An asymptotic theory of wind tunnel wall interference on subsonic slender bodies

An asymptotic theory of solid cylindrical wind-tunnel-wall interference about subsonic slender bodies has been developed. The basic approximation used is one of large wall-radius to body-length ratio. Matched asymptotic expansions show that in contrast to the analogous two-dimensional problem of a confined airfoil, three regions exist. Besides the incompressible crossflow and nearly axisymmetric zones, a wall layer exists where reflection in the wall of the line source representing the body becomes of dominant importance. From the theory, the interference pressures are shown to be approximately constant for closed bodies. Also demonstrated is that D'Alembert's paradox holds for interference drag of such shapes. Numerical studies comparing the exact theory to the asymptotic model which provides drastic simplifications, show that the latter can be used with reasonable accuracy to describe flows, even where the characteristic tunnel-radius to body-length ratio is as low as 1.5.