Aerodynamic Forces on Biconvex Aerofoils Oscillating in a Supersonic Airstream + Effect of Thickness on the Aerodynamic Forces on Biconvex Aerofoils Oscillating in a Supersonic Airstream, and Calculation of Forces for Aerofoil with Flap

Abstract

A method for the calculation of the aerodynamic forces on an oscillating aerofoil which allows for the effect of thickness is developed. The steady flow regime for zero or mean incidence is first determhaed for isentropic, irrotational and inviscid flow conditions. A small disturbance is then assumed and the non-linear equation defining the subsequent motion is reduced to a linear equation for the velocity potential of the disturbance. This is expressed in difference form and solved numerically by a step-by-step process. The results obtained show good agreement with the known solutions for a thick aerofoil at incidence in steady flow, and for the case of an oscillating flat plate. Consequently, it is believed that the results derived for an oscillating biconvex aerofoil are reasonably accurate. Aerodynamic lift and pitching moment derivatives for a 5 per cent thick, symmetrical, circular-arc aerofoil at Mach numbers M = 1.4, 1.5 and 2.0 are given for a range of frequencies and compared with values obtained on the basis of the flat plate theory. The effect of thickness appears to be important at the lower values of M, and the results indicate that the flat plate theory is not sufficiently accurate. + The lift distribution and the aerodynamic force coefficients are calculated for a 7.5 per cent thick symmetrical circular-arc aerofoil at Mach numbers Mo = 2.0, 1.7, 1.5 for a range of frequencies. These results are compared wffh those given in an earlier report (Ref. 1) for a 5 per cent thick aerofoil, and with the values derived on the basis of flat plate theory. A limited comparison is also made between the calculated results and those obtained experimentally.