A Numerical Analysis of the Effect of Condensation on Plume Rise

T. M. L. Wigley Department of Mechanical Engineering, University of Waterloo, Waterloo, Ontario, Canada

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Abstract

This paper presents the results of a numerical solution of the equations of moist plume rise and compares the trajectories of wet and dry cooling tower and scrubbed industrial plumes under a wide range of atmospheric stability conditions. Similar comparisons have been made previously by Wigley and Slawson, Hanna, and Weil, and the results of these authors are discussed. It is found that their results are all qualitatively correct, but that there are important quantitative differences between their results and the numerical solution. Previous approximate analytic results have shown that the critical lapse rate for the transition to unstable plume behavior for wet plumes is close to the saturated adiabatic lapse rate. The more-complete numerical solution confirms this result when one allows for the variation of the saturated adiabatic lapse rate with height. The approximate analytic formula for the maximum height of rise of dry plumes is also examined and found to overestimate plume rise by 6–20% when compared with the numerical solution.

Abstract

This paper presents the results of a numerical solution of the equations of moist plume rise and compares the trajectories of wet and dry cooling tower and scrubbed industrial plumes under a wide range of atmospheric stability conditions. Similar comparisons have been made previously by Wigley and Slawson, Hanna, and Weil, and the results of these authors are discussed. It is found that their results are all qualitatively correct, but that there are important quantitative differences between their results and the numerical solution. Previous approximate analytic results have shown that the critical lapse rate for the transition to unstable plume behavior for wet plumes is close to the saturated adiabatic lapse rate. The more-complete numerical solution confirms this result when one allows for the variation of the saturated adiabatic lapse rate with height. The approximate analytic formula for the maximum height of rise of dry plumes is also examined and found to overestimate plume rise by 6–20% when compared with the numerical solution.

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