An Equivalent Spherical Particle System to Describe Characteristics of Flow in a Dense Packing of Non-spherical Particles

Effective characteristics, such as the effective particle diameter and hydraulic radius, are usually used to determine the pressure loss associated with single-phase flow through an isotropic, dense non-spherical granular packing. These quantities can be considered as those of an equivalent spherical particle system. This paper reviews different methods to select effective particle diameters taking into account the effect of particle shape. A new method is proposed to determine an equivalent spherical particle system with both the hydraulic radius and the pressure loss equivalent to those in the actual non-spherical particle packing. This equivalent system can be used to determine the characteristics of flow in the actual system. The analyses provide theoretical justification for adoption of proper effective particle diameters and porosity as well as the dependency of Ergun-Kozeny constant on the shape factor of particles. It is also shown theoretically that the critical Reynolds number for Darcian flow depends on the porosity and the shape factor of particles.