Development of a rarefaction wave at discharge initiation in a storage silo—DEM simulations
The generation of a rarefaction wave at the initiation of discharge from a storage silo is a phenomenon of scientific and practical interest. The effect, sometimes termed the dynamic pressure switch, may create dangerous pulsations of the storage structure. Owing to the nonlinearity, discontinuity, and heterogeneity of granular systems, the mechanism of generation and propagation of stress waves is complex and not yet completely understood.
The present study conducted discrete element simulations to model the formation and propagation of a rarefaction wave in a granular material contained in a silo. Modeling was performed for a flat-bottom cylindrical container with diameter of 0.1 or 0.12 m and height of 0.5 m. The effects of the orifice size and the shape of the initial discharging impulse on the shape and extent of the rarefaction wave were examined. Positions, velocities, and forces of particles were recorded every 10−5 s and used to infer the location of the front of the rarefaction wave and loads on construction members. Discharge through the entire bottom of the bin generates a plane rarefaction wave that may be followed by a compaction wave, depending on the discharge rate.
Discharge through the orifice generates a spherical rarefaction wave that, after reflection from the silo wall, travels up the silo as a sequence of rarefaction–compaction cycles with constant wavelength equal to the silo diameter. During the travel of the wave along the bin height, the wave amplitude increases with the distance traveled. Simulations confirmed earlier findings of laboratory and numerical (finite element method) experiments and a theoretical approach, estimating the speed of the front of the rarefaction wave to range from 70 to 80 m/s and the speed of the tail to range from 20 to 60 m/s.
Keywords: granular flow, dynamic pressure switch, silo discharge, stress wave, rarefaction wave.