The object of this work is to develop methods for the quantitative prediction of all the major features of flow of a gas, together with solid particulate material, through a duct of arbitrary size and inclination. Flows of this sort are of great technical importance in pneumatic transport of particulate material, 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 tend to distribute themselves over the cross section of the duct in a markedly non-uniform way, making it very difficult to predict the hold up of solid material and the pressure drop along the duct, or even to extrapolate these quantities from measurements made with the same materials in ducts of other sizes. In addition, the crowding of the particles into limited parts of the cross section can lead to undesirable effects, such as recirculation of the solid material against the direction of the main flow.
The key to making useful predictions for these systems is to understand and quantify the mechanism that determines the distribution of particle concentration over the cross section. In many situations of practical interest the gas flow is highly turbulent, and it is tempting to attribute the observed distribution of the particles to their interaction with turbulent eddies. However, a closer examination shows that this could produce the observed effects only in quite restrictive circumstances, where the particles are almost, but not quite light enough to follow the gas motion exactly. In this work we investigate an alternative mechanism, which attributes the stratification of the concentration distribution to collisions between particles, We have derived a criterion (presented in this report) to judge whether this mechanism is likely to be important in any given system, and have developed a complete mathematical model to predict the distribution of particle concentration and the velocity profiles for both gas and particles in steady flows of this kind. A computer program has been constructed to solve the model equations, and extensive sets of solutions have been found for ducts of different sizes and inclinations.
The solutions obtained appear to simulate most of the characteristic observed properties of flows of this sort, including the undesirable recirculation patterns referred to above. There is a dearth of good quantitative experimental data covering ranges of design and operating conditions broad enough to provide a searching test of the theory, but we intend to seek out what is available for comparison with our predictions. For systems where collisions between particles mediate the pattern of flow our program provides, for the first time, a rational basis for the design of particle-gas transport systems and, perhaps of equal importance, for identifying those circumstances in which their performance is likely to be unsatisfactory. It is not a very large step to extend the method to include developing flows, where the particles are accelerating under the influence of forces exerted on them by the gas stream. To the extent that turbulence can be modelled, it is also possible to introduce into the model some effects of turbulent fluctuations in the gas velocity.