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A numerical and analytical study of the effect of aspect ratio on the behavior of a round thermal

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Abstract

A round thermal is formed when an element of buoyant fluid is released instantaneously into a quiescent ambient. Although the thermal spreading rate is of primary importance to mathematical modeling, the reported values in the literature vary greatly. To identify possible factors affecting the thermal spreading rate, we investigated the effect of different initial conditions numerically by solving the unsteady Reynolds-averaged Navier–Stokes equations with a two-equation turbulence closure. The initial aspect ratio (i.e. length-to-diameter ratio) of the thermal was varied between 0.125–4.0, and the initial density differences was changed from 1 to 10 %. Results show that the spreading rate is greatly affected by the initial aspect ratio, which also explains the variations in earlier reported values. Following the numerical study, an analytical model using buoyant vortex ring theory is developed to predict the spreading rate of a thermal. The predictions show good agreement with the results from both the numerical simulations and previous experimental studies. Another simple analytical model is also presented to approximate the thermal induced flow, and is validated using the numerical simulations.

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Acknowledgments

This research was supported by the National Research Foundation Singapore through the Singapore-MIT Alliance for Research and Technology’s CENSAM IRG research programme.

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Authors and Affiliations

  1. Center for Environmental Sensing and Modeling, Singapore-MIT Alliance for Research and Technology Centre, 1 CREATE Way, Singapore , 138602, Singapore

    Adrian C. H. Lai

  2. DHI-NTU Centre, Nanyang Environment and Water Research Institute, Nanyang Technological Univeristy, 1 Cleantech Loop, Singapore , 637141, Singapore

    Bing Zhao & Adrian Wing-Keung Law

  3. Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA , 02139, USA

    E. Eric Adams

Authors
  1. Adrian C. H. Lai
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  2. Bing Zhao
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  4. E. Eric Adams
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Correspondence to Adrian C. H. Lai.

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Lai, A.C.H., Zhao, B., Law, A.WK. et al. A numerical and analytical study of the effect of aspect ratio on the behavior of a round thermal. Environ Fluid Mech 15, 85–108 (2015). https://doi.org/10.1007/s10652-014-9362-3

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  • DOI: https://doi.org/10.1007/s10652-014-9362-3

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