Interface-resolved simulations of small inertial particles in turbulent channel flow

Abstract

We present a direct comparison between interface-resolved and one-way-coupled point-particle direct numerical simulations (DNS) of gravity-free turbulent channel flow laden with small inertial particles, with high particle-to-fluid density ratio and diameter of about $3$ viscous units. The most dilute flow considered, solid volume fraction $O(10^{-5})$, shows the particle feedback on the flow to be negligible, whereas differences with respect to the unladen case, noteworthy a drag increase of about $10\%$, are found for a volume fraction $O(10^{-4})$. This is attributed to a dense layer of particles at the wall, caused by turbophoresis, flowing with large particle-to-fluid apparent slip velocity. The most dilute case is therefore taken as the benchmark for assessing the validity of a widely used point-particle model, where the particle dynamics results only from inertial and nonlinear drag forces. In the bulk of the channel, the first- and second-order moments of the particle velocity from the point-particle DNS agree well with those from the interface-resolved DNS. Close to the wall, however, most of the statistics show major qualitative differences. We show that this difference originates from the strong shear-induced lift force acting on the particles in the near-wall region. This mechanism is well captured by the lift force model due to Saffman (J. Fluid Mech., vol. 22 (2), 1965, pp. 385--400), while other widely used, more elaborate, approaches aiming at extending the lift model for a wider range of particle Reynolds numbers can actually underpredict the magnitude of the near-wall particle velocity fluctuations for the cases analysed here.