The aerofoil in a wind tunnel of elliptic section

Abstract

The lift and drag experienced by an aerofoil in a wind tunnel differ from the lift and drag experienced by the same aerofoil under free air conditions. These differences, which are the induced effects due to the walls of the enclosure, can be determined by the aid of general considerations laid down by Prandtl. In a closed tunnel, that is, a tunnel with rigid walls, the necessary boundary condition is that the velocity normal to the walls shall be zero. In an open tunnel, or free jet, the condition is that the pressure is constant over the boundary. Assuming that trailing vortices spring from the aerofoil and extend downstream without distortion, Prandtl has shown that the problem can be converted into one dealing with the flow in a section of the wake far behind the aerofoil, the necessary boundary condition being that the velocity potential is constant over the trace of the open tunnel. Prandtl ( loc. cit .) himself has investigated the interference experienced by an aerofoil in a tunnel of circular section for an elliptic distribution of lift across the span. Glauert, to whom a considerable extension of the theory is due, found approximate values of the induced drag in a rectangular tunnel when the span of the aerofoil is indefinitely small. Terazawa modified Glauert’s method and obtained the exact solution for an aerofoil with uniform distribution of circulation in a rectangular channel. Rosenhead obtained exact results for uniform and elliptic distributions both in circular and rectangular tunnels. More recently, in connection with the building of a wind tunnel of elliptic section, Glauert was led to reconsider the general problem of wind tunnel interference, and his conclusions are embodied in three valuable papers. In the first of these he pointed out that the problem discussed by previous investigators is that in which the lift distribution is prescribed to be the same as that in free air, and the aerofoil is twisted in the tunnel to a position in which this distribution is maintained. In general, if the aerofoil is not twisted in this way, there is a change in the distribution of circulation. If this change is taken into account, Glauert has shown for a tunnel of circular section “that the formulæ derived from the assumption of elliptic distribution of lift are sufficiently accurate for all conventional shapes of aerofoil, but that those derived from the assumption of a uniform distribution over-estimate the effect of increasing span of the aerofoil.”