Effect of collisions on the dispersed phase fluctuation in a dilute tube flow: Experimental and theoretical analysis

Abstract

Measurements of particle fluctuation in a fully developed pipe flow at moderate Reynolds number is performed in this study. The present data are obtained by using a two-component phase Doppler anemometer. The radial profiles are measured at a distance of 0.2 diameter downstream the exit of the tube. At this location, the core flow still carries all the properties of the tube turbulence. A low mass loading of partly responsive particles is considered. The Stokes number of these partly responsive particles is of order 3 when the integral turbulent time scale on the axis of the tube flow is used. The velocity statistics are analyzed up to the third-order moments and we show that the radial turbulent transport of fluctuating kinetic energy is much higher for the particles than for the fluid. Radial balances of longitudinal and radial kinetic stresses of the particles are examined. Particle–particle collisions have a negligible direct effect on the evolution of the longitudinal fluctuating velocity. However, even at this low mass loading, we prove that particle–particle collisions and redistribution from the very large streamwise velocity variance to the radial velocity variance in the near wall region strongly influence the radial fluctuation of the particles. In the core region, a quadrant analysis enables the detection of low streamwise velocities focusing toward the axis and the corresponding quadrants are strongly dominant for the glass beads. We expect that the partly responsive particles, because of their inertia, keep some memory of the lower streamwise velocity existing in the near wall region while they fly across the tube. The collisions in the near wall region are, therefore, expected to have a strong indirect influence on the whole kinetic-energy balance in the tube by partly driving the radial transport of the fluctuating kinetic energy of the particles. This effect should be particularly strong in this circular geometry because events from any azimuthal directions converge in the central region.