932 resultados para Non-uniform flow


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Glaciations had a profound impact on the global sea-level and particularly on the Arctic environments. One of the key questions related to this topic is, how did the discharge of the Siberian Ob and Yenisei rivers interact with a proximal ice sheet? In order to answer this question high-resolution (1-12 kHz), shallow-penetration seismic profiles were collected on the passive continental margin of the Kara Sea Shelf to study the paleo-drainage pattern of the Ob and Yenisei rivers. Both rivers incised into the recent shelf, leaving filled and unfilled river channels and river canyons/valleys connecting to a complex paleo-drainage network. These channels have been subaerially formed during a regressive phase of the global sea-level during the Last Glacial Maximum. Beyond recent shelf depths of 120 m particle transport is manifested in submarine channel-levee complexes acting as conveyor for fluvial-derived fines. In the NE area, uniform draping sediments are observed. Major morphology determining factors are (1) sea-level fluctuations and (2) LGM ice sheet influence. Most individual channels show geometries typical for meandering rivers and appear to be an order of magnitude larger than recent channel profiles of gauge stations on land. The Yenisei paleo-channels have larger dimensions than the Ob examples and could be originated by additional water release during the melt of LGM Putoran ice masses. Asymmetrical submarine channel-levee complexes with channel depths of 60 m and more developed, in some places bordered by glacially dominated morphology, implying deflection by the LGM ice masses. A total of more than 12,000 km of acoustic profiles reveal no evidence for an ice-dammed lake of greater areal extent postulated by several workers. Furthermore, the existence of the channel-levee complexes is indicative of unhindered sediment flow to the north. Channels situated on the shelf above 120-m water depth exhibit no phases of ponding and or infill during sea-level lowstand. These findings denote the non-existence of an ice sheet on large areas of the Kara Sea shelf.

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Pore water and turnover rates were determined for surface sediment cores obtained in 2009 and 2010. The pore water was extracted with Rhizons (Rhizon CSS: length 5 cm, pore diameter 0.15 µm; Rhizosphere Research Products, Wageningen, Netherlands) in 1 cm-resolution and immediately fixed in 5% zinc acetate (ZnAc) solution for sulfate, and sulfide analyses. The samples were diluted, filtered and the concentrations measured with non-suppressed anion exchange chromatography (Waters IC-Pak anion exchange column, waters 430 conductivity detector). The total sulfide concentrations (H2S + HS- + S**2-) were determined using the diamine complexation method (doi:10.4319/lo.1969.14.3.0454). Samples for dissolved inorganic carbon (DIC) and alkalinity measurements were preserved by adding 2 µl saturated mercury chloride (HgCl2) solution and stored headspace-free in gas-tight glass vials. DIC and alkalinity were measured using the flow injection method (detector VWR scientific model 1054) (doi:10.4319/lo.1992.37.5.1113). Dissolved sulfide was eliminated prior to the DIC measurement by adding 0.5 M molybdate solution (doi:10.4319/lo.1995.40.5.1011). Nutrient subsamples (10 - 15 ml) were stored at - 20 °C prior to concentration measurements with a Skalar Continuous-Flow Analyzer (doi:10.1002/9783527613984).

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Pore water and turnover rates were determined for surface sediment cores obtained in 2009 and 2010. The pore water was extracted with Rhizons (Rhizon CSS: length 5 cm, pore diameter 0.15 µm; Rhizosphere Research Products, Wageningen, Netherlands) in 1 cm-resolution and immediately fixed in 5% zinc acetate (ZnAc) solution for sulfate, and sulfide analyses. The samples were diluted, filtered and the concentrations measured with non-suppressed anion exchange chromatography (Waters IC-Pak anion exchange column, waters 430 conductivity detector). The total sulfide concentrations (H2S + HS- + S**2-) were determined using the diamine complexation method (doi:10.4319/lo.1969.14.3.0454). Samples for dissolved inorganic carbon (DIC) and alkalinity measurements were preserved by adding 2 µl saturated mercury chloride (HgCl2) solution and stored headspace-free in gas-tight glass vials. DIC and alkalinity were measured using the flow injection method (detector VWR scientific model 1054) (doi:10.4319/lo.1992.37.5.1113). Dissolved sulfide was eliminated prior to the DIC measurement by adding 0.5 M molybdate solution (doi:10.4319/lo.1995.40.5.1011). Nutrient subsamples (10 - 15 ml) were stored at - 20 °C prior to concentration measurements with a Skalar Continuous-Flow Analyzer (doi:10.1002/9783527613984).

