Motion of a Slender Body in Flow

Abstract

The motion of fibers in a fluid is a fundamental phenomenon for the textile technology. In this paper, a slender body is used as the simplest model of a single fiber. Equations of motion of a slender body in the flow have been de rived and they have been applied to the falling motion in horizontal uniform flow. Influences of fluid velocity and slender body length on the behaviors of the body have been investigated by numerical calculation. The obtained results are as follows : (1) A slender body, which begins to move in an inclined direction to the vertical, approaches to the vertical direction immediately after the beginning of the motion. Thereafter, its direction of the motion slowly approaches to the horizontal direction and the trajectory of its mass center has an inflection point. then the body begins to approach to the vertical direction again. Finally it approaches to the horizontal posture asymptotically, it falls vertically at the same constant speed as that in still liquid and moves horizontally at the same speed as the fluid velocity without rotation.(2) The fluid velocity influences the motion of the body only within the small region after the starting in motion (until the body inclines to about 15° to the vertical for 30 mm in length). Beyond this region the relative translation al motion of the body to the fluid is independent of the fluid velocity. Therefore, the body rotation is also unaffected by the fluid velocity. And there is a tendency for fluid velocity to have more remarkable influences on the behaviors with decreasing length.