Foundations and applications of non-equilibrium statistical mechanics

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Finite volume modelling of an icefield with subglacial lake

Momentum, mass and energy balance laws provide the tools for the study of the evolution of an icefield covering a subglacial lake. The ice is described as a non-Newtonian fluid with a power-law constitutive relationship with temperature- and stress-dependent viscosity (Glen?s law) [1]. The phase transition mechanisms at the air/ice and ice/water interfaces yield moving boundary formulations, and lake hydrodynamics requires equation reduction for treating the turbulence.

Linear global instability of non-orthogonal incompressible swept attachment-line boundary layer flow

Instability of the orthogonal swept attachment line boundary layer has received attention by local1, 2 and global3–5 analysis methods over several decades, owing to the significance of this model to transition to turbulence on the surface of swept wings. However, substantially less attention has been paid to the problem of laminar flow instability in the non-orthogonal swept attachment-line boundary layer; only a local analysis framework has been employed to-date.6 The present contribution addresses this issue from a linear global (BiGlobal) instability analysis point of view in the incompressible regime. Direct numerical simulations have also been performed in order to verify the analysis results and unravel the limits of validity of the Dorrepaal basic flow7 model analyzed. Cross-validated results document the effect of the angle _ on the critical conditions identified by Hall et al.1 and show linear destabilization of the flow with decreasing AoA, up to a limit at which the assumptions of the Dorrepaal model become questionable. Finally, a simple extension of the extended G¨ortler-H¨ammerlin ODE-based polynomial model proposed by Theofilis et al.4 is presented for the non-orthogonal flow. In this model, the symmetries of the three-dimensional disturbances are broken by the non-orthogonal flow conditions. Temporal and spatial one-dimensional linear eigenvalue codes were developed, obtaining consistent results with BiGlobal stability analysis and DNS. Beyond the computational advantages presented by the ODE-based model, it allows us to understand the functional dependence of the three-dimensional disturbances in the non-orthogonal case as well as their connections with the disturbances of the orthogonal stability problem.

Reentrant hexagons in non-Boussinesq convection.

While non-Boussinesq hexagonal convection patterns are known to be stable close to threshold (i.e. for Rayleigh numbers R ? Rc ), it has often been assumed that they are always unstable to rolls for slightly higher Rayleigh numbers. Using the incompressible Navier?Stokes equations for parameters corresponding to water as the working fluid, we perform full numerical stability analyses of hexagons in the strongly nonlinear regime ( ? (R ? Rc )/Rc = O(1)). We find ?re-entrant? behaviour of the hexagons, i.e. as is increased they can lose and regain stability. This can occur for values of as low as = 0.2. We identify two factors contributing to the re-entrance: (i) far above threshold there exists a hexagon attractor even in Boussinesq convection as has been shown recently and (ii) the non-Boussinesq effects increase with . Using direct simulations for circular containers we show that the re-entrant hexagons can prevail even for sidewall conditions that favour convection in the form of competing stable rolls. For sufficiently strong non-Boussinesq effects hexagons even become stable over the whole -range considered, 0 6 6 1.5.

Analysis of Meshfree Methods for Lagrangian Fluid-Structure Interaction

In this dissertation a new numerical method for solving Fluid-Structure Interaction (FSI) problems in a Lagrangian framework is developed, where solids of different constitutive laws can suffer very large deformations and fluids are considered to be newtonian and incompressible. For that, we first introduce a meshless discretization based on local maximum-entropy interpolants. This allows to discretize a spatial domain with no need of tessellation, avoiding the mesh limitations. Later, the Stokes flow problem is studied. The Galerkin meshless method based on a max-ent scheme for this problem suffers from instabilities, and therefore stabilization techniques are discussed and analyzed. An unconditionally stable method is finally formulated based on a Douglas-Wang stabilization. Then, a Langrangian expression for fluid mechanics is derived. This allows us to establish a common framework for fluid and solid domains, such that interaction can be naturally accounted. The resulting equations are also in the need of stabilization, what is corrected with an analogous technique as for the Stokes problem. The fully Lagrangian framework for fluid/solid interaction is completed with simple point-to-point and point-to-surface contact algorithms. The method is finally validated, and some numerical examples show the potential scope of applications.