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Pore water and turnover rates were determined for surface sediment cores obtained in 2009 and 2010. The pore water was extracted with Rhizons (Rhizon CSS: length 5 cm, pore diameter 0.15 µm; Rhizosphere Research Products, Wageningen, Netherlands) in 1 cm-resolution and immediately fixed in 5% zinc acetate (ZnAc) solution for sulfate, and sulfide analyses. The samples were diluted, filtered and the concentrations measured with non-suppressed anion exchange chromatography (Waters IC-Pak anion exchange column, waters 430 conductivity detector). The total sulfide concentrations (H2S + HS- + S**2-) were determined using the diamine complexation method (doi:10.4319/lo.1969.14.3.0454). Samples for dissolved inorganic carbon (DIC) and alkalinity measurements were preserved by adding 2 µl saturated mercury chloride (HgCl2) solution and stored headspace-free in gas-tight glass vials. DIC and alkalinity were measured using the flow injection method (detector VWR scientific model 1054) (doi:10.4319/lo.1992.37.5.1113). Dissolved sulfide was eliminated prior to the DIC measurement by adding 0.5 M molybdate solution (doi:10.4319/lo.1995.40.5.1011). Nutrient subsamples (10 - 15 ml) were stored at - 20 °C prior to concentration measurements with a Skalar Continuous-Flow Analyzer (doi:10.1002/9783527613984).

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Pore water and turnover rates were determined for surface sediment cores obtained in 2009 and 2010. The pore water was extracted with Rhizons (Rhizon CSS: length 5 cm, pore diameter 0.15 µm; Rhizosphere Research Products, Wageningen, Netherlands) in 1 cm-resolution and immediately fixed in 5% zinc acetate (ZnAc) solution for sulfate, and sulfide analyses. The samples were diluted, filtered and the concentrations measured with non-suppressed anion exchange chromatography (Waters IC-Pak anion exchange column, waters 430 conductivity detector). The total sulfide concentrations (H2S + HS- + S**2-) were determined using the diamine complexation method (doi:10.4319/lo.1969.14.3.0454). Samples for dissolved inorganic carbon (DIC) and alkalinity measurements were preserved by adding 2 µl saturated mercury chloride (HgCl2) solution and stored headspace-free in gas-tight glass vials. DIC and alkalinity were measured using the flow injection method (detector VWR scientific model 1054) (doi:10.4319/lo.1992.37.5.1113). Dissolved sulfide was eliminated prior to the DIC measurement by adding 0.5 M molybdate solution (doi:10.4319/lo.1995.40.5.1011). Nutrient subsamples (10 - 15 ml) were stored at - 20 °C prior to concentration measurements with a Skalar Continuous-Flow Analyzer (doi:10.1002/9783527613984).

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Pore water and turnover rates were determined for surface sediment cores obtained in 2009 and 2010. The pore water was extracted with Rhizons (Rhizon CSS: length 5 cm, pore diameter 0.15 µm; Rhizosphere Research Products, Wageningen, Netherlands) in 1 cm-resolution and immediately fixed in 5% zinc acetate (ZnAc) solution for sulfate, and sulfide analyses. The samples were diluted, filtered and the concentrations measured with non-suppressed anion exchange chromatography (Waters IC-Pak anion exchange column, waters 430 conductivity detector). The total sulfide concentrations (H2S + HS- + S**2-) were determined using the diamine complexation method (doi:10.4319/lo.1969.14.3.0454). Samples for dissolved inorganic carbon (DIC) and alkalinity measurements were preserved by adding 2 µl saturated mercury chloride (HgCl2) solution and stored headspace-free in gas-tight glass vials. DIC and alkalinity were measured using the flow injection method (detector VWR scientific model 1054) (doi:10.4319/lo.1992.37.5.1113). Dissolved sulfide was eliminated prior to the DIC measurement by adding 0.5 M molybdate solution (doi:10.4319/lo.1995.40.5.1011). Nutrient subsamples (10 - 15 ml) were stored at - 20 °C prior to concentration measurements with a Skalar Continuous-Flow Analyzer (doi:10.1002/9783527613984).

