On The Role of Higher-Order Terms in Local Piston Theory

The use of second- and third-order classical piston theory [1] (CPT) is commonplace, with the role of the higher-order terms being well understood [2]. The advantages of local piston theory (LPT) relative to CPT have been demonstrated previously [3]. Typically, LPT has been used to perturb a mean-steady solution obtained from the Euler equations, and recently, from the Navier-Stokes equations [4]. The applications of LPT in the literature have been limited to first-order LPT [5–7]. The reasoning behind this has been that the dynamic linearization used assumes small perturbations. The present note clarifies the role of higher-order terms in LPT. It is shown that second-order LPT makes a non-zero contribution to the normal-force prediction, in contrast to second-order CPT

Aeroelastic prediction methods in supersonic flows for missile design

The prediction of aeroelastic instabilities such as flutter is important in the multi-disciplinary design and preliminary testing of missiles. Flutter prediction software varies in the fidelity of analysis, with accurate solutions being computationally expensive and involving the use of CFD. In this dissertation, a review is given of approximate methods for supersonic aeroelastic analysis. A general formulation of piston theory is developed to encompass both classical and local piston theory, and the literature on piston theory and its application in aeroelastic analysis is reviewed. An aeroelastic prediction method is developed for cantilevered trapezoidal plates in supersonic flows based on shock-expansion theory and local piston theory. The method is validated against 3D unsteady Euler aeroelastic computations in the Edge CFD solver and against experimental flutter data in literature. The prediction method is shown to be suitable for computationally inexpensive aeroelastic parametric studies applicable to missile fin design

Quantifying non-linearity 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 parameterised 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 parameterisation is used to assess the magnitude of non-linear 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

Zeroth-order flutter prediction for cantilevered plates in supersonic flow

An aeroelastic prediction framework in MATLAB with modularity in the quasi-steady aerodynamic methodology is developed. Local piston theory (LPT) is integrated with quasi-steady methods including shock-expansion theory and the Supersonic Hypersonic Arbitrary Body Program (SHABP) as a computationally inexpensive aerodynamic solver. Structural analysis is performed using bilinear Mindlin–Reissner quadrilateral plate elements. Strong coupling of the full-order system and linearization of the modal-order system are implemented. The methodology is validated against published experimental data in the literature and benchmarked against Euler computation in the Edge CFD code. The flutter dynamic pressure is predicted to be within 10% of the experimental value for 140 times lower computational cost compared to CFD. Good agreement in other cases is obtained with the industry-standard ZONA7 and ZONA7U codes

Local Piston Theory as an Alternative to Mesh Deformation: Slender Wing/Body Configurations

The suitability of local piston theory for modeling static loads on a deforming low-aspect-ratio wing in the presence of aerodynamic interference is investigated. Predictions using Euler-based local piston theory are compared to Euler solutions for the deformed geometry. Moderate to large deformations are investigated for the leeside wing on a cruciform wing/body configuration. It is shown that local piston theory is suitable even for large deformations, with the perturbation downwash/Mach number supersonic, provided that the loading induced by deformation is not dominated by interaction with body vortices or other sources of aerodynamic interference. Second-order local piston theory is recommended for deformations producing downwash/Mach numbers approaching sonic. The influence of the choice of piston theory coefficients is in producing an estimation band for the local piston theory load prediction, with insignificant influence on the load slope in the present investigation. In conclusion, local piston theory is put forward as a viable alternative to mesh deformation toward reduction of the computational cost of aerodynamic load prediction for static aeroelasticity, provided that perturbation loads are dominated by local twist and not by vortex interaction