Apuntes de Mecánica de Fluidos

Esta publicacion contiene unos apuntes para la parte de Mecánica de Fluidos de las asignaturas de la ETSAM, junto con cierta cantidad de material adicional que excede el ámbito del curso. Aunque está lejos de ser completa y de estar libre de errores, el autor espera sea útil.

Estudio paramétrico del conjunto tractor-trailer mediante aplicación de mecánica de fluidos computacional

La mejora del comportamiento aerodinámico de vehículos pesados en la carretera ha adquirido una mayor importancia estos últimos años debido a la crisis y su consecuente aumento del precio de los combustibles. Dado que una reducción en la resistencia aerodinámica del vehículo conlleva un menor empleo de combustible, el objetivo de este proyecto es realizar un estudio paramétrico del conjunto tractor-tráiler mediante la mecánica de fluidos computacional (CFD) para así obtener la geometría que proporciona un menor gasto de combustible cuando ésta es expuesta a viento frontal. La influencia de 3 parámetros, que son la separación existente entre cabina y remolque, la altura del remolque y el radio de curvatura de las aristas frontales de la cabina, es analizada en este estudio dividido en varias etapas que implican el uso de programas específicos como son: la parametrización y creación de las geometrías en 3D que es llevada a cabo mediante CATIA, el mallado del dominio (realizado con Gambit) y resolución de las ecuaciones mediante FLUENT. Finalmente se obtendrá una relación entre la resistencia aerodinámica (representada mediante el coeficiente de arrastre) y la combinación de los 3 parámetros, que nos permitirá decidir que geometría es la óptima. Abstract The improvement of the heavy vehicle’s aerodynamic behavior on the road has gained a great importance for these last years because of the economic crisis and the consequent increase of the price of the fuels. Due to the fact that a reduction in the aerodynamic resistance of the vehicle involves using a smaller amount of fuel, the objective of this project is to carry out a parametric study about the ensemble tractor-trailer by computational fluid dynamics methods (CFD) in order to obtain the geometry which expense of fuel is the lowest when it’s exposed to frontal wind. The influence of the three parameters, which are the space between cab and trailer, the height of the trailer and the curvature of the frontal cab edges, is analysed in this study which is divided into different parts involving specific programs: choosing the parameters and building the geometries, which is done by using CATIA, the mesh is built by Gambit, and the program equations-solver is FLUENT. Finally a ratio between aerodynamic resistance and a combination of the three parameters will be obtained and it will allow us to choose the best geometry.

Optimización de la agitación de un digestor anaerobio mediante mecánica de fluidos computacional