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Pore water and turnover rates were determined for surface sediment cores obtained in 2009 and 2010. The pore water was extracted with Rhizons (Rhizon CSS: length 5 cm, pore diameter 0.15 µm; Rhizosphere Research Products, Wageningen, Netherlands) in 1 cm-resolution and immediately fixed in 5% zinc acetate (ZnAc) solution for sulfate, and sulfide analyses. The samples were diluted, filtered and the concentrations measured with non-suppressed anion exchange chromatography (Waters IC-Pak anion exchange column, waters 430 conductivity detector). The total sulfide concentrations (H2S + HS- + S**2-) were determined using the diamine complexation method (doi:10.4319/lo.1969.14.3.0454). Samples for dissolved inorganic carbon (DIC) and alkalinity measurements were preserved by adding 2 µl saturated mercury chloride (HgCl2) solution and stored headspace-free in gas-tight glass vials. DIC and alkalinity were measured using the flow injection method (detector VWR scientific model 1054) (doi:10.4319/lo.1992.37.5.1113). Dissolved sulfide was eliminated prior to the DIC measurement by adding 0.5 M molybdate solution (doi:10.4319/lo.1995.40.5.1011). Nutrient subsamples (10 - 15 ml) were stored at - 20 °C prior to concentration measurements with a Skalar Continuous-Flow Analyzer (doi:10.1002/9783527613984).

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Contaminated soil reuse was investigated, with higher profusion, throughout the early 90’s, coinciding with the 1991 Gulf War, when efforts to amend large crude oil releases began in geotechnical assessment of contaminated soils. Isolated works referring to geotechnical testing with hydrocarbon ground contaminants are described in the state-of-the-art, which have been extended to other type of contaminated soil references. Contaminated soils by light non-aquous phase liquids (LNAPL) bearing capacity reduction has been previously investigated from a forensic point of view. To date, all the research works have been published based on the assumption of constant contaminant saturation for the entire soil mass. In contrast, the actual LNAPLs distribution plumes exhibit complex flow patterns which are subject to physical and chemical changes with time and distance travelled from the release source. This aspect has been considered along the present text. A typical Madrid arkosic soil formation is commonly known as Miga sand. Geotechnical tests have been carried out, with Miga sand specimens, in incremental series of LNAPL concentrations in order to observe the soil engineering properties variation due to a contamination increase. Results are discussed in relation with previous studies and as a matter of fact, soil mechanics parameters change in the presence of LNAPL, showing different tendencies according to each test and depending on the LNAPL content, as well as to the specimen’s initially planned relative density, dense or loose. Geotechnical practical implications are also commented on and analyzed. Variation on geotechnical properties may occur only within the external contour of contamination distribution plume. This scope has motivated the author to develop a physical model based on transparent soil technology. The model aims to reproduce the distribution of LNAPL into the ground due to an accidental release from a storage facility. Preliminary results indicate that the model is a potentially complementary tool for hydrogeological applications, site-characterization and remediation treatment testing within the framework of soil pollution events. A description of the test setup of an innovative three dimensional physical model for the flow of two or more phases, in porous media, is presented herein, along with a summary of the advantages, limitations and future applications for modeling with transparent material. En los primeros años de la década de los años 90, del siglo pasado, coincidiendo con la Guerra del Golfo en 1991, se investigó intensamente sobre la reutilización de suelos afectados por grandes volúmenes de vertidos de crudo, fomentándose la evaluación geotécnica de los suelos contaminados. Se describen, en el estado del arte de esta tésis, una serie de trabajos aislados en relación con la caracterización geotécnica de suelos contaminados con hidrocarburos, descripción ampliada mediante referencias relacionadas con otros tipos de contaminación de suelos. Existen estudios previos de patología de cimentaciones que analizan la reducción de la capacidad portante de suelos contaminados por hidrocarburos líquidos ligeros en fase no acuosa (acrónimo en inglés: LNAPL de “Liquid Non-Aquous Phase Liquid”). A fecha de redacción de la tesis, todas las publicaciones anteriores estaban basadas en la consideración de una saturación del contaminante constante en toda la extensión del terreno de cimentación. La distribución real de las plumas de contaminante muestra, por el contrario, complejas trayectorias de flujo que están sujetas a cambios físico-químicos en función del tiempo y la distancia recorrida desde su origen de vertido. Éste aspecto ha sido considerado y tratado en el presente texto. La arena de Miga es una formación geológica típica de Madrid. En el ámbito de esta tesis se han desarrollado ensayos geotécnicos con series de muestras de arena de Miga contaminadas con distintas concentraciones de LNAPL con el objeto de estimar la variación de sus propiedades geotécnicas debido a un incremento de contaminación. Se ha realizado una evaluación de resultados de los ensayos en comparación con otros estudios previamente analizados, resultando que las propiedades mecánicas del suelo, efectivamente, varían en función del contenido de LNAPL y de la densidad relativa con la que se prepare la muestra, densa o floja. Se analizan y comentan las implicaciones de carácter práctico que supone la mencionada variación de propiedades geotécnicas. El autor ha desarrollado un modelo físico basado en la tecnología de suelos transparentes, considerando que las variaciones de propiedades geotécnicas únicamente deben producirse en el ámbito interior del contorno de la pluma contaminante. El objeto del modelo es el de reproducir la distribución de un LNAPL en un terreno dado, causada por el vertido accidental de una instalación de almecenamiento de combustible. Los resultados preliminares indican que el modelo podría emplearse como una herramienta complementaria para el estudio de eventos contaminantes, permitiendo el desarrollo de aplicaciones de carácter hidrogeológico, caracterización de suelos contaminados y experimentación de tratamientos de remediación. Como aportación de carácter innovadora, se presenta y describe un modelo físico tridimensional de flujo de dos o más fases a través de un medio poroso transparente, analizándose sus ventajas e inconvenientes así como sus limitaciones y futuras aplicaciones.

