Collisional mechanics in solid-liquid flows

Experimental measurements of the particle pressure were obtained for a liquid fluidized bed and for a vertical gravity driven liquid-solid flow. The particle, or granular, pressure is defined as the extra pressure generated by the action of particles in a particulate multi-phase flow. Using a high-frequency-response pressure transducer, individual collisions of particles were collected and measured to obtain a time-averaged particle pressure. Results were obtained for a number of different particles and for two different test section diameters. Results show that the particle pressure experiences a maximum at intermediate concentrations, and that its magnitude is scaled with the particle density and the square of the terminal velocity of the particles. The particle pressure was found to be composed of two main contributions: one from pressure pulses generated by direct collisions of particles against the containing walls (direct component), and a second one from pressure pulses due to collisions between individual particles that are transmitted through the liquid (radiated component). The direct component of the particle pressure was studied by an analysis of particle collisions submerged in a liquid. A simple pendulum experiment provides controlled impacts in which measurements are made of the particle trajectories for different particles immersed in water. The velocity of the approaching particle is measured using a high speed digital camera; the magnitude of the collision is quantified using a high frequency response pressure transducer at the colliding surface. The measurements show that most of the particle deceleration occurs at less than half a particle diameter away from the wall. The measured collision pressure appears to increase with the impact velocity. Comparisons are drawn between the measured pressures and the predictions by Hertzian theory. A simple control-volume model is proposed to account for the effects of fluid inertia and viscosity. The pressure profile is estimated, and then integrated over the surface of the particle to obtain a force. The model predicts a critical Reynolds number at which the particle reaches the wall with zero velocity. Comparisons between the proposed model and the experimental measurements show qualitative agreement. Experiments involving binary collisions of particles were performed to investigate the radiated component of the particle pressure. This component results from the pressure front generated by the impulsive motion of a fluid resulting from a collision of particles in a liquid. When the two particles come into contact, the impulsive acceleration due to the elastic rebound produces a pressure pulse, which is transmitted through the fluid. A simple dual pendulum experiment was set up to generate controlled collisions. Measurements were obtained for a range of impact velocities, angles of incidence, and distances away from the wall for different pairs of particles. The magnitude of the impulse pressure appears to scale with the particle impact velocity and the density of the fluid. Based on the impulse pressure theory, a prediction for pressure generated due to the collision can be obtained. The model appears to agree well with the experimental measurements. The fluctuating component of the solid fraction was studied, as one of the sources of the particle pressure. The instantaneous cross-sectional averaged solid fraction was measured using an impedance meter. The root-mean square fluctuation of the solid fraction signal was measured in a liquid fluidized bed and a vertical gravity-driven flow, for different particle sizes and densities. Two types of fluctuations were identified: low-frequency large-scale fluctuations which dominate at high concentrations, and high-frequency small-scale fluctuations which are dominant at intermediate solid fractions. The effect of each type was isolated by filtering. When the large-scale fluctuations were present, the magnitude of the rms fluctuation was found to scale with particle diameter, but when eliminated the mean fluctuation appeared to scale with the particle mass instead