Data-assimilation and stability analysis of turbulent mean flows around airfoils close to stall

Abstract

The prediction of turbulent mean flows around airfoil near stalling conditions is still nowadays a challenge for numerical simulation based on Reynolds Averaged Navier Stokes equations. Transition and linear-eddy viscosity turbulence models classicaly used in the aeronautical industry do not properly capture the separation and reattachment of laminar/turbulent boundary layers that occur when increasing the angle of attack. This lack of accuracy prevents such turbulence models from properly predicting not only the mean flow but also the onset of low–frequency oscillations [3] or transverse cellular patterns [2] that are observed experimentally close to the stall angle. In this talk, we will show recent results of our group to improve (i) the turbulence mean flow estimation thanks to adjoint-based data-assimilation techniques [1] and (ii) the prediction of low-frequency oscillations and stall cells using global stability analysis of assimilated mean flows. Firstly, we will consider the onset of stall cells around a NACA4412 airfoil at Reynolds number Re=350 000. A transition/turbulence model is corrected using a full-state mean flow velocity field obtained from Direct Numerical Simulation. The stability analysis of the assimilated mean flow, based on the linearization of the RANS and turbulence models, reveals the existence of a three-dimensional steady global mode that gets unstable for angle of attack and transverse wavenumber in agreement with the experimental results. Those results will be discussed and compared to those obtained with methods recently proposed in the litterature and based on frozen eddy-viscosity approaches and eddy-viscosity fields estimated from DNS mean-flow. Secondly, we will consider the low-frequency flow-oscillations around a NACA0012 airfoil at angles of attack 10 degrees and various Reynolds numbers in the range [30000-50000]. In that case, velocity fields measured with Particle Image Velocimetry (PIV) are used to calibrate the turbulence model. The stability analysis of those assimilated mean flows predicts the existence of an unstable low-frequency global mode that may explain bursting events observed in the mean flow. We will conclude this talk by discussing the limit of our approach and the remaining challenges.