Two-dimensional transonic aerodynamic design method

Abstract

This paper demonstrates the capabilities of a new transonic, two-dimensional design method, based on the simultaneous solution of multiple streamtubes, coupled through the position of, and pressure at, the streamline interfaces. This allows the specification of either the airfoil shape (direct, analysis mode) or the airfoil surface pressure distribution (inverse, design mode). The nonlinear system of equations is formulated in a conservative manner, which guarantees the correct treatment of shocks, and is solved by a rapid Newton solution method. Viscous effects can also be included through a coupled integral boundary-layer analysis. The first set of results shows the effect of different far-field treatments, demonstrating the improvement in accuracy obtained by including the second-order doublet terms in addition to the usual first-order vortex term. The results are also compared to those obtained by specifying straight far-field streamlines (corresponding to solid-wall wind-tunnel experiments) or constant far-field pressure (corresponding to freejet experiments) to show the sensitivity to the farfield distance. In the second set of results, the design method is used to design a transonic airfoil with C/ = 1.000 at A/oo = 0.70. It is shown that the off-design performance is improved by specifying a surface pressure distribution with a very weak shock.