Mixing of dense fluid in a turbulent pipe flow Part 2. Dependence of transfer coefficients on local stability

Abstract

This paper continues an investigation into the mixing of a dense layer of salt solution in a turbulent pipe flow in order to obtain a more detailed understanding of the underlying physical processes. The effect of the density difference on the velocity profile in a sloping pipe is calculated using a simplified model, and the results compared with direct measurements obtained by timing streaks of dye at various levels in the pipe. These velocity profiles are also used in conjunction with density profiles to estimate the dependence of the transfer coefficients for salt and momentum KS and KM, on stability.It is found that KS is much more greatly affected by the density gradient than KM, and that the ratio KS/KM may be represented, to the accuracy of the experiments, as a function of the local Richardson Number Ri. The results agree with what is known of KS/KM in neutral and very stable conditions, and they confirm an earlier prediction by Ellison that the critical flux Richardson number, at which KS becomes zero, is much less than unity.Finally, a crude semi-empirical method is outlined which indicates how the new measurements of the transfer coefficients may be related to the overall properties of the flow discussed in the first part of the paper.