On the Similarity of Velocity and Temperature Profiles In Strong (Variable Density) Turbulent Buoyant Plumes

Abstract

Various similarity hypothesis for axisymmetric turbulent buoyant plumes with large density differences (strong plumes) are discussed in this paper, In contrast to buoyant flows having small density variations (Boussinesqu limit), controversies remain in modeling strong buoyant flows for which (▵e/e₀=(e₀-e)/e₀=O(1)), We review: 1) previous attempts to model such flows. 2) experimental evidence that the flow properties for strong plumes have similar profiles. and 3) a consistent derivation of the similarity relations. A significant conclusion from this analysis is that the similarity profiles for velocity and density defect (or temperature rise) should be expressed in terms of an average stream function or equivalently the Howarth variable (e.g.,n=∫₀ ^r(e/e₀rdr for axisymmetric plumes) which includes variable density effects. Others have suggested, instead, that the plume property profiles might be expressed by using a laboratory radial coordinate normalized by a local characteristic flow width, in analogy to weak buoyant plumes. We demonstrate that these latter similarity assumptions are inconsistent with the conservation equations for both overall momentum flow and overall mass flow. In addition, these latter similarity arguments encounter difficulties with generally accepted entrainment laws for strong plumes. These problems are overcome by using the somewhat more cumbersome stream function similarity. However, we point out that final resolution of the controversy may have to await definitive experimental examination of the radial similarity in strong plumes.