Debido al gran interés existente en el ahorro y recuperación de energía, y en el deseo de obtener productos que permitan usos beneficiosos del fango procedente de la depuración del agua residual, la digestión anaerobia es el proceso de estabilización de uso más extendido. El tiempo de retención de sólidos es un factor clave en el proceso de digestión anaerobia. En base al tiempo de retención de sólidos, se dimensiona el volumen de los digestores anaerobios para así obtener la reducción de materia orgánica deseada, con la correspondiente producción de biogás. La geometría del digestor y su sistema de agitación deben ser adecuados para alcanzar el tiempo de retención de sólidos de diseño. Los primeros trabajos sobre la agitación de los digestores realizaban únicamente experimentos con trazadores y otros métodos de medición. En otros casos, la mezcla era evaluada mediante la producción de biogás. Estas técnicas tenían el gran hándicap de no conocer lo que sucedía realmente dentro del digestor y sólo daban una idea aproximada de su funcionamiento. Mediante aplicación de la mecánica de fluidos computacional (CFD) es posible conocer con detalle las características del fluido objeto de estudio y, por lo tanto, simular perfectamente el movimiento del fango de un digestor anaerobio. En esta tesis se han simulado mediante CFD diferentes digestores a escala real (unos 2000 m3 de volumen) agitados con bomba/s de recirculación para alcanzar los siguientes objetivos: establecer la influencia de la relación entre el diámetro y la altura, de la pendiente de la solera, del número de bombas y del caudal de recirculación en dichos digestores, definir el campo de velocidades en la masa de fango y realizar un análisis energético y económico. Así, es posible conocer mejor cómo funciona el sistema de agitación de un digestor anaerobio a escala real equipado con bomba/s de recirculación. Los resultados obtenidos muestran que una relación diámetro/altura del digestor por encima de 1 empeora la agitación del mismo y que la pendiente en la solera del digestor favorece que la masa de fango esté mejor mezclada, siendo más determinante la esbeltez del tanque que la pendiente de su solera. No obstante, también es necesario elegir adecuadamente los parámetros de diseño del sistema de agitación, en este caso el caudal de recirculación de fango, para obtener una agitación completa sin apenas zonas muertas. En el caso de un digestor con una geometría inadecuada es posible mejorar su agitación aumentando el número de bombas de recirculación y el caudal de las mismas, pero no se llegará a alcanzar una agitación total de la masa de fango debido a su mal diseño original. Anaerobic digestion is the process for waste water treatment sludge stabilization of more widespread use due to the huge interest in saving and recovering energy and the wish to obtain products that allow beneficial uses for the sludge. The solids retention time is a key factor in the anaerobic digestion. Based on the solids retention time, volume anaerobic digester is sized to obtain the desired reduction in organic matter, with the corresponding production of biogas. The geometry of the digester and the stirring system should be adequate to achieve the design solid retention time. Early works on digesters stirring just performed tracer experiments and other measurement methods. In other cases, mixing was evaluated by biogas production. These techniques had the great handicap of not knowing what really happened inside the digester and they only gave a rough idea of its operation. By application of computational fluid dynamics (CFD), it is possible to know in detail the characteristics of the fluid under study and, therefore, simulate perfectly the sludge movement of an anaerobic digester. Different full-scale digesters (about 2000 m3 of volume) agitated with pump/s recirculation have been simulated by CFD in this thesis to achieve the following objectives: to establish the influence of the relationship between the diameter and height, the slope of the bottom, the number of pumps and the recirculation flow in such digesters, to define the velocity field in the mass of sludge and carry out an energy and economic analysis. Thus, it is possible to understand better how the agitation system of a full-scale anaerobic digester equipped with pump/s recirculation works. The results achieved show that a diameter/height ratio of the digester above 1 worsens its stirring and that the slope of the digester bottom favors that the mass of sludge is better mixed, being more decisive the tank slenderness than the slope of its bottom. However, it is also necessary to select properly the design parameters of the agitation system, in this case the sludge recirculation flow rate, for a complete agitation with little dead zones. In the case of a digester with inadequate geometry, its agitation can be improved by increasing the number of recirculation pumps and flow of them, but it will not reach a full agitation of the mass of sludge because of the poor original design.

Resonadores piezoeléctricos de cizalladura: estudio de la formación de biofilms y caracterización de fluidos magneto‐reológicos

