The oscillating aerofoil in subsonic flow

Abstract

A relatively simple method for calculating the aerodynamic forces on an oscillating aerofoil is developed and used to derive the aerodynamic coefficients for M = 0.7, 0.8 and 0.9 for a range of frequency parameter values. The two-dimensional aerofoiI is represented by a flat plate and the usual assumptions of linearized theory for unsteady flow are made. The problem is reduced to one of finding the solution of an integral equation for the velocity potential of the disturbed flow. This is solved by the use of the known solution of a related problem in incompressible flow in which the aerofoil oscillates at a frequency increased by the factor (1 - M²)-1 and for which the condition for tangential flow is suitably modified. By successive approximation to this modified boundary condition, it is possible to obtain solutions to any desired accuracy. Formulae for the aerodynamic coefficients may also be derived for each approximation. Those given by the first approximation are of sufficient accuracy for use in stability calculations when the frequency parameters involved are low. For higher values, more complicated formulae corresponding to higher-order approximations could be derived if required. The results obtained confirm that values given in Ref. 6 which were derived by Dietze's method for M = 0.7 and by Schade for M = 0.8 are substantially correct.