Michel Y. Louge

Measurements of the collision properties of small spheres

An experiment to measure the properties of the collisions between two small spheres or between a small sphere and a semi‐infinite flat wall are described. The apparatus releases the particles in a free‐fall without initial spin. The impacts are modeled in terms of three coefficients. The first is the coefficient of normal restitution. The second represents the frictional properties of the contact surfaces. The last characterizes the restitution of the tangential components of the velocity of the contact point for impacts that do not involve sliding. The coefficients are calculated from stroboscopic photographs of the ballistics of the particles near the collision. The results establish that the collision model provides an accurate description of the dynamics of the impacts.

Inelastic microstructure in rapid granular flows of smooth disks

Computer simulations of two‐dimensional rapid granular flows of uniform smooth inelastic disks under simple shear reveal a dynamic microstructure characterized by the local, spatially anisotropic agglomeration of disks. A spectral analysis of the concentration field suggests that the formation of this inelastic microstructure is correlated with the magnitude of the total stresses in the flow. The simulations confirm the theoretical results of Jenkins and Richman [J. Fluid Mech. 192, 313 (1988)] for the kinetic stresses in the dilute limit and for the collisional stresses in the dense limit, when the size of the periodic domain used in the simulations is a small multiple of the disk diameter. However, the kinetic and, to a lesser extent, collisional stresses both increase significantly with the size of the periodic domain, thus departing from the predictions of the theory that assumes spatial homogeneity and isotropy.

The role of particle collisions in pneumatic transport

We analyse the dilute, steady, fully developed flow of relatively massive particles in a turbulent gas in the context of a vertical pipe. The idea is that the exchange of momentum in collisions between the grains and between the grains and the wall plays a significant role in the balance of forces in the particle phase. Consequently, the particle phase is considered to be a dilute system of colliding grains, in which the velocity fluctuations are produced by collisions rather than by the gas turbulence. The balance equations for rapid granular flow are modified to incorporate the drag force from the gas, and boundary conditions, based on collisional exchanges of momentum and energy at the wall, are employed. The turbulence of the gas is treated using a one-equation closure. A numerical solution of the resulting governing equations provides velocity and turbulent energy profiles in agreement with the measurements of Tsuji et al. (1984).

Measurements of impact properties of small, nearly spherical particles

The authors report impact properties for collisions of small, nearly spherical particles that present interesting experimental challenges. They consider difficulties arising with surface reflectivity, slight asphericity, surface damage and collisions with particles affixed to a rigid plate. To measure these impact properties, the authors refine the experimental technique of Foersteret al. To permit straightforward incorporation in rapid granular theories, the impacts are described with three coefficients. The first is the Newtonian coefficient of normal restitution. The second represents the frictional properties of the contact surfaces. The last characterizes the restitution of the tangential component of the contact point velocity for impacts that involve negligible sliding.

Computer simulations of rapid granular flows of spheres interacting with a flat, frictional boundary

This paper employs computer simulations to test the theory of Jenkins [J. Applied Mech. 59, 120 (1992)] for the interaction between a rapid granular flow of spheres and a flat, frictional wall. This paper examines the boundary conditions that relate the shear stress and energy flux at the wall to the normal stress, slip velocity, and fluctuation energy, and to the parameters that characterize a collision. It is found that while the theory captures the trends of the boundary conditions at low friction, it does not anticipate their behavior at large friction. A critical evaluation of Jenkins’ assumptions suggests where his theory may be improved.

On dense granular flows down flat frictional inclines

We consider dense, relatively shallow flows of 3 mm glass spheres moving down a chute with a flat, frictional base of 3.6 m length. Sustained flows are observed at inclinations corresponding to an effective friction between the static and dynamic friction of individual grains. A capacitance instrument records the formation of waves with a dominant component traveling upstream. Simultaneous measurements of granular temperature at the base using a load cell reveal that the waves are accompanied by substantial reduction in granular agitation. A theory incorporating contributions from impulsive and enduring interactions with the base produces quantitative predictions for the range of sustained flows observed in the experiments. Closure of the theory is achieved using a balance between the production and dissipation of angular momentum in a narrow basal shear layer. A linear stability analysis of the corresponding hydraulic equations further suggests the origin of the waves.

On the flux of fluctuation energy in a collisional grain flow at a flat, frictional wall

We consider a flow of colliding spheres that interacts with a flat, frictional wall and calculate the flux of fluctuation energy in two limits. In the first limit, all spheres slide upon contact with the wall. Here, we refine the calculations of Jenkins [J. Appl. Mech. 59, 120 (1992)] and show that a correlation between two orthogonal components of the fluctuation velocity of the point of contact of the grains with the wall provides a substantial correction to the flux originally predicted. In the other limit, the granular material is agitated but the mean velocity of the contact points with respect to the wall is zero and Jenkins’ earlier calculation is improved by distinguishing between those contacts that slide in a collision and those that stick. The new expressions for the flux agree well with the computer simulations of Louge [Phys. Fluids 6, 2253 (1994)]. Finally, we extend the expression for zero mean sliding to incorporate small sliding and obtain an approximate expression for the flux between th...

Fluid dynamic similarity of circulating fluidized beds

Abstract The effects of scale-up on the fluid dynamics of circulating fluidized beds (CFB) are investigated using a single cold laboratory facility with the ability to recycle fluidization gas mixtures of adjustable density and viscosity. By matching five dimensionless parameters, experiments employing plastic, glass and steel powders achieve fluid dynamic similarity with high-temperature CFB risers of 0.32, 0.46 and 1 m diameter. Comparisons of results obtained with the plastic and glass powders indicate that static pressure and its fluctuations scale with the riser and particle diameters, respectively. Experiments with the steel powder exhibit incipient choking behavior consistent with the greater analogous bed size that they simulate. The onset of choking with plastic and steel powders is well predicted by the correlation of Yang [Powder Technol., 35 (1983) 143]. Experiments with coated glass beads suggest that the magnitude of the particle Coulomb friction coefficient affects the fluid dynamics of the CFB in the limit where this coefficient is small.

Pressure and voidage gradients in vertical gas-solid risers

Abstract The customary practice of inferring average voidage from measurements of vertical pressure gradients may lead to significant errors at the transition between the dense and the dilute regions of a circulating fluidized bed riser. In this context, a one-dimensional model is developed to account for rapid variations of vertical voidage in these calculations In particular, the model explains the discrepancy observed by Arena et. al between the voidage profiles inferred from pressure gradients and those measured by quick-closing valve technique. The significance of this effect is discussed.

Application of capacitance instrumentation to the measurement of density and velocity of flowing snow

Abstract We describe capacitance instrumentation suitable for the measurement of density and velocity of flowing snow with moderate liquid-phase water content. A wand, consisting of two adjacent sensors protected by guard circuits, produces signals that are related to snow density through calibration. Cross-correlation of the signals permits velocity measurements. Calibration is accomplished using a capacitance device that records the dielectric properties of a snow sample while subjecting it to controlled levels of compaction and volume change. Non-invasive probe geometries are also presented. The instrumentation is tested in artificial and natural avalanches.