Suspensions in turbulent liquid pipe flow: Kinetic modelling and added mass effects

We find that the radial component of the particle kinetic stress controls the radial diffusivity and the scale height of the concentration profile. It is shown that the axial and radial normal stresses are larger than the corresponding fluid stresses, mainly due to the virtual mass force. A model for hydrodynamic (long-range) interaction between the particles is invoked to account for the radial normal stress profile. As has been found previously in gas-solid flow, this interaction serves to redistribute the axial normal stress to the radial normal stress. The transport of kinetic stress is insignificant, leading to local relations between particle and fluid stresses, and a local particle diffusivity. The axial normal stress induced by the mean velocity shear is small compared to the virtual mass contribution.