Numerical solutions of turbulent buoyant jet problems

Theoretical solutions were obtained for four classes of turbulent buoyant jet problems, namely, 1) an inclined, round buoyant jet in a stagnant, uniform ambient fluid; 2) an inclined, round buoyant jet in a stagnant ambient fluid with linear density-stratification; 3) an inclined, slot buoyant jet in a stagnant, uniform ambient fluid; 4) an inclined, slot buoyant jet in a stagnant ambient fluid with linear density-stratification. This report is a summary of the numerical simulations on buoyant jets in stagnant environments carried out in connection with previous investigations by Fan (10), Fan and Brooks (12) and Brooks and Koh (8). Using the integral type of analysis, assuming similarity, predictions can be made for jet trajectory, widths, and dilution ratios, in a uniform or density-stratified environment without ambient currents. Numerical solutions have been presented in dimensionless form for a wide range of initial conditions including the effect of the initial angle of discharge. Problems with non-linear density profiles are not readily treated in generalized non-dimensional form. Rather it is more feasible to make case by case calculations using dimensional variables. A program for such calculations for a round jet is available in a technical memorandum by Ditmars (16). These solutions are useful in the design of disposal systems for sewage effluent into the ocean or cooling water into a lake.