Local Piston Theory with Viscous Correction and Its Application

Abstract

This paper introduces a local piston theory with viscous correction for the prediction of hypersonic unsteady aerodynamic loads at high attitudes and large Mach numbers. A semi-empirical relation accounting for the viscous interaction effects to determine the effective shape is proposed. The method is validated by applying to thin airfoils at various Mach numbers, angles of attack, and operating altitudes. Sample two- and three-dimensional aerodynamic forces calculations are conducted demonstrating this method. Furthermore, flutter boundary predictions for a two-dimensional airfoil and pitching-in-damping derivative evaluations for a three-dimensional waverider configuration are performed with this unsteady aerodynamic model. Compared with the Euler-based local piston theory, this model performs much better at high altitudes for a wide range of Mach numbers, angles of attack, and shapes. Results suggest the feasibility of using the effective shape of hypersonic vehicles to efficiently and accurately obtain the unsteady aerodynamic characteristics in hypersonic flow environment.