Buoyant formation number of a starting buoyant jet

Understanding the influence of buoyancy on the formation number is important for analyzing the development of a starting buoyant jet and the interactions between its vortex ring and trailing stem. Numerical simulations with a large-eddy simulation model are performed to reproduce the starting buoyant jet in conditions ranging from pure jet to lazy plume. From the results, an improved method to determine the formation number is proposed based on the occurrence of a step jump in the vortex ring circulation. A comparison of the numerical results with the experimental data for a starting pure jet is first performed. The widely accepted formation number (approximate to 4.0) is obtained, which implies that the method is satisfactory. The effect of buoyancy on the formation number is then investigated for two turbulent discharge conditions of Re=2000 and 2500 and with a wide range of buoyancy flux. Best-fit results are obtained that correlate the formation number with the Richardson number. Finally, a slug model that incorporates buoyancy is developed to allow prediction of the buoyant formation number for the starting buoyant jet using a limiting value of 0.33 for the dimensionless energy, which is the same value for a pure jet.