Active attenuation of a trailing vortex inspired by a parabolized stability analysis

TL;DR

This paper demonstrates how a linear parabolized stability analysis can guide the design of active control strategies to effectively attenuate trailing vortices in a flow field, leading to shorter vortices and reduced circulation.

Contribution

The study introduces a stability-analysis-guided control approach for trailing vortices, showing its effectiveness in reducing vortex length and circulation.

Findings

The fifth wake mode excites vortex instability leading to vortex attenuation.

Controlling the principal wake mode shortens vortex length.

Controlling the fifth wake mode further reduces vortex length and circulation.

Abstract

Designing effective control for complex three-dimensional flow fields proves to be non-trivial. Oftentimes, intuitive control strategies lead to suboptimal control. To navigate the control space, we utilize a linear parabolized stability analysis to guide the design of a control scheme for a trailing vortex flow field aft of a NACA0012 half-wing at an angle of attack $\alpha = 5^\circ$ and a chord-based Reynolds number $Re = 1000$. The stability results show that the unstable mode with the smallest growth rate (fifth wake mode) provides a pathway to excite a vortex instability, whereas the principal unstable mode remains in the wake of the wing. Inspired by this finding, we perform direct numerical simulations that excite each mode with body forces matching the shape function from the stability analysis. Relative to the baseline uncontrolled case, the principal wake mode reduces the vortex length, while the fifth wake mode further shortens the tip vortex. Analogously, the streamwise circulation of the trailing vortex is found to be significantly reduced. From these results, we conclude that a rudimentary linear stability analysis can provide key insight into the underlying physics and help engineers design more effective control.