Force Production Mechanisms for a Flat Plate Wing at Low Reynolds Numbers

Abstract

Micro Air Vehicles (MAVs) operate in highly unsteady and often separated flow conditions which are well outside the usual design space of conventional lifting surfaces. This paper aims to coalesce theory and simply explain the physical mechanisms behind force production for such unsteady and separated flows with regards to added mass and circulatory (vortex dynamics) effects. Particle Image Velocimetry (PIV) and flow visualisation are additionally used to show that the 'non-circulatory' added mass forces are responsible for production of vorticity bound to the wing surface, thus can be confused with free vortices in the flow field. Changes to the 'added mass vorticity' and thus forces derived from this are shown to be independent of flow topology and perhaps viscous effects in general with exception to edge conditions. A technique to simply quantify the distribution of the bound vorticity from PIV measurements is additionally described and utilised. * Ph.D., sjc276@cam.ac.uk. † Professor, hb@eng.cam.ac.uk, AIAA Associate Fellow.

Linking the Unsteady Force Generation to Vorticity for a Translating and Rotating Cylinder

“…Comparing the theoretical added mass and the experimental non-circulatory vortex sheet clearly shows that it is possible to recover γ nc from PIV data. A similar result was previously shown by Corkery & Babinsky [9] for a translating thin flat plate. The data presented here confirms that this approach can be extended to objects of finite thickness.…”

“…These have further been linked to respective circulatory and non-circulatory vortex sheets [8]. The latter was experimentally shown by Corkery & Babinsky [9] to generate vorticity in the flow with zero total circulation for a thin flat plate. Separating the acting forces into their components is useful when building low order models, as the contributions can be modelled independently and superimposed at the end to yield the total force.…”

“…To recover the individual components for a rotating body of finite thickness the approach outlined by Graham et. al [10] and Corkery & Babinsky [9] is used and adapted. The boundary vortex sheet, γ b , is assumed to consist of three parts and defined as…”

“…The local vortex sheet strength on the cylinder surface γ c is now the velocity difference between a stationary cylinder and the induced velocity, U induced , γ c = 0 − U induced = −U induced (10) γ b is determined by adapting the method proposed by Corkery & Babinsky [9], thereafter referred to as the wedge method. The circumference of the cylinder is divided into a number of small wedges with an inner segment length δs n , as illustrated in figure 11.…”

“…The paper will begin by presenting an experimental set-up which allows the measurement of the complete flow field around a translating and rotating cylinder. To recover the surface vortex sheet components, the methodology proposed by Eldredge [8], Graham et al [10] and Corkery & Babinsky [9] is extended to a general case and demonstrated in an applied experimental setting. This consequently allows the forces and importantly the force components to be recovered purely from particle image velocimetery (PIV); as long as two-dimensional flow can be assumed.…”