Extreme vortex-gust airfoil interactions at Reynolds number 5000

We study interactions between an NACA0012 airfoil and a discrete vortex gust of extreme strength at a chord-based Reynolds number of 5000. This paper considers the gust ratios of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>G</a:mi><a:mo>≥</a:mo><a:mn>1</a:mn></a:mrow></a:math>, representative of conditions experienced by small-scale aircraft in adverse flight environments. We first carry out large-eddy simulations of spanwise periodic flows around an airfoil at the angle of attack of <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:msup><b:mn>14</b:mn><b:mo>∘</b:mo></b:msup></b:math>, exhibiting a turbulent separated wake. Introducing a vortex gust as a Taylor vortex upstream of the wing, the dependence of aerodynamic forces and vortical flows on gust parameters such as magnitude, rotational direction (positive and negative signs), size, and orientation is investigated. The lift responses and flow fields exhibit primarily two-dimensional behavior up to the gust ratio <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mo>|</c:mo><c:mi>G</c:mi><c:mo>|</c:mo></c:mrow></c:math> of 3, while three-dimensionality with very fine-scale structures emerges for <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mo>|</d:mo><d:mi>G</d:mi><d:mo>|</d:mo><d:mo>≥</d:mo><d:mn>4</d:mn></d:mrow></d:math>, triggering instabilities during the interaction. Once the gust becomes large in size, the fluctuation of aerodynamic loads is further enlarged, and the deformation of vortical flows and lift response is experienced earlier compared with cases with a small-sized gust, which reveals the dangerous aerodynamic situation hindering stable flights. The current study also shows that the fluctuation of the unsteady lift strongly depends on the gust location and rotational direction, providing hints for lift attenuation. Scale-decomposition analysis is performed to further examine the energy-transfer dynamics in extreme vortex-airfoil interaction across a range of spatial length scales. We reveal that the energy from large-scale vortex cores is transferred to the shear layers that emerge due to the interaction. Based on the current findings, we also consider unsupervised machine learning-based data compression of the present extreme vortex-gust airfoil interactions with an observable-augmented nonlinear autoencoder. A collection of vortical flow snapshots for <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:mo>|</e:mo><e:mi>G</e:mi><e:mo>|</e:mo><e:mo>≤</e:mo><e:mn>3</e:mn></e:mrow></e:math> whose interaction dynamics are primarily two-dimensional can be compressed to three variables while extracting the important vortical structures associated with the lift coefficient. The findings throughout this study suggest that modeling and control strategies developed for two-dimensional problems could be considered for analyzing extreme vortex-airfoil interactions at higher Reynolds numbers.