The calculation of lift taking account of the boundary layer

Abstract

The purpose of this paper is to fred a sound approach to the problem of the theoretical prediction of sectional characteristics taking account of the boundary layer. Attention is mainly concentrated on the lift, since it is on the accuracy of this calculation that the accuracy of calculations for other characteristics such as pressure distribution and moments must depend. Calculations of the lift and of the velocity at the edge of the boundary layer near tile trailing edge have been made for two dissimilar symmetrical aerofoils at an incidence of 6 deg, using boundary-layer data taken from experiment. The method of calculation satisfies the fundamental theorem that no net vorticity is discharged into tile wake at the trailing edge and in contrast to tile earlier calculations of R. & M. 1996, full account is now taken of the effect of the boundary layer on the velocity field outside tile boundary layer, so that the empiricism of that report is avoided. The present calculations harmonise the two different methods of approach which have been used in the past, namely, the one in which the loss of lift below the Joukowski value was attributed entirely to the incidence and camber effects of the boundary layer, and the other in which the vorticity theorem was satisfied, but boundary-layer camber effects were ignored. The main conclusions are as follows :--The calculated values of the lift and the velocity at the edge of the boundary layer at the trailing edge are in satisfactory agreement with experiment. Incidence and camber effects of the boundary layer account for a large proportion of the loss of lift, which is much greater for the Piercy 1240 aerofoil (trailing edge angle 22.15 deg) than for the cusped Joukowski aerofoil. Curvature effects may be important near the trailing edge. Prediction of the other characteristics such as pressure distribution and moments should be possible, but the work involved will be considerable. Given a satisfactory method of computing the details of tile turbulent boundary layer up to the separation position, prediction of scale effects and Mach number effects on sectional characteristics below the stall should also be possible, using the methods of this paper in conjunction with an iterative process. More boundary-layer explorations should be undertaken in the neighbourhood of the trailing edge of large chord aerofoils with zero and finite trailing-edge angles.