420 research outputs found

    A robustness result for a von Kármán plate

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    Wall-bounded turbulent flows at high Reynolds numbers: Recent advances and key issues

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    Wall-bounded turbulent flows at high Reynolds numbers have become an increasingly active area of research in recent years. Many challenges remain in theory, scaling, physical understanding, experimental techniques, and numerical simulations. In this paper we distill the salient advances of recent origin, particularly those that challenge textbook orthodoxy. Some of the outstanding questions, such as the extent of the logarithmic overlap layer, the universality or otherwise of the principal model parameters such as the von Kármán “constant,” the parametrization of roughness effects, and the scaling of mean flow and Reynolds stresses, are highlighted. Research avenues that may provide answers to these questions, notably the improvement of measuring techniques and the construction of new facilities, are identified. We also highlight aspects where differences of opinion persist, with the expectation that this discussion might mark the beginning of their resolution

    On unidirectional flight of a free flapping wing

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    International audienceWe study the dynamics of a rigid, symmetric wing that is flapped vertically in a fluid. The motion of the wing in the horizontal direction is not constrained. Above a critical flapping frequency, forward flight arises as the wing accelerates to a terminal state of constant speed. We describe a number of measurements which supplement our previous work. These include (a) a study of the initial transition to forward flight near the onset of the instability, (b) the separate effects of flapping amplitude and frequency, (c) the effect of wing thickness, (d) the effect of asymmetry of the wing planform, and (e) the response of the wing to an added resistance. Our results emphasize the robustness of the mechanisms determining the forward flight speed as observed in our previous study

    Improved Reduced Order Mechanical Model and Finite Element Analysis of Three-Dimensional Deformations of Epithelial Tissues

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    In this chapter, we analyse non-uniform bending of single-layer cell tissues—epithelia, surrounding organs throughout the body. Dimensionally reduced model is suggested, which is equivalent to membranes with bending stiffness: the total elastic energy of the tissue is a combination of stretching and bending energies. The energy, suggested in this chapter, is a piecewise function, the branches of which correspond to a specific deformation regime: compression, pure bending and stretch

    Nonlinear analysis of layered structures with weak interfaces

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    This work addresses nonlinear finite element analysis of laminated structures with weak interfaces. Considered first are shallow laminated beams subject to arbitrary large displacements, small layer strains and moderate interface slippage. Under these requirements rigorous development of layer-wise kinematic field is performed assuming First order Shear Deformation Theory (FSDT) at the layer level. The final form of this field is highly nonlinear and thus awkward in direct finite element (FE) implementation. However, the small strain assumption allows decomposition of element displacements into large rigid-body-motion and small deforming displacement field. In this case, the conjunction of linearized kinematic relations and the von Kármán strain measure applied in moving element frame allows for robust co-rotational FE formulation. This formulation is here extended to account for material nonlinear behaviour of layers and interfaces. To complete the development, means of obtaining efficient FE implementation are indicated. Discussed topics include the choice of suitable element interpolation schemes, proficient methods of alleviating numerical locking, evaluation of element deforming displacement field and management of layer-wise boundary conditions. In addition, a novel approach is proposed for a posteriori enhancement of the transverse shear stress distribution. Finally, the proposed model is tested with a number of demanding benchmark tests. The above modelling approach is next extended to geometric nonlinear analysis of laminated plates. Constraining plate displacements to be moderate (in von Kármán's sense) and using Total-Lagrangian FE formulation it is shown that the simplicity and robustness of the beam formulation can be preserved also in plate analysis. FE solutions obtained with the adopted approach are again shown to provide reliable results in global and local scale. However, it is also indicated that methods used to alleviate shear locking in single-layer plate elements are not entirely satisfactory in multi-layer ones. Thus, FE implementation allowing for non-regular meshes needs yet to be identified. Considered next is the possibility of extending the developed plate model to the corotational FE analysis of shallow laminated shells. Primary concern here is assuring consistency of 3D rotations of element vectors and matrices. This problem is resolved here by modifying the description of interface displacement field and including vertex rotations in finite element kinematics. With these enhancements FE matrix formulation is constructed to allow geometric nonlinear analysis of shallow laminated shells subject to arbitrary large displacements, small layer strains and moderate interface slippage

