Experiments on continuous, steady flows of granular materials down an inclined channel or chute have been conducted with the objectives of understanding the characteristics of chute flows and of acquiring information on the rheological behavior of granular material flow. Two neighboring fiber-optic displacement probes provide a means to measure (1) the mean velocity by cross-correlating two signals from the probes, (2) the unsteady or random component of the particle velocity in the longitudinal direction by a procedure of identifying particles, and (3) the mean particle spacing at the boundaries by counting the frequency of passage of the particles. In addition, a strain-gauged plate built into the chute base has been employed to make direct measurement of shear stress at the base. With the help of these instruments, the vertical profiles of mean velocity, velocity fluctuation, and linear concentration were obtained at the sidewalls. Measurements of some basic flow properties such as solid fraction, velocity, shear rate, and velocity fluctuation were analyzed to understand the characteristics of the chute flow. Finally, the rheological behavior of granular materials was studied with the experimental data. In particular, the rheological models of Lun et al. (1984) for general flow and fully developed flow were compared with the present data.

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Existing constitutive relations and governing equations have been used to solve for fully developed chute flows of granular materials. In particular, the results of Lun et al. (1984) have been employed and the boundary value problem has been formulated with two parameters (the coefficient of restitution between particles, and the chute inclination), and three boundary values at the chute base wall, namely the values of solid fraction, granular temperature, and mean velocity at the wall. The boundary value problem has been numerically solved by the “shooting method.” The results show the significant role played by granular conduction in determining the profiles of granular temperature, solid fraction, and mean velocity in chute flows. These analytical results are also compared with experimental measurements of velocity fluctuation, solid fraction, and mean velocity made by Ahn et al. (1989), and with the computer simulations by Campbell and Brennen (1985b).

Rapid granular flow through an orifice (nozzle-shaped flow restrictor) located at the bottom of a vertical tube has been studied using three-dimensional direct computer simulation with the purpose of investigating (1) characteristics of rapid granular flows through the flow restrictor, (2) the choking condition of rapid flow at the orifice and thus conditions at which the maximum discharge rate takes place for the given orifice, and (3) a functional relationship between the discharge rate and flow quantities such as granular temperature and solid fraction. In the present simulation, where the frictional hard-sphere collision operator was employed, it was possible to obtain both rapid and slow (choked) flows through the orifice by controlling the number of particles in the system. The results show that the profile of granular temperature in the vicinity of the orifice plays an important role in determining the choking condition at the orifice. Flow appears to be choked when an adverse granular conduction occurs locally at the orifice in the direction opposite to the mean flow. On the other hand, flow is not choked when the fluctuation energy is conducted in the mean flow direction near the orifice. When flow is not choked, the discharge rate through the orifice increases with increasing solid fraction or normal stress. Once the flow becomes choked, however, the discharge rate decreases as the solid fraction or normal stress increases. Also for inelastic, rough particles, the discharge rate is found to be proportional to the granular temperature to the power of 1.5 and inversely proportional to the gravitational acceleration and the tube length.

The characteristics of pressure drop in corrugated pipes were experimentally studied in both straight and helically coiled configurations. The present study employed the stainless-steel pipes with the corrugation of circular cross section, which are widely used in boilers and pipe systems between solar panels and boilers. The diameters of corrugated pipes were 20.4, 25.4, 34.5 and 40.5 mm. The corrugated pipe, approximately 10 m in length, was configured either in the straight manner or in the helical coil with the helix diameter of 0.43 or 0.64 m. Water stored in a tank was fed into a corrugated pipe by a pump while the flow rate was controlled by a control valve. The friction factors of the pipes remain constant over the range of Reynolds number from 4,000 to 50,000, indicating that the flow in the pipe was fully turbulent. When the pipe was straightly configured, the friction factors were measured to be 0.070, 0.075, 0.12 and 0.22 for the diameter of 20.4, 25.4, 34.5 and 40.5 mm, respectively. Thus the present study showed that the friction factors increased with the increasing diameter of the pipe. This result is clearly contrary to a rare experimental result available in the literature. On the other hand, as expected, the friction factor for the helically coiled configuration was higher than that of the straight configuration with the same tube diameter, and the configuration of the smaller helix diameter yielded the larger friction factor. The reason for the increasing friction factor with the increasing pipe diameter remains to be explored further.