Dispersion in slowly moving fluids.

Abstract

This work is concerned with the characterization of slowly moving fluids and was carried out on the flow of water through a narrow sedimentation tank. Dispersion in the type of flow structure involved is caused mainly by the presence of large eddies and, due to the fact that shear stresses are small, these eddies persist for a considerable period of time. Two flow models are presented : The first model assumes the X- Y- velocity component pair to form a discrete state Markov process in time and dispersion equations for the mean concentration at a point, the variance as well as concentration cross correlations are generated. In the second model the velocity fluctuation components are assumed to be independent, time-stationary Markov processes with normal probability density functions. The stochastic differential equation describing dispersion of tracer is formulated with and without the effect of molecular diffusion and solutions to both cases are presented. Comparison of the model with experimental data obtained from tracer and anemometer measurements show that the model is capable of describing mean dispersion in a relatively small region of the tank and that the tracer experiments were insensitive to molecular diffusion.