Optimal pressure reconstruction based on planar particle image velocimetry and sparse sensor measurements

An adjoint-based approach for the accurate estimation of pressure of steady turbulent flows is developed and validated using both numerical and experimental data. The approach considers a simple algorithm to correct for the pressure in the domain solely based on sensor measurements at the wall. Adjoint looping is shown to provide both an accurate and fast algorithm where only minor modifications are required to implement the present procedure in an existing pressure solver. The algorithm is first validated using a set of time-averaged unsteady Reynolds-averaged Navier–Stokes equation in the wake of a D-shaped bluff body. The effect of noise is also investigated and shows that combining both a Helmholtz decomposition to recover a divergence-free velocity field and the adjoint-based correction provides consistent results for the pressure field. The approach is then applied to a wind-tunnel experiment for the same geometry. An independent comparison of drag, estimated between pressure measurements at the wall and the corrected pressure field shows good agreement. Finally, the role of domain size for the adjoint-based approach is addressed. The present algorithm naturally extends to time-dependent measurements without additional modifications.