The dynamics of axisymmetric slender liquid bridges between unequal disks

n this paper the influence of an axial microgravity on the dynamic stability of axisymmetric slender liquid bridges between unequal disks is numerically studied by using a one-dimensional theory. The breaking of such liquid configurations is analyzed and the dependence of some overall characteristics of the breaking process on the value of axial microgravity, the geometry and the volume of the liquid bridge, as well as stability limits are obtained.

Experiments with liquid bridges in simulated microgravity

A feature of stability diagrams of liquid bridges between unequal disks subjected to small axial gravity forces is that, for each separation of disks, there is a value of microgravity for which an absolute minimum volume limit is reached. The dependence of such microgravity values on the liquid bridge geometry has been experimentally checked by using the neutral buoyancy technique, experimental results being in complete agreement with theoretical ones. Analytical background assuring the experimental procedure used is presented, and a second order analytical expression for the equilirium interface is also calculated.

Numerical and experimental study of the dynamics of axisymmetric slender liquid bridges

A one-dimensional inviscid slice model has been used to study numerically the influence of axial microgravity on the breaking of liquid bridges having a volume close to that of gravitationless minimum volume stability limit. Equilibrium shapes and stability limits have been obtained as well as the dependence of the volume of the two drops formed after breaking on both the length and the volume of the liquid bridge. The breaking process has also been studied experimentally. Good agreement has been found between theory and experiment for neutrally buoyant systems

One-dimensional linear analysis of the compound jet

The stability of an infinitely long compound liquid column is analysed by using a one-dimensional inviscid slice model. Results obtained from this one-dimensional linear analysis are applicable to the study of compound capillary jets, which are used in the ink-jet printing technique. Stability limits and the breaking regimes of such fluid configurations are established, and, whenever possible, theoretical results are compared with experimental ones.

A wind tunnel two-dimensional parametric investigation of biplane configurations

This paper presents an experimental and systematic investigation about how geometric parameters on a biplane configuration have an influence on aerodynamic parameters. This experimental investigation has been developed in a two-dimensional approach. Theoretical studies about biplanes configurations have been developed in the past, but there is not enough information about experimental wind tunnel data at low Reynolds number. This two-dimensional study is a first step to further tridimensional investigations about the box wing configuration. The main objective of the study is to find the relationships between the geometrical parameters which present the best aerodynamic behavior: the highest lift, the lowest drag and the lowest slope of the pitching moment. A tridimensional wing-box model will be designed following the pattern of the two dimensional study conclusions. It will respond to the geometrical relationships that have been considered to show the better aerodynamic behavior. This box-wing model will be studied in the aim of comparing the advantages and disadvantages between this biplane configuration and the plane configuration, looking for implementing the box-wing in the UAV?s field. Although the box wing configuration has been used in a small number of existing UAV, prestigious researchers have found it as a field of high aerodynamic and structural potential.

Métodos computacionales para visco-hiperelasticidad anisótropa en grandes deformaciones

