Investigation on the drag force and flow field of an accelerating plate

Abstract

We present results on the instantaneous drag force acting on a rectangular plate that accelerates in a direction normal to the plate surface. Conventionally the drag force on an accelerating object is divided into a steady state term and an added mass term, which can both be time-dependent. However, for prolonged accelerations this theory does not hold. This paper shows a different method to scale the forces that act on an accelerating plate. We base this scaling on an experiment in which a plate was accelerated from rest through a water tank using an industrial gantry robot. In this experiment both the forces that act on the plate and the velocity fields, using PIV, were measured for a large range of accelerations and final velocities. The vorticity fields, obtained from the velocity fields, qualitatively show the same process of vortex formation across the whole range of accelerations. However, the instantaneous drag force and total circulation clearly differ for different accelerations. Shortly after the acceleration period ends, and the plate reaches its final velocity, the drag force and the circulation for different accelerations coincide and do not depend on the acceleration history anymore. We divided the force into two components: the steady state force, which can be scaled by using the drag coefficient, and an instationary force, for which we found a new scaling. This scaling, which involves the square root of both the velocity and the acceleration, can predict the instationary force significantly better than the conventional scaling.