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Typical streak computations present in the literature correspond to linear streaks or to small amplitude nonlinear streaks computed using DNS or nonlinear PSE. We use the Reduced Navier-Stokes (RNS) equations to compute the streamwise evolution of fully non-linear streaks with high amplitude in a laminar flat plate boundary layer. The RNS formulation provides Reynolds number independent solutions that are asymptotically exact in the limit $Re \gg 1$, it requires much less computational effort than DNS, and it does not have the consistency and convergence problems of the PSE. We present various streak computations to show that the flow configuration changes substantially when the amplitude of the streaks grows and the nonlinear effects come into play. The transversal motion (in the wall normal-streamwise plane) becomes more important and strongly distorts the streamwise velocity profiles, that end up being quite different from those of the linear case. We analyze in detail the resulting flow patterns for the nonlinearly saturated streaks and compare them with available experimental results.

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Based on our needs, that is to say, through precise simulation of the impact phenomena that may occur inside a jet engine turbine with an explicit non-linear finite element code, four new material models are postulated. Each one of is calibrated for four high-performance alloys that can be encountered in a modern jet engine. A new uncoupled material model for high strain and ballistic is proposed. Based on a Johnson-Cook type model, the proposed formulation introduces the effect of the third deviatoric invariant by means of three different Lode angle dependent functions. The Lode dependent functions are added to both plasticity and failure models. The postulated model is calibrated for a 6061-T651 aluminium alloy with data taken from the literature. The fracture pattern predictability of the JCX material model is shown performing numerical simulations of various quasi-static and dynamic tests. As an extension of the above-mentioned model, a modification in the thermal softening behaviour due to phase transformation temperatures is developed (JCXt). Additionally, a Lode angle dependent flow stress is defined. Analysing the phase diagram and high temperature tests performed, phase transformation temperatures of the FV535 stainless steel are determined. The postulated material model constants for the FV535 stainless steel are calibrated. A coupled elastoplastic-damage material model for high strain and ballistic applications is presented (JCXd). A Lode angle dependent function is added to the equivalent plastic strain to failure definition of the Johnson-Cook failure criterion. The weakening in the elastic law and in the Johnson-Cook type constitutive relation implicitly introduces the Lode angle dependency in the elastoplastic behaviour. The material model is calibrated for precipitation hardened Inconel 718 nickel-base superalloy. The combination of a Lode angle dependent failure criterion with weakened constitutive equations is proven to predict fracture patterns of the mechanical tests performed and provide reliable results. A transversely isotropic material model for directionally solidified alloys is presented. The proposed yield function is based a single linear transformation of the stress tensor. The linear operator weighs the degree of anisotropy of the yield function. The elastic behaviour, as well as the hardening, are considered isotropic. To model the hardening, a Johnson-Cook type relation is adopted. A material vector is included in the model implementation. The failure is modelled with the Cockroft-Latham failure criterion. The material vector allows orienting the reference orientation in any other that the user may need. The model is calibrated for the MAR-M 247 directionally solidified nickel-base superalloy.

