Prediction of freeplay-induced aeroelastic limit cycle oscillations using the Loewner framework

Kurzfassung

Abstract Freeplay in control-surface mechanisms can generate finite-amplitude limit cycle oscillations (LCOs) that are not captured by linear aeroelastic stability analysis. This paper investigates an efficient reduced-order approach for predicting such responses using frequency-domain aerodynamic data. Unsteady aerodynamic forces are represented in state-space form by means of the Loewner framework and coupled with a three-degree-of-freedom typical-section model including heave, pitch and control-surface rotation. The freeplay nonlinearity is introduced in the control-surface hinge. The formulation is applicable to aerodynamic data from different fidelity levels, including incompressible two-dimensional potential flow, the doublet-lattice method (DLM) and linearized frequency-domain (LFD) Reynolds-averaged Navier-Stokes solutions. The resulting nonlinear aeroelastic system is solved by time-domain integration and harmonic balance. A describing-function extension of the p-L flutter method is used to provide amplitude-dependent initial guesses for the harmonic-balance solver. The method is applied to a scaled typical section representative of a transport-aircraft airfoil. In incompressible flow, time-domain and harmonic-balance solutions are compared. In the transonic regime, DLM- and LFD-based Loewner models are shown to yield different LCO predictions. For the small freeplay gap considered, the LFD-Loewner state-space model reproduces the high-fidelity computational-fluid-dynamics/computational-structural-mechanics (CFD-CSM) response, demonstrating its potential for efficient small-amplitude freeplay-induced LCO prediction.