Identification of freeplay and aerodynamic nonlinearities in a 2D aerofoil system with via higher-order spectra

Abstract

Higher-Order Spectra (HOS) are used to characterise the nonlinear aeroelastic behaviour of a plunging and pitching 2-degree-of-freedom aerofoil system by diagnosing structural and/or aerodynamic nonlinearities via the nonlinear spectral content of the computed displacement signals. The nonlinear aeroelastic predictions are obtained from high-fidelity viscous fluid-structure interaction simulations. The power spectral, bi-spectral and tri-spectral densities are used to provide insight into the functional form of both freeplay and inviscid/viscous aerodynamic nonlinearities with the system displaying both low- and high-amplitude Limit Cycle Oscillation (LCO). It is shown that in the absence of aerodynamic nonlinearity (low-amplitude LCO) the system is characterised by cubic phase coupling only. Furthermore, when the amplitude of the oscillations becomes large, aerodynamic nonlinearities become prevalent and are characterised by quadratic phase coupling. Physical insights into the nonlinearities are provided in the form of phase-plane diagrams, pressure coefficient distributions and Mach number flowfield contours.

Parameterization of nonlinear aeroelastic reduced order models via direct interpolation of Taylor partial derivatives

“…Excellent agreement can be observed between the FOM and ROM solutions -demonstrating that the nonlinear parameter space can indeed be captured with excellent precision using a biquadratic interpolation scheme. Although not presented here, almost identical trends are observed for the tip response using ROM 1 4 and ROM 2 9 .…”

“…Although this was not by design, it is an excellent finding that the inclusion of this ROM in the library allows robust identification of the nonlinear flutter point. Figure 10(b) demonstrates that at δ s = 0.5 • the bilinear ROM 1 4 captures the LCO amplitudes at the root rotational axis with very good precision and reasonable precision for δ s = 0.625 • . However, for freeplay values above this, discrepancies can be observed through under prediction of the LCO amplitude as the dynamic pressure increases beyond q ∞ = 3846 [Pa].…”

“…With a freeplay of δ s = 0.875 • the biquadratic ROM 2 9 is generally in very good agreement with the FOM, however, slightly over predicts the amplitude, making it more conservative. The bilinear ROM 1 4 slightly under predicts the amplitude and over predicts the depth of the inflections at the rotational velocity maxima.…”

“…In Figure 7 the contours demonstrate that the biquadratic ROM 2 9 is able to capture the entire parameter space with excellent precision while the bilinear ROM 1 4 is less accurate. The discrepancies are larger in regions of the space that are furthest from the sampled ROM 4 1 locations.…”

“…One of the challenges in modeling aeroelastic systems with discrete structural nonlinearities such as, freeplay, in the transonic flow regime, is the potential for nonlinear aerodynamic loads that coexist with the structural nonlinearity [1], [2]. While linearization of the nonlinear structural model is common practice in aeroelastic problems involving freeplay (employing techniques such as fictitious masses [3] or residual vectors [4]), the assumption of aerodynamic linearization may, for some transonic systems, be invalid with small parameter changes [5].…”