Turbulent buoyant jets into stratified or flowing ambient fluids
Creators: name: Fan, Loh-Nien
Publisher: name: California Institute of Technology
Year: 1967

description: Theoretical and experimental studies were made on two classes of buoyant jet problems, namely:

1) an inclined, round buoyant jet in a stagnant environment with linear density-stratification;

2) a round buoyant jet in a uniform cross stream of homogeneous density.

Using the integral technique of analysis, assuming similarity, predictions can be made for, jet trajectory, widths, and dilution ratios, in a density-stratified or flowing environment. Such information is of great importance in the design of disposal systems for sewage effluent into the ocean or waste gases into the atmosphere. 

The present study of a buoyant jet in a stagnant environment has extended the Morton type of analysis to cover the effect of the initial angle of discharge. Numerical solutions have been presented for a range of initial conditions. Laboratory experiments were conducted for photographic observations of the trajectories of dyed jets. In general the observed jet forms agreed well with the calculated trajectories and nominal half widths when the value of the entrainment coefficient was taken to be α = 0.082, as previously suggested by Morton. 

The problem of a buoyant jet in a uniform cross stream was analyzed by assuming an entrainment mechanism based upon the vector difference between the characteristic jet velocity and the ambient velocity. The effect of the unbalanced pressure field on the sides of the jet flow was approximated by a gross drag term. Laboratory flume experiments with sinking jets which are directly analogous to buoyant jets were performed. Salt solutions were injected into fresh water at the free surface in a flume. The jet trajectories, dilution ratios and jet half widths were determined by conductivity measurements. The entrainment coefficient, α, and drag coefficient, Cd, were found from the observed jet trajectories and dilution ratios. In the ten cases studied where jet Froude number ranged from 10 to 80 and velocity ratio (jet: current) k from 4 to 16, a varied from 0.4 to 0.5 and Cd from 1.7 to 0.1. The jet mixing motion for distances within 250D was found to be dominated by the self-generated turbulence, rather than the free-stream turbulence. Similarity of concentration profiles has also been discussed.
description: © 1967 W. M. Keck Laboratory of Hydraulics and Water Resources. California Institute of Technology. 

The writer wishes to express his deep gratitude to his advisor, Professor Norman H. Brooks, for suggestion of this project as well as guidance and encouragement offered throughout the investigation. He would also like to thank Dr. Robert C. Y. Koh for discussions and help given in the early stage of this study. To Professors Vito A. Vanoni and Fredric Raichlen he expresses thanks for their kind advice and assistance. For design and construction of laboratory equipment, the writer is much indebted to Mr. Elton F. Daly, supervisor of the shop and laboratory. The assistance of Mr. Robert L. Greenway is also much appreciated.
The writer would like to express his gratitude to Messrs.
Jiin-jen Lee, Josephat K. Okoye and William W. Owens, Graduate Research Assistants, for their assistance in performing laboratory experiments and reducing data; to Mr. Carl T. Eastvedt for taking motion pictures and laboratory photographs; to Mr. Carl A. Green, Jr., for preparation of graphs and to Mrs. Patricia Rankin for her typing of the manuscript. This research was supported by research grants WP-00428 and WP-00680 of the U. S. Public Health Service, National Institutes of Health, and research grant WP-01256-01 of the U.S. Federal Water Pollution Control Administration. The experiments were conducted in the W. M. Keck Laboratory of Hydraulics and Water Resources at the California Institute of Technology. This report was submitted by the writer in May, 1967, as a thesis with the same title to the California Institute of Technology
in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Civil Engineering.
description: Submitted - KH-R-15.pdf