The onset of unsteadiness of two-dimensional bodies falling or rising freely in a viscous fluid: a linear study

We consider the transition between the steady vertical path and the oscillatory path of two-dimensional bodies moving under the effect of buoyancy in a viscous fluid. Linearization of the Navier–Stokes equations governing the flow past the body and of Newton’s equations governing the body dynamics leads to an eigenvalue problem, which is solved numerically. Three different body geometries are then examined in detail, namely a quasi-infinitely thin plate, a plate of rectangular cross-section with an aspect ratio of 8, and a rod with a square cross-section. Two kinds of eigenmodes are observed in the limit of large body-to-fluid mass ratios, namely ‘fluid’ modes identical to those found in the wake of a fixed body, which are responsible for the onset of vortex shedding, and four additional ‘aerodynamic’ modes associated with much longer time scales, which are also predicted using a quasi-static model introduced in a companion paper. The stability thresholds are computed and the nature of the corresponding eigenmodes is investigated throughout the whole possible range of mass ratios. For thin bodies such as a flat plate, the Reynolds number characterizing the threshold of the first instability and the associated Strouhal number are observed to be comparable with those of the corresponding fixed body. Other modes are found to become unstable at larger Reynolds numbers, and complicated branch crossings leading to mode switching are observed. On the other hand, for bluff bodies such as a square rod, two unstable modes are detected in the range of Reynolds number corresponding to wake destabilization. For large enough mass ratios, the leading mode is similar to the vortex shedding mode past a fixed body, while for smaller mass ratios it is of a different nature, with a Strouhal number about half that of the vortex shedding mode and a stronger coupling with the body dynamics

Flow around an oscillating circular disk at low to moderate Reynolds numbers

Direct numerical simulations of the flow induced by a circular disk oscillating sinusoidally along its axis are performed. The aspect ratio of the disk is 10. The Reynolds number , based on the maximum speed and the diameter of the disk, is in the range of . The Keulegan-Carpenter number is in the range of . Five flow regimes are observed in the considered-space: (I) axisymmetric flow (AS), (II) planar symmetric flow in the low-region (PSL), (III) azimuthally rotating flow in the low-region (ARL), (IV) planar symmetric flow in the high-region (PSH) and (V) azimuthally rotating flow in the high-region (ARH). The critical boundaries between different flow regimes are identified based on the evolutions of the magnitude and direction of transverse force acting on the disk. For the non-axisymmetric flow regimes, the flow is one-sided with respect to the axis of the disk and is associated with a non-zero mean value of the transverse force acting on the disk

