The spreading phase in Lighthill's model of the Weis-Fogh lift mechanism

摘要

Lighthill's analysis (J. Fluid Mech., vol. 60, 1973, p. 1) of the Weis-Fogh lift mechanism is extended to include the spreading phase of the cycle. Lighthill proposed a two-dimensional inviscid irrotational analytical model to compute the circulation around two flat plates (the wings) as they open out, in opposite directions, about a common centre of rotation taken to be at the point of contact of an edge of each plate (the 'opening phase'). At a critical opening angle, the plates separate and move apart horizontally (the 'spreading phase'). During this second phase, the fluid region becomes doubly connected and is not: analysed by Lighthill. It can, however, also be Studied analytically and the results are presented here. We also extend a similar analysis, in an application to turbomachinery, due to Furber & Ffowcs Williams (J. Fluid Mech., vol. 94, 1979, p. 519).