Global Linear Instability at the Dawn of its 4th Decade: A List of Challenges (A Practical Guide on how to Contain the Euphoria and Avoid the Oversell)

Global linear instability theory is concerned with the temporal or spatial development of small-amplitude perturbations superposed upon laminar steady or time-periodic threedimensional flows, which are inhomogeneous in two (and periodic in one) or all three spatial directions.1 The theory addresses flows developing in complex geometries, in which the parallel or weakly nonparallel basic flow approximation invoked by classic linear stability theory does not hold. As such, global linear theory is called to fill the gap in research into stability and transition in flows over or through complex geometries. Historically, global linear instability has been (and still is) concerned with solution of multi-dimensional eigenvalue problems; the maturing of non-modal linear instability ideas in simple parallel flows during the last decade of last century2–4 has given rise to investigation of transient growth scenarios in an ever increasing variety of complex flows. After a brief exposition of the theory, connections are sought with established approaches for structure identification in flows, such as the proper orthogonal decomposition and topology theory in the laminar regime and the open areas for future research, mainly concerning turbulent and three-dimensional flows, are highlighted. Recent results obtained in our group are reported in both the time-stepping and the matrix-forming approaches to global linear theory. In the first context, progress has been made in implementing a Jacobian-Free Newton Krylov method into a standard finite-volume aerodynamic code, such that global linear instability results may now be obtained in compressible flows of aeronautical interest. In the second context a new stable very high-order finite difference method is implemented for the spatial discretization of the operators describing the spatial BiGlobal EVP, PSE-3D and the TriGlobal EVP; combined with sparse matrix treatment, all these problems may now be solved on standard desktop computers.

