Inviscid Flow About Airfoils at High Supersonic Speeds

Steady flow about curved airfoils is investigated analytically at high supersonic speeds. Assuming air behaves as an ideal diatomic gas, it is found that small pressure disturbances emanating from the surface of an airfoil are almost completely absorbed in the leading-edge shock wave (or a shock wave emanating from any other location on the surface), provided the flow deflection angles are not too close to those corresponding to shock detachment. This result is found to be essentially independent of Mach number. As a consequence, it is shown that within the limitations of the assumption of ideal gas flow, the shock-expansion method may be used with good accuracy to predict pressure distributions on curved airfoils at arbitrarily high Mach numbers. This observation is verified with the aid of the method of characteristics applied to a 10-percent-thick, biconvex airfoil at 0 deg angle of attack. It is further shown that the shock-expansion method can be easily employed to construct the entire flow field about a curved airfoil, accounting for shock-wave curvature and resulting entropy gradients in the flow.