Analysis of unsteady aerodynamics for elastic bodies in supersonic flow

Abstract

The harmonic potential panel method (HPP, also known as HGM) developed for nonplanar wings in supersonic flight is generalized in its capability to include flexible bodies performing bending oscillations. Three different coordinate systems (namely, the wind-fixed, body-fixed, and pseudo-wind-fixed) are first investigated. It is shown that the singularity at the apex is removed in the last two coordinate systems. The present HPP method is based on the formulation of a line-doublet paneling scheme, which is general for axisymmetric bodies of arbitrary shapes, allows for slope discontinuity, and is valid in the full frequency range. Because of the harmonic gradient model, the number of elements required is least affected by the given Mach number and reduced frequency. To validate the present HPP method, the computed results in various limits are verified with slenderbody theory, piston theory, measured stability derivatives, and steady velocities, as calculated by other methods for different body shapes.