Modelización de contactos termoelastohidrodinámicos

La mejora en la eficiencia energética y la reducción de la tasa de fallos en los contactos lubricados son aspectos que resultan de gran interés en numerosos sectores de la industria, y plantean en estos momentos nuevas dificultades operativas y retos para un futuro próximo. Los avances tecnológicos han incrementado las exigencias técnicas que se requieren a los aceites para cumplir su función al extender sus variables operativas a un mayor espectro de aplicaciones, tanto de condiciones de funcionamiento como a la gran variedad de nuevos materiales constitutivos de los engranajes en los que se tiene que utilizar. Por ello, actualmente se está incentivado el desarrollo de nuevos procedimientos que permitan comprender el comportamiento de este tipo de contactos lubricados, con el fin de lograr mejoras técnicas en su diseño y la correcta selección del aceite. En esta Tesis Doctoral se presenta una metodología de cálculo numérico que permite simular el comportamiento de contactos elastohidrodinámicos (EHD) puntuales, como puede ser el caso de un rodamiento. La resolución de este problema presenta diversas complejidades matemáticas y exige el desarrollo de un elaborado procedimiento de cálculo basado en técnicas multinivel. Para hacer del procedimiento una herramienta válida en un gran número de condiciones de funcionamiento y tipos de lubricantes, se ha tenido en cuenta en el cálculo la posible aparición de comportamientos no-Newtonianos del lubricante y fenómenos de generación y disipación de calor, provocados por el movimiento relativo del fluido y las superficies en contacto. Para la validación del procedimiento, se han contrastado los resultados numéricos obtenidos con nuestro método, con los resultados numéricos y experimentales publicados por otros autores y con valores experimentales propios medidos en un equipo de ensayo de contacto puntual tipo MTM. El desarrollo de este programa ha dotado a la División de Ingeniería de Máquinas de una herramienta que ha permitido, y sobre todo va permitir, evaluar la importancia de cada uno de los parámetros reológicos en los diferentes problemas que va a tener que abordar, evaluación que hasta el momento se realizaba con métodos aproximados que describen la fenomenología con mucha menos precisión. A la hora de emplear nuestro procedimiento numérico para simular situaciones reales, nos hemos encontrado con el obstáculo de que es muy complicado encontrar, en la bibliografía y bases de datos, los parámetros que caracterizan el comportamiento reológico del lubricante en las condiciones de presión, temperatura y grado de cizallamiento habituales en las que se trabaja en este tipo de contactos, y las pocas medidas que existen para estas condiciones de funcionamiento son poco fiables. Por ello como complemento al objetivo principal de esta Tesis hemos desarrollado una metodología para caracterizar los lubricantes en estas condiciones extremas. Dicha metodología está basada en la buena descripción que hace nuestro programa del coeficiente de fricción, lo que nos ha permitido obtener los parámetros reológicos del III lubricante a partir de las medidas experimentales del coeficiente de fricción generado en un equipo MTM lubricado con el lubricante que se desea caracterizar. Madrid, Octubre de 2012 IV Improving energy efficiency and reducing the failure rate in lubricated contacts are issues that are of great interest in many sectors of industry, and right now posed operational difficulties and new challenges for the near future. Technological advances have increased the technical demands required to oils to fulfil its role by extending its operational variables to a wider range of applications, both operating conditions and to the wide variety of new materials which constitute the gear in which must be used. For this reason, has being encouraged currently to develop new procedures to understand the behaviour of this type of lubricated contacts, in order to achieve improvements in design techniques and the correct oil selection. In this Thesis we present a numerical methodology to simulate the puntual elastohydrodynamic contact behaviour (EHD), such as a roller bearing. The resolution of this problem presents various mathematical complexities and requires the development of an elaborate calculation procedure based on multilevel techniques. To make the procedure a valid tool in a wide range of operating conditions and types of lubricants, has been taken into account in calculating the possible occurrence of non-Newtonian behaviour of the lubricant and phenomena of generation and dissipation of heat, caused by the fluid relative motion and contacting surfaces. For the validation of the method, we have compared the numerical results obtained with our method with numerical and experimental results published by other authors also with own experimental values measured on point-contact test equipment MTM. The development of this program has provided the Machines Engineering Division of a tool that has allowed, and especially will allow to evaluate the importance of each of the rheological parameters on the various problems that will have to be addressed, evaluation performed hitherto described methods that phenomenology approximated with much less accuracy. When using our numerical procedure to simulate real situations we have encountered the obstacle that is very difficult to find, in the literature and database, parameters characterizing the rheological behaviour of the lubricant in the usual conditions of pressure, temperature and shear rate in which you work in this type of contact, and the few measures that exist for these operating conditions are unreliable. Thus in addition to the main objective of this thesis, we have developed a methodology to characterize the lubricants in these extreme conditions. This methodology is based on the good description, which makes our program, of the coefficient of friction, that allowed us to obtain the lubricant rheological parameters from experimental measurements of the friction coefficient generated on lubricated MTM equipment with the lubricant to be characterized.

