to 15° (average~6°), whereas the concentric bands are located on flatter terrain (average slope~2–3°). Crater-size frequency analysis yields an Amazonian-Hesperian boundary crater retention age for the terrain (~3 Gyr), which together, with the presence of very few degraded craters, either implies a recent emplacement, resurfacing, or intense erosion. The apparent sensitivity to local topography and preference for concentrating in localized depressions is compatible with deformation as a viscous fluid. In addition, the bands display clear signs of degradation and slumping at their margins along with a suite of other features that include fractured mounds, polygonal cracks at variable size-scales, and knobby/hummocky textures. Together, these features suggest an ice-rich composition for at least the upper layers of the terrain, which is currently being heavily modified through loss of ice and intense weathering, possibly by wind.

Study of the influence of actin-binding proteins using linear analyses of cell deformability

The actin cytoskeleton plays a key role in the deformability of the cell and in mechanosensing. Here we analyze the contributions of three major actin cross-linking proteins, myosin II, a-actinin and filamin, to cell deformability, by using micropipette aspiration of Dictyostelium cells. We examine the applicability of three simple mechanical models: for small deformation, linear viscoelasticity and drop of liquid with a tense cortex; and for large deformation, a Newtonian viscous fluid. For these models, we have derived linearized equations and we provide a novel, straightforward methodology to analyze the experiments. This methodology allowed us to differentiate the effects of the cross-linking proteins in the different regimes of deformation. Our results confirm some previous observations and suggest important relations between the molecular characteristics of the actin-binding proteins and the cell behavior: the effect of myosin is explained in terms of the relation between the lifetime of the bond to actin and the resistive force; the presence of a-actinin obstructs the deformation of the cytoskeleton, presumably mainly due to the higher molecular stiffness and to the lower dissociation rate constants; and filamin contributes critically to the global connectivity of the network, possibly by rapidly turning over crosslinks during the remodeling of the cytoskeletal network, thanks to the higher rate constants, flexibility and larger size. The results suggest a sophisticated relationship between the expression levels of actinbinding proteins, deformability and mechanosensing.

Energetic considerations of ciliary beating and the advantage of metachronal coordination

The internal mechanism of cilia is among the most ancient biological motors on an evolutionary scale. It produces beat patterns that consist of two phases: during the effective stroke, the cilium moves approximately as a straight rod, and during the recovery stroke, it rolls close to the surface in a tangential motion. It is commonly agreed that these two phases are designed for efficient functioning: the effective stroke encounters strong viscous resistance and generates thrust, whereas the recovery stroke returns the cilium to starting position while avoiding viscous resistance. Metachronal coordination between cilia, which occurs when many of them beat close to each other, is believed to be an autonomous result of the hydrodynamical interactions in the system. Qualitatively, metachronism is perceived as a way for reducing the energy expenditure required for beating. This paper presents a quantitative study of the energy expenditure of beating cilia, and of the energetic significance of metachronism. We develop a method for computing the work done by model cilia that beat in a viscous fluid. We demonstrate that for a single cilium, beating in water, the mechanical work done during the effective stroke is approximately five times the amount of work done during the recovery stroke. Investigation of multicilia configurations shows that having neighboring cilia beat metachronally is energetically advantageous and perhaps even crucial for multiciliary functioning. Finally, the model is used to approximate the number of dynein arm attachments that are likely to occur during the effective and recovery strokes of a beat cycle, predicting that almost all of the available dynein arms should participate in generating the motion.

Pendant drop formation of shear-thinning and yield stress fluids

A volume-of-fluid numerical method is used to predict the dynamics of shear-thinning liquid drop formation in air from a circular orifice. The validity of the numerical calculation is confirmed for a Newtonian liquid by comparison with experimental measurements. For particular values of Weber number and Froude number, predictions show a more rapid pinch-off, and a reduced number of secondary droplets, with increasing shear-thinning. Also a minimum in the limiting drop length occurs for the smallest Weber number as the zero-shear viscosity is varied. At the highest viscosity, the drop length is reduced due to shear-thinning, whereas at lower viscosities there is little effect of shear-thinning. The evolution of predicted drop shape, drop thickness and length, and the configuration at pinch-off are discussed for shear-thinning drops. The evolution of a drop of Bingham yield stress liquid is also considered as a limiting case. In contrast to the shear-thinning cases, it exhibits a plug flow prior to necking, an almost step-change approach to pinch-off of a torpedo shaped drop following the onset of necking, and a much smaller neck length; no secondary drops are formed. The results demonstrate the potential of the numerical model as a design tool in tailoring the fluid rheology for controlling drop formation behaviour. (c) 2006 Elsevier Inc. All rights reserved.

Dynamics of pulsed flow in an elastic tube

Internal haemorrhage, often leading to cardio-vascular arrest happens to be one of the prime sources of high fatality rates in mammals. We propose a simplistic model of fluid flow in our attempt to specify the location of the haemorrhagic spot, which, if located accurately, could possibly be operated leading to an instant cure. The model we employ for the purpose is basically fluid mechanical in origin and consists of a viscous fluid, pumped by a periodic force and flowing through an elastic tube. The analogy is with that of blood, pumped from the heart and flowing through an artery or vein. Our results, aided by graphical illustrations, match reasonably well with experimental observations.