An experimental study of the flow of glass beads in quasi-2d half-filled cylinders with different cross-sectional shapes (square, star, circle with 2 wedges or 4 wedges) rotated about their axes is carried out using flow visualization. The flow of particles in such geometries is time-periodic and the length and thickness of the flowing layer shrink and expand with rotation of the cylinder. The surface angle increases and decreases with the layer length. The shape of the layer in different geometries, however, is qualitatively similar to that for a circular cylinder. A depth-averaged flow model to predict the time-varying layer thickness profile is presented, along with a perturbation solution in terms of a small parameter, k, which is the ratio of the layer thickness at midpoint to the half-length of the layer at the cross-section orientation when the length is minimum. The O(k) perturbation solution and the full theory both predict that the scaled layer thickness varies periodically; the deviations are proportional to the rate of change of the length. The perturbation solution gives results close to those from numerical solution except at cylinder orientations when the length of the flowing layer changes sharply. Measured variation of the scaled midlayer thickness with time for all geometries is well predicted by the theory.
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