Effects of settling on inertial particle slip velocity statistics in wall-bounded flows

Developing reduced-order models for the transport of solid particles in turbulence typically requires a statistical description of the particle-turbulence interactions. In this work, we utilize a statistical framework to derive continuum equations for the moments of the slip velocity of inertial, settling Lagrangian particles in a turbulent boundary layer. Using coupled Eulerian-Lagrangian direct numerical simulations, we then identify the dominant mechanisms controlling the slip velocity variance, and find that for a range of Stokes number (Formula presented), Settling number (Formula presented) and Reynolds number (Formula presented) (based on frictional scales),the slip variance is primarily controlled by local differences between the ‘seen’ variance and the particle velocity variance, while terms appearing due to the inhomogeneity of the turbulence are subleading until (Formula presented) becomes large. We also consider several comparative metrics to assess the relative magnitudes of the fluctuating slip velocity and the mean slip velocity, and we find that the vertical mean slip increases rapidly with (Formula presented), rendering the variance relatively small - an effect found to be most substantial for (Formula presented). Finally, we compare the results with a model of the acceleration variance (Berk & Coletti 2021 J. Fluid Mech. 917, A47) based the concept of a response function described in Csanady (1963 J. Atmos. Sci. 20, 201-208), highlighting the role of the crossing trajectories mechanism. We find that while there is good agreement for low (Formula presented), systematic errors remain, possibly due to implicit non-local effects arising from rapid particle settling and inhomogeneous turbulence. We conclude with a discussion of the implications of this work for modelling the transport of coarse dust grains in the atmospheric surface layer.

Duke Scholars

Author Andrew Bragg Civil and Environmental Engineering