Fluid structure interaction in bioinspired locomotion problems

Mención Internacional en el título de doctorNature offers a vast amount of examples of efficient locomotion. Millions of years of evolution have allowed animals —such as fish, insects and birds—, and even plants —such as winged-seeds or dandelions— to achieve outstanding locomotive skills. Therefore, it is not a surprise that scientists and engineers have tried to replicate the flight and swimming capabilities of the former examples in order to develop efficient aerial and nautical robots. In fact, these efforts have led to the design and development of several successful bioinspired robots. However, their performance is still far below their living counterparts. One of the main reasons is that the understanding of the physics underlying biological locomotion is still limited. This is due to the complexity of the problem under consideration: the locomotion of a body through a fluid medium. This can be considered fluid structure interaction (FSI) problem where the dynamics of the specimens is the result from the hydrodynamic interaction with the surrounding fluid, which in turn is modified by the motion of the specimens. Consequently, the resulting problem is highly nonlinear and complex from a mathematical standpoint. This dissertation attempts to contribute to further understand the fluid structure interactions in bioinspired locomotion problems. To that end, direct numerical simulations of several examples of bioinspired FSI problems are performed. These examples include the auto-rotation of a winged-seed, the flow interactions between the wings of a dragonfly, and the schooling patterns that emerge between two fish. In the first part of this dissertation, the algorithm which has been developed to perform part of the aforementioned studies is presented. The proposed algorithm allows the study of the FSI of systems of connected rigid bodies —which serve as a model for the actual specimens— immersed in an incompressible fluid. It is built based on a preexisting flow solver, coupled with a robotic algorithm for the computation of the dynamic equations of the bodies. The use of robotic algorithms endows the proposed methodology with a great fiexibility, allowing to simulate a large variety of problems with different geometries and configurations. The second part of the thesis is devoted to the analysis of the aforementioned examples. In this regard, we first consider the flight of a winged-seed. This is a very interesting, yet complex, problem of fluid-dynamic interaction; in which the auto-rotative motion is the result of a subtle equilibrium between the aerodynamic forces and the inertia properties of the winged-seed. In our study, the dynamics and the flow surrounding the auto-rotating seed are characterized in a range of Reynolds numbers, Re. Specifically, we focus on the study of the leading edge vortex (LEV) that is developed on the upper surface of the seed's wing as it auto-rotates. Our findings suggest that, in the explored range Re = [80 — 240], LEV's stability is not driven by vorticity transport along the spanwise direction nor viscous effects, as reported in the literature of rotating wings. Instead, fictitious accelerations (i.e., Coriolis and centrifugal accelerations) are the most suitable candidates to stabilize the LEV over the seed's wing. In the second example, we study the effect of the three-dimensional (3D) interactions in the performance of two tandem wings, resembling those of a dragonfly. To that end, the wings undergo a two-dimensional (2D) optimum kinematics which is a combination of heaving and pitching. We first analyze the effect of wings' aspect ratio, AR, by comparing the 3D and 2D simulations. The results show that 3D vertical interactions are detrimental for the thrust production of the hindwing, but they do not significantly affect the propulsive efficiency of the tandem arrangement. Next, a more realistic flapping kinematics of the 3D is considered and compared to the previous heaving kinematics. We find a decrease in the propulsive efficiency of the flapping wings compared to their heaving counterparts, which has been linked to a non-desired shedding of vorticity on the inboard region of the wings. The last bioinspired example corresponds to the collective motion of two self-propelled three-dimensional bodies. These bodies are idealized as rectangular, flat plates with flexibility along their chordwise direction, and that self-propels thanks to a prescribed vertical motion of their leading edges. We observe that tandem configurations emerge where both plates swim at a constant mean horizontal velocity and with a mean equilibrium horizontal distance. These configurations can be classified, attending to the resulting flow interactions, into compact and regular configurations. In the former, the performance of the upstream flapper is modified due to the close interaction with the downstream flapper. However, in the regular configurations, the performance of the upstream flapper is similar to that of an isolated flapper. Conversely, the performance of the downstream flapper is affected in both configurations by the interaction with the wake of the upstream flapper. We are able to link the changes in the downstream flapper's performance to its interaction with the vertical jet induced by vortex rings of the upstream flapper's wake. Finally, we propose a model to qualitatively predict the performance of a hypothetical downstream flapper based on the flow field of and isolated flapper, showing good agreement with the actual simulations.La naturaleza ofrece una gran cantidad de ejemplos de locomoción eficiente. Millones de años de evolución han permitido a animales —tales como peces, insectos o pájaros— e incluso plantas —como sainaras o dientes de león— lograr unas habilidades de lomoción excepcionales. Por lo tanto, no es una sorpresa que científicos e ingenieros hayan intentado replicar la capacidades de vuelo y nado de los anteriores ejemplos, con el objetivo de desarrollar robots aéreos y nadadores más eficientes. De hecho, estos esfuerzos han dado lugar al diseño y desarrollo exitoso de varios robots bioinsipirados. Sin embargo, el rendimiento de éstos es todavía