El comportamiento mecánico de muchos materiales biológicos y poliméricos en grandes deformaciones se puede describir adecuadamente mediante formulaciones isocóricas hiperelásticas y viscoelásticas. Las ecuaciones de comportamiento elástico y viscoelástico y las formulaciones computacionales para materiales incompresibles isótropos en deformaciones finitas están ampliamente desarrolladas en la actualidad. Sin embargo, el desarrollo de modelos anisótropos no lineales y de sus correspondientes formulaciones computacionales sigue siendo un tema de investigación de gran interés. Cuando se consideran grandes deformaciones, existen muchas medidas de deformación disponibles con las que poder formular las ecuaciones de comportamiento. Los modelos en deformaciones cuadráticas facilitan la implementación en códigos de elementos finitos, ya que estas medidas surgen de forma natural en la formulación. No obstante, pueden dificultar la interpretación de los modelos y llevar a resultados pocos realistas. El uso de deformaciones logarítmicas permite el desarrollo de modelos más simples e intuitivos, aunque su formulación computacional debe ser adaptada a las exigencias del programa. Como punto de partida, en esta tesis se demuestra que las deformaciones logarítmicas representan la extensión natural de las deformaciones infinitesimales, tanto axiales como angulares, al campo de las grandes deformaciones. Este hecho permite explicar la simplicidad de las ecuaciones resultantes. Los modelos hiperelásticos predominantes en la actualidad están formulados en invariantes de deformaciones cuadráticas. Estos modelos, ya sean continuos o microestructurales, se caracterizan por tener una forma analítica predefinida. Su expresión definitiva se calcula mediante un ajuste de curvas a datos experimentales. Un modelo que no sigue esta metodología fue desarrollado por Sussman y Bathe. El modelo es sólo válido para isotropía y queda definido por una función de energía interpolada con splines, la cual reproduce los datos experimentales de forma exacta. En esta tesis se presenta su extensión a materiales transversalmente isótropos y ortótropos utilizando deformaciones logarítmicas. Asimismo, se define una nueva propiedad que las funciones de energía anisótropas deben satisfacer para que su convergencia al caso isótropo sea correcta. En visco-hiperelasticidad, aparte de las distintas funciones de energía disponibles, hay dos aproximaciones computational típicas basadas en variables internas. El modelo original de Simó está formulado en tensiones y es válido para materiales anisótropos, aunque sólo es adecuado para pequeñas desviaciones con respecto al equilibrio termodinámico. En cambio, el modelo basado en deformaciones de Reese y Govindjee permite grandes deformaciones no equilibradas pero es, en esencia, isótropo. Las formulaciones anisótropas en este último contexto son microestructurales y emplean el modelo isótropo para cada uno de los constituyentes. En esta tesis se presentan dos formulaciones fenomenológicas viscoelásticas definidas mediante funciones hiperelásticas anisótropas y válidas para grandes desviaciones con respecto al equilibrio termodinámico. El primero de los modelos está basado en la descomposición multiplicativa de Sidoroff y requiere un comportamiento viscoso isótropo. La formulación converge al modelo de Reese y Govindjee en el caso especial de isotropía elástica. El segundo modelo se define a partir de una descomposición multiplicativa inversa. Esta formulación está basada en una descripción co-rotacional del problema, es sustancialmente más compleja y puede dar lugar a tensores constitutivos ligeramente no simétricos. Sin embargo, su rango de aplicación es mucho mayor ya que permite un comportamiento anisótropo tanto elástico como viscoso. Varias simulaciones de elementos finitos muestran la gran versatilidad de estos modelos cuando se combinan con funciones hiperelásticas formadas por splines. ABSTRACT The mechanical behavior of many polymeric and biological materials may be properly modelled be means of isochoric hyperelastic and viscoelastic formulations. These materials may sustain large strains. The viscoelastic computational formulations for isotropic incompressible materials at large strains may be considered well established; for example Ogden’s hyperelastic function and the visco-hyperelastic model of Reese and Govindjee are well known models for isotropy. However, anisotropic models and computational procedures both for hyperelasticity and viscohyperelasticity are still under substantial research. Anisotropic hyperelastic models are typically based on structural invariants obtained from quadratic strain measures. These models may be microstructurallybased or phenomenological continuum formulations, and are characterized by a predefined analytical shape of the stored energy. The actual final expression of the stored energy depends on some material parameters which are obtained from an optimization algorithm, typically the Levenberg-Marquardt algorithm. We present in this work anisotropic spline-based hyperelastic stored energies in which the shape of the stored energy is obtained as part of the procedure and which (exactly in practice) replicates the experimental data. These stored energies are based on invariants obtained from logarithmic strain measures. These strain measures preserve the metric and the physical meaning of the trace and deviator operators and, hence, are interesting and meaningful for anisotropic formulations. Furthermore, the proposed stored energies may be formulated in order to have material-symmetries congruency both from a theoretical and from a numerical point of view, which are new properties that we define in this work. On the other hand, visco-hyperelastic formulations for anisotropic materials are typically based on internal stress-like variables following a procedure used by Sim´o. However, it can be shown that this procedure is not adequate for large deviations from thermodynamic equilibrium. In contrast, a formulation given by Reese and Govindjee is valid for arbitrarily large deviations from thermodynamic equilibrium but not for anisotropic stored energy functions. In this work we present two formulations for visco-hyperelasticity valid for anisotropic stored energies and large deviations from thermodynamic equilibrium. One of the formulations is based on the Sidoroff multiplicative decomposition and converges to the Reese and Govindjee formulation for the case of isotropy. However, the formulation is restricted to isotropy for the viscous component. The second formulation is based on a reversed multiplicative decomposition. This last formulation is substantially more complex and based on a corotational description of the problem. It can also result in a slightly nonsymmetric tangent. However, the formulation allows for anisotropy not only in the equilibrated and non-equilibrated stored energies, but also in the viscous behavior. Some examples show finite element implementation, versatility and interesting characteristics of the models.

