A theory of two-dimensional airfoils with strong inlet flow on the upper surfaceud

摘要

The two-dimensional theory of airfoils with arbitrarily strong inletudflow into the upper surface was examined with the aim of developing a thin-airfoiludtheory which is valid for this condition. Such a theory has, in fact,udbeen developed and reduces uniformly to the conventional thin-wing theoryudwhen the inlet flow vanishes. The integrals associated with the arbitraryudshape, corresponding to the familiar Munk integrals, are somewhat moreudcomplex but not so as to make calculations difficult.udTo examine the limit for very high ratios of inlet to free-streamudvelocity, the theory of the Joukowski airfoil was extended to incorporateudan arbitrary inlet on the upper surface. Because this calculation is exact,udphenomena observed in the limit cannot be attributed to the linearized calculation. These results showed that airfoil theory, in the conventional sense,udbreaks down at very large ratios of inlet to free-stream velocity. Thisudoccurs where the strong induced field of the inlet dominates the free-streamudflow so overwhelmingly that the flow no longer leaves the trailing edge butudflows toward it. Then the trailing edge becomes, in fact a leading edgeudand the Kutta condition is physically inapplicable. For the example in thisudwork, this breakdown occurred at a ratio of inlet to free-stream velocityudof about 10. This phenomena suggests that for ratios in excess of theudcritical value, the flow separates from the trailing edge and the circulationudis dominated by conditions at the edges of the inlet.