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Fluxes across double-diffusive interfaces: a one-dimensional-turbulence study

Published online by Cambridge University Press:  12 April 2011

ESTEBAN GONZALEZ-JUEZ ,
ALAN R. KERSTEIN  and
DAVID O. LIGNELL
ESTEBAN GONZALEZ-JUEZ
Affiliation:
Combustion Research Facility, Sandia National Laboratories, Livermore, CA 94551-0969, USA
ALAN R. KERSTEIN*
Affiliation:
Combustion Research Facility, Sandia National Laboratories, Livermore, CA 94551-0969, USA
DAVID O. LIGNELL
Affiliation:
Department of Chemical Engineering, Brigham Young University, Provo, UT 84602, USA
*
†Email address for correspondence: [email protected]
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Abstract

This work is a parametric study of the fluxes of heat and salt across unsheared and sheared double-diffusive interfaces using one-dimensional-turbulence (ODT) simulations. It is motivated by the need to understand how these fluxes scale with parameters related to the fluid molecular properties and background shear. Comparisons are made throughout with previous models and available measurements. In unsheared interfaces, ODT simulations show that the dimensionless heat flux Nu scales with the stability parameter Rρ, Rayleigh number Ra and Prandtl number Pr as Nu ~ (Ra/Rρ)0.37±0.03 when Pr varies from 3 to 100 and as Nu ~ (Ra/Rρ)0.31Pr0.22±0.04 when Pr varies from 0.01 to 1. Here Ra/Rρ can be seen as the ratio of destabilizing and stabilizing effects. The simulation results also indicate that the ratio of salt and heat fluxes Rf is independent of Pr, scales with the Lewis number Le as Rf ~ Le0.41±0.04 when Rρ is large enough and deviates from this expression for low values of Rρ, when the interface becomes heavily eroded. In sheared interfaces, the simulations show three flow regimes. When the Richardson number Ri ≪ 1, shear-induced mixing dominates, the heat flux scales with the horizontal velocity difference across the interface and Rf = Rρ. Near Ri ~ 1 the heat and salt fluxes are seen to increase abruptly as the shear increases. The flow structure and scaling of the fluxes are similar to those of unsheared interfaces when Ri ≫ 1.

JFM classification

Turbulent Flows: Turbulent convection Turbulent Flows: Turbulence modelling
Type
Papers
Information
Journal of Fluid Mechanics , Volume 677 , 25 June 2011 , pp. 218 - 254
Copyright
Copyright © Cambridge University Press 2011

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References

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