We propose a novel cluster-based reduced-order modelling (CROM) strategy of unsteady flows. CROM combines the cluster analysis pioneered in Gunzburger's group (Burkardt et al. 2006) and and transition matrix models introduced in fluid dynamics in Eckhardt's group (Schneider et al. 2007). CROM constitutes a potential alternative to POD models and generalises the Ulam-Galerkin method classically used in dynamical systems to determine a finite-rank approximation of the Perron-Frobenius operator. The proposed strategy processes a time-resolved sequence of flow snapshots in two steps. First, the snapshot data are clustered into a small number of representative states, called centroids, in the state space. These centroids partition the state space in complementary non-overlapping regions (centroidal Voronoi cells). Departing from the standard algorithm, the probabilities of the clusters are determined, and the states are sorted by analysis of the transition matrix. Secondly, the transitions between the states are dynamically modelled using a Markov process. Physical mechanisms are then distilled by a refined analysis of the Markov process, e.g. using finite-time Lyapunov exponent and entropic methods. This CROM framework is applied to the Lorenz attractor (as illustrative example), to velocity fields of the spatially evolving incompressible mixing layer and the three-dimensional turbulent wake of a bluff body. For these examples, CROM is shown to identify non-trivial quasi-attractors and transition processes in an unsupervised manner. CROM has numerous potential applications for the systematic identification of physical mechanisms of complex dynamics, for comparison of flow evolution models, for the identification of precursors to desirable and undesirable events, and for flow control applications exploiting nonlinear actuation dynamics.Comment: 48 pages, 30 figures. Revised version with additional material. Accepted for publication in Journal of Fluid Mechanic

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Large-Eddy Simulation (LES) has become a potent tool to investigate instabilities in swirl flows even for complex, industrial geometries. However, the accurate prediction of pressure losses on these complex flows remains difficult. The paper identifies localised near-wall resolution issues as an important factor to improve accuracy and proposes a solution with an adaptive mesh h-refinement strategy relying on the tetrahedral fully automatic MMG3D library of Dapogny et al. (J. Comput. Phys. 262, 358-378, 2014) using a novel sensor based on the dissipation of kinetic energy. Using a joint experimental and numerical LES study, the methodology is first validated on a simple diaphragm flow before to be applied on a swirler with two counter-rotating passages. The results demonstrate that the new sensor and adaptation approach can effectively produce the desired local mesh refinement to match the target losses, measured experimentally. Results shows that the accuracy of pressure losses prediction is mainly controlled by the mesh quality and density in the swirler passages. The refinement also improves the computed velocity and turbulence profiles at the swirler outlet, compared to PIV results. The significant improvement of results confirms that the sensor is able to identify the relevant physics of turbulent flows that is essential for the overall accuracy of LES. Finally, in the appendix, an additional comparison of the sensor fields on tetrahedral and hexahedral meshes demonstrates that the methodology is broadly applicable to all mesh types.

For the last ten years, large eddy simulations have become a major tool for investigating jet noise sources because of their intrinsic ability to capture broadband turbulent features. However, many challenges still arise when dealing with complex geometries in terms of method accuracy and computational costs. Two different approaches to compute jet noise in an industrial context are here validated and compared. Both approaches are based on a hybrid methodology combining Large Eddy Simulation of jet flows for sources computations and a Ffowcs Williams and Hawkings' analogy for far field noise prediction but they differ on their grid topologies. The first approach uses classical block structured grids. The numerical scheme is a low dispersive, low dissipative finite volume compact scheme. The second approach uses fully unstructured tetrahedral grids with a low dispersive, low dissipative Taylor-Galerkin finite-element scheme. Both approaches are used to compute a 0.9 Mach, cold jet at moderate Reynolds number 4 × 10 5 without accounting for the nozzle geometry. Comparisons between simulations and experimental measurements highlight the need to correctly capture the initial turbulent development of the mixing layer at the nozzle exit. In the present simulations, since the nozzle geometry is not discretized, the turbulent transition is done by injecting perturbations as vortex ring modes. Results obtained

A generalized non-reflecting inlet boundary condition for steady and forced compressible flows with injection of vortical and acoustic waves. (2019) Computers and Fluids, 190. 503-513.

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International audienceCharacterizing and controlling nonlinear, multi-scale phenomena are central goals in science and engineering. Cluster-based reduced-order modeling (CROM) was introduced to exploit the underlying low-dimensional dynamics of complex systems. CROM builds a data-driven discretization of the Perron–Frobenius operator, resulting in a probabilistic model for ensembles of trajectories. A key advantage of CROM is that it embeds nonlinear dynamics in a linear framework, which enables the application of standard linear techniques to the nonlinear system. CROM is typically computed on high-dimensional data; however, access to and computations on this full-state data limit the online implementation of CROM for prediction and control. Here, we address this key challenge by identifying a small subset of critical measurements to learn an efficient CROM, referred to as sparsity-enabled CROM. In particular, we leverage compressive measurements to faithfully embed the cluster geometry and preserve the probabilistic dynamics. Further, we show how to identify fewer optimized sensor locations tailored to a specific problem that outperform random measurements. Both of these sparsity-enabled sensing strategies significantly reduce the burden of data acquisition and processing for low-latency in-time estimation and control. We illustrate this unsupervised learning approach on three different high-dimensional nonlinear dynamical systems from fluids with increasing complexity, with one application in flow control. Sparsity-enabled CROM is a critical facilitator for real-time implementation on high-dimensional systems where full-state information may be inaccessible