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An algebraic model for the turbulent flux of a passive scalar

Published online by Cambridge University Press:  26 April 2006

Michael M. Rogers ,
Nagi N. Mansour  and
William C. Reynolds
Michael M. Rogers
Affiliation:
NASA Ames Research Center, Moffett Field, CA 94035, USA
Nagi N. Mansour
Affiliation:
NASA Ames Research Center, Moffett Field, CA 94035, USA
William C. Reynolds
Affiliation:
NASA Ames Research Center, Moffett Field, CA 94035, USA Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA
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Abstract

The behaviour of passive-scalar fields resulting from mean scalar gradients in each of three orthogonal directions in homogeneous turbulent shear flow has been studied using direct numerical simulations of the unsteady incompressible Navier-Stokes equations with 128 × 128 × 128 grid points. It is found that, for all orientations of the mean scalar gradient, the sum of the pressure-scalar gradient and velocity gradient-scalar gradient terms in the turbulent scalar flux balance equation are approximately aligned with the scalar flux vector itself. In addition, the time derivative of the scalar flux is also approximately aligned with the flux vector for the developed fields (corresponding to roughly constant correlation coefficients). These alignments lead directly to a gradient transport model with a tensor turbulent diffusivity. The simulation results are used to fit a dimensionless model coefficient as a function of the turbulence Reynolds and Péclet numbers. The model is tested against two different passive-scalar fields in fully developed turbulent channel flow (also generated by direct numerical simulation) and is found to predict the scalar flux quite well throughout the entire channel.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 203 , June 1989 , pp. 77 - 101
Copyright
© 1989 Cambridge University Press

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