Luc Pastur

A dynamic mode decomposition approach for large and arbitrarily sampled systems

Detection of coherent structures is of crucial importance for understanding the dynamics of a fluid flow. In this regard, the recently introduced Dynamic Mode Decomposition (DMD) has raised an increasing interest in the community. It allows to efficiently determine the dominant spatial modes, and their associated growth rate and frequency in time, responsible for describing the time-evolution of an observation of the physical system at hand. However, the underlying algorithm requires uniformly sampled and time-resolved data, which may limit its usability in practical situations. Further, the computational cost associated with the DMD analysis of a large dataset is high, both in terms of central processing unit and memory. In this contribution, we present an alternative algorithm to achieve this decomposition, overcoming the above-mentioned limitations. A synthetic case, a two-dimensional restriction of an experimental flow over an open cavity, and a large-scale three-dimensional simulation, provide exampl...

Dynamical analysis of an intermittency in an open cavity flow

When open flows pass an open cavity, it is known that for medium or large Reynolds numbers, self-sustained oscillations generally appear. When more than one mode is excited, some nonlinear competition between modes may occur. In the configuration investigated here, the underlying dynamics are mainly driven by two dominant modes. The interplay between these two modes is investigated using phase portraits, Poincare sections, and return maps. The toroidal structure of the phase portrait is then investigated using a symbolic dynamics built from an angular return map. Each symbol can be associated with a specific mode and the interplay described in terms of symbolic sequences, leading to exhibit a switching mode process.

Investigating mode competition and three-dimensional features from two-dimensional velocity fields in an open cavity flow by modal decompositions

Shear-layer driven open cavity flows are known to exhibit strong self-sustained oscillations of the shear-layer. Over some range of the control parameters, a competition between two modes of oscillations of the shear layer can occur. We apply both Proper Orthogonal Decomposition and Dynamic Mode Decomposition to experimental two-dimensional two-components time and spaced velocity fields of an incompressible open cavity flow, in a regime of mode competition. We show that, although proper orthogonal decomposition successes in identifying salient features of the flow, it fails at identifying the spatial coherent structures associated with dominant frequencies of the shear-layer oscillations. On the contrary, we show that, as dynamic mode decomposition is devoted to identify spatial coherent structures associated with clearly defined frequency channels, it is well suited for investigating coherent structures in intermittent regimes. We consider the velocity divergence field, in order to identify spanwise coherent features of the flow. Finally, we show that both coherent structures in the inner-flow and in the shear-layer exhibit strong spanwise velocity gradients, and are therefore three-dimensional.

Flow coherent structures and frequency signature: application of the dynamic modes decomposition to open cavity flow

The dynamic dimension of an impinging flow may be significantly reduced by its boundary conditions and self-sustained oscillations they induce. The spectral signature is associated with remarkable spatial coherent structures. Dynamic modes decomposition (DMD) makes it possible to directly extract the dynamical properties of a non-linearly saturated flow. We apply DMD to highlight the spectral contribution of the longitudinal and transverse structures of an experimental open-cavity flow.

Closed-Loop Analysis and Control of Cavity Shear Layer Oscillations

This paper focuses on the closed-loop control of an incompressible flow past an open cavity. We propose a delayed feedback controller to suppress the self-sustained oscillations of the shear layer. The control law shows robustness to changes in flow conditions. An extension of the Eigensystem Realization Algorithm (ERA) to closed-loop identification, the so-called OCID technique, is used to extract the unstable linear dynamics of the cavity flow. The model-based analysis actually captures the modes against which the steady flow becomes unstable. The identified model is used to design an optimal controller, which shows both efficiency and robustness to stabilize the cavity flow.

Three-Dimensional Waves Inside an Open Cavity and Interactions with the Impinging Shear Layer

A separated flow over an open cavity (Fig. 1) is primarily characterised by the enhancement of self-sustained oscillations

An adaptive compressed-sensing equation-free approach for closed-loop nonlinear control

We present a method which seeks to combine the efficiency of an optimal control command with the robustness of a closed-loop controller. While the performance of optimal control is excellent, it cannot account for perturbations to the system under control which make the resulting performance to drop. On the other hand, a closed-loop control makes use of the actual state of the system and is thus robust, at the price of limited performance. We here present a control method which is both robust (closed-loop) and achieves a nearoptimal performance. The controller relies on an approximation of the optimal control command in the state space where the system lies upon reduction. The command can then be updated when a new observation of the system becomes available, hence achieving a closed-loop control. The approximation of the command in the state space is a computationally costly step but is achieved off-line and only once. To minimize its cost while achieving a good accuracy in the approximation, an adaptive multi-wavelets approach, combined with compressed-sensing acceleration exploiting compressibility, is here proposed. The control algorithm is demonstrated on the control of a cylinder wake in a 2-D flow.