Submitted to: International Association of Hydraulic Research International Symposium
Publication Type: Proceedings
Publication Acceptance Date: 7/25/2011
Publication Date: 9/6/2011
Citation: Prasad, S.N., Suryadevara, M.R., Romkens, M.J. 2011. Phenomena of drag reduction on saltating sediment in shallow, supercritical flows. International Association of Hydraulic Research International Symposiumon Ruver, Coastal, and Estuarine Morphodynamics, Tsinghua University Press, Beijing, PRC. Theme A: 14-22. CDROM. Interpretive Summary: Well known examples of locomotion include the maneuvering and clustering of racing automobiles and bicyclists, queuing of lobsters during underwater migrations, and flying of birds in air. These phenomena are explained by conventional hydrodynamic drafting, for which rigid bodies enjoy drag reduction when situated behind a leader. Similarly, sediment particles in transport experience the influence of neighboring particles in motion. This article represents a quantitative analysis of calculating the reduction in drag due to the presence of other sediment particles in transport. An expression was obtained which shows that, for a row of an infinite number of identical spherical particles of diameter d, spaced a distance s apart, the ratio of the drag coefficients is related to the linear concentration, d/s. This information is helpful in quantifying sediment transport and deposition processes.
Technical Abstract: ABSTRACT: When a group of objects move through a fluid, it often exhibits coordinated behavior in which bodies in the wake of a leader generally experience reduced drag. Locomotion provides well known examples including the maneuvering and clustering of racing automobiles and bicyclists and queuing of lobsters during underwater migrations and flying of birds in air. These phenomena are explained by conventional hydrodynamic drafting, for which rigid bodies enjoy drag reduction when situated behind a leader. Though flow field around drafting bodies is complicated, the effect is qualitatively understood by considering that the body sits in the lower velocity wake of the leader. The resulting force arrangement leads to passive aggregation and offers net drag reduction for locomotion. Does this rationalization of interactions among rigid bodies manifest its effect in sediment transport processes? It turns out that the present research, whose overall goal is to develop physically based models of sediment transport in shallow flows, does reveal the existence of drag reduction on particles when the transport mode is in a pure saltation phase. This phase exists when the solid concentration is small, less than 5%, where particle collisions are negligible. Our experiments were limited to shallow supercritical flows in which uniformed sized sands and glass beads in the range of diameters between 300-1400 microns were used for sediment behavior. Photonic probe measurements were carried out to determine concentration and particle velocities. It is found that the velocity increases with concentration until particle collisions become significant resulting in bed evolution with identifiable structures. Results are presented for coarse and medium sized sand and glass beads for hydraulic conditions with Froude numbers 1.92 and 1.45. In shallow supercritical flows boundary layer thickness is very small and, therefore, coarse particle sediments move primarily under the influence of hydrodynamic and bed collisional forces. When the particle collision is insignificant, the redistribution of energy during non-frontal bed collision funnels a part of the tangential momentum in the normal direction so that the particles move in a pure saltation mode. The paper develops an impact model in which relative tangential and normal velocities are related by the coefficients of tangential and normal restitutions. The model yields a functional relation between particle velocity, saltation height and the restitution coefficients. The drag reduction effect is modeled by the superposition of two flow fields. First the drag coefficient is determined for the case of a single particle and the second part consists of a similar coefficient due to the flow field behind the leading particle. Thus, for a row of infinite number of spherical particles of diameter, d, equally spaced center to center distance, s, the ratio of the drag coefficients (multiple to single particle) is found to be (1-alpha^2) where alpha is the linear concentration, d/s , and c is a constant which depends on the particle Reynolds number.