muy inferior al de sus referentes biológicos. Una de las principales razones es que la comprensión de la física subyacente de la lomococión de sistemas biológicos es aún limitada. Esto es debido a la complejidad del problema, a saber, el movimiento de un cuerpo a través de un medio fluido. Este se puede considerar como un problema de interacción fluido estructura (FSI) donde la dinámica del espécimen es el resultado de la interacción fluidodinámica con el fluido de alrededor, el cual es a su vez modificado por el movimiento del cuerpo. Consecuentemente, el problema resultante es altamente no lineal y complejo desde un punto de vista matemático. Con esta disertación se pretende contribuir a una mayor comprensión de la interacción fluido estructura en problemas de locomoción bioninspirados. Con tal propósito, se han realizado simulaciones numéricas directas de varios ejemplos bioinspirados de interacción fluido estructura. Estos ejemplos incluyen la autorrotación de una sámara, las interaccionés fluidas entre las alas de una libélula y los patrones de nado que surgen entre dos peces. Durante la primera parte de esta disertación, se describe el algoritmo que ha sido desarrollado con el propósito de simular alguno de los problemas anteriormente citados. El algoritmo propuesto permite el estudio de la interacción fluido estructura de sistemas de cuerpos rígidos conectados —los cuales sirven como modelo de los especímenes reales— que están sumergidos en un fluido incompresible. Está construido sobre un solver fluido pre-existente, acoplado a un algoritmo robótico que se encarga de calcular las ecuaciones dinámicas de los cuerpos. El uso de algoritmos robóticos proporciona a la metodología propuesta una gran flexibilidad, permitiendo simular una gran variedad de problemas con diversas geometrías y configuraciones. La segunda parte de esta tesis está dedicada al análisis de los ejemplos mencionados anteriormente. En este respecto, consideramos primero el vuelo de una sámara, el cual es un problema muy interesante, aunque complejo, de interacción fluido dinámica en el cual el movimiento autorrotativo es el resultado de un sutil equilibrio entre las fuerzas aerodinámicas y las propiedades inerciales de la semilla. En nuestro estudio, caracterizamos la dinámica y el flujo alrededor de la semilla autorrotante en un rango de números de Reynolds, Re. En concreto, nos centramos en el estudio del vórtice del borde de ataque (LEV) que se forma en la parte superior del ala de la sámara cuando ésta autorrota. Nuestros hallazgos sugieren que, en el rango explorado de Re = [80 — 240], la estabilidad del LEV no se debe a un transporte de vorticidad a lo largo de la dirección de la envergadura del ala, ni a efectos viscosos —como se ha mencionado en la literatura de alas rotativas—, sino que las aceleraciones ficticias (es decir, las aceleraciones centrífugas y de Coriolis), son las candidatas más probables responsables de la estabilización del LEV. En el segundo ejemplo, se estudia el efecto de las interacciones tridimensionales (3D) en el rendimiento de dos alas en configuración tándem, basadas en las de una libélula. Para ello, se prescribe que el movimiento de las alas sea una combinación de cabeceo y oscilación vertical que es óptimo en 2 dimensiones (2D). Primero analizamos el efecto de la relación de aspecto de las alas, A% comparando los resultados de las simulaciones en 3D y en 2D. Los resultados revelan que las interacciones vorticales en 3D son perjudiciales para la generación de empuje del ala trasera, pero estas interacciones no afectan de forma significativa a la eficiencia propulsiva del conjunto. Posteriormente, se considera un movimiento de batimiento más realista de las alas, y se compara su eficiencia con la obtenida previamente para las alas en movimiento oscilatorio vertical. Se observa una menor eficiencia de las alas en batimiento en comparación con las mismas alas en movimiento oscilatorio vertical. Este deterioro es asociado a un desprendimiento de estructuras vorticales cerca de los bordes marginales de las alas en batimiento. El último ejemplo bioinspirado es el del movimiento colectivo de dos cuerpos tridimiensionales que se auto propulsan. Estos cuerpos se idealizan como placas planas rectangulares, siendo flexibles a lo largo de su cuerda, y que se auto propulsan gracias a un movimiento vertical impuesto de sus bordes de ataque. Los resultados muestran la aparición de configuraciones tándem donde sendas placas nadan con una velocidad inedia constante y separadas a una distancia de equilibrio que es también constante. Estas configuraciones son clasificadas —atendiendo a las interacciones fluidas— entre compactas y regulares. En las primeras, el rendimiento de la placa que nada aguas arriba (a la que llamaremos líder) se ve afectado por las interacciones cercanas con el cuerpo que nada aguas abajo (al que denominaremos seguidor). En cambio, en las configuraciones regulares el redimiento del líder es el mismo que el de una placa similar nadando de forma aislada. Por el contrario, el rendimiento del seguidor se ve afectado en ambas configuraciones debido a las interacciones con la estela del líder. Se ha podido relacionar estos cambios en la eficiencia del seguidor con la interacción con el chorro inducido por los anillos vorticales de la estela del líder. Finalmente, hemos propuesto un modelo que permite predecir, de forma cualitativa, el rendimiento de un seguidor hipotético basándonos en el campo fluido de una placa aislada. El modelo muestra una buena correlación con los datos obtenidos de las simulaciones numéricas.This thesis has been carried out in the Bioengineering and Aerospace Engineering Department at Universidad Carlos III de Madrid. The financial support has been provided by the Spanish Ministry of Economy and Competitiveness through grant DPI2016-76151-C2-2-R (AEI/FEDER, UE).Programa de Doctorado en Mecánica de Fluidos por la Universidad Carlos III de Madrid; la Universidad de Jaén; la Universidad de Zaragoza; la Universidad Nacional de Educación a Distancia; la Universidad Politécnica de Madrid y la Universidad Rovira i VirgiliPresidente: Francisco Javier Huera-Huarte.- Secretario: Javier Rodríguez Rodríguez.- Vocal: Ignazio María Viol