Numerical Error Prediction and its applications in CFD using tau-estimation

Nowadays, Computational Fluid Dynamics (CFD) solvers are widely used within the industry to model fluid flow phenomenons. Several fluid flow model equations have been employed in the last decades to simulate and predict forces acting, for example, on different aircraft configurations. Computational time and accuracy are strongly dependent on the fluid flow model equation and the spatial dimension of the problem considered. While simple models based on perfect flows, like panel methods or potential flow models can be very fast to solve, they usually suffer from a poor accuracy in order to simulate real flows (transonic, viscous). On the other hand, more complex models such as the full Navier- Stokes equations provide high fidelity predictions but at a much higher computational cost. Thus, a good compromise between accuracy and computational time has to be fixed for engineering applications. A discretisation technique widely used within the industry is the so-called Finite Volume approach on unstructured meshes. This technique spatially discretises the flow motion equations onto a set of elements which form a mesh, a discrete representation of the continuous domain. Using this approach, for a given flow model equation, the accuracy and computational time mainly depend on the distribution of nodes forming the mesh. Therefore, a good compromise between accuracy and computational time might be obtained by carefully defining the mesh. However, defining an optimal mesh for complex flows and geometries requires a very high level expertize in fluid mechanics and numerical analysis, and in most cases a simple guess of regions of the computational domain which might affect the most the accuracy is impossible. Thus, it is desirable to have an automatized remeshing tool, which is more flexible with unstructured meshes than its structured counterpart. However, adaptive methods currently in use still have an opened question: how to efficiently drive the adaptation ? Pioneering sensors based on flow features generally suffer from a lack of reliability, so in the last decade more effort has been made in developing numerical error-based sensors, like for instance the adjoint-based adaptation sensors. While very efficient at adapting meshes for a given functional output, the latter method is very expensive as it requires to solve a dual set of equations and computes the sensor on an embedded mesh. Therefore, it would be desirable to develop a more affordable numerical error estimation method. The current work aims at estimating the truncation error, which arises when discretising a partial differential equation. These are the higher order terms neglected in the construction of the numerical scheme. The truncation error provides very useful information as it is strongly related to the flow model equation and its discretisation. On one hand, it is a very reliable measure of the quality of the mesh, therefore very useful in order to drive a mesh adaptation procedure. On the other hand, it is strongly linked to the flow model equation, so that a careful estimation actually gives information on how well a given equation is solved, which may be useful in the context of _ -extrapolation or zonal modelling. The following work is organized as follows: Chap. 1 contains a short review of mesh adaptation techniques as well as numerical error prediction. In the first section, Sec. 1.1, the basic refinement strategies are reviewed and the main contribution to structured and unstructured mesh adaptation are presented. Sec. 1.2 introduces the definitions of errors encountered when solving Computational Fluid Dynamics problems and reviews the most common approaches to predict them. Chap. 2 is devoted to the mathematical formulation of truncation error estimation in the context of finite volume methodology, as well as a complete verification procedure. Several features are studied, such as the influence of grid non-uniformities, non-linearity, boundary conditions and non-converged numerical solutions. This verification part has been submitted and accepted for publication in the Journal of Computational Physics. Chap. 3 presents a mesh adaptation algorithm based on truncation error estimates and compares the results to a feature-based and an adjoint-based sensor (in collaboration with Jorge Ponsín, INTA). Two- and three-dimensional cases relevant for validation in the aeronautical industry are considered. This part has been submitted and accepted in the AIAA Journal. An extension to Reynolds Averaged Navier- Stokes equations is also included, where _ -estimation-based mesh adaptation and _ -extrapolation are applied to viscous wing profiles. The latter has been submitted in the Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering. Keywords: mesh adaptation, numerical error prediction, finite volume Hoy en día, la Dinámica de Fluidos Computacional (CFD) es ampliamente utilizada dentro de la industria para obtener información sobre fenómenos fluidos. La Dinámica de Fluidos Computacional considera distintas modelizaciones de las ecuaciones fluidas (Potencial, Euler, Navier-Stokes, etc) para simular y predecir las fuerzas que actúan, por ejemplo, sobre una configuración de aeronave. El tiempo de cálculo y la precisión en la solución depende en gran