43508-AC9
Instabilities in Granular Taylor-Couette Flow
As a critical technology for the petroleum industry, understanding of many aspects of particulate processing operations is surprisingly limited. A large number of petrochemical processes stand to benefit from improved understanding of granular flows. The processing of granular materials necessarily involves flow and the associated complexities of such flows. However, a fundamental understanding of granular flows is far from complete. Poor understanding and control of granular flows causes processing inefficiencies at best, and failures at worst. More globally speaking, there is an increasing need for engineers and scientists to develop technologies that increase process yields, reduce waste production, and improve protection of health, safety and the environment. In many cases, the success of future technologies hinge on improved fundamental understanding and control of granular flow and mixing.
In fluids, analysis of paradigmatic or model experiments, like Benard, Couette, Taylor-Couette, and Kelvin-Helmholtz, has served to uncover aspects of shear transmission that have led to a better understanding of flows of engineering importance. For granular flows, we believe improved understanding will hinge on analysis of analogous paradigmatic or model experiments. The focus of this work is Taylor-Couette flows which are one of the simplest model geometries encompassing both shear and boundary interactions – essential ingredients of practical flows.
The Taylor-Couette geometry provides an ideal geometry for examining the rheological responses of granular materials undergoing shear. The Taylor-Couette geometry also provides a means to control and study granular flow instabilities. Since most industrial or natural flows are not steady or uniform it is crucial to examine flow instabilities and the resulting spatio-temporal dynamics. The azimuthal symmetry of the Taylor-Couette experiment means that structures that are coherent in space and time can be studied in a compact experiment. While there is ongoing work examining rapid granular shear flows of spheres in small systems (to avoid instabilities and maintain nearly homogeneous flows) we have begun to examine larger systems in order to provoke instabilities.
During the past year, we have continued to make use of both physical and computational experiments in Couette and Taylor-Couette flows. We have also continued to examine shear in cylindrical mixers, which share some of the features of Couette flows. For Taylor-Couette flows, we have been characterizing the spatial instabilities that arise. In the past year, two continuum models using kinetic theory have been examined in our work, and their results are compared with particle dynamic (PD) simulations. A notable difference between the two continuum models is their treatment of energy partition (equipartition vs. non-equipartition). We consider mixtures of particles with different sizes, masses and densities. For Couette flows, we find that energy equipartition breaks down with an increase in the system inelasticity and the mass ratio. The effect of the size ratio on non-equipartition of granular energy is very small if the two particle species have the same mass. Two forms of segregation are studied in the present work: total solids segregation in the system and solids species segregation. Total solids segregation is related to the distribution of the granular energy across the walls. Solids species segregation is due to a competition of three diffusion forces: the thermal diffusion force, the ordinary diffusion force and the pressure diffusion force. For equal density but different size particles, we observe quantitative differences between the two continuum models, where one model predicts a much greater degree of both total solids and solids species segregation than the other model. For equal size but different mass particles, we observe qualitative differences between the models where one model and PD simulations predict a segregation transition based on the particle mass, which is not seen in the other model for the conditions we have examined.
Students involved in the research have received training in particle technology which has been recognized as an area of national need as it has traditionally been neglected in the
