Application of the unsteady compressible source and doublet panel method to flutter calculations

The Source and Doublet Panel Method (SDPM) developed by Morino in the 1970s can model unsteady compressible ideal flow around wings and bodies. In this work, the SDPM is adapted to the calculation of aeroelastic solutions for wings. A second order nonlinear version of Bernoulli’s equation is transformed to the frequency domain and written in terms of the generalized mode shapes and displacements. It is shown that the unsteady pressure component at the oscillating frequency is a linear function of the generalized displacements and can therefore be used to formulate a linear flutter problem. The proposed approach has several advantages: the exact geometry is modelled, including thickness, camber, twist and dihedral effects, the motion of the surface can be represented using all six degrees of freedom, the pressure calculation is of higher order and the generalised aerodynamic mass, damping and stiffness load terms are calculated separately. The complete procedure is validated using the experimental data from the weakened AGARD 445.6 wing and three rectangular wings with pitch and plunge degrees of freedom.