Effects of ambient crossflows and density stratification on the characteristic behavior of round turbulent buoyant jets

Abstract

This investigation considers a round, turbulent buoyant jet in an ambient crossflow that is either of uniform density or with a linear density stratification. The primary emphasis is the development of a fundamental understanding of the jet properties that are of interest in engineering design problems. These include jet trajectories, characteristic dilutions, and in the case of a stratified crossflow, the maximum and equilibrium heights of rise. Most previous studies of similar buoyant jet flows have used the integral method to solve for the jet characteristics. This approach requires an assumed relation for the rate of entrainment of ambient fluid by the jet, and also depends upon experimental evidence to estimate values for the coefficients in the assumed relation. Most previous experimental studies have been directed toward evaluating entrainment coefficients and have not considered a systematic investigation of the effects of the various jet and ambient flow parameters. A major objective of this investigation is to provide a basis for the interpretation and extension of the results from previous theoretical and experimental investigations. A systematic dimensional analysis is performed to define the basic problem and to provide approximate solutions without using the integral equations. The analysis indicates the types of experiments necessary to adequately describe general buoyant jet behavior and also provides a framework for the presentation of experimental data. The approximate solutions for the jet characteristics were derived from the dimensional analysis by considering asymptotic descriptions of a general buoyant jet as different effects become predominant in determining the flow behavior. The limiting cases considered are for the jet behavior controlled by either its initial momentum or by its buoyancy for situations where the ambient velocity either is relatively large or approaches zero. Combinations of these four asymptotic descriptions can be used to approximately describe a general buoyant jet. Several different types of flow behavior can be expected, depending upon the relative magnitudes of various characteristic length scales associated with these buoyant jet flows. These different types of flow can be compared to the theoretical solutions proposed by other researchers, providing a basis for better understanding previous research. Experiments were performed to confirm the asymptotic relations developed in the analysis, to evaluate the coefficients in the relations, and to determine the limits of their applicability. The experimental configuration was a salt water jet discharged downward into a tank of less dense fluid with either uniform density or linear density stratification. The Boussinesq approximation implies that these results will be comparable to a buoyant jet rising in a less dense ambient fluid. The crossflow was simulated by towing the jet source along the water surface in the tank. Jet trajectories and dilutions were measured for the experiments with an unstratified crossflow. For the experiments performed with the tank stratified, maximum and equilibrium heights of rise, a few trajectories, and jet dilutions were measured. The results of these various experimental measurements are presented in a unified manner to facilitate the application to design problems. The experimental evidence indicated that the coefficients in the asymptotic relations were somewhat dependent upon the initial jet volume flux, an observation that has not been previously noted by other researchers. This variation can be expected from the dimensional analysis and is shown to be significant in some instances.

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