Effects of the Boussinesq Approximation on the Results of Strongly-Buoyant Plume Calculations

M. Schatzmann Meteorological Institute, University of Hamburg, Hamburg, W. Germany

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A. J. Policastro Environmental Research Division, Argonne National Laboratory, Argonne, IL 60439

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Abstract

Nearly all mathematical models which are commonly used to predict the dispersion of chimney gases in the atmosphere or heated water discharges in the aquatic environment employ the so-called Boussinesq approximation. It is part of this approximation that density variations appear solely in the buoyancy term of the momentum equation and are neglected in all other terms.

The exact limits of validity of the Boussinesq approximation and the precise effects the simplifications have on model performance are known only qualitatively.

The objective of this paper is to present, for a variety of industrial stack plumes with different initial density ratios, comparisons of predictions which have been obtained employing 1) a model which makes the Boussinesq approximation and 2) a version of the same model in which this approximation has not been introduced. It was found that the difference in jet-property predictions between the two models increases with increasing initial density defect ratio. In the case of the largest ratio tested (Δρ/ρ∞= 0.5), the maximum height of rise predicted with the Boussinesq approximated model was ∼20% larger than predicted with the non-Boussinesq approximated model. These differences in predictions are, of course, to some extent model-specific but provide, nevertheless, a first quantitative estimate on how the Boussinesq approximation affects the performance of plume models.

Abstract

Nearly all mathematical models which are commonly used to predict the dispersion of chimney gases in the atmosphere or heated water discharges in the aquatic environment employ the so-called Boussinesq approximation. It is part of this approximation that density variations appear solely in the buoyancy term of the momentum equation and are neglected in all other terms.

The exact limits of validity of the Boussinesq approximation and the precise effects the simplifications have on model performance are known only qualitatively.

The objective of this paper is to present, for a variety of industrial stack plumes with different initial density ratios, comparisons of predictions which have been obtained employing 1) a model which makes the Boussinesq approximation and 2) a version of the same model in which this approximation has not been introduced. It was found that the difference in jet-property predictions between the two models increases with increasing initial density defect ratio. In the case of the largest ratio tested (Δρ/ρ∞= 0.5), the maximum height of rise predicted with the Boussinesq approximated model was ∼20% larger than predicted with the non-Boussinesq approximated model. These differences in predictions are, of course, to some extent model-specific but provide, nevertheless, a first quantitative estimate on how the Boussinesq approximation affects the performance of plume models.

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