Validity of several approximations for the turbulent buoyant jet in a stagnant neutrally-stratified ambient

A series of approximations are usually made in deriving integral model equations for the dispersion of a round turbulent buoyant jet into a stagnant neutrally-stratified ambient fluid. The magnitudes of differences in model predictions caused by making four of these approximations are calculated as a function of the initial densimetric Froude number and the initial relative density difference. The four approximations studied are (1) the Boussinesq approximation, (2) the use of a common Gaussian width for both mean axial velocity and mean temperature (or concentration) excess, (3) the neglect of fluctuation-correlation terms, and (4) the assumption of a linear relationship between excess density and excess temperature (or concentration). The four approximations are studied singly and then cumulatively as the predictions of the two models, one with and one without all approximations, are compared to seven low Froude number data cases. Results show that the Boussinesq approximation produces percentage differences in predictions which are about half of the initial relative density difference expressed in percentage. Use of a common Gaussian width for velocity and temperature produces differences from 6% to 30% depending on the entrainment assumption used. Fluctuation correlation effects rarely exceed 8%. Lastly, at Froude numbers below about 10 the correct nonlinear equation of state must often be used for heated waste jets to acheive accurate results, and the correct air equation of state may also be needed for low Froude number heated air jets, depending on the initial diameter and velocity