Interacting flow theory and trailing edge separation – no stall

Abstract

The central question addressed here concerns the occurrence of laminar separation near a non-symmetric trailing edge, on one surface only of an airfoil, and whether or not such an event heralds a ‘catastrophic stall’ in the sense that the flow structure changes significantly from the triple-deck or interactive-boundary-layer form holding for attached flow. Virtually all previous works have conjectured, assumed or argued that there is such a catastrophic stall. The present work, however, points (strongly, we believe) to the opposite view, based on a combination of analytical and numerical grounds. First, the argument for a catastrophic stall, although tempting, is shown to contain a fundamental flaw. Secondly, the present numerical work deliberately aims at including the most important separated-flow features, the acknowledgement of the discontinuities at the trailing-edge station and the effects of reversed flow, in a systematic fashion. This appears to be the first such attempt. As a result the trailing-edge requirements are found to be swept upstream, forcing any flow reversal on just one surface to be followed by a reattachment, however abruptly, just before the trailing-edge point. Thirdly, an analysis of the nearly separated and the just-separated regimes confirms the natural emergence of the reattachment phenomenon and ties in closely with the observed numerical features. In particular, the distance of the reattachment point from the trailing edge is found to be of the tiny order $\overline{\triangle^4} $ or less, where $\overline{\triangle}$ is the small upstream separation distance. Finally, there is shown to be a logical tie-in also with trailing-edge flows involving two-sided separation where no catastrophic stall arises. It is concluded that there is no catastrophic stall and that inter alia the triple-deck/interactive-boundary-layer approach can continue to be used with one-sided separation present.

The study implies some fairly striking features associated with one-sided separating flows, but these do bear a firm resemblance to recent laminar and even turbulent flow computations and experiments. This indicates that, contrary to previous proposals, such computations and experiments are explicable within the realms of interactive-boundary-layer theory.