Two models and the generation mechanisms of the drag on an accelerating starting disk

Abstract

As a canonical problem, the impulsive starting of a circular disk contains the fundamental mechanisms of the force generation of the drag-based propulsions. In this paper, a circular disk is uniformly accelerated to a constant target velocity along a straight path, the instantaneous drag on and the flow fields around the disk are measured. A series of experiments were conducted by varying the two dimensionless numbers, i.e., the Reynolds number ( Re) ranging from 40 000 to 80 000 and the acceleration number ([Formula: see text]) (double normalized uniform-acceleration distance) ranging from 0.5 to 2. Based on the quasi-steady and the impulse-based ideas, two analytical models are proposed for predicting and accounting for the drag force on the disk. Moreover, the two models distinguish the generation of the drag force into three phases. In the acceleration phase, the growth rate and initial peak of the drag on the disk strongly depend on [Formula: see text], which make the drag-force histories exhibit a good scaling law for a given [Formula: see text], and the whole drag is generally contributed by the increased growth rate of the vortex ring circulation. In the transition phase, the drag decreases owing to the decrease in the circulation growth rate of the vortex ring. In the vortex pinch-off phase, the circulation of the vortex ring nearly no longer grows and the size growth rate of vortex ring gradually plays a dominant role in the drag generation. The present results suggest two implications. The peak of the drag in the accelerating phase implies an alternative perspective for understanding the high-lift generation in the reversal of wing stroke in flapping flight, and three-phase drag generation implies a controllable principle based on vortex formation for enhancing the force generation in drag-based propulsions.