Iterative method for thick cambered wings in subcritical flow

Abstract

A method of computing the steady, inviscid flow around a thick, cambered and twisted wing (neglecting dihedral) is presented. The flow field is represented by distributions of sources and doublets in the chordal surface, the strengths of which are determined iteratively from the boundary conditions on the wing upper and lower surfaces. To save computing time, these conditions are transferred to the surface of the related uncambered wing (the 'thickness surface') by a two-term Taylor series expansion in the camber ordinate. This approximate boundary condition is now correct to second order. In order to improve the approximations for the singularity distributions at each stage, and so to speed up convergence, an inner iteration scheme is employed, based on a similar Taylor expansion centred on the mean chordal surface. The method is extended to compressible (subcritical) flow with the help of the Prandtl-Glauert rule. The method is tested on R.A.E. Wing 'B', a research wing with rapid spanwise changes in camber and twist near the root and tip. Results from two runs with different numbers of chordwise and spanwise stations agree well, which suggests that the method is well-conditioned and reliable; agreement with some results from the B.A.C. (Roberts) program is satisfactory; and the predictions of the latest version of the R.A.E. Standard Method agree with these reasonably well, in view of the marked spanwise deformation of the wing.