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Generalized Vortex Lattice Method for Oscillating Thin Airfoil in Subsonic Flow

The mathematical model for two-dimensional unsteady sonic flow, based on the classical diffusion equation with imaginary coefficient, is presented and discussed. The main purpose is to develop a rigorous formulation in order to bring into light the correspondence between the sonic, supersonic and subsonic panel method theory. Source and doublet integrals are obtained and Laplace transformation demonstrates that, in fact, the source integral is the solution of the doublet integral equation. It is shown that the doublet-only formulation reduces to a Volterra integral equation of the first kind and a numerical method is proposed in order to solve it. To the authors' knowledge this is the first reported solution to the unsteady sonic thin airfoil problem through the use of doublet singularities. Comparisons with the source-only formulation are shown for the problem of a flat plate in combined harmonic heaving and pitching motion.

Panel Method Formulation for Oscillating Airfoils in Sonic Flow

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Estudo numérico de uma asa com controle ativo de flutter por realimentação da pressão medida num ponto

Unsteady Lifting Surface Theory in Sonic Flow: The Problem Revisited

/pdf/modelo-numerico-para-simulacao-da-resposta-aeroelastica-de-4r3kr3f732.pdf

Modelo numérico para simulação da resposta aeroelástica de asas fixas.

A numerical method for calculating the unsteady pressure distribution on harmonically oscillating lifting surfaces in subsonic flow is presented. The Helmholtz equation for the complex velocity potential is written in integral form and solved by discrete panels superposition, which can be recognized as a generalization of the well-known vortex lattice method. Numerical calculations are carried out for a rectangular wing and are compared with well-established literature data. The influence of chordwise and spanwise discretization, as well as wake length, on the convergence rate, is also numerically studied

Marcos V. Bortolus

Papers

Generalized vortex lattice method for oscillating lifting surfaces in subsonic flow