Michele Alessandro Bucci

Dynamique souscritique et supercritique d’un écoulement incompressible autourd’éléments de micro-rugosité: Cette thèse vise à mettre en évidence les limites du contrôle passif en utilisant des éléments de rugosité miniaturisés. La topologie des écoulements induite par la présence d’une rugosité cylindrique et des générateurs de tourbillons miniaturisés a été étudiée pour analyser la dynamique pour des temps court et long. Différentes bifurcations supercritiques ont été examinées au moyen d’une analyse de stabilité globale. La bifurcation souscritique est déclenchée par des mécanismes de croissance transitoire de l'énergie ou par la réceptivité de modes globaux stables. Des structures deforçage optimal 3D sont extraites pour comprendre la distribution spatiale liée à la fréquence de résonance du système. La simulation numérique directe perturbée révèle le rôle central du mode global le moins stable dans les instationnarités non-linéaires observées. Une analyse détaillée des structures tourbillonnaires montre qu’elles sont principalement liées aux mécanismes linéaires sous-jacents. La principale caractéristique globale du mode propre est liée à la présence d’une zone de séparation en aval de la rugosité cylindrique. En utilisant des générateurs de tourbillon miniaturisés, cette zone de séparation est fortement diminuée et aucun mode global isolé est alors présent. La dynamique de l’écoulement se révèle être conduit non seulement par le nombre de Reynolds de rugosité et par son rapport d'aspect géométrique, mais aussi par le rapport entre la hauteur de la rugosité et l’epaisseur de couche limite.

The volume of fluid (VoF) method is widely used in multiphase flow simulations to track and locate the interface between two immiscible fluids. The relative volume fraction in each cell is used to recover the interface properties (i.e., normal, location, and curvature). Accurate computation of the local interface curvature is essential for evaluation of the surface tension force at the interface. However, this interface reconstruction step is a major bottleneck of the VoF method due to its high computational cost and low accuracy on unstructured grids. Recent attempts to apply data-driven approaches to this problem have outperformed conventional methods in many test cases. However, these machine learning-based methods are restricted to computations on structured grids. In this work, we propose a machine learning-enhanced VoF method based on graph neural networks (GNNs) to accelerate interface reconstruction on general unstructured meshes. We first develop a methodology for generating a synthetic dataset based on paraboloid surfaces discretized on unstructured meshes to obtain a dataset akin to the configurations encountered in industrial settings. We then train an optimized GNN architecture on this dataset. Our approach is validated using analytical solutions and comparisons with conventional methods in the OpenFOAM framework on a canonical test. We present promising results for the efficiency of GNN-based approaches for interface reconstruction in multiphase flow simulations in the industrial context.

Model order reduction through the POD-Galerkin method can lead to dramatic gains in terms of computational efficiency in solving physical problems. However, the applicability of the method to non linear high-dimensional dynamical systems such as the Navier-Stokes equations has been shown to be limited, producing inaccurate and sometimes unstable models. This paper proposes a deep learning based closure modeling approach for classical POD-Galerkin reduced order models (ROM). The proposed approach is theoretically grounded, using neural networks to approximate well studied operators. In contrast with most previous works, the present CD-ROM approach is based on an interpretable continuous memory formulation, derived from simple hypotheses on the behavior of partially observed dynamical systems. The final corrected models can hence be simulated using most classical time stepping schemes. The capabilities of the CD-ROM approach are demonstrated on two classical examples from Computational Fluid Dynamics, as well as a parametric case, the Kuramoto-Sivashinsky equation.