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En esta tesis se integran numéricamente las ecuaciones reducidas de Navier Stokes (RNS), que describen el flujo en una capa límite tridimensional que presenta también una escala característica espacial corta en el sentido transversal. La formulación RNS se usa para el cálculo de “streaks” no lineales de amplitud finita, y los resultados conseguidos coinciden con los existentes en la literatura, obtenidos típicamente utilizando simulación numérica directa (DNS) o nonlinear parabolized stability equations (PSE). El cálculo de los “streaks” integrando las RNS es mucho menos costoso que usando DNS, y no presenta los problemas de estabilidad que aparecen en la formulación PSE cuando la amplitud del “streak” deja de ser pequeña. El código de integración RNS se utiliza también para el cálculo de los “streaks” que aparecen de manera natural en el borde de ataque de una placa plana en ausencia de perturbaciones en la corriente uniforme exterior. Los resultados existentes hasta ahora calculaban estos “streaks” únicamente en el límite lineal (amplitud pequeña), y en esta tesis se lleva a cabo el cálculo de los mismos en el régimen completamente no lineal (amplitud finita). En la segunda parte de la tesis se generaliza el código RNS para incluir la posibilidad de tener una placa no plana, con curvatura en el sentido transversal que varía lentamente en el sentido de la corriente. Esto se consigue aplicando un cambio de coordenadas, que transforma el dominio físico en uno rectangular. La formulación RNS se integra también expresada en las correspondientes coordenadas curvilíneas. Este código generalizado RNS se utiliza finalmente para estudiar el flujo de capa límite sobre una placa con surcos que varían lentamente en el sentido de la corriente, y es usado para simular el flujo sobre surcos que crecen en tal sentido. Abstract In this thesis, the reduced Navier Stokes (RNS) equations are numerically integrated. This formulation describes the flow in a three-dimensional boundary layer that also presents a short characteristic space scale in the spanwise direction. RNS equations are used to calculate nonlinear finite amplitude “streaks”, and the results agree with those reported in the literature, typically obtained using direct numerical simulation (DNS) or nonlinear parabolized stability equations (PSE). “Streaks” simulations through the RNS integration are much cheaper than using DNS, and avoid stability problems that appear in the PSE when the amplitude of the “streak” is not small. The RNS integration code is also used to calculate the “streaks” that naturally emerge at the leading edge of a flat plate boundary layer in the absence of any free stream perturbations. Up to now, the existing results for these “streaks” have been only calculated in the linear limit (small amplitude), and in this thesis their calculation is carried out in the fully nonlinear regime (finite amplitude). In the second part of the thesis, the RNS code is generalized to include the possibility of having a non-flat plate, curved in the spanwise direction and slowly varying in the streamwise direction. This is achieved by applying a change of coordinates, which transforms the physical domain into a rectangular one. The RNS formulation expressed in the corresponding curvilinear coordinates is also numerically integrated. This generalized RNS code is finally used to study the boundary layer flow over a plate with grooves which vary slowly in the streamwise direction; and this code is used to simulate the flow over grooves that grow in the streamwise direction.

