Transport phenomena in multi-particle systems—I. Pressure drop and friction factors: Unifying the hydraulic-radius and submerged-object approaches

Abstract

A submerged-object model which accounts for the presence of stagnant zones is developed for predicting the pressure drop in random multi-particle systems. This model is then combined with the hydraulic-radius approach. With appropriate definition of the parameters involved, these approaches are found to yield complementary results. The tortuosity factor is considered as a velocity enhancement coefficient and is then related to the stagnant bed voidage. An expression for the tortuosity factor in random multi-particle systems is obtained. A definition for the multi-particle Reynolds number is developed which is applicable to the entire range of void fractions. A generalized friction factor is also developed from the definition of the friction factor for flow in a conduit and is related to the porosity-dependent drag coefficient for individual spheres. The friction factor reduces to the single-sphere drag coefficient in the limit ε→1. The approach, in principle, permits the collapsing of the entire momentum transfer data for multi-particle systems to a single curve coincident with the single-sphere drag coefficient relation. Friction factors calculated from the experimental data reported in the literature on packed, fluidized and distended beds, as well as sedimenting systems, are in good agreement with the theory for laminar as well as turbulent regimes. An expression for the relative velocity of sedimenting suspensions, applicable to a wide range of Reynolds number and void fractions, is obtained. An approximation for the estimation of the minimum fluidizing velocity is also developed and compared with the data available in the literature.