On the entrainment assumption in Schatzmann's integral plume model

Teixeira, M. A. C. ORCID: https://orcid.org/0000-0003-1205-3233 and Miranda, P. M. A. (1997) On the entrainment assumption in Schatzmann's integral plume model. Applied Scientific Research, 57. pp. 15-42. ISSN 1573-1987 doi: 10.1007/BF02528762

Abstract/Summary

The behaviour of stationary, non-passive plumes can be simulated in a reasonably simple and accurate way by integral models. One of the key requirements of these models, but also one of their less well-founded aspects, is the entrainment assumption, which parameterizes turbulent mixing between the plume and the environment. The entrainment assumption developed by Schatzmann and adjusted to a set of experimental results requires four constants and an ad hoc hypothesis to eliminate undesirable terms. With this assumption, Schatzmann’s model exhibits numerical instability for certain cases of plumes with small velocity excesses, due to very fast radius growth. The purpose of this paper is to present an alternative entrainment assumption based on a first-order turbulence closure, which only requires two adjustable constants and seems to solve this problem. The asymptotic behaviour of the new formulation is studied and compared to previous ones. The validation tests presented by Schatzmann are repeated and it is found that the new formulation not only eliminates numerical instability but also predicts more plausible growth rates for jets in co-flowing streams.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/29257
Item Type	Article
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology No Reading authors. Back catalogue items
Publisher	Springer Verlag
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