Generalized formulation and review of piston theory for airfoils

The present work presents a brief review of some of the notable contributions to piston theory and of its theoretical basis. A generalized formulation of piston theory is given, applicable to both local and classical piston theory. A consistent generalized formulation of the downwash equation is given, accounting for arbitrary motion in the plane of the airfoil. The formulation reduces to established downwash equations through appropriate definition of the cylinder orientation. The theoretical range of validity of Lighthill’s classical piston theory is examined, and the relative accuracy of a number of approximate theories encapsulated by the formulation as applied to a planar wedge is considered. The relative importance of higher-order terms in piston theory is examined, with the significance of recent literature extending the fidelity of the firstorder term highlighted. It is subsequently suggested that current implementations of local piston theory may be improved through the use of a first-order term of suitable accuracy.Armaments Corporation of South Africa through the Fluxion grant.http://arc.aiaa.org/loi/aiaajhb2016Mechanical and Aeronautical Engineerin

Quantifying nonlinearity in planar supersonic potential flows

An analysis is presented which allows the engineer to quantitatively estimate the validity bounds of aerodynamic methods based in linear potential flows a-priori. The development is limited to quasi-steady planar flows with attached shocks and small body curvature. Perturbation velocities are parametrised in terms of Mach number and flow turning-angle by means of a series-expansion for flow velocity based in the method of characteristics. The parametrisation is used to assess the magnitude of nonlinear term-groupings relative to linear groups in the full potential equation. This quantification is used to identify dominant nonlinear terms and to estimate the validity of linearising the potential flow equation at a given Mach number and flow turning angle. Example applications include the a-priori estimation of the validity bounds for linear aerodynamic models for supersonic aeroelastic analysis of lifting surfaces and panels.http://journals.cambridge.org/action/displayJournal?jid=AFR2017-06-30hb2017Mechanical and Aeronautical Engineerin

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

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.Thesis (PhD)--University of Pretoria, 2019.Armscor (Fluxion / Ledger)Mechanical and Aeronautical EngineeringPhDUnrestricte