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Length of near-wall plumes in turbulent convection

Published online by Cambridge University Press:  20 September 2011

Baburaj A. Puthenveettil ,
G. S. Gunasegarane ,
Yogesh K. Agrawal ,
Daniel Schmeling ,
Johannes Bosbach  and
Jaywant H. Arakeri
Baburaj A. Puthenveettil*
Affiliation:
Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai, 600036, India
G. S. Gunasegarane
Affiliation:
Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai, 600036, India
Yogesh K. Agrawal
Affiliation:
Department of Mechanical Engineering, National Institute of Technology, Durgapur, 713209, India
Daniel Schmeling
Affiliation:
Institute of Aerodynamics and Flow Technology, German Aerospace Center (DLR), Göttingen, 37073, Germany
Johannes Bosbach
Affiliation:
Institute of Aerodynamics and Flow Technology, German Aerospace Center (DLR), Göttingen, 37073, Germany
Jaywant H. Arakeri
Affiliation:
Department of Mechanical Engineering, Indian Institute of Science, Bangalore, 560012, India
*
†Email address for correspondence: apbraj@iitm.ac.in
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Abstract

We present planforms of line plumes formed on horizontal surfaces in turbulent convection, along with the length of line plumes measured from these planforms, in a six decade range of Rayleigh numbers () and at three Prandtl numbers (). Using geometric constraints on the relations for the mean plume spacings, we obtain expressions for the total length of near-wall plumes on horizontal surfaces in turbulent convection. The plume length per unit area (), made dimensionless by the near-wall length scale in turbulent convection (), remains constant for a given fluid. The Nusselt number is shown to be directly proportional to for a given fluid layer of height . The increase in has a weak influence in decreasing . These expressions match the measurements, thereby showing that the assumption of laminar natural convection boundary layers in turbulent convection is consistent with the observed total length of line plumes. We then show that similar relationships are obtained based on the assumption that the line plumes are the outcome of the instability of laminar natural convection boundary layers on the horizontal surfaces.

JFM classification

Convection: Buoyant boundary layers Convection: Plumes/thermals Turbulent Flows: Turbulent convection
Type
Papers
Information
Journal of Fluid Mechanics , Volume 685 , 25 October 2011 , pp. 335 - 364
Copyright
Copyright © Cambridge University Press 2011

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