Errors from Using Conservation of Buoyancy Concept in Plume Computations

The conservation of buoyancy concept as currently applied to buoyant jets and plumes in water is reviewed with regard to its origin, validity, and accuracy. Although the original buoyant plume model was based on the assumption of a constant thermal coefficient of volumetric expansion, and thus was limited to temperature differences of a few degrees, the original model has been widely applied to cases involving temperature differences as high as 17°C (30.6°F). Such application results in buoyancy forces which are significantly larger than the more accurate values based on models using conservation of energy instead of buoyancy. In the case of the computed trajectories the errors are most noticeable for lower ambient temperatures and lower jet exit velocities. The basic point is that conservation of buoyancy is an approximation and not a fundamental conservation principle. Because of the current use of numerical solutions to the governing equations there is no real justification for its use in place of the more rigorous conservation of energy equation.