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Keywords:

  • turbulent transport;
  • Lagrangian methods;
  • source diffusion

Abstract

Turbulent dispersion of a scalar emitted from a source in homogeneous turbulence has been placed in a solid theoretical context by Taylor, Saffman, and Batchelor. However, the case of source diffusion in the near-wall region, where the turbulence is not Gaussian, and the effects of the molecular Prandtl number (Pr) on the effective dispersion have not been explored to similar depth. The present work studies the behavior of elevated sources in turbulent channel flow and in turbulent-plane Couette flow. The trajectories of heat markers are monitored in space and time as they move in a hydrodynamic field created by a direct numerical simulation. The fluids span several orders of magnitude of Pr (or Schmidt number), Pr = 0.1, 0.7, 3, 6, 10, 100, 200, 500, 1000, 2400, 7500, 15,000, and 50,000 (liquid metals, gases, liquids, lubricants, and electrochemical fluids). It is found that the molecular Pr has negligible effects in the evolution of the marker cloud for Pr ≥ 3, when the point of marker release is away from the viscous wall sublayer. However, when the markers are released close to the wall, the molecular effects on dispersion are strong. It is also found that total effective dispersion is higher in the case of plane Couette flow, where the total stress across the channel is constant. © 2005 American Institute of Chemical Engineers AIChE J, 2005