Vertical mass transfer in open channel flow

The vertical mass transfer coefficient and particle fall velocity were determined in an open channel shear flow. Three dispersants, dye, fine sand and medium sand, were used with each of three flow conditions. The dispersant was injected as a continuous line source across the channel and downstream concentration profiles were measured. From these profiles along with the measured velocity distribution both the vertical mass transfer coefficient and the local particle fall velocity were determined.

The effects of secondary currents on the vertical mixing process were discussed. Data was taken and analyzed in such a way as to largely eliminate the effects of these currents on the measured values.

A procedure was developed by which the local value of the fall velocity of sand sized particles could be determined in an open channel flow. The fall velocity of the particles in the turbulent flow was always greater than their fall velocity in quiescent water.

Reynolds analogy between the transfer of momentum and marked fluid particles was further substantiated. The turbulent Schmidt number was shown to be approximately 1.03 for an open channel flow with a rough boundary. Eulerian turbulence measurements were not sufficient to predict the vertical transfer coefficient.

Vertical mixing of sediment is due to three semi-independent processes. These processes are: secondary currents, diffusion due to tangential velocity fluctuations and diffusion due to the curvature of the fluid particle path lines. The diffusion coefficient due to tangential velocity fluctuations is approximately proportional to the transfer coefficient of marked fluid particles. The proportionality constant is less than or equal to 1.0 and decreases with increasing particle size. The diffusion coefficient due to the curvature of the fluid particle path lines is not related to the diffusion coefficient for marked fluid particles and increases with particle size, at least for sediment particles in the sand size range. The total sediment transfer coefficient is equal to the sum of the coefficient due to tangential velocity fluctuations and the coefficient due to the curvature of the fluid particle path lines. 

A numerical solution to the conservation of mass equation is given. The effects of the transfer coefficient, fall velocity and bed conditions on the predicted concentration profiles are illustrated.