Drag force on an accelerating flat plate at low Reynolds numbers

The accelerating flat plate is a useful model for studying the drag-based flapping flight (where drag is used to provide the weight-supporting force or thrust). Previous studies have mainly focused on the high Reynolds number (Re) regime pertaining to the flight of relatively large insects and birds. In this study, we numerically investigate the unsteady drag and flows of a uniformly accelerating flat plate at low Re that is typical of miniature insect flight (Re = 10-40). The following is shown. Unlike high-Re cases where the acceleration effect on drag is insensitive to Re, at low Re, the effect exhibits a strong dependence on Re: As Re decreases below 100, the acceleration effect increases rapidly, becoming 33%-56% greater than that of high-Re cases in the Re range of 10-40, before gradually decreasing. A simple model that consists of the quasi-steady, added-mass, and history force terms is proposed for drag at low Re. The scalings of the quasi-steady and added-mass force terms are well known; we find that the history force term scales approximately with the square root of the acceleration and velocity. The above result that relatively large drag is produced by the accelerating wing at Re = 10-40 is especially interesting and might explain why miniature insects fly in this Re range.