Prédiction hybride d'écoulements autour de profils par assimilation de données

Overview & Synopsis

This thesis focuses on the characterization of unsteady flows by coupling experimental and numerical approaches (CFD). PIV (Particle Image Velocimetry) is an optical experimental method that provides velocity fields on a planar or volumetric domain whose spatial and temporal resolution limitations reduce access to certain quantities of interest, for example in the near-wall region. CFD can resolve very fine scales but remains limited due to uncertainties in the input specifications of the simulations. The combination of experimental and numerical methods by data assimilation (DA) is a way to overcome these limitations to improve the prediction and characterization of complex flows.A first part of the thesis focused on characterizing the flow around a low-Reynolds-number airfoil by PIV measurements and studying a low frequency oscillation phenomenon appearing near stall. A processing of the experimental data was performed using spectral techniques and an analysis of coherent spatio-temporal structures by Spectral Proper Orthogonal Decomposition (SPOD). However, the total acquisition time of the PIV limits the analysis of this low-frequency phenomenon. The assimilation of the mean flow fields obtained experimentally with Reynolds Averaged Navier-Stokes (RANS) simulations followed by a resolvent analysis allows to complete these data and to address the limitations observed. Assimilation is then a way to observe the low frequency oscillation phenomenon as well as a laminar separation bubble in the poorly resolved region by PIV measurements.The second part of the thesis focuses on the filtering of unsteady data with the aim of developing assimilation techniques to complement experimental measurements in real time. In this context, a low complexity data assimilation method based on Kalman filtering and model reduction by Dynamic Mode Decomposition (DMD) is developed. The proposed methodology, the Catalogue Kalman Filter (CatKF), is multi-model and allows to handle uncertainties resulting from the lack of knowledge of experimental parameters such as wind tunnel speed or the angle of attack of an airfoil. The efficiency of CatKF is tested on a 2D cylinder wake and the flow around two 2D side-by-side square cylinders. The fundamental idea of CatKF is also extended to propose two original methodologies for estimating uncertain parameters.