La presente tesis revisa y analiza algunos aspectos fundamentales relativos al comportamiento de los sensores basados en resonadores piezoeléctricos TSM (Thickness Shear Mode), así como la aplicación de los mismos al estudio y caracterización de dos medios viscoelásticos de gran interés: los fluidos magnetoreológicos y los biofilms microbianos. El funcionamiento de estos sensores está basado en la medida de sus propiedades resonantes, las cuales varían al entrar en contacto con el material que se quiere analizar. Se ha realizado un análisis multifrecuencial, trabajando en varios modos de resonancia del transductor, en algunas aplicaciones incluso de forma simultánea (excitación pulsada). Se han revisado fenómenos como la presencia de microcontactos en la superficie del sensor y la resonancia de capas viscoelásticas de espesor finito, que pueden afectar a los sensores de cuarzo de manera contraria a lo que predice la teoría convencional (Sauerbrey y Kanazawa), pudiéndonos llevar a incrementos positivos de la frecuencia de resonancia. Además, se ha estudiado el efecto de una deposición no uniforme sobre el resonador piezoeléctrico. Para ello se han medido deposiciones de poliuretano, modelándose la respuesta del resonador con estas deposiciones mediante FEM. El modelo numérico permite estudiar el comportamiento del resonador al modificar distintas variables geométricas (espesor, superficie, no uniformidad y zona de deposición) de la capa depositada. Se ha demostrado que para espesores de entre un cuarto y media longitud de onda aproximadamente, una capa viscoelástica no uniforme sobre la superficie del sensor, amplifica el incremento positivo del desplazamiento de la frecuencia de resonancia en relación con una capa uniforme. Se ha analizado también el patrón geométrico de la sensibilidad del sensor, siendo también no uniforme sobre su superficie. Se han aplicado sensores TSM para estudiar los cambios viscoelásticos que se producen en varios fluidos magneto-reológicos (FMR) al aplicarles distintos esfuerzos de cizalla controlados por un reómetro. Se ha podido ver que existe una relación directa entre diversos parámetros reológicos obtenidos con el reómetro (fuerza normal, G’, G’’, velocidad de deformación, esfuerzo de cizalla…) y los parámetros acústicos, caracterizándose los FMR tanto en ausencia de campo magnético, como con campo magnético aplicado a distintas intensidades. Se han estudiado las ventajas que aporta esta técnica de medida sobre la técnica basada en un reómetro comercial, destacando que se consigue caracterizar con mayor detalle algunos aspectos relevantes del fluido como son la deposición de partículas (estabilidad del fluido), el proceso de ruptura de las estructuras formadas en los FMR tanto en presencia como en ausencia de campo magnético y la rigidez de los microcontactos que aparecen entre partículas y superficies. También se han utilizado sensores de cuarzo para monitorear en tiempo real la formación de biofilms de Staphylococcus epidermidis y Eschericia coli sobre los propios resonadores de cristal de cuarzo sin ningún tipo de recubrimiento, realizándose ensayos con cepas que presentan distinta capacidad de producir biofilm. Se mostró que, una vez que se ha producido una primera adhesión homogénea de las bacterias al sustrato, podemos considerar el biofilm como una capa semi-infinita, de la cual el sensor de cuarzo refleja las propiedades viscoelásticas de la región inmediatamente contigua al resonador, no siendo sensible a lo que sucede en estratos superiores del biofilm. Los experimentos han permitido caracterizar el módulo de rigidez complejo de los biofilms a varias frecuencias, mostrándose que el parámetro característico que indica la adhesión de un biofilm tanto en el caso de S. epidermidis como de E. coli, es el incremento de G’ (relacionado con la elasticidad o rigidez de la capa), el cual viene ligado a un incremento de la frecuencia de resonancia del sensor. ABSTRACT This thesis reviews and analyzes some key aspects of the behavior of sensors based on piezoelectric resonators TSM (Thickness Shear Mode) and their applications to the study and characterization in two viscoelastic media of great interest: magnetorheological fluids and microbial biofilms. The operation of these sensors is based on the analysis of their resonant properties that vary in contact with the material to be analyzed. We have made a multi-frequency analysis, working in several modes of resonance of the transducer, in some applications even simultaneously (by impulse excitation). We reviewed some phenomena as the presence of micro-contacts on the sensor surface and the resonance of viscoelastic layers of finite thickness, which can affect quartz sensors contrary to the conventional theory predictions (Sauerbrey and Kanazawa), leading to positive resonant frequency shifts. In addition, we studied the effect of non-uniform deposition on the piezoelectric resonator. Polyurethane stools have been measured, being the resonator response to these depositions modeled by FEM. The numerical model allows studying the behavior of the resonator when different geometric variables (thickness, surface non-uniformity and deposition zone) of the deposited layer are modified. It has been shown that for thicknesses between a quarter and a half of a wavelength approximately, non-uniform deposits on the sensor surface amplify the positive increase of the resonance frequency displacement compared to a uniform layer. The geometric pattern of the sensor sensitivity was also analyzed, being also non-uniform over its surface. TSM sensors have been applied to study the viscoelastic changes occurring in various magneto-rheological fluids (FMR) when subjected to different controlled shear stresses driven by a rheometer. It has been seen that there is a direct relationship between various rheological parameters obtained with the rheometer (normal force, G', G'', stress, shear rate ...) and the acoustic parameters, being the FMR characterized both in the absence of magnetic field, and when the magnetic field was applied at different intensities. We have studied the advantages of this technique over the characterization methods based on commercial rheometers, noting that TSM sensors are more sensitive to some relevant aspects of the fluid as the deposition of particles (fluid stability), the breaking process of the structures formed in the FMR both in the presence and absence of magnetic field, and the rigidity of the micro-contacts appearing between particles and surfaces. TSM sensors have also been used to monitor in real time the formation of biofilms of Staphylococcus epidermidis and Escherichia coli on the quartz crystal resonators themselves without any coating, performing tests with strains having different ability to produce biofilm. It was shown that, once a first homogeneous adhesion of bacteria was produced on the substrate, the biofilm can be considered as a semi-infinite layer and the quartz sensor reflects only the viscoelastic properties of the region immediately adjacent to the resonator, not being sensitive to what is happening in upper layers of the biofilm. The experiments allow the evaluation of the biofilm complex stiffness module at various frequencies, showing that the characteristic parameter that indicates the adhesion of a biofilm for the case of both S. epidermidis and E. coli, is an increased G' (related to the elasticity or stiffness of the layer), which is linked to an increase in the resonance frequency of the sensor.

