Nonlinear aerodynamics of a pitching wing: Experiments and data-driven modelling

The rotating blades of a helicopter or a wind turbine are subject to unsteady
aerodynamic loads. These may cause vibration, fatigue, and even catastrophic
failure in the underlying structure. A major challenge when modelling such
unsteady loads is to accurately capture aerodynamic nonlinearities. The most
pronounced nonlinear effects are associated with stall, when the flow separates
from the wing surface, which is most likely to occur when the angle of attack
is large or changes rapidly.
The increasing availability of high-quality data both from experiments and
simulations has paved the way for modelling unsteady aerodynamics in a
data-driven manner. Non-linear system identification provides a powerful
framework to fully account for nonlinearity in data-driven models. In this dis-
sertation, we investigate the potential of such models for a canonical system in
unsteady nonlinear aerodynamics: the pitching wing. A flexible and robust
model structure is provided by polynomial nonlinear state-space (PNLSS)
models, where the classical linear state- space model is extended with nonlin-
ear functions.
The quality of a data-driven model depends critically on the quality of the
data on which it is trained. We use wind-tunnel experiments of a pitching wing
performed with a dedicated wind tunnel setup that allows the user to impose
an arbitrary motion to the wing, including the high offset angles and pitch
rates that lead to stall. PNLSS models are most suitably trained on broad-
band signals. The wing is therefore pitched with swept- sine and random-
i
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phase multisine excitation signals. PNLSS models are then constructed from
those data.
This work demonstrates the first use of the multisine signal for modelling
the unsteady aerodynamics of the pitching wing. The PNLSS models trained
on swept sines and multisines are validated on harmonically pitching wing
data with different degrees of nonlinearity. The harmonic pitching resembles
the load condition encountered in wind turbines and helicopters. The results
show that the PNLSS models can estimate the nonlinear aerodynamic forces
more accurately than a linear model or semi-empirical model. Furthermore,
it is shown that the same modelling procedure can handle a range of nonlin-
earity in the different operating regimes of the pitching wing. Thus, a single
PNLSS model can be obtained which represents both linear and nonlinear
behaviour. The identified nonlinear models can be used in a model-based
controller to accurately predict the fluctuating loads on the aerodynamic sur-
face. The modelling procedure requires minimum user intervention which
makes it attractive for use in industry.