    Empirical eigenfunctions: application in unsteady aerodynamics

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    Mención Internacional en el título de doctorThe main aim of modal decompositions is to obtain a set of functions which can describe in a compact way the variability contained in a set of observables/data. While this can be easily obtained by means of the eigenfunctions of the operator from which the observables depends, the empirical eigenfunctions allow to obtain a similar result from a set of data, without the knowledge of the problem operator. In Fluid Mechanics and related sciences one of the most prominent techniques to obtain empirical eigenfunctions is referred to as Proper Orthogonal Decomposition (POD). This thesis contains applications of the empirical eigenfunctions to (Experimental) Aerodynamics data. The mathematical framework of the POD is introduced following the bi-orthogonal approach by Aubry (1991). The mathematical derivation of the POD is given, wherever possible, in its most general formulation, without bounding it to the decomposition of a specific quantity. This choice of the author depends on the variety of POD applications which are included in this dissertation, ranging from signal processing problems to applications more strictly related with flow physics. The mathematical framework includes also one of the POD extensions, the Extended POD (EPOD), which allows to extract modes linearly correlated to the empirical eigenfunctions of a second quantity. The first two applications of the empirical eigenfunctions are strictly connected with the signal treatment in experimental techniques for Fluid Mechanics. In Chapter 3, the empirical eigenfunctions are identified as an optimal basis in which perform a "low-pass" spectral filter of experimental fluid data, such as velocity fields measured with Particle Image Velocimetry (PIV). This filtering is extremely beneficial to reduce the random errors contained in the PIV fields and obtain a more accurate estimate of derivative quantities (such as, for instance, vorticity), which are more affected by random errors. In Chapter 4 the POD is exploited for the pre-treatment of a sequence of PIV images. The aim is to remove background and reflections, which are sources of uncertainty in PIV measurements. In this case a "high-pass" spectral filtering is applied to the PIV image ensemble in order to remove the highly-coherent part of the signal corresponding to the background. In the third and fourth applications, the POD is applied to recover the underlying dynamics of a flow. More specifically, in Chapter 5 the POD is applied to the complex wake of a pair of cylinders in tandem arrangement with the additional perturbation of the wall proximity. Through this technique it is possible to track the changes in the oscillatory behaviour of the wake instabilities ascribed to different geometrical configurations of the cylinders. In Chapter 6 the POD and the EPOD are applied respectively to the flow fields around an airfoil in plunging and pitching motion and to the unsteady aerodynamic forces acting on the airfoil. The decomposition allows to extract a reduced set of modes of the flow field which are related to the force generation mechanism. These modes correspond to well-recognizable phenomena of the flow which can be identified for diverse airfoil kinematics. This flow-field driven force decomposition is analysed on the light of existing force models, enabling their reinterpretation and driving towards possible corrections. The final application is devoted to overcome the low temporal resolution of typical flow field measurements, such as PIV, by proposing a robust estimation of turbulent flows dynamics. The method employs a modified version of the EPOD to identify the correlation between a non-time-resolved field measurement and a time-resolved point measurement. The estimation of the time-resolved flow fields is obtained exploiting the correlation of the flow fields with the temporal information contained in the point measurements.El objetivo principal de las descomposiciones modales es obtener un conjunto de funciones que sean capaces de describir de una manera compacta la variabilidad contenida en un conjunto de observables/datos. Si bien este objetivo puede ser fácilmente realizado mediante el uso de las autofunciones del operador del cual los observables dependen, las autofunciones empíricas permiten obtener un resultado similar partiendo de un conjunto de datos sin la necesidad de conocer el operador del problema. En Mecánica de Fluidos y en ciencias relacionadas con esta disciplina, una de las técnicas más relevantes