Apuntes de Mecánica de Fluidos

Esta publicacion contiene unos apuntes para la parte de Mecánica de Fluidos de las asignaturas de la ETSAM, junto con cierta cantidad de material adicional que excede el ámbito del curso. Aunque está lejos de ser completa y de estar libre de errores, el autor espera sea útil.

Estudo da dinâmica e destino ambiental dos fluidos usados na usinagem industrial de peças metálicas

Este estudo consistiu na investigação sobre a interação dos lubrificantes empregados na usinagem de metais com a matéria orgânica natural (substâncias húmicas), a sua mobilidade no solo, a degradação microbiológica e a remoção dos mesmos do solo. Realizou-se, também, um estudo sobre as mudanças nas características dos fluidos após a sua utilização. Para o processo de degradação das amostras de fluido, submetidos aos efeitos de diferentes fatores ambientais, foram utilizados quatro tratamentos : (i) microrganismos nativos, chamada amostra controle; (ii) amostra controle com matéria orgânica proveniente de turfa; (iii) amostra controle acrescida de microrganismos existentes nos efluentes de máquinas de corte; e (iv) amostra controle com adição de microrganismos de compostagem. Para a pesquisa da degradação sem o efeito dos parâmetros climáticos, foram utilizadas amostras de solo contaminadas mantendo-se em estufa, e a inoculação dos microrganismos em meios de cultura com e sem acréscimo de fonte alternativa de carbono. Como técnicas analíticas, foram utilizadas a CG-DIC e a CG-EM. Essas técnicas são indicadas tanto para estudar a composição dos fluidos quanto dos produtos de degradação microbiológica, tendo sido otimizados métodos analíticos para serem empregados no monitoramento ambiental e de estudos de degradação. As análises por IVTF e por EF também foram empregadas na identificação e quantificação dos fluidos. Observou-se uma considerável interação dos fluidos solúveis com a matéria orgânica do solo, embora tenham se apresentado com alta mobilidade para alguns constituintes, bem como um acelerado processo de degradação durante o uso. De outro modo, os fluidos insolúveis se apresentaram mais imóveis, ficando retidos na matéria orgânica do solo, entretanto, foram mais prontamente degradados no ambiente que os solúveis. A adição de matéria orgânica e de microrganismos de compostagem acelerou o processo de degradação para todos os fluidos de corte investigados.

Tema 1. Mecánica de sólidos y fluidos (Curso 2009-2010)

Sólidos, líquidos y gases: densidad; Elasticidad en sólidos: tensión y deformación; Elasticidad en fluidos: presión; Temperatura y dilatación térmica; Estática de fluidos; Fenómenos de superficie: tensión superficial, capilaridad; Dinámica de fluidos ideales; Fluidos reales: viscosidad.

Relaciones de los fluidos imponderables entre sí : Discurso leído ante el claustro de la Universidad Central en el solemne acto de recibir la investidura de doctor en la Facultad de Ciencias, Sección de Físicas... /

Tesis de la Univesidad Central (Madrid), leída el 16-05-1865.

