Fully determined three-dimensional velocity field in a divergence-free convection experiment with rigid boundary conditions

Various velocity measurements techniques for fluid dynamics experiments have been developed over the last four decades. These include Particle Image Velocimetry (PIV) and Particle Tracking Velocimetry (PTV), both of which rely on imaging the flow with passive particles. While these techniques now allow for an accurate determination of velocity fields at high particle densities, they still suffer from significant inaccuracies when it comes to measurements near boundaries, due to smaller particle concentrations and imaging difficulties in these regions. To improve such measurements, we developed a correction technique for measured velocity fields. Using a PTV approach, we reconstructed the 3D velocity field from an experimental setup designed to study Rayleigh–Bénard convection in a tank. We corrected the obtained velocity field to ensure its accurate, rigid boundary conditions corresponding to the tank walls, while keeping the flow divergence-free. We then assessed the quality of the corrected velocity fields by comparing them with the outputs of 3D numerical simulations that reproduced the precise experimental conditions. The experimentally obtained divergence-free velocity fields with exact boundary conditions compare well with the results of the numerical simulations, which validates our approach. Using synthetic images, we estimated that our corrected fields are in better agreement with numerical simulations (Pearson coefficient \(R = 0.96\) $R=0.96$ ) than the raw measured fields (Pearson coefficient \(R = 0.91\) $R=0.91$ ). We find that at high Reynolds numbers, our results can be described by scaling laws that are consistent with previous results from the literature. The correction technique could be useful for a wide range of fluid dynamics experiments where accurate measurements near the walls are needed. These include the advection of passive tracers, where the boundary conditions need to be exact, or turbulence measurements, where the flow gradient at the walls must be precisely determined.