Wind-tunnel interference effects on measurements of aerodynamic coefficients for oscillating aerofoils

Abstract

A theory is developed for estimating the effect of wind-tunnel walls on measured values of aerodynamic coefficients for two-dimensional aerofoils oscillating in an incompressible fluid. The case of an aerofoil describing translational and pitching oscillations in a wind tunnel of rectangular cross-section is considered, and it is shown in Table 1 and Figs. 3 and 4 that the damping derivatives associated with the pitching degree of freedom are very sensitive to wall effects when the frequency parameter for the motion is small, and when the axis of oscillation is not at, or near, quarter chord. When the axis is at quarter chord, the pitching-moment damping-derivative is hardly affected by the presence of the tunnel walls. The values of the derivatives given in Table 1 refer to an axis of oscillation at mid-chord and correspond to a ratio of tunnel height to aerofoil chord of 4.75. They are used to determine the pitching-moment derivatives for an axis of oscillation at 0.445c for comparison with values obtained by J. B. Bratt from measurements on a 2-in. chord aerofoil in a 9½-in. square wind tunnel. The theoretical values corresponding to free-stream conditions differ considerably from the experimental results, but, as shown in Figs. 4 and 5, better agreement is obtained when an allowance for tunnel-wall interference is made. The remaining difference between theory and experiment may he attributed to the influence of aerofoil thickness and to boundary-layer effects. By the use of the method developed in (R. & M. 2654), these effects can also be taken into account and incorporated in the theory presented for estimating pure interference corrections for the aerodynamic derivatives. When this is done, the results given in Table 2, and plotted in Figs. 4 and 5, are obtained. A comparison of theory and experiment then shows satisfactory agreement.