Variational data assimilation of 3D wake flows using limited experimental observations.*

In this study, we use variational data assimilation to reconstruct the mean velocity field around a wake generator using limited experimental observations. Stereo PIV is employed to obtain mean velocity fields along the spanwise plane at ten equally spaced locations in the streamwise direction in the wake of the wake generator. The available data on discrete planes makes it challenging to compute quantities such as vorticity. Spalart-Allmaras (SA) RANS turbulence model is used to conduct a baseline simulation of the same test case but suffers from errors particularly in the regions of strong recirculation. We improve the prediction of the SA model and expand the field of view offered by the limited experimental observations using data assimilation. We use variational data assimilation with the discrete adjoint method to optimize a control parameter by minimizing the discrepancy between the experimental and RANS mean velocity fields. The topological differences between the CFD mesh and the experimental grid are resolved by using a cell-averaging method which is fully implemented in the discrete adjoint solver DAFoam.  We test two control parameters – a scalar multiplier to the SA turbulence transport equation and a source term to the momentum equations. The performance of the two control parameters in using limited experimental data to accurately reconstruct the mean velocity field is assessed. We also quantify the influence of data sparsity on accuracy of reconstruction.