Strong Turbulent Buoyant Plumes. I. Similarity

Abstract

It is shown that similarity solutions in strong buoyant plumes (plane or axisymmctric) exist if a local characteristic turbulent diffusion coefficient varies inversely proportional to the square of the local gas density in the plume. The similarity formulation implies that the proper dependent variable for the temperature (density) defect is ΔT/₀(Δρ/ρ), where ΔT( Δρ) is the temperature (density) defect from the ambient temperature (density), T₀(ρ0), and ρ is the local density in the plume. The same variable is applicable further downstream from the source when the plume becomes weak. The form of the variable, ΔT/T₀, proposed for both strong and weak plumes is different from the form of the variable, ΔT/T( Δρ/ρ₀), previously used for weak plumes. Long experience with strong plumes from fires and recent experimental results of temperature variations along the plume axis support the use of the variable ΔT/T₀. The similarity solution is consistent with Morton's (1965) model of strong plumes and the form of the entrainment function for strong density variations in plumes or jets proposed by Ricou and Spalding (1961). In a subsequent paper, a simple model will be presented, based on the similarity solutions, to predict flame heights and the location of the virtual source in turbulent diffusion flames (momentum or buoyancy controlled). The model is similar to Steward's (1970), developed for buoyancy controlled flames.