medida de los modelos utilizados, así como de la dimensión espacial del problema considerado. Mientras que modelos simples basados en flujos perfectos, como modelos de flujos potenciales, se pueden resolver rápidamente, por lo general aducen de una baja precisión a la hora de simular flujos reales (viscosos, transónicos, etc). Por otro lado, modelos más complejos tales como el conjunto de ecuaciones de Navier-Stokes proporcionan predicciones de alta fidelidad, a expensas de un coste computacional mucho más elevado. Por lo tanto, en términos de aplicaciones de ingeniería se debe fijar un buen compromiso entre precisión y tiempo de cálculo. Una técnica de discretización ampliamente utilizada en la industria es el método de los Volúmenes Finitos en mallas no estructuradas. Esta técnica discretiza espacialmente las ecuaciones del movimiento del flujo sobre un conjunto de elementos que forman una malla, una representación discreta del dominio continuo. Utilizando este enfoque, para una ecuación de flujo dado, la precisión y el tiempo computacional dependen principalmente de la distribución de los nodos que forman la malla. Por consiguiente, un buen compromiso entre precisión y tiempo de cálculo se podría obtener definiendo cuidadosamente la malla, concentrando sus elementos en aquellas zonas donde sea estrictamente necesario. Sin embargo, la definición de una malla óptima para corrientes y geometrías complejas requiere un nivel muy alto de experiencia en la mecánica de fluidos y el análisis numérico, así como un conocimiento previo de la solución. Aspecto que en la mayoría de los casos no está disponible. Por tanto, es deseable tener una herramienta que permita adaptar los elementos de malla de forma automática, acorde a la solución fluida (remallado). Esta herramienta es generalmente más flexible en mallas no estructuradas que con su homóloga estructurada. No obstante, los métodos de adaptación actualmente en uso todavía dejan una pregunta abierta: cómo conducir de manera eficiente la adaptación. Sensores pioneros basados en las características del flujo en general, adolecen de una falta de fiabilidad, por lo que en la última década se han realizado grandes esfuerzos en el desarrollo numérico de sensores basados en el error, como por ejemplo los sensores basados en el adjunto. A pesar de ser muy eficientes en la adaptación de mallas para un determinado funcional, este último método resulta muy costoso, pues requiere resolver un doble conjunto de ecuaciones: la solución y su adjunta. Por tanto, es deseable desarrollar un método numérico de estimación de error más asequible. El presente trabajo tiene como objetivo estimar el error local de truncación, que aparece cuando se discretiza una ecuación en derivadas parciales. Estos son los términos de orden superior olvidados en la construcción del esquema numérico. El error de truncación proporciona una información muy útil sobre la solución: es una medida muy fiable de la calidad de la malla, obteniendo información que permite llevar a cabo un procedimiento de adaptación de malla. Está fuertemente relacionado al modelo matemático fluido, de modo que una estimación precisa garantiza la idoneidad de dicho modelo en un campo fluido, lo que puede ser útil en el contexto de modelado zonal. Por último, permite mejorar la precisión de la solución resolviendo un nuevo sistema donde el error local actúa como término fuente (_ -extrapolación). El presenta trabajo se organiza de la siguiente manera: Cap. 1 contiene una breve reseña de las técnicas de adaptación de malla, así como de los métodos de predicción de los errores numéricos. En la primera sección, Sec. 1.1, se examinan las estrategias básicas de refinamiento y se presenta la principal contribución a la adaptación de malla estructurada y no estructurada. Sec 1.2 introduce las definiciones de los errores encontrados en la resolución de problemas de Dinámica Computacional de Fluidos y se examinan los enfoques más comunes para predecirlos. Cap. 2 está dedicado a la formulación matemática de la estimación del error de truncación en el contexto de la metodología de Volúmenes Finitos, así como a un procedimiento de verificación completo. Se estudian varias características que influyen en su estimación: la influencia de la falta de uniformidad de la malla, el efecto de las no linealidades del modelo matemático, diferentes condiciones de contorno y soluciones numéricas no convergidas. Esta parte de verificación ha sido presentada y aceptada para su publicación en el Journal of Computational Physics. Cap. 3 presenta un algoritmo de adaptación de malla basado en la estimación del error de truncación y compara los resultados con sensores de featured-based y adjointbased (en colaboración con Jorge Ponsín del INTA). Se consideran casos en dos y tres dimensiones, relevantes para la validación en la industria aeronáutica. Este trabajo ha sido presentado y aceptado en el AIAA Journal. También se incluye una extensión de estos métodos a las ecuaciones RANS (Reynolds Average Navier- Stokes), en donde adaptación de malla basada en _ y _ -extrapolación son aplicados a perfiles con viscosidad de alas. Este último trabajo se ha presentado en los Actas de la Institución de Ingenieros Mecánicos, Parte G: Journal of Aerospace Engineering. Palabras clave: adaptación de malla, predicción del error numérico, volúmenes finitos

