Theoretical use of variable porosity in slotted tunnels for minimizing wall interference on dynamic measurements

Abstract

In parallel with a recent experimental study of the use of slotted tunnel liners with variable perforated screens to give interference-free aerodynamic damping derivatives, the corresponding problem is considered theoretically. The principle, that wall interference usually changes sign when slots in the roof and floor of a rectangular tunnel are completely sealed, has prompted these complementary studies with systematic variation of a porosity parameter that can govern the intermediate wall conditions. A theory for small frequency parameter and subsonic compressible flow, which has already explained serious interference effects observed experimentally, is extended to the more general tunnel boundary conditions. With the aid of a special similarity rule for compressible flow, the six necessary interference parameters are determined by a judicious amalgam of exact and approximate data for incompressible flow, including allowance for elliptic loading over a finite wing span. The corrections to oscillatory lift and pitching moment are formulated. By iterative calculation the theoretical method is applied to pitching motion of the unswept tapered and cropped delta planforms chosen for the related half-model experiments. The most favourable wall porosity for low interference is similar in theory and experiment for the two wings. A recommended practical procedure for approximating to interference-free wall conditions is thus corroborated by theoretical calculation and is also extended to give residual corrections. The extended procedure is illustrated for the larger cropped delta half-model. It is concluded that the uncertainties from ventilated wall interference on pitching derivatives can be reduced to about 5 per cent of the in-phase lift derivative, provided that the model span does not exceed 40 per cent of the tunnel breadth, nor the planform area 15 per cent of the working cross section. Theory and experiment combine to show that the optimum ventilated wall is hardly influenced by Mach number, so that there are good prospects of eliminating the major interference effects at transonic speeds.