Lift and drag in intruders moving through hydrostatic granular media at high speeds

摘要

Recently, experiments showed that forces on intruders dragged horizontally through dense, hydrostatic granularnpackings mainly depend on the local surface orientation and can be seen as the sum of the forces exerted on smallnsurface elements. In order to understand such forces more deeply, we perform a two-dimensional soft-spherenmolecular dynamics simulation, on a similar setup, of an intruder dragged through a 50–50 bi-disperse granularnpacking, with diameters 0.30 and 0.34 cm. We measure, for both circular and half-circle shapes, the forcesnparallel (drag) and perpendicular (lift) to the drag direction as functions of the drag speed, with V = 10.3–n309 cm/s, and intruder depths, with D = 3.75–37.5 cm. The drag forces on an intruder monotonically increasenwith V and D, and are larger for the circle. However, the lift force does not depend monotonically on V and D,nand this relationship is affected by the shape of the intruder. The vertical force was negative for the half-circle,nbut for a small range of V and D, we measure positive lift. We find no sign change for the lift on the circle,nwhich is always positive. The explanation for the nonmonotonic dependence is related to the decrease in contactsnon the intruder as V increases. This is qualitatively similar to supersonic flow detachment from an obstacle. Thendetachment picture is supported by simulation measurements of the velocity field around the intruder and forcenprofiles measured on its surface.