Effect of Mass Ratio on the Vortex-Induced Vibrations of a Long Tensioned Beam in Shear Flow

The flow past a cylindrical tensioned beam of aspect ratio 200 is predicted by direct numerical simulation of the threedimensional Navier-Stokes equations. The beam is free to oscillate in inline and crossflow directions and submitted to a linearly sheared oncoming flow. The ratio between high and low inflow velocities is 3.67, with a maximum Reynolds number of 330. Two structure/fluid mass ratios are considered, 6 and 3. Structure vortex-induced vibrations are characterized by mixed standingtraveling wave patterns. A reduction of mass ratio from 6 to 3 leads to purer, more pronounced traveling wave responses and larger amplitude vibrations in both directions. While multifrequency structure vibrations are observed at m = 6, case m = 3 exhibits monofrequency responses. A large zone of synchronization between vortex shedding and structure vibration (lock-in) is identified in the high velocity region. The topology of fluidstructure energy exchanges shows that the flow can excite the structure at lock-in and damps its vibrations in non-lock-in region. Inline/crossflow motion synchronization is monitored. Similar zigzagging patterns of inline/crossflow motion phase difference are put forward for both mass ratios, highlighting a predominant character of counterclockwise orbits in the excitation region. Topics: Shear flow, Vortex-induced vibrationBP-MIT Major Projects Progra

Mono- and multi-frequency vortex-induced vibrations of a long tensioned beam in shear flow

The mono-frequency as well as multi-frequency vortex-induced vibrations of a tensioned beam of aspect ratio 200, immersed in a linear shear flow at Reynolds number 330 and free to move in both the in-line and cross-flow directions, are studied by means of direct numerical simulation. The structural responses are composed of mixed standing traveling wave patterns. We observe a switch between mono-and multi-frequency vibrations when the mass ratio changes from a value of 3 to 6, while keeping constant the non dimensional cable and beam phase velocities. This switch is attributed to the accompanying change in the time-averaged in-line curvature of the beam, which alters the oncoming flow velocity component normal to the structure configuration. It is shown, in general, that the mono- or multi-frequency nature of the response is controlled by the form of the profile of the normal component of the oncoming flow. Mono- and multi-frequency vibrations may occur in both the in-line and cross-flow directions, with a frequency ratio close to 2. Each excited frequency is associated with a single structural wavenumber. The local synchronization between the vortex shedding and the cross-flow oscillation, i.e. the lock-in condition, occurs in the high velocity zone and covers a similar spanwise extent in both the mono- and multi-frequency cases. Counter-clockwise figure-eight trajectories are very likely to occur within the lock-in region. In both the mono- and multi-frequency types of response, the flow excites the structural vibrations within the lock-in region and damps the structural motions in the non-lock-in region. The multi-frequency character of the response impacts both the lock-in phenomenon and the fluid–structure energy transfer

Physics-informed neural networks modeling for systems with moving immersed boundaries: application to an unsteady flow past a plunging foil

Recently, physics informed neural networks (PINNs) have been explored extensively for solving various forward and inverse problems and facilitating querying applications in fluid mechanics applications. However, work on PINNs for unsteady flows past moving bodies, such as flapping wings is scarce. Earlier studies mostly relied on transferring to a body attached frame of reference which is restrictive towards handling multiple moving bodies or deforming structures. Hence, in the present work, an immersed boundary aware framework has been explored for developing surrogate models for unsteady flows past moving bodies. Specifically, simultaneous pressure recovery and velocity reconstruction from Immersed boundary method (IBM) simulation data has been investigated. While, efficacy of velocity reconstruction has been tested against the fine resolution IBM data, as a step further, the pressure recovered was compared with that of an arbitrary Lagrange Eulerian (ALE) based solver. Under this framework, two PINN variants, (i) a moving-boundary-enabled standard Navier-Stokes based PINN (MB-PINN), and, (ii) a moving-boundary-enabled IBM based PINN (MB-IBM-PINN) have been formulated. A fluid-solid partitioning of the physics losses in MB-IBM-PINN has been allowed, in order to investigate the effects of solid body points while training. This enables MB-IBM-PINN to match with the performance of MB-PINN under certain loss weighting conditions. MB-PINN is found to be superior to MB-IBM-PINN when {\it a priori} knowledge of the solid body position and velocity are available. To improve the data efficiency of MB-PINN, a physics based data sampling technique has also been investigated. It is observed that a suitable combination of physics constraint relaxation and physics based sampling can achieve a model performance comparable to the case of using all the data points, under a fixed training budget

Résolution de problème inverse et propagation d'incertitudes (application à la dynamique des gaz compressibles)

