Sequential Data Assimilation of Turbulent Flow and Pressure Fields over Aerofoil

The present study concentrates on the global velocity and pressure fields recovery over a NACA0012 aerofoil using the adjoint-based sequential data assimilation (DA) approach. Planar particle image velocimetry (PIV) measurement is conducted in the water channel to capture the time-resolved velocity field above the aerofoil, and the velocity field data are then used for DA. The attack angle is fixed at , and the Reynolds number, based on the inflow velocity and chord length , is . Conventional pressure determination methods that use either integration or a solution of the Poisson equation are applied to compute the instantaneous pressure field from the PIV data. Dynamic detached-eddy simulation (DDES) and Reynolds-averaged Navier–Stokes (RANS) simulations using the shear strain transport model are also performed for comparison. The conventional pressure determination methods yield large errors due to the error accumulation and boundary effects, whereas the RANS simulation seriously mispredicts the flow separation, and the DDES also fails due to low mesh resolution. By solving the primary-adjoint equation system and updating the correction for the governing equations at time steps for which observations exist, DA accurately reproduces the instantaneous flowfield in the observational region, which substantially improves the prediction of pressure distribution on the aerofoil surface and the flow in the wake region. Using the observational data in half of the region, DA also improves the flow and pressure prediction in the other half region. The present DA method is therefore able to reproduce the global fields from limited measurement data.