ON VERTICAL TURBULENT BUOYANT JETS

Plane and round buoyant jets in a quiescent ambient have three distinc tive regions; an initial variable-density, non-buoyant region, a trans ition region and a final plume region. Decay laws in the first and thi rd regions can be derived from dimensional similarity considerations. However, the decay relations in the transition region are usually dete rmined empirically. This paper presents an approach whereby decay laws valid for all three regions are derived for plane and round buoyant j ets. The analysis is carried out by assuming self-preservation of the mean field in each of the regions and Gaussian error distributions for the mean properties, With this formulation, the eddy diffusivities fo r momentum and temperature (or mass fraction) are determined by solvin g the turbulent mean flow equations subject to appropriate boundary co nditions and are found to vary along and across the jet. An auxiliary equation is derived by requiring the eddy viscosity to correctly appro ach its corresponding limiting value for an incompressible free plane or round jet. The auxiliary equation thus derived is physically relate d to jet entrainment. Growth rate and decay laws are deduced and they correctly predict their dependence on the jet density ratio in the fir st region and the densimetric Froude number in the third region. Calcu lations of decays of centerline properties in these two regions correl ate well with plane and round jet measurements. On the other hand, dec ays of centerline properties in the transition region are dependent on both the jet density ratio and the densimetric Froude number and are in good agreement with plane and round jet data.