Compressible Flow Over Moderate Aspect Ratio Wings

In this section, small disturbance theories for both subsonic and supersonic wings are discussed. As in two-dimensional cases, the symmetric and the lifting problems are treated separately, thanks to the linearity of the governing equations and boundary conditions, for thin wings with small relative camber and at small angles of attack. The linearized boundary condition on the plane z = 0 are

_ w(x, у, 0+) = d(x, у,0+) = U (Ш(x, у) +1 ш(x, у)- a)

w(x, y, 0-) = ^(x, y, 0-) = U Ц(x, y) – 1 ^(x, y) – a

where d(x, y) and e(x, y) represent the camber and thickness of the thin wing, respec­tively.

Notice that in the symmetric problem involving the wing thickness distribution only, the potential is symmetric with ф(x, y, – z) = ф(x, y, z), whereas for the lifting problem the potential is antisymmetric with ф(x, y, – z) = —ch(x, y, z). As in two­dimensional thin airfoil theory, across the wing surface, u is continuous and w jumps for the symmetric problem and u jumps and w is continuous for the lifting problem. The solution will be obtained as superposition of sources and their derivatives in three-dimensional flow, such that the boundary conditions are satisfied.

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