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Turbophoresis of small inertial particles: theoretical considerations and application to wall-modelled large-eddy simulations

Published online by Cambridge University Press:  26 November 2019

Perry L. Johnson Open the ORCID record for Perry L. Johnson [Opens in a new window] ,
Maxime Bassenne Open the ORCID record for Maxime Bassenne [Opens in a new window]  and
Parviz Moin
Perry L. Johnson*
Affiliation:
Center for Turbulence Research, Stanford University, Stanford, CA94305, USA
Maxime Bassenne
Affiliation:
Center for Turbulence Research, Stanford University, Stanford, CA94305, USA
Parviz Moin
Affiliation:
Center for Turbulence Research, Stanford University, Stanford, CA94305, USA
*
†Email address for correspondence: perryj@stanford.edu
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Abstract

In wall-bounded turbulent flows, the wall-normal gradient in turbulence intensity causes inertial particles to move preferentially toward the wall, leading to elevated concentration levels in the viscous sublayer. At first glance, wall-modelled large-eddy simulations may seem ill suited for accurately simulating this behaviour, given that the sharp gradients and coherent structures in the viscous sublayer and buffer region are unresolved in this approach. In this paper, a detailed inspection of conservation equations describing the influence of turbophoresis and near-wall structures on particle concentration profiles reveals a more nuanced view depending on the friction Stokes number. The dynamics of low and moderate Stokes number particles indeed depends strongly on the complex spatio-temporal details of streaks, ejections, and sweeps in the near-wall region. This significantly impacts the near-wall particle concentration through a biased sampling effect which provides a net force away from the wall on the particle ensemble caused by the tendency of inertial particles to accumulate in low-speed ejection regions. At higher Stokes numbers, however, this biased sampling is of minimal importance, and the particle concentration becomes inversely proportional to the wall-normal particle velocity variance at a given distance from the wall. As a result, wall-modelled large-eddy simulations can predict concentration profiles with more accuracy in the high Stokes number regime than low Stokes numbers simply by modifying the interpolation scheme for particles between the first grid point and the boundary. However, accurate representation of low and moderate Stokes number particles depends critically on information not present in standard wall-modelled large-eddy simulations.

JFM classification

Multiphase and Particle-laden Flows: Particle/fluid flow Turbulent Flows: Turbulence simulation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 883 , 25 January 2020 , A27
Copyright
© 2019 Cambridge University Press

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