Summary
The object of this work is to extend our earlier research on the flow of gas and particles through ducts to the situation in which the flow is turbulent. Such flows are of great technical importance in pneumatic transport of particulates and in the circulation of particulate materials within chemical processes. Examples of the latter type include the riser reactors and standpipes which form components of the catalyst circulation loop in catalytic crackers, used in the refining of oil, and the long standpipes used in certain coal liquefaction plants, In all these systems the particles are found to distribute themselves in a very non-uniform way over the width of the duct. Unless the nature of this distribution can be predicted, it is not possible to calculate the pressure drop along the duct or other quantities, such as the statistical distribution of particle residence times, which are needed in the design of these systems.
The key to making useful predictions is, therefore, to understand and quantify the mechanism responsible for the distribution of particle concentration over the cross section of the duct. In earlier work, sponsored by TFPRI, we have established that collisions among the particles can endow the assembly of particles with properties analogous to those of a molecular fluid, and that this can generate a distribution of the particles which is, in many ways, realistic. However, the behavior is found to be very sensitive to mechanical properties of the particles which affect the elasticity of collisions, and this is not at all realistic behavior for most systems of technical interest.
The present work examines the effect of turbulent flow on the cross sectional distribution of the particles, and indicates that there will be sharply enhanced concentration in the vicinity of the walls of the duct, as observed in practice. In contrast to the findings of our earlier work the predicted distribution of particle concentration appears to be rather insensitive to the properties of the particles or the parameters of the turbulence model used. In must be emphasized that these conclusions are tentative, since difficulties encountered in generating numerical solutions of the governing equations have not yet been entirely overcome, but the results obtained so far are encouraging.