Two independent mechanisms with distinct laws for the generation of drag force on accelerating plates

Acceleration of objects in fluids widely exists in biological propulsions and contains rich unsteady fluid mechanisms. In this paper, the instantaneous drag force on accelerating normal flat plates (circular, elliptical, square, and rectangular plates) in a wide range of dimensionless acceleration (a*=16∼2) is measured, and the underlying mechanism for force generation is investigated. At first, we find that the drag force coefficient generally scales with the square root of a* when a*1.0, coinciding with the scaling law given by Reijtenbagh et al. (PRL. 2023,130,174001). However, the drag force coefficient more linearly scales with a* rather than a* when a*1.0, thereby indicating acceleration plays two distinct roles on the force generation depending on a*. Moreover, two scaling laws are built to quantitatively describe the two distinct roles of a* on the drag force generation. Based on fluid impulse, the drag force is largely contributed by the added mass of the accelerating plates (added mass force) and vorticity generation fed by the shear layer on the edge of the plates (vortex creation force). When a*1.0, the vortex creation force scales with a* and almost contributes to the total drag force. When a*1.0, the added mass force scaling with a* contributes to most of the drag force. Furthermore, the two force generation mechanisms associated with acceleration (a*) are independent, and a criterion based on the energy ratio is proposed to identify the transition of the two force generation mechanisms. The present results uncover the role of acceleration in force generation and explain the inconsistencies of using one quasi-steady model in describing the force on accelerating plates.