Modelos sin malla en simulación numérica de estructuras aeroespaciales

La presente Tesis Doctoral aborda la introducción de la Partición de Unidad de Bernstein en la forma débil de Galerkin para la resolución de problemas de condiciones de contorno en el ámbito del análisis estructural. La familia de funciones base de Bernstein conforma un sistema generador del espacio de funciones polinómicas que permite construir aproximaciones numéricas para las que no se requiere la existencia de malla: las funciones de forma, de soporte global, dependen únicamente del orden de aproximación elegido y de la parametrización o mapping del dominio, estando las posiciones nodales implícitamente definidas. El desarrollo de la formulación está precedido por una revisión bibliográfica que, con su punto de partida en el Método de Elementos Finitos, recorre las principales técnicas de resolución sin malla de Ecuaciones Diferenciales en Derivadas Parciales, incluyendo los conocidos como Métodos Meshless y los métodos espectrales. En este contexto, en la Tesis se somete la aproximación Bernstein-Galerkin a validación en tests uni y bidimensionales clásicos de la Mecánica Estructural. Se estudian aspectos de la implementación tales como la consistencia, la capacidad de reproducción, la naturaleza no interpolante en la frontera, el planteamiento con refinamiento h-p o el acoplamiento con otras aproximaciones numéricas. Un bloque importante de la investigación se dedica al análisis de estrategias de optimización computacional, especialmente en lo referente a la reducción del tiempo de máquina asociado a la generación y operación con matrices llenas. Finalmente, se realiza aplicación a dos casos de referencia de estructuras aeronáuticas, el análisis de esfuerzos en un angular de material anisotrópico y la evaluación de factores de intensidad de esfuerzos de la Mecánica de Fractura mediante un modelo con Partición de Unidad de Bernstein acoplada a una malla de elementos finitos. ABSTRACT This Doctoral Thesis deals with the introduction of Bernstein Partition of Unity into Galerkin weak form to solve boundary value problems in the field of structural analysis. The family of Bernstein basis functions constitutes a spanning set of the space of polynomial functions that allows the construction of numerical approximations that do not require the presence of a mesh: the shape functions, which are globally-supported, are determined only by the selected approximation order and the parametrization or mapping of the domain, being the nodal positions implicitly defined. The exposition of the formulation is preceded by a revision of bibliography which begins with the review of the Finite Element Method and covers the main techniques to solve Partial Differential Equations without the use of mesh, including the so-called Meshless Methods and the spectral methods. In this context, in the Thesis the Bernstein-Galerkin approximation is subjected to validation in one- and two-dimensional classic benchmarks of Structural Mechanics. Implementation aspects such as consistency, reproduction capability, non-interpolating nature at boundaries, h-p refinement strategy or coupling with other numerical approximations are studied. An important part of the investigation focuses on the analysis and optimization of computational efficiency, mainly regarding the reduction of the CPU cost associated with the generation and handling of full matrices. Finally, application to two reference cases of aeronautic structures is performed: the stress analysis in an anisotropic angle part and the evaluation of stress intensity factors of Fracture Mechanics by means of a coupled Bernstein Partition of Unity - finite element mesh model.

