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

We develop a Eulerian model for a particle suspension in fully developed turbulent liquid in a horizontal pipe. Virtual mass effects and hydrodynamic interactions are accounted for by an extension of the kinetic theory of Reeks and Swailes. del input is provided by the fluid–turbulence statistics measured using PIV. The model output is compared to PTV data in terms of concentration and particle kinetic stresses. We use water as carrier fluid, and polystyrene particles of diameter 950 μ m . The flow Reynolds numbers are 43,000, 64,000 and 115,000, with corresponding particle Stokes numbers (in terms of the turbulence timescale seen by the particles) of 1.3, 2.5 and 3.0. d 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.