Development of an Aeroprediction Method for Slender Bodies Including Aeroelastic Effects Using Euler-Based Local Piston Theory

Abstract

Euler-based local piston theory (LPT) has received significant interest in recent literature. The method utilizes a simple, algebraic relation to predict between perturbation pressures directly from local surface deformation and from the local fluid conditions obtained from a steady Euler solution. Early applications of Euler-based LPT to simple, non-interfering geometries and flows yielded the accurate (<5% error) prediction of unsteady pressures at orders-of-magnitude lower computational expense compared to unsteady CFD. These successes led to the broader application of Euler-based LPT to more complex scenarios, such as full-vehicle geometries and interference flows. However, a degradation in the prediction accuracy was noted. This motivated the present work, in which the suitability of Euler-based LPT as an aeroprediction method for slender bodies with aeroelastic effects is assessed.

An extensive and thorough review of the literature revealed that no investigation into higher-order terms in the pressure equation of LPT had been made. More significantly, the mathematical basis for LPT had yet been developed. Finally, no controlled numerical investigation into the application of Euler-based LPT under aerodynamic interference associated with cruciform control surfaces on slender bodies could be found in the literature.

The present work addresses the above gaps in the literature. The first is addressed analytically, and shows that second-order LPT provides a non-zero contribution to aerodynamic stiffness. To address the second gap, a derivation of LPT from the 3D unsteady Euler equations is presented, with an in-depth discussion of the required assumptions. A number of significant conclusions regarding the validity of Euler-based LPT are drawn. It is argued that the method will be in significant error when applied in regions involving, amongst others, viscous boundary-layers, concentrated vorticity, transonic or embedded subsonic flows, sharp curvature, wing-body junctions, subsonic leading-edges, wing-tips, and trailing-edges. Furthermore, it is argued that Euler-based LPT will be in error when applied to mode-shapes of deformation involving localized bending and camber or point-local deformations. Finally, it is stressed that an algebraic pressure equation in LPT cannot account for flowfield interaction, which may be significant in the aforementioned scenarios. These conclusions are supported by a numerical investigation performed in the present work, which addresses the third gap in the literature.