Abstract

Interface-resolved direct numerical simulations of downward particle-laden turbulent channel flows are performed by using a direct-forcing fictitious domain method. The effects of the particle settling coefficient, the density ratio (2, 10, and 100), and the particle size on fluid-turbulence interactions are investigated at a bulk Reynolds number of 5746 and a particle volume fraction of 2.36%. Our results indicate that the significant particle-induced reduction in the turbulence intensity does not take place for the downflow at a low density ratio of 2, and the turbulence intensity generally increases with an increasing particle Reynolds number at the same other control parameters, unlike the upflow case. The total turbulent kinetic energy (TKE) in the channel is larger for the downflow than for the upflow at the same particle Reynolds number, whereas the TKE at the channel center is roughly independent of the flow direction when the particle inertia is very large. For a density ratio of 2, the particles aggregate and are preferentially located in the low-speed streaks in the near-wall region, whereas for a density ratio of 10, the particles migrate toward the channel center, similar to the zero-gravity case. The flow friction increases with an increasing settling coefficient for the same density ratio and particle size, and the friction at the density ratio of order (10) is smallest. The pair distribution function shows the transition from the turbulence-dominated feature to the sedimentation-dominated feature, as the settling coefficient increases.

The effects of the particle collision model in a direct-forcing fictitious domain method on the fluid and particle statistics of a fully developed turbulent channel flow laden with finite-size neutrally buoyant particles are numerically investigated. The particle collisions are described by a combination of the discrete element method and the lubrication force correction model. We first validate our code via several benchmark tests, including the normal particle–wall collisions at different impact Stokes numbers and the oblique collisions with varied incidence angles. Subsequently, the effects of the lubrication correction and the particle stiffness on the fluid and particle statistics of the particle-laden turbulent flows are examined. The results show that the lubrication force correction has an important effect on the particle pair statistics at the near-contact regime. Both the lubrication force between the particles and the decrease in the particle stiffness result in the decrease in the flow friction mainly due to the increase in the fluid Reynolds stress. The flow friction is always larger for smaller particles at the same particle volume fraction irrespective of the lubrication correction. The particle–particle lubrication force decreases the near-wall particle concentration, whereas the particle–wall lubrication force has the opposite effect.

In this paper we demonstrate that the original Troshko-Hassan model with the correction coefficient being unity should be chosen for the interfacial term in the turbulent kinetic energy equation at the statistically steady state, based on theoretical analysis and interface-resolved direct numerical simulations of the particle sedimentation in a periodic domain and an upward turbulent channel flow. In addition, the computational schemes for the viscous dissipation near the particle surface with the non-boundary-fitted mesh are examined, and the results show that the second-order single-sided differentiation for the velocity gradient at the fluid grids in the immediate vicinity of the particle surface can reduce the computational error significantly, compared to the two-sided differentiation.

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