Yann Fraigneau

A Reconstruction Method for the Flow Past an Open Cavity

In this paper we propose a method to reconstruct the flow at a given time over a region of space using partial instantaneous measurements and full-space proper orthogonal decomposition (POD) statistical information. The procedure is tested for the flow past an open cavity. 3D and 2D POD analysis are used to characterize the physics of the flow. We show that the full 3D flow can be estimated from a 2D section at an instant in time provided that some 3D statistical information — i.e., the largest POD modes of the flow — is made available.

Synthetic wall boundary conditions for the direct numerical simulation of wall-bounded turbulence

We report on the simulation of a turbulent channel flow in a reduced computational domain where the wall no-slip boundary condition is replaced with a synthetic boundary condition on a horizontal plane in the wall layer. The simulation is carried out at a moderate Reynolds number (R τ=180). The boundary condition consists of a planar velocity field reconstructed at each instant from a combination of proper orthogonal decomposition (POD) spatial eigenfunctions, which are supposed to be known a priori. Two different techniques are used to reconstruct the temporal coefficients of the combination. The coefficients are first integrated from a dynamical model [29] (B. Podvin, A pod-based model for the wall layer of a turbulent channel flow, Phys. Fluids 21(1) (2009), p. 015111) derived for one wall-normal POD mode. The coefficients are then estimated from flow information on the reduced domain as described in [30] (Podvin et al., On self-similarity in the wall layer of a turbulent channe flow, J. Fluids Eng. 134 (2010), p. 042102). Synthetic wall conditions are tested at y+=17 and y+=50. When only one wall-normal POD mode is used, the low-dimensional model appears to provide some agreement, while the estimation technique fails to reproduce the statistics of a full channel flow. The statistics improved significantly when the higher order wall-normal POD modes were included in the estimation procedure. Contributions to the Reynolds stress were examined: Vortex stretching was more easily reproduced than vorticity transfer, and adjusted more rapidly to the feedback-estimated boundary condition.

A few thoughts on proper orthogonal decomposition in turbulence

Proper orthogonal decomposition was originally introduced in turbulence to identify large-scale patterns in turbulent flows. Over the years, several extensions have been formulated in order to strengthen its model-predictive abilities, with limited success in the case of fully developed turbulence. We argue that physics-based insight obtained from the proper orthogonal decomposition structures and other turbulence analysis techniques could lead to significant developments in that respect. Numerical results from channel flow simulations are used to illustrate our conjectures.

Numerical simulation of the turbulent separation reattachment flow around a thick flat plate

This work concerns the turbulent flow generated around a thick flat plate to study the relationship between instantaneous flow structures and the unsteady pressure field. LES results compare favorably to experiments thanks to using a high order scheme. Mean and fluctuating quantities are very well predicted in both the detachment and the reattachment regions. Dimensionless frequencies, characteristic of flapping and shedding phenomena, have also been recorded that are in agreement with experiments.

On Self-Similarity in the Inner Wall Layer of a Turbulent Channel Flow

We use proper orthogonal decomposition (POD) to estimate the flow in the near-wall region based on information from the outer buffer layer. Our goal is to assess how the flow structures in the inner wall region are connected to those further away from the wall, and to investigate the nature of the coupling between the inner and the outer region in the POD framework. Reconstructions are carried out for numerical simulations of a plane channel flow at two different Reynolds numbers. We show that elongated structures with a spanwise wavelength smaller than a critical value tend to be concentrated in the inner layer. The critical wavelength is shown to scale with the inner layer height, and interactions between the inner and the outer layer appear to take place predominantly over a self-similar, height-dependent, range of wavenumbers, in agreement with Townsend’s attached eddy hypothesis. The reconstructed field appears to capture an adequate energy content and to remain correlated with the real field even close to the wall, which reflects the persistence of energetic structures over the extent of the buffer layer.

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.

POD-based wall boundary conditions for the numerical simulation of turbulent channel flows

Simulation of turbulent wall-bounded flows requires a high spatial resolution in the wall region, which limits the range of Reynolds numbers which can be effectively reached. In previous work, we proposed proper orthogonal decomposition (POD) based wall boundary conditions to bypass the simulation of the inner wall region. Tests were carried out for direct numerical simulation at a low Reynolds number Reτ = 180. The boundary condition is based on the POD spatial eigenfunctions which are determined a priori in the full channel. It consists of a three-component velocity field on the plane y+ = 50 which is reconstructed at each instant from a combination of selected eigenfunctions. The coefficients of the combination are estimated from the simulation in the reduced domain using the threshold-based reconstruction method described in Podvin et al. The study is now extended to large-eddy simulation at higher Reynolds numbers Reτ = 295 and Reτ = 590. Two versions of the reconstruction method are considered. In the first version, both the phases and the moduli of the coefficients are allowed to vary. In the second version, only the phases are adjusted. We find that the latter method is associated with improved statistics and is relatively robust with respect to the reconstruction threshold. However, it is sensitive to the details of the numerical simulation, unlike the former method, which is associated with less accurate statistics and is more dependent on the reconstruction threshold.

A POD-based reconstruction method for the flow in the near-wall region

We present a reconstruction method to estimate the instantaneous flow close to the wall of a turbulent channel. The motivation for the procedure is to come up with suitable wall models for large-eddy simulations. The idea is to apply the Proper Orthogonal Decomposition to the velocity field u over a zone extending over the lower wall region to be modelled \( \Omega _1 :0 \le y + \le y_1 \) and the LES numerical domain, \( \Omega _2 : y_1 \le y + \le y_2 \). The reconstruction method is a straightforward extension of the procedure described in Podvin et al. [Podvin et al., Journal of Fluids Engineering 2006]. The POD modes an(t) are estimated by solving a linear system where the right-hand side contains information about the flow in the upper region, and the operator is the inner product of the empirical eigenfunctions restricted to the lower region.