para obtener autofunciones empíricas es la conocida como Descomposición Modal Ortogonal (Proper Orthogonal Decomposition, POD). Esta tesis contiene diversas aplicaciones de las autofunciones empíricas en datos de Aerodinámica (Experimental). La base matemática de la POD es introducida siguiendo la aproximación biortogonal realizada por Aubry (1991). La formulación matemática de la POD es expresada siempre que es posible en el marco más general posible, sin condicionarla a la descomposición de una variable en concreto. La elección del autor dependerá de las diferentes aplicaciones de la POD, todas ellas descritas en la presente tesis, las cuales abarcan desde problemas de procesado de señales hasta aplicaciones más estrictamente relacionadas con el análisis de la física del flujo. La formulación matemática incluye también uno de las extensiones de la POD, la POD Extendida (EPOD), la cual permite extraer modos linealmente correlacionados con las autofunciones empíricas de una segunda variable. Las dos primeras aplicaciones de las autofunciones empíricas están estrictamente relacionadas con el tratamiento de señales en técnicas experimentales de Mecánica de Fluidos. En el Capítulo 3, las autofunciones empíricas son identificadas como una base optima, la cual se puede utilizar para realizar un filtro pasa bajos espectral para datos experimentales de flujos, tales como campos de velocidad obtenidos mediante la técnica de Velocimetría por Imágenes de Partículas, (Particle Image Velocimetry, PIV). Este tipo de filtro es muy beneficioso para reducir los errores de carácter aleatorio contenidos en los campos de PIV y por tanto obtener una estimación más precisa en las cantidades que precisan del uso de derivadas (por ejemplo, la vorticidad), ya que están más afectadas por este tipo de errores. En el Capítulo 4, la POD es utilizada para el pretratamiento de una secuencia de imágenes de PIV. El objetivo es reducir el fondo de la imagen y las reflexiones, ambas fuentes de incertidumbre en las medidas de PIV. En este caso, un filtro pasa altos espectral es aplicado al conjunto de imágenes de PIV para poder quitar la parte mayormente correlacionada de la señal, la cual corresponde con el fondo de la imagen. En la tercera y cuarta aplicación de la POD, está técnica es utilizada para reconstruir las dinámicas fundamentales de un flujo. Concretamente, en el Capítulo 5 la POD es utilizada para analizar la estela compleja que se produce en una pareja de cilindros en tándem con la perturbación adicional de una pared próxima a ellos. A través de esta técnica, es posible poder estudiar los cambios en el comportamiento oscilatorio de las inestabilidades de la estela, las cuales están relacionadas con las diferentes configuraciones geométricas de los cilindros. En el capítulo 6, la POD y la EPOD son aplicadas respectivamente a campos fluidos y fuerzas aerodinámicas producidos por un perfil aerodinámico en movimiento (de rotación y desplazamiento vertical) no estacionario. La técnica de descomposición permite extraer un conjunto reducido de modos del campo fluido que están relacionados con el mecanismo que genera las fuerzas aerodinámicas. Estos modos corresponden con fenómenos característicos del flujo que pueden ser identificados para diferentes cinemáticas de perfiles aerodinámicos. Estas dinámicas del flujo que están conectadas con las fuerzas aerodinámicas son analizadas teniendo en cuenta los modelos ya existentes en la literatura que describen las fuerzas aerodinámicas, permitiendo su reinterpretación e incluso pudiendo añadir posibles correcciones. La última aplicación propuesta está destinada a subsanar la baja resolución temporal típica de las medidas de campo fluido, como en aquellas realizadas utilizando PIV, mediante una estimación robusta de las dinámicas del flujo turbulento. El método propuesto emplea una versión modificada de la EPOD para identificar para correlación entre un campo fluido medido que no está resuelto en el tiempo y una medida puntual que sí que está resulta en el tiempo. La estimación del campo fluido resuelto en el tiempo es obtenida mediante la correlación de los campos de flujo con la información temporal contenida en la medida puntual.This work has been partially supported by the Grant TRA2013-41103-P of the Spanish Ministry of Economy and Competitiveness, which includes FEDER funding, and by the Grant DPI2016-79401-R, funded by the Spanish State Research Agency (SRA) and European Regional Development Fund (ERDF).Programa Oficial de Doctorado en Mecánica de FluidosPresidente: Bharathram Ganapathisubramani.- Secretario: Francisco Javier Rodríguez Rodríguez.- Vocal: Francisco J. Huera-Huart

