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Mixed convection in turbulent channels with unstable stratification

Published online by Cambridge University Press:  25 May 2017

Sergio Pirozzoli Open the ORCID record for Sergio Pirozzoli [Opens in a new window] ,
Matteo Bernardini ,
Roberto Verzicco Open the ORCID record for Roberto Verzicco [Opens in a new window]  and
Paolo Orlandi
Sergio Pirozzoli*
Affiliation:
Dipartimento di Ingegneria Meccanica e Aerospaziale, Sapienza Università di Roma, Via Eudossiana 18, 00184 Roma, Italy
Matteo Bernardini
Affiliation:
Dipartimento di Ingegneria Meccanica e Aerospaziale, Sapienza Università di Roma, Via Eudossiana 18, 00184 Roma, Italy
Roberto Verzicco
Affiliation:
Dipartimento di Ingegneria Industriale, Università di Roma Tor Vergata, 00133 Roma, Italy Physics of Fluids Group, University of Twente, 7500 AE Enschede, The Netherlands
Paolo Orlandi
Affiliation:
Dipartimento di Ingegneria Meccanica e Aerospaziale, Sapienza Università di Roma, Via Eudossiana 18, 00184 Roma, Italy
*
†Email address for correspondence: [email protected]
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Abstract

We study turbulent flows in pressure-driven planar channels with imposed unstable thermal stratification, using direct numerical simulations in a wide range of Reynolds and Rayleigh numbers and reaching flow conditions which are representative of fully developed turbulence. The combined effect of forced and free convection produces a peculiar pattern of quasi-streamwise rollers occupying the full channel thickness, with aspect ratio considerably higher than unity; it has been observed that they have an important redistributing effect on temperature and momentum, providing for a substantial fraction of the heat and momentum flux at bulk Richardson numbers larger than $0.01$. The mean values and the variances of the flow variables do not appear to follow Prandtl’s scaling in the free-convection regime, except for the temperature and vertical velocity fluctuations, which are more directly affected by wall-attached turbulent plumes. We find that the Monin–Obukhov theory nevertheless yields a useful representation of the main flow features. In particular, the widely used Businger–Dyer flux-profile relationships are found to provide a convenient way of approximately accounting for the bulk effects of friction and buoyancy, although the individual profiles may have wide scatter from the alleged trends. Significant deviations are found in direct numerical simulations with respect to the commonly used parametrization of the momentum flux in the light-wind regime, which may have important practical impact in wall models of atmospheric dynamics. Finally, for modelling purposes, we devise a set of empirical predictive formulae for the heat flux and friction coefficients, which are within approximately $10\,\%$ standard deviation from the numerical results in a wide range of flow parameters.

JFM classification

Turbulent Flows: Stratified turbulence Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulent convection
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Papers
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Journal of Fluid Mechanics , Volume 821 , 25 June 2017 , pp. 482 - 516
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© 2017 Cambridge University Press 

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