A Special Perturbation Method in Orbital Dynamics

Bead models are used in dynamical simulation of tethers. These models discretize a cable using beads distributed along its length. The time evolution is obtained nu- merically. Typically the number of particles ranges between 5 and 50, depending on the required accuracy. Sometimes the simulation is extended over long periods (several years). The complex interactions between the cable and its spatial environment require to optimize the propagators —both in runtime and precisión that constitute the central core of the process. The special perturbation method treated on this article conjugates simpleness of computer implementation, speediness and precision, and is capable to propagate the orbit of whichever material particle. The paper describes the evolution of some orbital elements, which are constants in a non-perturbed problem, but which evolve in the time scale imposed by the perturbation. It can be used with any kind of orbit and it is free of sin- gularities related to small inclination and/or small eccentricity. The use of Euler parameters makes it robust.

A Spectral Analysis of LDA Turbulent Flow Measurements in a Ship Air Wake

Helicopters are one of the most important tactical elements in maritime operations. The necessity for an improvement in the conditions in which the landing and take-off operations are carried out leads to the study of the flow that separates from the ship?s superstructure over the flight deck. To investigate this flow a series of wind tunnel experiments have been performed by testing a sub-scale model of a generic frigate. Measurements of the flow?s velocity have been taken by means of Laser Doppler Anemometry (LDA) in five points that simulate the last path of the landing trajectory. The data obtained in these experiments is manipulated in a frequency analysis where the corresponding spectra are calculated. Onboard measurements from an actual full scale frigate are analyzed and compared with the wind tunnel results. Conclusions obtained consist of a series of illustrative values of turbulent energy frequency ranges which can be valuable for any study in this field. The comparison shows a clear similarity between both experiments, reasserting the wind tunnel measurements and its reliability.

The development of a wind tunnel DAQ system by using Labview tools

This paper presents the experimental three-year learning activity developed by a group of teachers in a wind tunnel facility. The authors, leading a team of students, carried out a project consisting of the design, assembly and testing of a wind tunnel. The project included all stages of the process from its initial specifications to its final quality flow assessments, going through the calculation of each element, and the building of the whole wind tunnel. The group of (final year) students was responsible for the whole wind tunnel project as a part of their bachelor degree project. The paper focuses on the development of wind tunnel data acquisition software. This automatic tool is essential to improve the automation of the data acquisition of the wind tunnel facility systems, in particular for a 6DOF multi-axis force/torque sensor. This work can be considered as a typical example of real engineering practice: a set of specifications that has to be modified due to the constraints imposed throughout the project, in order to obtain the final result

Transverse galloping of two-dimensional bodies having a rhombic cross-section

Transverse galloping is a type of aeroelastic instability characterized by oscillations perpendicular to wind direction, large amplitude and low frequency, which appears in some elastic two-dimensional bluff bodies when they are subjected to an incident flow, provided that the flow velocity exceeds a threshold critical value. Understanding the galloping phenomenon of different cross-sectional geometries is important in a number of engineering applications: for energy harvesting applications the interest relies on strongly unstable configurations but in other cases the purpose is to avoid this type of aeroelastic phenomenon. In this paper the aim is to analyze the transverse galloping behavior of rhombic bodies to understand, on the one hand, the dependence of the instability with a geometrical parameter such as the relative thickness and, on the other hand, why this cross-section shape, that is generally unstable, shows a small range of relative thickness values where it is stable. Particularly, the non-galloping rhombus-shaped prism?s behavior is revised through wind tunnel experiments. The bodies are allowed to freely move perpendicularly to the incoming flow and the amplitude of movement and pressure distributions on the surfaces is measured.

Un Método de Perturbaciones Especiales en la Dinámica de Tethers

En la simulación dinámica de tethers se usan "bead models" que discretizan el cable mediante "cuentas" distribuidas en toda su longitud y cuya evolución temporal se aborda numéricamente. Dependiendo de la precisión deseada, el número de partículas oscila, típicamente, entre 5 y 50. En ocasiones la simulación se extiende sobre tiempos largos (varios años). La complejidad de las interacciones del cable con el medio espacial exige optimizar, en tiempo y precisión, los propagadores que constituyen el núcleo central del proceso. El "método de perturbaciones especiales" objeto de este artículo conjuga sencillez de programación, rapidez y precisión, y permite propagar la órbita de cualquier partícula material. Describe la evolución de ciertos "elementos orbitales", constantes del problema "no perturbado}"que, en el "perturbado", evolucionan en la escala de tiempos impuesta por la perturbación. Puede usarse con cualquier tipo de órbita, está libre de singularidades asociadas a inclinación y/o excentricidad pequeñas, y el uso de parámetros de Euler le confiere robustez.