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Corrosion of steel bars embedded in concrete has a great influence on structural performance and durability of reinforced concrete. Chloride penetration is considered to be a primary cause of concrete deterioration in a vast majority of structures. Therefore, modelling of chloride penetration into concrete has become an area of great interest. The present work focuses on modelling of chloride transport in concrete. The differential macroscopic equations which govern the problem were derived from the equations at the microscopic scale by comparing the porous network with a single equivalent pore whose properties are the same as the average properties of the real porous network. The resulting transport model, which accounts for diffusion, migration, advection, chloride binding and chloride precipitation, consists of three coupled differential equations. The first equation models the transport of chloride ions, while the other two model the flow of the pore water and the heat transfer. In order to calibrate the model, the material parameters to determine experimentally were identified. The differential equations were solved by means of the finite element method. The classical Galerkin method was employed for the pore solution flow and the heat transfer equations, while the streamline upwind Petrov Galerkin method was adopted for the transport equation in order to avoid spatial instabilities for advection dominated problems. The finite element codes are implemented in Matlab® . To retrieve a good understanding of the influence of each variable and parameter, a detailed sensitivity analysis of the model was carried out. In order to determine the diffusive and hygroscopic properties of the studied concretes, as well as their chloride binding capacity, an experimental analysis was performed. The model was successfully compared with experimental data obtained from an offshore oil platform located in Brazil. Moreover, apart from the main objectives, numerous results were obtained throughout this work. For instance, several diffusion coefficients and the relation between them are discussed. It is shown how the electric field set up between the ionic species depends on the gradient of the species’ concentrations. Furthermore, the capillary hysteresis effects are illustrated by a proposed model, which leads to the determination of several microstructure properties, such as the pore size distribution and the tortuosity-connectivity of the porous network. El fenómeno de corrosión del acero de refuerzo embebido en el hormigón ha tenido gran influencia en estructuras de hormigón armado, tanto en su funcionalidad estructural como en aspectos de durabilidad. La penetración de cloruros en el interior del hormigón esta considerada como el factor principal en el deterioro de la gran mayoría de estructuras. Por lo tanto, la modelización numérica de dicho fenómeno ha generado gran interés. El presente trabajo de investigación se centra en la modelización del transporte de cloruros en el interior del hormigón. Las ecuaciones diferenciales que gobiernan los fenómenos a nivel macroscópico se deducen de ecuaciones planteadas a nivel microscópico. Esto se obtiene comparando la red porosa con un poro equivalente, el cual mantiene las mismas propiedades de la red porosa real. El modelo está constituido por tres ecuaciones diferenciales acopladas que consideran el transporte de cloruros, el flujo de la solución de poro y la transferencia de calor. Con estas ecuaciones se tienen en cuenta los fenómenos de difusión, migración, advección, combinación y precipitación de cloruros. El análisis llevado a cabo en este trabajo ha definido los parámetros necesarios para calibrar el modelo. De acuerdo con ellas, se seleccionaron los ensayos experimentales a realizar. Las ecuaciones diferenciales se resolvieron mediante el método de elementos finitos. El método clásico de Galerkin se empleó para solucionar las ecuaciones de flujo de la solución de poro y de la transferencia de calor, mientras que el método streamline upwind Petrov-Galerkin se utilizó para resolver la ecuación de transporte de cloruros con la finalidad de evitar inestabilidades espaciales en problemas con advección dominante. El código de elementos finitos está implementado en Matlab® . Con el objetivo de facilitar la comprensión del grado de influencia de cada variable y parámetro, se realizó un análisis de sensibilidad detallado del modelo. Se llevó a cabo una campaña experimental sobre los hormigones estudiados, con el objeto de obtener sus propiedades difusivas, químicas e higroscópicas. El modelo se contrastó con datos experimentales obtenidos en una plataforma petrolera localizada en Brasil. Las simulaciones numéricas corroboraron los datos experimentales. Además, durante el desarrollo de la investigación se obtuvieron resultados paralelos a los planteados inicialmente. Por ejemplo, el análisis de diferentes coeficientes de difusión y la relación entre ellos. Así como también se observó que el campo eléctrico establecido entre las especies iónicas disueltas en la solución de poro depende del gradiente de concentración de las mismas. Los efectos de histéresis capilar son expresados por el modelo propuesto, el cual conduce a la determinación de una serie de propiedades microscópicas, tales como la distribución del tamaño de poro, además de la tortuosidad y conectividad de la red porosa.

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We study the renormalization group flow of the average action of the stochastic Navier-Stokes equation with power-law forcing. Using Galilean invariance, we introduce a nonperturbative approximation adapted to the zero-frequency sector of the theory in the parametric range of the Hölder exponent 4−2 ɛ of the forcing where real-space local interactions are relevant. In any spatial dimension d, we observe the convergence of the resulting renormalization group flow to a unique fixed point which yields a kinetic energy spectrum scaling in agreement with canonical dimension analysis. Kolmogorov's −5/3 law is, thus, recovered for ɛ=2 as also predicted by perturbative renormalization. At variance with the perturbative prediction, the −5/3 law emerges in the presence of a saturation in the ɛ dependence of the scaling dimension of the eddy diffusivity at ɛ=3/2 when, according to perturbative renormalization, the velocity field becomes infrared relevant.

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We develop a simplified model of choked flow in pipes for CO2-water solutions as an important step in the modelling of a whole hydraulic system with the intention of eliminating the carbon dioxide generated in air-independent submarine propulsion. The model is based on an approximate fitting of the homogeneous isentropic solution upstream of a valve (or any other area restriction), for given fluid conditions at the entrance. The relative maximum choking back-pressure is computed as a function of area restriction ratio. Although the procedure is generic for gas solutions, numeric values for the non-dimensional parameters in the analysis are developed only for choking in the case of carbon dioxide solutions up to the pure-water limit.