To stall-cell or not to stall-cell: Variational data assimilation of 3D mean flow past a stalled airfoil

Abstract: The full-field reconstruction of three-dimensional (3D) turbulent flows from sparse experimental measurements remains a significant challenge, particularly for flows exhibiting complex 3D flow separation. In this work, we address this challenge for the case of stall cells - spanwise coherent structures that form on the suction surface of wings at post-stall conditions. Planar particle image velocimetry (PIV) experiments are performed on a NACA 0012 wing at a chord-based Reynolds number of $Re_c \approx 450{,}000$ and angle of attack $α= 14^\circ$, acquiring two-component mean velocity data on four spanwise planes. The experimental data show clear spanwise variation in the extent of the separation and flow dynamics, consistent with the presence of stall cells. Three-dimensional variational (3DVar) data assimilation (DA) within the field inversion framework is then employed to reconstruct the full 3D mean flow field by augmenting these sparse planar measurements with the Spalart--Allmaras (SA) Reynolds-averaged Navier--Stokes (RANS) turbulence model. The performance of the reconstruction is assessed on planes not used in the assimilation. It is shown that a single plane of sparse experimental data is sufficient to recover the essential features of a stall cell, including counter-rotating vortices around focal points on the suction surface. The lowest reconstruction error is obtained when two planes of data that are close together but exhibit markedly different separation extents are used, and the complementary roles of the reference data placement and the computational boundary conditions in shaping the reconstructed stall cell structure are explained. These results demonstrate the capability of 3DVar DA to reconstruct the full 3D physics of stall cells from two-component velocity data acquired on select spanwise planes.