The reliable prediction of the temporal behavior of complex systems is key in numerous scientific fields. This strong interest is however hindered by modeling issues: often, the governing equations describing the physics of the system under consideration are not accessible or, if known, their solution might require a computational time incompatible with the prediction time constraints. Not surprisingly, approximating complex systems in a generic functional format and informing it ex-nihilo from available observations has become common practice in the age of machine learning, as illustrated by the numerous successful examples based on deep neural networks. However, generalizability of the models, margins of guarantee and the impact of data are often overlooked or examined mainly by relying on prior knowledge of the physics. We tackle these issues from a different viewpoint, by adopting a curriculum learning strategy. In curriculum learning, the dataset is structured such that the training process starts from simple samples towards more complex ones in order to favor convergence and generalization. The concept has been developed and successfully applied in robotics and control of systems. Here, we apply this concept for the learning of complex dynamical systems in a systematic way. First, leveraging insights from the ergodic theory, we assess the amount of data sufficient for a-priori guaranteeing a faithful model of the physical system and thoroughly investigate the impact of the training set and its structure on the quality of long-term predictions. Based on that, we consider entropy as a metric of complexity of the dataset; we show how an informed design of the training set based on the analysis of the entropy significantly improves the resulting models in terms of generalizability, and provide insights on the amount and the choice of data required for an effective data-driven modeling.

The effect of freestream turbulence on the dynamics of an incompressible flow past a cylindrical roughness element in subcritical conditions (i.e., for Reynolds numbers below the onset of linear instability) has been investigated by the joint application of direct numerical simulations, linear modal and nonmodal stability analyses, and dynamic mode decomposition. At first, the influence of the Reynolds number and the ratio of the boundary layer's thickness to roughness height on the three-dimensional spatiotemporal (global) stability of the flow has been investigated. Depending on the operating conditions, the leading instability can either be varicose (symmetric) or sinuous (antisymmetric). In both cases, when the flow is excited by broadband frequency forcing, dynamic mode decomposition extracts only varicose coherent structures even though optimal response analysis predicts a strong amplification of sinuous disturbances having frequency close to that of the marginally stable sinuous eigenmode. This apparent discrepancy is attributed to the fact that the sinuous instability is sensitive to a very limited range of frequencies barely excited by freestream turbulence while varicose disturbances are associated with high amplification in a much wider frequency range. Hence, in this case the flow behaves as an amplifier of varicose perturbations rather than a resonator. Consequences on the subsequent transition to turbulence have been studied, highlighting that varicose perturbations extract energy from the near-wake region, get continuously amplified due to the excitation provided by freestream turbulence, and eventually give rise to a shedding of hairpin vortices.

Deep reinforcement learning (DRL) is applied to control a nonlinear, chaotic system governed by the one-dimensional Kuramoto–Sivashinsky (KS) equation. DRL uses reinforcement learning principles for the determination of optimal control solutions and deep neural networks for approximating the value function and the control policy. Recent applications have shown that DRL may achieve superhuman performance in complex cognitive tasks. In this work, we show that using restricted localized actuation, partial knowledge of the state based on limited sensor measurements and model-free DRL controllers, it is possible to stabilize the dynamics of the KS system around its unstable fixed solutions, here considered as target states. The robustness of the controllers is tested by considering several trajectories in the phase space emanating from different initial conditions; we show that DRL is always capable of driving and stabilizing the dynamics around target states. The possibility of controlling the KS system in the chaotic regime by using a DRL strategy solely relying on local measurements suggests the extension of the application of RL methods to the control of more complex systems such as drag reduction in bluff-body wakes or the enhancement/diminution of turbulent mixing.

The onset of unsteadiness in a boundary-layer flow past a cylindrical roughness element is investigated for three flow configurations at subcritical Reynolds numbers, both experimentally and numerically. On the one hand, a quasi-periodic shedding of hairpin vortices is observed for all configurations in the experiment. On the other hand, global stability analyses have revealed the existence of a varicose isolated mode, as well as of a sinuous one, both being linearly stable. Nonetheless, the isolated stable varicose modes are highly sensitive, as ascertained by pseudospectrum analysis. To investigate how these modes might influence the dynamics of the flow, an optimal forcing analysis is performed. The optimal response consists of a varicose perturbation closely related to the least stable varicose isolated eigenmode and induces dynamics similar to that observed experimentally. The quasi-resonance of such a global mode to external forcing might thus be responsible for the onset of unsteadiness at subcritical Reynolds numbers, hence providing a simple explanation for the experimental observations.