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Controversial turbulent Schmidt number value in particle-laden boundary layer flows

J. Chauchat*, D. Hurther, and T. Revil-Baudard

Z. Cheng† and T.-J. Hsu

  • Univ. Grenoble Alpes, CNRS, Grenoble INP, LEGI, 38000 Grenoble, France

  • Civil and Environmental Engineering, Center for Applied Coastal Research, University of Delaware, Newark, Delaware 19711, USA

  • *julien.chauchat@univ-grenoble-alpes.fr
  • †Now at Convergent Science Inc., Madison, WI 53719, USA.
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Phys. Rev. Fluids 7, 014307 – Published 18 January, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.014307

Abstract

One of the most enigmatic science questions concerning inertial particle transport by a turbulent boundary layer flow is the value of the turbulent Schmidt number defined as the ratio of turbulent eddy viscosity to particle concentration diffusivity. Using direct acoustic measurement of turbulent particle flux profile, and two-phase flow turbulence-resolving numerical simulation, it is demonstrated that turbulent dispersion of particles is reduced rather than enhanced as predicted by many existing literature models. The explanation lies in the misleading assumption of settling velocity in quiescent water to estimate the turbulent particle diffusivity, while direct measurements and simulations of turbulent particle flux support the occurrence of settling retardation. The analysis presented herein suggests that the value of the turbulent Schmidt number is always larger than unity with values between 3 and 4 based on the directly measured turbulent particle flux. The observed settling reduction cannot be explained by the well-known hindrance effects related to particle concentration. This effect seems to be related to turbulence-particle interactions and correlates more with the Stokes number. Finally, our parameters, namely, the turbulent Schmidt number higher than unity, modified von Kármán constant, and settling retardation, are successfully tested for the modeling of particle concentration profile using the well-known Rouse formulation. This result suggests that alternative parametrizations are possible to reduce the degree of empiricism to predict suspended particle transport by a boundary layer flow.

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Phys. Rev. Fluids 7, 014307– Published 18 January, 2022
  • Received 18 December 2020
  • Accepted 29 November 2021
Article part of CHORUS
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