SUMMARY
This report covers research under the auspices of IFPRI during the period January 1986 - December 1989. Mr. M. C. Turner has continued in the appointment of a Research Studentship throughout this period of the IFPRI research project.
Results are reported of investigations into the flow properties of idealised powders (monodisperse spherical particles) using experimental techniques, computer simulations of idealised models, and fundamental theoretical studies. The objective of the research is to predict constitutive rheological relations for use in fluid mechanics calculations of the flow of powders in given geometric devices.
Experimental studies have been based on measurements of the behaviour of well-characterised powders of monodisperse spheres in a rotating fluidised bed, and also on direct laboratory measurements of the coefficient of restitution for glass ballotini spherical beads, Results are reported for glass ballotini particles in the size range from 10m4 to 10-3 m. Experinental measurements of the properties of *ideal powders* are required to test the accuracy of computer simulation models alongside the development of the computational approach.
Computer simulation results are reported for four different types of model system.
The first approach was to set up a computer simulation mode1 of chute flow closely resembling the simple experimental geometry. This gives information on boundary effects but it rtalistd early on that, whilst this may also give some information on the constitutive rheology, "particulate fluid mechanics"on relatively tiny numbers of particles is not the way * forward.
Computational rheology and computational fluid mechanics must be treated seperately.
The calculations of the constitutive rheology of an idealised powder requires the use of homogenous periodic boundary systems with well-defined particle and system state variables similar to non-equilibrium molecular dynamics used to determine transport properties of molecular systems. In this case the computations are properly described as steady-state granular dynamics.
The three types of system for which we report results are:
(1) an isokinetic system of the ideal powder of frictionless, monodisperse, elastic hard spheres where the *granular temperature" (total kinetic energy) is held constant by uniform continuous velocity renormalisation. This artificial system has no direct experimental counterpart but it relates to real-granular systems by analytical scaling laws which we have developed.
(ii) The direct simulation of flowing systems of inelastic frictionless spheres with a constant coefficient of restitution for comparisons with available theoretical and experimental results. These are essentially exact computations of the constitutive rheology of that model and can be used to test the approximations in the kinetic theory approach previously advocated by other researchers , in this area.
(iii) The steady-state granular dynamics simulations have been extended to incorporate surface friction. By comparing the results for systems with and without surface friction we are able to estimate its effect on the constitutive rheology and examine means of incorporating surface friction besides inelasticity into simple analytic forms for the rheology using scaling prediction methods.
The scaling laws which we report have been developed to predict the dependence of the pressure tensor initially in the region of rapid granular flow, on the rate of strain deformation. Using known properties of the thermal equilibrium hard-sphere fluid and its steady-state isokinetic flow curves, these scaling laws enable the constitutive rheology for systems over a wide range of particle and state variables to be presented analytically. Results have been obtained for various forms of the coefficient-of-restitution, since this is not known experimentally for even the simplest real powders, to give some insight into how it affects the rheology in the rapid flow domain. The scaling predictions have been compared with both experimental results and predictions of kinetic theory.
The scaling laws also predict the shear-rate dependent granular *temperatures” (particle kinetic energies), kinetic conductivities and particle diffurivities from available hard-sphere fluid transport data. This produces all the input data necessary to proceed with a finite difference or finite element fluid mechanics prediction, either transient or steady, of laminar shear flow. The methods of predicting the conatitutive rheology are easily extended to elongational and bulk deformations for more general flows.