    Laser Guide Star Only Adaptive Optics: The Development of Tools and Algorithms for the Determination of Laser Guide Star Tip-Tilt

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    Adaptive Optics (AO) is a technology which corrects for the effects of the atmosphere and so improves the optical quality of ground based astronomical observations. The bright “guide stars” required for correction are not available across the entire sky, so Laser Guide Stars (LGSs) are created. A Natural Guide Star (NGS) is still required to correct for tip-tilt as the LGS encounters turbulence on the uplink path resulting in unpredictable “jitter”, hence limiting corrected sky coverage. In this thesis an original method is proposed and investigated that promises to improve the correction performance for tomographic AO systems using only LGSs, and no NGS, by retrieving the LGS uplink tip-tilt. To investigate the viability of this method, two unique tools have been developed. A new AO simulation has been written in the Python programming language which has been designed to facilitate the rapid development of new AO concepts. It features realistic LGS simulation, ideal to test the method of LGS uplink tip-tilt retrieval. The Durham Real-Time Adaptive Optics Generalised Optical Nexus (DRAGON) is a laboratory AO test bench nearing completion, which features multiple LGS and NGS Wavefront Sensors (WFSs) intended to further improve tomographic AO. A novel method of LGS emulation has been designed, which re-creates focus anisoplanatism, elongation and uplink turbulence. Once complete, DRAGON will be the ideal test bench for further development of LGS uplink tip-tilt retrieval. Performance estimates from simulation of the LGS uplink tip-tilt retrieval method are presented. Performance is improved over tomographic LGS AO systems which do not correct for tip-tilt, giving a modest improvement in image quality over the entire night sky. Correction performance is found to be dependent on the atmospheric turbulence profile. If combined with ground layer adaptive optics, higher correction performance with a very high sky coverage may be achieved

    Incorporating basic calibrations in existing machine-learned turbulence modeling

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    This work aims to incorporate basic calibrations of Reynolds-averaged Navier-Stokes (RANS) models as part of machine learning (ML) frameworks. The ML frameworks considered are tensor-basis neural network (TBNN), physics-informed machine learning (PIML), and field inversion & machine learning (FIML) in J. Fluid Mech., 2016, 807, 155-166, Phys. Rev. Fluids, 2017, 2(3), 034603 and J. Comp. Phys., 2016, 305, 758-774, and the baseline RANS models are the one-equation Spalart-Allmaras model, the two-equation kk-ω\omega model, and the seven-equation Reynolds stress transport models. ML frameworks are trained against plane channel flow and shear-layer flow data. We compare the ML frameworks and study whether the machine-learned augmentations are detrimental outside the training set. The findings are summarized as follows. The augmentations due to TBNN are detrimental. PIML leads to augmentations that are beneficial inside the training dataset but detrimental outside it. These results are not affected by the baseline RANS model. FIML's augmentations to the two eddy viscosity models, where an inner-layer treatment already exists, are largely neutral. Its augmentation to the seven-equation model, where an inner-layer treatment does not exist, improves the mean flow prediction in a channel. Furthermore, these FIML augmentations are mostly non-detrimental outside the training dataset. In addition to reporting these results, the paper offers physical explanations of the results. Last, we note that the conclusions drawn here are confined to the ML frameworks and the flows considered in this study. More detailed comparative studies and validation & verification studies are needed to account for developments in recent years
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