Lift on Two-Dimensional Symmetrical Airfoil of Finite Thickness in Supersonic Flow

Author: Li, Ting-Yi

Year: 1947

Degree: Engineer's thesis

Advisor: Puckett, Allen E.

Committee Member: Unknown, Unknown

Option: Aeronautics

DOI: 10.7907/zajs-cy52

Abstract

This research consists of a study of several methods of computing the slope of lift curve for a two-dimensional symmetrical airfoil of finite thickness in completely supersonic potential flow. An "exact" formula is derived by considering the flow conditions over the airfoil surface including the effects of the oblique shock waves emitted from the leading edge of the airfoil. This "exact" formula is applied to two simple cases: (1) a 5% thick circular arc airfoil, and (2) a 10% thick circular arc airfoil. The computation results are compared with (1) Ackeret's linearized theory, (2) Busemann's second order theory and (3) Busemann's third order theory. It is found that the presence of shock waves at the airfoil leading edge will lead to a reversal in sign of the slope of lift curve at low Mach numbers close to 1.00, this effect is also sometimes observed experimentally. Furthermore, it has been shown that the linearized theory and the second order theory give too low dC∠ /doℒ values at high Mach numbers. The third order theory agrees with the "exact" theory in general tendency but is not quite so accurate in very high Mach number region and at Mach numbers close to 1.00. Thus, for accurate determination of the slope of lift curve, the "exact" formula may find some engineering uses. To facilitate future computations, charts for the necessary coefficients are prepared and steps in applying the formula for engineering cases are outlined and discussed in some detail.

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