Minimization of divergence error in volumetric velocity measurements and implications for turbulence statistics

Volumetric velocity measurements taken in incompressible fluids are typically hindered by a nonzero divergence error due to experimental uncertainties. Here, we present a technique to minimize divergence error by employing continuity of mass as a constraint, with minimal change to the measured velocity field. The divergence correction scheme (DCS) is implemented using a constraint-based nonlinear optimization. An assessment of DCS is performed using direct numerical simulations (DNS) velocity fields with random noise added to emulate experimental uncertainties, together with a Tomographic particle image velocimetry data set measured in a channel flow facility at a matched Reynolds number to the DNS data (Reτ ≈ 937). Results indicate that the divergence of the corrected velocity fields is reduced to near zero, and a clear improvement is evident in flow statistics. In particular, significant improvements are observed for statistics computed using spatial gradients such as the velocity gradient tensor, enstrophy, and dissipation, where having zero divergence is most important.