Fluidos de perfuração aquosos: a contribuição da goma xantana e carboximetilcelulose no controle de filtrado

This study aimed mainly to evaluate the influence of xanthan gum (XG) and carboxymethylcellulose (CMC) in the filtration process of water-based drilling fluids, considering the conformational changes suffered by the polyelectrolyte with the addition of sodium chloride (NaCl) in different concentrations (0.17, 0.34 and 0.51 mol.L-1). It was also evaluated the behavior of the fluid by the addition of calcium carbonate (CaCO3) in pure water and in brine. Seeking a better understanding of the interaction between the polymers used and CaCO3, polymer adsorption analyzes were performed using a depletion method, which yielded a higher percentage of adsorption of Xanthan Gum in this material (29%), which can justify the formation of a thin and waterproof filter cake for drilling fluids containing this polymer. However, the best values of apparent viscosity (20 and 24 mPa.s) and volume of filtrate (8.0 and 8.1 mL) were obtained for the systems consisting of xanthan gum, CMC and CaCO3, in NaCl aqueous solutions concentrations of 0.34 and 0.51 mol.L-1, respectively. The values can be related to the presence of CMC that increases the apparent viscosity and reduces the volume of filtrate. In addition, the CaCO3 added acts as a bridging agent, promoting the formation of a less permeable filter cake

Uso de água produzida na formulação de fluidos de perfuração

Drilling fluids have fundamental importance in the petroleum activities, since they are responsible for remove the cuttings, maintain pressure and well stability, preventing collapse and inflow of fluid into the rock formation and maintain lubrication and cooling the drill. There are basically three types of drilling fluids: water-based, non-aqueous and aerated based. The water-based drilling fluid is widely used because it is less aggressive to the environment and provide excellent stability and inhibition (when the water based drilling fluid is a inhibition fluid), among other qualities. Produced water is generated simultaneously with oil during production and has high concentrations of metals and contaminants, so it’s necessary to treat for disposal this water. The produced water from the fields of Urucu-AM and Riacho da forquilha-RN have high concentrations of contaminants, metals and salts such as calcium and magnesium, complicating their treatment and disposal. Thus, the objective was to analyze the use of synthetic produced water with similar characteristics of produced water from Urucu-AM and Riacho da Forquilha-RN for formulate a water-based drilling mud, noting the influence of varying the concentration of calcium and magnesium into filtered and rheology tests. We conducted a simple 32 factorial experimental design for statistical modeling of data. The results showed that the varying concentrations of calcium and magnesium did not influence the rheology of the fluid, where in the plastic viscosity, apparent viscosity and the initial and final gels does not varied significantly. For the filtrate tests, calcium concentration in a linear fashion influenced chloride concentration, where when we have a higher concentration of calcium we have a higher the concentration of chloride in the filtrate. For the Urucu’s produced water based fluids, volume of filtrate was observed that the calcium concentration influences quadratically, this means that high calcium concentrations interfere with the power of the inhibitors used in the formulation of the filtered fluid. For Riacho’s produced water based fluid, Calcium’s influences is linear for volume of filtrate. The magnesium concentration was significant only for chloride concentration in a quadratic way just for Urucu’s produced water based fluids. The mud with maximum concentration of magnesium (9,411g/L), but minimal concentration of calcium (0,733g/L) showed good results. Therefore, a maximum water produced by magnesium concentration of 9,411g/L and the maximum calcium concentration of 0,733g/L can be used for formulating water-based drilling fluids, providing appropriate properties for this kind of fluid.

Tensoativo derivado do ácido cítrico: síntese e aplicação em fluidos de perfuração de emulsão inversa

This work describes the synthesis and study of the application of a new surfactant (Triester Lipophilic – TEL) obtained by citric acid with octanol. It is reaction was followed by thin layer chromatography (TLC) and after purification the product was characterized by proton and 13 – carbon nuclear magnetic resonance spectroscopy ( H and 13C NMR), thermogravimetric analysis (TGA) and surface tension analysis of oil-in-water emulsions. The TEL performance as surfactant in ester, n-paraffin and biodiesel based drilling fluids on the 70/30 and 60/40 water- oil rations (WOR) was evaluated by comparative tests of two commercial products used in the fields. These drilling fluids were aged in roller oven at 200 0 F during 16 h. The rheological and electric stability measurements were carried out at 135 ºF, the phase separation was evaluated after seven days at rest and the filtrate volume of drilling fluids was determined at high temperature and high pressure. The rheological behavior of the drilling fluids was evaluated by the flow curves. The results showed that the drilling fluids studied here presented Binghamian behavior as well as the used in the oil fields. The laboratory tests showed that the TEL reduced the filtrate volume and promoted the enhance of the thermal and mechanical stabilities.

