Nonlinear aeroelastic modeling via conformal mapping and vortex method for a flat-plate airfoil in arbitrary motion

•A nonlinear aerodynamic modeling for flat plates in arbitrary motion is proposed.•The model uses conformal mapping and a complex-potential representation of the flow.•The assumptions of linearized body kinematics and flat wake are removed.•Validation with linearized formulations and experimental data is performed.•The aeroelastic response to sudden starts and body–vortex interactions is studied.

A nonlinear aerodynamic modeling based on conformal mapping is presented to obtain semi-analytical formulas for the unsteady aerodynamic force and pitching moment on a flat-plate airfoil in arbitrary motion. The aerodynamic model accounts for large amplitudes and non-planar wake and is used to study the aeroelastic behavior of a flat-plate airfoil elastically connected to a support. The fluid is assumed to be inviscid and incompressible, while the flow is assumed to be attached, planar, and potential. Within these hypotheses, conformal mapping and a complex-potential representation of unsteady aerodynamics are used to simplify the theoretical formulation. The vorticity shed at the trailing edge is discretized in desingularized point vortices in order to allow free-wake dynamics. The unsteady aerodynamic model is validated with classical linearized formulations based on the assumption of small disturbances, and with experimental data and theoretical predictions for a large-amplitude pitch-up, hold, pitch-down maneuver. The aeroelastic model is then used to simulate the response of a flat-plate airfoil to sudden starts and body–vortex interactions. Numerical results show that the proposed approach can be an effective tool to model the aeroelastic behavior of an arbitrarily-moving wing section in a time-dependent potential stream of incompressible fluid.

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