A first order theory for Newtonian flow over two-dimensional airfoils

Abstract

Summary A simple closed-form formula for the coefficient of surface pressure, Cp is given in this paper. The formula is based on first and second approximations of the full problem and can be used for the Newtonian flow past two-dimensional thin airfoils at small angles of attack and with attached shock waves. It thus extends Cole's zero order theory to the effects of non-zero (γ – 1) and finite values of Mx where γ is the ratio of the specific heats of the gas and Mx is the free stream Mach number. The analysis presented relies on a previous recent formulation of the hypersonic small disturbance theory which has proved to be more advantageous than the hypersonic small disturbance theory. The results are compared with other approximate methods and the agreement is found to be generally good.