Quantitative PIV measurement in narrow channels

This work focuses on making quantitative velocity measurements with a large depth-of-focus within a thin-gap channel, typical of Hele-Shaw cells. The inherent difficulty in such flows is due to the large velocity gradient across the gap and effects due to particle migration. In the simplest case of no particle migration, the PIV correlation peak is broadened due to the parabolic velocity profile, with an expected peak value at the maximum centerline velocity. However, there is an inevitable under-estimation that is typically up to 33{\%} of the centerline velocity for all but the smallest particle images and largest displacements, due to particle image size effects. In addition, inertial particle migration within the channel results in a second correlation peak as the particles rapidly move away from the wall. In later times, as the particles reach their equilibrium position, the particles sample only a single velocity value, and present conditions similar to traditional PIV interrogation. A practical procedure is proposed to make PIV quantitative by manipulating the particles to their equilibrium position prior to performing measurements and a reliable PIV measurement under appropriate working conditions is discussed for diffusive Rayleigh-B\'{e}nard convection in a Hele Shaw cell.