Multi-fluid Eulerian model of an electrospray in a host gas.

An Eulerian multifluid model is used to describe the evolution of an electrospray plume and the flow induced in the surrounding gas by the drag of the electrically charged spray droplets in the space between an injection electrode containing the electrospray source and a collector electrode. The spray is driven by the voltage applied between the two electrodes. Numerical computations and order-of-magnitude estimates for a quiescent gas show that the droplets begin to fly back toward the injection electrode at a certain critical value of the flux of droplets in the spray, which depends very much on the electrical conditions at the injection electrode. As the flux is increased toward its critical value, the electric field induced by the charge of the droplets partially balances the field due to the applied voltage in the vicinity of the injection electrode, leading to a spray that rapidly broadens at a distance from its origin of the order of the stopping distance at which the droplets lose their initial momentum and the effect of their inertia becomes negligible. The axial component of the electric field first changes sign in this region, causing the fly back. The flow induced in the gas significantly changes this picture in the conditions of typical experiments. A gas plume is induced by the drag of the droplets whose entrainment makes the radius of the spray away from the injection electrode smaller than in a quiescent gas, and convects the droplets across the region of negative axial electric field that appears around the origin of the spray when the flux of droplets is increased. This suppresses fly back and allows much higher fluxes to be reached than are possible in a quiescent gas. The limit of large droplet-to-gas mass ratio is discussed. Migration of satellite droplets to the shroud of the spray is reproduced by the Eulerian model, but this process is also affected by the motion of the gas. The gas flow preferentially pushes satellite droplets from the shroud to the core of the spray when the effect of the inertia of the droplets becomes negligible, and thus opposes the well-established electrostatic/inertial mechanism of segregation and may end up concentrating satellite droplets in an intermediate radial region of the spray.

Long wave theory for experimental devices with compressed/expanded surfactant monolayers

Surfactant monolayers are of interest in a variety of phenomena, including thin film dynamics and the formation and dynamics of foams. Measurement of surface properties has received a continuous attention and requires good theoretical models to extract the relevant physico- chemical information from experimental data. A common experimental set up consists in a shallow liquid layer whose free surface is slowly com- pressed/expanded in periodic fashion by moving two slightly immersed solid barriers, which varies the free surface area and thus the surfactant concentration. The simplest theory ignores the fluid dynamics in the bulk fluid, assuming spatially uniform surfactant concentration, which requires quite small forcing frequencies and provides reversible dynamics in the compression/expansion cycles. Sometimes, it is not clear whether depar- ture from reversibility is due to non-equilibrium effects or to the ignored fluid dynamics. Here we present a long wave theory that takes the fluid dynamics and the symmetries of the problem into account. In particular, the validity of the spatially-uniform-surfactant-concentration assumption is established and a nonlinear diffusion equation is derived. This allows for calculating spatially nonuniform monolayer dynamics and uncovering the physical mechanisms involved in the surfactant behavior. Also, this analysis can be considered a good means for extracting more relevant information from each experimental run.

Wind tunnel analysis on the influence of cantilever parapets on the wind loads on curved roofs

Different methods to reduce the high suction caused by conical vortices have been reported in the literature: vertical parapets, either solids or porous, placed at the roof edges being the most analysed configuration. Another method for alleviating the high suction peaks due to conical vortices is to round the roof edges. Very recently, the use of some non-standard parapet configurations, like cantilever parapets, has been suggested. In this paper, its efficiency to reduce suction loads on curved roofs is experimentally checked by testing the pressure distribution on the curved roof of a low-rise building model in a wind tunnel. Very high suction loads have been measured on this model, the magnitude of these high suction loads being significantly decreased when cantilever...

