Improved prediction of bending plumes

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Abstract
Integral plume models harbor a fundamental, often significant error because the standard implementation of control volumes, or elements, is inconsistent with the overall geometry of the problem. The error, called the negative volume anomaly, occurs irregularly, being contingent on there being strong bending and large plume diameter. When present it causes entrainment, i.e., dilution, to be overestimated. It is of practical significance because dilution estimates are used to design and assess diffusers. The anomaly arises when constructed round element faces intersect, as they do when plume diameters are large and plume bending is pronounced, inadvertently generating negative volume and a faulty integration of the governing equations. A modified control volume is proposed to correct the error, and its performance is demonstrated. Its development yields clues to other plume behavior, for example, how plume trajectories may respond to the asymmetrical addition of mass and its distribution in the element.

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