Error reduction for time-resolved PIV data based on Navier–Stokes equations

The post-processing of the measured velocity in particle image velocimetry (PIV) is a critical step in reducing error and predicting missing information of the flow field. In this work, time-resolved PIV data are incorporated with the incompressible Navier–Stokes (N–S) equations to reduce the measurement error and improve the accuracy. A pressure correction scheme (PCS) based on the projection method is adopted to solve the N–S equations, and an optimization algorithm is introduced to balance the fidelity between the PIV data and the numerical solutions. The PCS for PIV data, called PIV–PCS, cannot only reduce the errors in the velocity divergence and the curl of the pressure gradient but also ensure that the flow field satisfies the dynamic constraints imposed by the momentum equation. An important weight coefficient s that balances the level of the velocity modification with the residual of the governing equation is defined and numerically assessed. A method for optimizing the value of s is provided. The new approach is evaluated by two time-resolved PIV experiments: one on the 2D wake flow of a circular cylinder at low Reynolds number and one on tomographic PIV for the 3D wake flow of a hemisphere at high Reynolds number. All the numerical assessments and experimental applications are compared with the divergence-free smoothing (DFS) method. The results indicate that the presented PIV–PCS method is superior to the DFS method in terms of reducing the measurement error and recovering the real physical flow structures.