Quantitative velocity measurement in thin-gap Poiseuille flows

Abstract

Quantitative in-plane velocity measurement by means of particle image velocimetry (PIV) within thin-gap devices subject to a large depth of focus and Poiseuille flow conditions across the gap is investigated. The primary obstacles to a reliable quantitative measurement are due to the effects of the inherent wall-normal velocity gradient and the inertial migration of particles in the wall-normal direction. Specifically, in the simplest case of no particle migration, the PIV correlation peak is broadened due to velocity variations within the interrogation region, and the result is expected to predict the maximum centerline velocity. The current work demonstrates, however, that there is an inevitable underestimation of the peak velocity due to the convolution of the fluid displacement probability distribution function (PDF) by the particle image size that introduces a biased error typically up to 33 % of the centerline velocity for all but the smallest particle images and largest displacements. Due to the low signal-to-noise ratio caused by the velocity gradient, the probability of a valid estimate is significantly impaired, demanding an unrealistically high concentration of tracer particles. In addition, inertial particle migration within the channel introduces a selective sampling of the velocity PDF, causing a second correlation peak to emerge as the particles rapidly move away from the wall, making a reliable measurement troublesome. In later times, the particles reach their equilibrium position and hence sample only a single velocity value, presenting conditions similar to traditional PIV interrogations, with the correlation function reduced to a single symmetric peak. A practical procedure is proposed to make PIV quantitative by manipulating the particles to their equilibrium position prior to performing measurements. A demonstration of a reliable PIV measurement under appropriate working conditions is discussed for diffusive Rayleigh–Bénard convection in a Hele-Shaw cell.