Wind-tunnel wall interference effects on oscillating aerofoils in subsonic flow

Abstract

A theory is developed for estimating the effect of wind-tunnel walls on the air forces acting on an aerofoil oscillating in a subsonic airstream. It can only be applied for a range of frequencies well below the frequency at which transverse vibrations of the air stream may be induced. The possibility of resonance occurring for certain combinations of tunnel height, frequency of oscillation of aerofoil, wind speed and Mach number was first pointed out by Runyan and Watkins, and the present paper confirms their conclusions. The method is applied to calculate aerodynamic derivatives for an oscillating flat plate in a wind tunnel of height equal to 4.75 aerofoil chord and a Mach number M = 0-7. Results obtained are tabulated for comparison with the known theoretical free-stream values. It is shown that the influence of the walls is considerable even at frequencies of oscillation well below that of resonance. Measurements of the pitching-moment damping coefficient for the RAE 104 aerofoil of 2-in. chord in:the 9.5-in. x 9.5-in. Wind Tunnel have been made by Bratt and his results for M = 0.7 differ appreciably from the corresponding estimated values given in this note. However, by the use of the equivalent profile method much better agreement may be obtained. This method is used to estimate the pitching-moment damping for a range of Much numbers and low-frequency parameter values corresponding to those used in the tests. Fairly good agreement between estimated and measured values is obtained up to M = 0.8, and the calculations indicate, in accordance with experiment, a loss of damping at the highest Mach numbers considered.