Dynamics of thermal ignition of spray flames in mixing layers

Conditions are identified under which analyses of laminar mixing layers can shed light on aspects of turbulent spray combustion. With this in mind, laminar spray-combustion models are formulated for both non-premixed and partially premixed systems. The laminar mixing layer separating a hot-air stream from a monodisperse spray carried by either an inert gas or air is investigated numerically and analytically in an effort to increase understanding of the ignition process leading to stabilization of high-speed spray combustion. The problem is formulated in an Eulerian framework, with the conservation equations written in the boundary-layer approximation and with a one-step Arrhenius model adopted for the chemistry description. The numerical integrations unveil two different types of ignition behaviour depending on the fuel availability in the reaction kernel, which in turn depends on the rates of droplet vaporization and fuel-vapour diffusion. When sufficient fuel is available near the hot boundary, as occurs when the thermochemical properties of heptane are employed for the fuel in the integrations, combustion is established through a precipitous temperature increase at a well-defined thermal-runaway location, a phenomenon that is amenable to a theoretical analysis based on activation-energy asymptotics, presented here, following earlier ideas developed in describing unsteady gaseous ignition in mixing layers. By way of contrast, when the amount of fuel vapour reaching the hot boundary is small, as is observed in the computations employing the thermochemical properties of methanol, the incipient chemical reaction gives rise to a slowly developing lean deflagration that consumes the available fuel as it propagates across the mixing layer towards the spray. The flame structure that develops downstream from the ignition point depends on the fuel considered and also on the spray carrier gas, with fuel sprays carried by air displaying either a lean deflagration bounding a region of distributed reaction or a distinct double-flame structure with a rich premixed flame on the spray side and a diffusion flame on the air side. Results are calculated for the distributions of mixture fraction and scalar dissipation rate across the mixing layer that reveal complexities that serve to identify differences between spray-flamelet and gaseous-flamelet problems.

Numerical study of ultrasound induced non-linear shape and size bubble oscillations in viscoelastic media

The theoretical study of forced bubble oscillations is motivated by the importance of cavitation bubbles and oscillating encapsulated microbubbles (i.e. contrast agents) in medical sciences. In more details,theoretical studies on bubble dynamics addressing the sound-bubble interaction phenomenon provide the basis for understanding the dynamics of contrast agent microbubbles used in medical diagnosis and of non-linearly oscillating cavitation bubbles in the case of high-intensity ultrasound therapy. Moreover, the inclusion of viscoelasticity is of vital importance for an accurate theoretical analysis since most biological tissues and fluids exhibit non-Newtonian behavior.

Hydrostatic instabilities in floating zone cristal growth process

If only Fluid Mechanics aspects are considered, the configuration appearing in the floating zone technique for crystal growth can be modelled as a mass of liquid spanning between two solid rods. Besides, if now the influence of temperature gradients and heat flow are not considered, the simplest fluid model consists of an isothermal liquid mass of constant properties (density and surface tension) held by capillary forces between two solid disks placed a distance L apart: the so called liquid bridge. As it is well known, if both supporting disks were parallel, coaxial and of the same diameter, 2R, the volume of liquid, V, were equal to that of a cylinder of the same L and R (V=KR~L) and no body forces were acting on the liquid column, the fluid configuration (under these conditions of cylindrical shape) will become unstable when the distance between the disks equals the length of the circumference of the supporting disks (L=2KR, the so-called Rayleigh stability limit). One should be aware that the Rayleigh stability limit can be dramatically modified when the geometry differs from the above described cylinder (due to having non-coaxial disks, different diameter disks, liquid volume different from the cylindrical one, etc) or when other external effects like accelerations either axial or lateral are considered. In this paper the stability limits of liquid bridges considering different types of perturbations are reviewed.

Fluid-solid interaction in arteries incorporating the autoregulation concept in boundary conditions

In pre-surgery decisions in hospital emergency cases, fast and reliable results of the solid and fluid mechanics problems are of great interest to clinicians. In the current investigation, an iterative process based on a pressure-type boundary condition is proposed in order to reduce the computational costs of blood flow simulations in arteries, without losing control of the important clinical parameters. The incorporation of cardiovascular autoregulation, together with the well-known impedance boundary condition, forms the basis of the proposed methodology. With autoregulation, the instabilities associated with conventional pressure-type or impedance boundary conditions are avoided without an excessive increase in computational costs. The general behaviour of pulsatile blood flow in arteries, which is important from the clinical point of view, is well reproduced through this new methodology. In addition, the interaction between the blood and the arterial walls occurs via a modified weak coupling, which makes the simulation more stable and computationally efficient. Based on in vitro experiments, the hyperelastic behaviour of the wall is characterised and modelled. The applications and benefits of the proposed pressure-type boundary condition are shown in a model of an idealised aortic arch with and without an ascending aorta dissection, which is a common cardiovascular disorder.