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Constitutive relations are derived for a gas-particle suspension in which the particles are subject to a fluid velocity field, and experience inter-particle collisions. The flow is driven by two types of energy sources, an imposed mean shear and fluid velocity fluctuations, in the limit where the time between collisions τ is small compared to the viscous relaxation time τ, so that the dissipation of energy between collisions is small compared to the energy of a particle. Constitutive relations from the kinetic theory of dense gases are used when the flow is driven by the mean shear. The effect of fluid velocity fluctuations is incorporated using an additional diffusive term in the Boltzmann equation for the particle velocity distribution, and this leads to an additional ‘diffusino’ stress.

This paper presents a method for integrating two-phase flow into the vector formulation of the One-Dimensional Turbulence model (ODT) without the introduction of any additional free parameters into the model. ODT is an unsteady turbulent flow simulation model implemented on a one-dimensional domain, representing flow evolution as observed along a line of sight through a 3D turbulent flow. Overturning motions representing individual eddies are implemented as instantaneous rearrangement events. Particles are simulated in a turbulent channel using one-way coupling.

Numerical simulations were run with turbulent friction Reynolds numbers, Re, 180 and 640. Validation was achieved by comparing wall-normal profiles of particle statistics with DNS, LES, and experiments.