Quasi-cylindrical approximation to the swirling flow in an atomizer chamber

A quasi-cylindrical approximation is used to analyse the axisymmetric swirling flow of a liquid with a hollow air core in the chamber of a pressure swirl atomizer. The liquid is injected into the chamber with an azimuthal velocity component through a number of slots at the periphery of one end of the chamber, and flows out as an anular sheet through a central orifice at the other end, following a conical convergence of the chamber wall. An effective inlet condition is used to model the effects of the slots and the boundary layer that develops at the nearby endwall of the chamber. An analysis is presented of the structure of the liquid sheet at the end of the exit orifice, where the flow becomes critical in the sense that upstream propagation of long-wave perturbations ceases to be possible. This nalysis leads to a boundary condition at the end of the orifice that is an extension of the condition of maximum flux used with irrotational models of the flow. As is well known, the radial pressure gradient induced by the swirling flow in the bulk of the chamber causes the overpressure that drives the liquid towards the exit orifice, and also leads to Ekman pumping in the boundary layers of reduced azimuthal velocity at the convergent wall of the chamber and at the wall opposite to the exit orifice. The numerical results confirm the important role played by the boundary layers. They make the thickness of the liquid sheet at the end of the orifice larger than predicted by rrotational models, and at the same time tend to decrease the overpressure required to pass a given flow rate through the chamber, because the large axial velocity in the boundary layers takes care of part of the flow rate. The thickness of the boundary layers increases when the atomizer constant (the inverse of a swirl number, proportional to the flow rate scaled with the radius of the exit orifice and the circulation around the air core) decreases. A minimum value of this parameter is found below which the layer of reduced azimuthal velocity around the air core prevents the pressure from increasing and steadily driving the flow through the exit orifice. The effects of other parameters not accounted for by irrotational models are also analysed in terms of their influence on the boundary layers.

Effects of radiation losses on very lean methane/air flames propagating upward in a vertical tube

The stationary upward propagation of a very lean methane/air flame in a long vertical tube open at the bottom and closed at the top is simulated numerically using a single overall chemical reaction to model combustion and assuming an optically thin gas and a transparent or non-reflecting tube wall to approximately account for radiation losses from CO2CO2 and H2OH2O. Buoyancy plays a dominant role in the propagation of these flames and causes a large region of low velocity of the burnt gas relative to the flame to appear below the flame front when the equivalence ratio is decreased. The size of this region scales with the radius of the tube, and its presence enhances the effect of radiation losses, which would be otherwise negligible for a standard flammability tube, given the small concentration of radiating species. Heat conduction is found to be important in the low velocity region and to lead to a conduction flux from the flame to the burnt gas that causes extinction at the flame tip for a value of the equivalence ratio near the flammability limit experimentally measured in the standard tube. The effect of radiation losses decreases with the radius of the tube. Numerical results and order-of-magnitude estimates show that, in the absence of radiation, a very lean flame front fails to propagate only after recirculation of the burnt gas extends to its reaction region and drastically changes its structure. This condition is not realized for the standard flammability tube, but it seems to account for the flammability limit measured in a tube of about half the radius of the standard tube.

Jovian Capture of a Spacecraft with a Self-Balanced Electrodynamic Bare Tether

This paper proposes and analyzes the use of a nonrotating tethered system for a direct capture in Jovian orbit using the electrodynamic force generated along the cable. A detailed dynamical model is developed showing a strong gravitational and electrodynamic coupling between the center of mass and the attitude motions. This paper shows the feasibility of a direct capture in Jovian orbit of a rigid tethered system preventing the tether from rotating. Additional mechanical–thermal requirements are explored, and preliminary operational limits are defined to complete the maneuver. In particular, to ensure that the system remains nonrotating, a nominal attitude profile for a self-balanced electrodynamic tether is proposed, as well as a simple feedback control.