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Turbulent flow over a liquid layer revisited: multi-equation turbulence modelling

Published online by Cambridge University Press:  25 August 2011

Lennon Ó Náraigh ,
Peter D. M. Spelt  and
Tamer A. Zaki
Lennon Ó Náraigh*
Affiliation:
School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland
Peter D. M. Spelt
Affiliation:
Department of Chemical Engineering, Imperial College London SW7 2AZ, UK Département Mécanique, Université Claude Bernard Lyon 1, France Laboratoire de la Mécanique des Fluides & Acoustique (LMFA), CNRS, Ecully, France
Tamer A. Zaki
Affiliation:
Department of Mechanical Engineering, Imperial College London SW7 2AZ, UK
*
†Email address for correspondence: lennon.onaraigh@ucd.ie
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Abstract

The mechanisms by which turbulent shear flow causes waves on a gas–liquid interface are studied analytically, with a critical assessment of the possible role played by wave-induced Reynolds stresses (WIRSs). First, turbulent flow past a corrugated surface of a small slope is analysed; the surface can either be stationary or support a travelling wave. This problem serves as a useful model because direct numerical simulation (DNS) and experimental data are available to test the analysis, and because this picture is itself a model for the fully coupled two-layer problem. It is demonstrated that the WIRSs play no significant role in shear-driven turbulent flow past a moving wavy wall, and that they alter the structure of the flow only in a quantitative fashion in the pressure-driven case. In the shear-driven case in particular, excellent agreement is obtained with previously reported DNS results. Two closure assumptions are made in our model: the first concerns the wave-induced dissipation of turbulent kinetic energy; the second concerns the importance of rapid distortion. The results of our calculations are sensitive to the assumptions used to close the wave-induced dissipation but are insensitive to the details of the rapid-distortion modelling. Finally, the fully coupled two-layer problem is addressed in the setting of waves of small amplitude, where it is demonstrated that the WIRSs do not play a significant role in the growth of interfacial waves, even at relatively high Reynolds numbers. Again, good agreement is obtained between data from experiments and DNS.

JFM classification

Multiphase and Particle-laden Flows: Gas/liquid flow Instability: Instability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 683 , 25 September 2011 , pp. 357 - 394
Copyright
Copyright © Cambridge University Press 2011

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