Three Dimensional Unsteady Flow and Active Morphing Effect in Flapping Wings

Bumble b ee cannot fly, if we ignore the significant differences b etween flappin

Unsteadiness in Flow over a Flat Plate at Angle-of-Attack at Low Reynolds Numbers

Flow over an impulsively started low-aspect-ratio flat plate at angle-of-attack is investigated for a Reynolds number of 300. Numerical simulations, validated by a companion experiment, are performed to study the influence of aspect ratio, angle of attack, and planform geometry on the interaction of the leading-edge and tip vortices and resulting lift and drag coefficients. Aspect ratio is found to significantly influence the wake pattern and the force experienced by the plate. For large aspect ratio plates, leading-edge vortices evolved into hairpin vortices that eventually detached from the plate, interacting with the tip vortices in a complex manner. Separation of the leading-edge vortex is delayed to some extent by having convective transport of the spanwise vorticity as observed in flow over elliptic, semicircular, and delta-shaped planforms. The time at which lift achieves its maximum is observed to be fairly constant over different aspect ratios, angles of attack, and planform geometries during the initial transient. Preliminary results are also presented for flow over plates with steady actuation near the leading edge

Permeability sets the linear path instability of buoyancy-driven disks

The prediction of trajectories of buoyancy-driven objects immersed in a viscous fluid is a key problem in fluid dynamics. Simple-shaped objects, such as disks, present a great variety of trajectories, ranging from zig-zag to tumbling and chaotic motions. Yet, similar studies are lacking when the object is permeable. We perform a linear stability analysis of the steady vertical path of a thin permeable disk, whose flow through the microstructure is modelled via a stress-jump model based on homogenization theory. The relative velocity of the flow associated with the vertical steady path presents a recirculation region detached from the body, which shrinks and eventually disappears as the disk becomes more permeable. In analogy with the solid disk, one non-oscillatory and several oscillatory modes are identified and found to destabilize the fluid-solid coupled system away from its straight trajectory. Permeability progressively filters out the wake dynamics in the instability of the steady vertical path. Modes dominated by wake oscillations are first stabilized, followed by those characterized by weaker, or absent, wake oscillations, in which the wake is typically a tilting induced by the disk inclined trajectory. For sufficiently large permeabilities, the disk first undergoes a non-oscillatory divergence instability, which is expected to lead to a steady oblique path with a constant disk inclination, in the nonlinear regime. A further permeability increase reduces the unstable range of all modes until quenching of all linear instabilities

The Numerical Simulation of Fluid Flow

This book collects the accepted contributions to the Special Issue "The Numerical Simulation of Fluid Flow" in the Energies journal of MDPI. It is focused more on practical applications of numerical codes than in its development. It covers a wide variety of topics, from aeroacoustics to aerodynamics and flow-particles interaction