A New Scaling Law for Drag Forces on Accelerating Plates

The drag force on an accelerating object is usually described by a quasi-steady force that scales with the square of the instantaneous velocity and an added mass force due to the acceleration. This description could lead to a significant underestimation of the actual drag force. We aim to find a better description of the drag force on a flat plate in an unsteady flow by measuring both the drag force and velocity field for a large range of constant accelerations and velocities. Our experiments show that the force due to acceleration scales with the square root of the acceleration, contrary to a linear scaling that is expected from added mass. This force is associated with the generation and advection of vorticity at the plate surface. We present a new scaling law for the drag force on accelerating plates, based on the history force for unsteady flow. This scaling avoids previous inconsistencies in using added mass forces in the description of forces on accelerating plates. This new scaling law has proved useful in predicting the drag force for different plate geometries and non-constant accelerations.