Turbulence characteristics of particle-laden pipe flow

Turbulence characteristics of vertical air–solid pipe flow are investigated in this paper. Direct numerical simulations of the gas phase have been performed, while the solid particles have been simulated by a Lagrangian approach, including particle collisions. The modelling of wall roughness is shown to be important to obtain agreement with experimental data. Reynolds stresses and Reynolds stress budgets are given for both phases and for a wide range of solid–air mass load ratios (mass loads), varying from 0.11 to 30. Air turbulence intensities, Reynolds shear stress, and turbulence production reduce with increasing mass load. The mean air profile does not alter for low mass loads. In this regime, a simple theory predicts that the reduction of air turbulent production relative to unladen turbulent production is approximately equal to the mass load ratio. The insight that the solids Reynolds shear stress can be significant, even for low mass loads, is essential for this explanation. It is shown that at least two mechanisms cause the turbulence reduction. In addition to the classically recognized mechanism of dissipation of turbulent fluctuations by particles, there is another suppressing mechanism in inhomogeneous flows: the non-uniform relative velocity of the phases, created because particles slip at the wall, collide, and slowly react with the continuous phase. Investigation of the air turbulent kinetic energy equation demonstrates that the relative reduction of air pressure strain is larger than the reduction of turbulent production and dissipation, and pressure strain may therefore be a cause of the reduction of the other quantities. The fluctuational dissipation induced by the drag forces from particles is small compared to the other terms, but not negligible. For intermediate and high mass loads the air turbulence remains low. The relatively small turbulence intensities are not generated by the standard turbulent mechanisms any more, but directly caused by the particle motions. The particle–fluid interaction term in the turbulent kinetic energy equation is no longer dissipative, but productive instead. On increasing the mass load, the radial and azimuthal fluctuations of the particles grow. The corresponding reduction of solids anisotropy is an effect of the inter-particle collisions, which act as a solids pressure strain term. For intermediate and high mass loads, fluctuational drag force and particle collisions appear to be the relevant dissipation mechanisms in the solids fluctuational energy equation. In contrast to the air turbulent production, the solids ‘turbulent’ production term has the same level for low and high mass loads, while it attains a clear local minimum between. With increasing mass load, large-scale coherent turbulent fluid structures weaken, and eventually disappear. Simultaneously, the fluid fluctuations at relatively small length scales are enhanced by the motion of the particles. The highest particle concentration occurs near the wall for low mass loads, but on increasing the mass load, the concentration profile becomes uniform, while for the highest mass load particles accumulate in the centre of the pipe. Two-point correlation functions indicate that the addition of a small number of small solid particles to a clean pipe flow increases the streamwise length scale of the turbulence.