Superficial Velocity in Heterogeneous Two-Phase Systems with Truncated Fractal Distribution of Particle Concentration

Abstract

The interplay of particles in a heterogeneous multiparticle two-phase system and its effect on superficial velocity have not been well quantified. In this study, a new model is developed to examine the superficial velocity in a heterogeneous multiparticle two-phase system. To examine the heterogeneous effects to the potentially maximum extent, the particle concentration is assumed to follow a truncated fractal distribution, which is integrated into the free surface cell model. In a statistical sense, the multiparticle two-phase system is stationary, so the mean of spatial heterogeneity can be replaced by the ensemble mean. Since the underlying physical concept is rooted in the free surface cell model, the validity of the model should be, therefore, limited to the low-Reynolds number conditions. The developed model is compared to data from three representative experimental studies in the literature and it is found that the model can better capture the scatters in experimental data than the original free surface cell model. The model is also compared with three representative models and demonstrates reasonable results. While the deterministic free surface cell model underestimates the velocity, the cell model with truncated fractal distribution being incorporated can predict high velocity with a wide range of particle concentration heterogeneity.