Coupled measurements of interface topography and three-dimensional velocity field of a free surface flow

Complete energy balance evaluations for interfacial flow require simultaneous coupled estimations of the free surface topography and the flow velocity beneath the surface. We describe here an extension of the tomographic PIV and volumetric LPT technique for this coupled measurement. We applied this optical measurement technique to the study of three-dimensional (3D) flow at the air–water interface during the controlled fall of a droplet. Our original setup made it possible to monitor, in real time, the 3D position of fluorescent tracer particles, both on the surface and in the bulk flow. We overcame the shadow effect due to the presence of waves at the interface by illuminating the flow through the underside of a truncated squared pyramidal water tank. We chose to use a water tank of this shape to ensure that optical access could be established orthogonally through the walls of the tank. Four high-speed cameras were focused on the illuminated volume of the flow through the four lateral sides of the pyramidal water tank. The images of the four cameras were analyzed by 3D Lagrangian particle tracking velocimetry (Schanz et al. 2016). With this technique, we were able to track particles accurately at seeding densities compatible with the thresholds for tomographic PIV and to reduce considerably the number of ghost particles. We then obtained local 3D velocities by interpolating vector volumes from the discrete particles. The energy balance was determined by evaluating interface position and bulk flow velocity. Surface curvature and potential energy were determined from surface topography. The kinetic energy of the flow was derived from the bulk flow velocities. We then compared the energy balance thus obtained with that derived from direct visualization of the impact of the same drop. Our findings demonstrate the ability of this technique to characterize such complex interfacial flows in terms of their energetics.