Cette thèse porte sur la propagation d'incertitudes et la résolution de problème inverse et leur accélération par Chaos Polynomial. L'objectif est de faire un état de l'art et une analyse numérique des méthodes spectrales de type Chaos Polynomial, d'en comprendre les avantages et les inconvénients afin de l'appliquer à l'étude probabiliste d'instabilités hydrodynamiques dans des expériences de tubes à choc de type Richtmyer-Meshkov. Le second chapitre fait un état de l'art illustré sur plusieurs exemples des méthodes de type Chaos Polynomial. Nous y effectuons son analyse numérique et mettons en évidence la possibilité d'améliorer la méthode, notamment sur des solutions irrégulières (en ayant en tête les difficultés liées aux problèmes hydrodynamiques), en introduisant le Chaos Polynomial généralisé itératif. Ce chapitre comporte également l'analyse numérique complète de cette nouvelle méthode. Le chapitre 3 a fait l'objet d'une publication dans Communication in Computational Physics, celle-ci a récemment été acceptée. Il fait l'état de l'art des méthodes d'inversion probabilistes et focalise sur l'inférence bayesienne. Il traite enfin de la possibilité d'accélérer la convergence de cette inférence en utilisant les méthodes spectrales décrites au chapitre précédent. La convergence théorique de la méthode d'accélération est démontrée et illustrée sur différents cas-test. Nous appliquons les méthodes et algorithmes des deux chapitres précédents à un problème complexe et ambitieux, un écoulement de gaz compressible physiquement instable (configuration tube à choc de Richtmyer-Meshkov) avec une analyse poussée des phénomènes physico-numériques en jeu. Enfin en annexe, nous présentons quelques pistes de recherche supplémentaires rapidement abordées au cours de cette thèse.This thesis deals with uncertainty propagation and the resolution of inverse problems together with their respective acceleration via Polynomial Chaos. The object of this work is to present a state of the art and a numerical analysis of this stochastic spectral method, in order to understand its pros and cons when tackling the probabilistic study of hydrodynamical instabilities in Richtmyer-Meshkov shock tube experiments. The first chapter is introductory and allows understanding the stakes of being able to accurately take into account uncertainties in compressible gas dynamics simulations. The second chapter is both an illustrative state of the art on generalized Polynomial Chaos and a full numerical analysis of the method keeping in mind the final application on hydrodynamical problems developping shocks and discontinuous solutions. In this chapter, we introduce a new method, naming iterative generalized Polynomial Chaos, which ensures a gain with respect to generalized Polynomial Chaos, especially with non smooth solutions. Chapter three is closely related to an accepted publication in Communication in Computational Physics. It deals with stochastic inverse problems and introduces bayesian inference. It also emphasizes the possibility of accelerating the bayesian inference thanks to iterative generalized Polynomial Chaos described in the previous chapter. Theoretical convergence is established and illustrated on several test-cases. The last chapter consists in the application of the above materials to a complex and ambitious compressible gas dynamics problem (Richtmyer-Meshkov shock tube configuration) together with a deepened study of the physico-numerical phenomenon at stake. Finally, in the appendix, we also present some interesting research paths we quickly tackled during this thesis.PARIS-JUSSIEU-Bib.électronique (751059901) / SudocSudocFranceF

Mixture of polynomial chaos expansions for uncertainty propagation

HydrodynamicsAbstrac

Analysis and prediction of vortex-induced vibrations of variable-tension vertical risers in linearly sheared currents

Many studies have tackled the problem of previous termvortex-induced vibrationsnext term (VIV) of a vertical riser with a constant tension and placed in uniform currents. In this study, attention is focused on the cross-flow VIV modelling, time-domain previous termanalysis and predictionnext term of variable-tension vertical risers in linearly sheared currents. The partial-differential equation governing the riser transverse motion is based on a flexural tensioned-beam model with typical pinned–pinned supports. The hydrodynamic excitation model describing the modulation of lift force is based on a distributed van der Pol wake oscillator whose nonlinear equation is also partial-differential due to the implementation of a diffusion term. The variation of empirical wake coefficients with system parameters and the water depth-dependent Reynolds number is introduced. Based on the assumed Fourier mode shape functions obtained by accounting for the effect of non-uniform tension, the Galerkin technique is utilized to construct a low-dimensional multi-mode model governing the coupled fluid-riser interaction system due to VIV. Numerical simulations in the case of varying sheared flow profiles are carried out to systematically evaluate riser nonlinear dynamics and highlight the influence of fluid–structure parameters along with associated VIV aspects. In particular, the effects of shear and tensioned-beam (tension versus bending) parameters are underlined. Some comparisons with published experimental results and observations are qualitatively and quantitatively discussed. Overall parametric previous termanalysis and predictionnext term results may be worthwhile for being a new benchmark against future experimental testing and/or numerical results predicted by an alternative model and methodology