The lift and moment acting on a thick aerofoil in unsteady motion

Abstract

A new approach to the problem of calculating the unsteady two-dimensional flow about aerofoils in an incompressible fluid is presented. While the flow is assumed to be inviscid throughout, the potential flow boundary conditions are modified semi-empirically to make some allowance for viscous effects. The method is applicable to thick aerofoils, the only limitation being that the velocities and displacements of the unsteady perturbations about the mean steady motion must be small. The dependent variable of the method is the complex harmonic function In ( U e ¹⁰ / q ), where U is the velocity at infinity, and ( q, 0 ) is the velocity vector in polar co-ordinates, while the independent variables are theory allows for (i) and (ii) but not for (iii). The theory yields three distinct effects of aerofoil thickness on the classical flat-plate oscillatory derivatives. These are: (i) the reduced frequency w is replaced by 8w , where 2 _n8 is the theoretical lift-slope, (ii) the force and moment derivatives are multiplied by factors of 8, and (iii) the reduction of the wake velocity due to the thickness of the aerofoil changes the flat-plate derivatives by an amount which is quite large at high values of w Tables are given from which it is possible to deduce with little effort the effects of aerofoil thickness and viscosity on the air-load coefficients. The theory yields results in close agreement with some recent Dutch measurements of the air-load coefficients and also with some earlier measurements at the National Physical Laboratory.