Quantifying nonlinearity in planar supersonic potential flows

Abstract

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.