Scientific and Technical Aerospace Reports Volume 39 April 6, 2001

During the past four years, we have worked to insure the success of a flight experiment on particle segregation in energetic
grain flows. The experiment is meant to test theory and numerical simulations as they apply to shearing flows of colliding grains
in micro-gravity. The experiment involves a binary mixture of spheres that differ in diameter and/or mass. A steady, fully-developed
flow of the mixture is established between parallel, bumpy boundaries that are in relative motion. Because the energy transferred
and dissipated in collisions between the flowing spheres and the boundaries is different from that transferred and dissipated
in collisions among the flowing spheres, the energy of the particle velocity fluctuations in the mixture varies across the flow. The
frequency of collisions among and between the two types of spheres depends upon the spatial gradient of this energy and upon
the spatial gradients of the concentrations of the two types of spheres. Consequently, the balances of momentum across the flow
require that gradients of concentration accompany the gradients of mixture fluctuation energy. In the experiment, we measure how
the energy of the velocity fluctuations and the concentrations vary across the flow. The object of the experiment is to determine
how well these measured fields compare with those predicted by theory and observed in numerical simulations and to understand
why any differences between them occur. The activities of the past four years involved physical experiments, computer simulations,
and theory. We carried out physical experiments on five flights in the KC-135. This involved the design and construction
of a prototype shear cell in the shape of a racetrack. We also developed a way to obtain images of flowing spheres made of plastic,
ceramic, and metal through the cell side wall and a means for computer interpretation of these images. We then measured profiles
of mixture velocity, mixture fluctuation velocity, mixture volume fraction, and species number density in the shear cell during
episodes of micro-gravity on the KC-135. The comparison of these profiles with those measured in computer simulations and the
predictions of theory led to adjustments in the operating conditions of the shear cell and gave indications of the advantages and
disadvantages of each material. We developed discrete particle dynamics simulations for the full racetrack cell and for a section
of fully developed flow that was periodic in the flow direction. The full computer simulation was used to design the racetrack shear
cell and to study the properties of the flow in it. We also tested the results of the fully developed simulation against the measurements
made in the shear cell during flight and predictions of theory. The latter were obtained in a numerical scheme that we developed
to solve the full equations and boundary conditions for the mean mixture velocity, fluctuation velocity, and mixture volume
fraction in steady, fully developed shearing flows over the cross section of the shear cell. Finally, we derived a simplified theory
for segregation for mixtures in which the diameters and/or the masses of the two spheres are not too different and a new theory
for segregation of disks in planar shearing flows. We extended existing boundary conditions for bumpy frictional boundaries to
include terms that are nonlinear in the ratio of the mean slip velocity to the strength of the velocity fluctuations. We developed
simple approximate differential equations with analytical solutions to describe segregation between bumpy boundaries with the
influence of the side walls taken into account in an averaged way. Future research will involve the evaluation of a new cell design.
Computer simulations of the full racetrack shear cell indicate that the flow along the straight sections never achieves a fully-developed
state. In earlier studies, we were led to believe that a fully-developed flow was attained because, near the ends of the straight
sections, the profiles of mixture mean velocity, fluctuation velocity, and volume fraction were all close to their fully-developed
values. The flow development seems to be controlled by the end regions in a way that we do not yet understand. Consequently,
we have begun to evaluate an axi-symmetric shear cell configuration in which the flow is fully developed at each section. Such
a shear cell involves concentric circular cylinders that are in relative motion. Cylindrical bumps on these are parallel to the axis
of the cylinders. When the cylinders rotate in opposite directions, so that there is a streamline of zero circumferential mixture
velocity inside the shearing flow, the centripetal accelerations are minimized. The advantage of such a cell is that the flows will
be fully developed at every section. Also, because both boundaries move with respect to the fixed sidewalls, the flows will be more
agitated across the gap. A possible disadvantage is that there is always some centripetal accelerations within the gap. However,
theory and computer simulations can incorporate at least modest centrifugal forces, so we regard this as an opportunity to test this
capability against the physical experiments. Finally, such an axi-symmetric cell is simpler to design and build than the racetrack
and its axi-symmetric design seems to offers greater flexibility for a variety of experiments that might involve cylindrical boundaries
of different diameters, depths, and bumpiness. Also, the design facilitates studies of time-dependent segregation and segregation
in flows that are a single particle in depth. Because the flow in the axi-symmetric cell is fully developed at every section, it
is possible to employ it to carry out unambiguous experiments on time-dependent segregation. In the racetrack design, the time-dependent
segregation associated with a change in boundary speed could be confused with that associated with the flow development.
The axi-symmetric geometry makes it possible to carry out measurements of diffusion velocities and time-dependent
concentrations across the cell that follow, for example, an abrupt change in boundary speed. The results of such experiments can
be tested against computer simulations and simplified versions of existing theories. The simplicity of the design of the axi-symmetric
cell makes it possible to reconfigure it to carry out experiments on segregation in flows that are a single particle in thickness.
This provides an opportunity to test theory for the segregation of binary mixtures of disks in planar shearing flows that we have
developed during the past four years. Also, this provides an opportunity to complement the work of researchers the University
of Rennes who are carrying out physical experiments on the segregation of binary mixtures of circular disks in shearing flows
carried out on an air table. We anticipate that because of the simplicity of the two-dimensional experiment, the prototype axisym-
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