Kinetic theory and boundary conditions for flows of highly inelastic spheres. Quarterly progress report, April 1, 1995--June 30, 1995

摘要

In this quarter, we continue the same parameter study as the last quarter by choosing other sets of values of r,delta, e, e(sub w), and phi for which we know that at least one solution of the type described in the last quarter may be maintained, and determine the complete range of T(y=beta) (within O < T(y=beta) < 10) for which such flows can be maintained. To each value of T(y=beta) in this range, there correspond values of mass hold-up (m(sub t)), mass flow rate (m), and depth beta. In addition, for each value of T(y=beta) in this range, we can calculate the total fluctuation energy per unit area (E), the slip velocity (v) at the base, the velocity (U(sub top)) at the top, and the depth-averaged values of solid fraction, velocity, and granular temperature. In this manner, we thoroughly characterize all the steady, fully developed, gravity driven flows that are possible for prescribed sets of r, delta, e, e(sub w), and phi. In this manner, we find that there are boundaries, flow particles, and inclinations for which the kinetic theory predicts that steady, fully developed flows can be maintained at all flow rates above a minimum value. These are qualitatively different from the results presented last quarter, in which maximum flow rates were determined for each case considered. The fact that it is possible to find circumstances under which there are no maximum flow rates that limits the occurrence of steady flows may be useful when in practice it is necessary to steadily transport extremely high volumes of granular materials.