Data assimilation for aerothermal mean flow reconstruction using aero-optical observations: accounting for RANS model-form uncertainty

International audienceIn this study, we investigate a Data Assimilation approach for the numerical reconstruction of turbulent aero-thermal flows, and more particularly of their average density fields. The proposed approach relies on an ensemble Bayesian inference method providing a derivative free optimization framework suitable for solving inverse problems and quantifying model uncertainties. The originality of this work lies in the use of minimally invasive measurements such as those obtained by the optical technique referred to as Background Oriented Schlieren (BOS). Such a measurement technique provides dense maps of light ray deviations through the flow of interest that can be obtained from multiple points of view and cameras. These deviations are obtained by integration through the volume of interest and projection into 2D planes, yielding an observation operator that can be modeled by numerical ray tracing. Such observations provide incomplete but spatially dense information about the 3D flow observed.Until now, restitution of density fields of turbulent aerothermal flows was mainly tackled with purely aero-optical modeling as in tomographic BOS. The present approach intends to provide additional physical constraints in the restitution process by relying on a flow model such as those obtained by Reynolds Averaged Navier-Stokes (RANS) equations. As it will be detailed, the developed DA framework is first applied as a calibration tool on the closure coefficients of a two-equation turbulence model, the k-omega SST model. Numerical simulations of a hot jet impinging on a flat plate with non-uniformly distributed temperature are considered as an example. The mean density field is reconstructed and compared to a reference synthetic experiment obtained by Large Eddy Simulation. Significant improvements in the RANS model predictions in terms of relative errors between the estimate samples mean and the LES data were obtained. However, some remaining local discrepancies are observed and can be understood as the consequence of the rigid nature of the model closure in the reconstruction of a multi-featured flow. To alleviate the current closure inadequacy, an inclusion of model-form uncertainties, found in a higher-dimensional space, is investigated.Finally, beyond providing an efficient data-driven reconstruction} technique, the proposed procedure enables working with high-dimensional turbulence models (e.g. second-order turbulence models such as Reynolds Stress Models), i.e. with a number of parameters of the same size as the state. This will allow investigation of more complex aerothermal flows and other modifications of turbulence closure models in future works