Contribuição da poliacrilamida parcialmente hidrolisada em associação com a bentonita em fluidos de perfuração aquosos

In this study, we investigated the effect of addition of partially hydrolyzed polyacrylamide (HPAM) and bentonite in the physicochemical properties of acquous drilling fluids. Two formulations were evaluated: F1 formulation, which was used as reference, containing carboxymethylcellulose (CMC), magnesium oxide (MgO), calcite (calcium carbonate - CaCO3 ), xanthan gum, sodium chloride (NaCl) and triazine (bactericidal); and F2, containig HPAM steady of CMC and bentonite in substituition of calcite. The prepared fluids were characterized by rheological properties, lubricity and fluid loss. Calcite was characterized by granulometry and thermal gravimetric analysis (TGA). The formulation F2 presented filtration control at 93◦C 34 mL while F1 had total filtration. The lubricity coefficient was 0.1623 for F2 and 0.2542 for F1, causing reduction in torque of 25% for F1 and 52 % for F2, compared to water. In the temperature of 49 ◦C and shear rate of 1022 s −1 , the apparent viscosities were 25, 5 and 48 cP for F1 and F2 formulation, respectively, showing greater thermal resistance to F2. With the confirmation of higher thermal stability of F2, factorial design was conducted in order to determine the HPAM and of bentonite concentrations that resulted in the better performance of the fluids. The statistical design response surfaces indicated the best concentrations of HPAM (4.3g/L) and bentonite (28.5 g/L) to achieve improved properties of the fluids (apparent viscosity, plastic viscosity, yield point and fluid loss) with 95% confidence, as well as the correlations between these factors (HPAM and bentonite concentrations). The thermal aging tests indicated that the formulations containing HPAM and bentonite may be used to the maximum temperature until 150 ◦C. The analyze of the filter cake formed after filtration of fluids by X-ray diffraction showed specific interactions between the bentonite and HPAM, explaining the greater thermal stability of F2 compared to the fluid F1, that supports maximum temperature of 93 ◦C.

Efeito da força iônica nas propriedades de fluidos de perfuração aquosos à base de polímeros carboxilados e sulfatados

In the well drilling operations problems caused by contamination of the drilling fluid are common. The dissolution of ions from the geological formations affects the rheological and filtration properties of the fluids. These ions shield the charges of ionic polymers, leading to its precipitation. In this work was performed a detailed study on the stability of the properties of aqueous solutions and aqueous drilling fluids in the presence of sulphated and carboxylated polymers, using carboxymethylcellulose and kappa-carrageenan as polymer compounds carboxylated and sulfated model, respectively. The effects of ionic strength of the aqueous medium containing Na+, Mg2+ and Ca2+ on rheological properties of the polymer and drilling fluids solutions were evaluated by varying the concentration of salts, pH and temperature. It was observed that the fluids with κ-carrageenan suffered less influence against the contamination by the ions at pH 9 to 10, even at higher concentrations, but higher influence on pH> 11. The fluids containing carboxymethylcellulose were more sensitive to contamination, with rapid reduction in viscosity and significant increase of the filtrate volume, while the fluid based polymer sulfated kappa-carrageenan showed evidence of interaction with cations and preserve the rheological properties and improved stability the volume of filtrate.

Efeito da força iônica nas propriedades de fluidos de perfuração aquosos à base de polímeros carboxilados e sulfatados

In the well drilling operations problems caused by contamination of the drilling fluid are common. The dissolution of ions from the geological formations affects the rheological and filtration properties of the fluids. These ions shield the charges of ionic polymers, leading to its precipitation. In this work was performed a detailed study on the stability of the properties of aqueous solutions and aqueous drilling fluids in the presence of sulphated and carboxylated polymers, using carboxymethylcellulose and kappa-carrageenan as polymer compounds carboxylated and sulfated model, respectively. The effects of ionic strength of the aqueous medium containing Na+, Mg2+ and Ca2+ on rheological properties of the polymer and drilling fluids solutions were evaluated by varying the concentration of salts, pH and temperature. It was observed that the fluids with κ-carrageenan suffered less influence against the contamination by the ions at pH 9 to 10, even at higher concentrations, but higher influence on pH> 11. The fluids containing carboxymethylcellulose were more sensitive to contamination, with rapid reduction in viscosity and significant increase of the filtrate volume, while the fluid based polymer sulfated kappa-carrageenan showed evidence of interaction with cations and preserve the rheological properties and improved stability the volume of filtrate.