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

Abstract

Designing effective control for complex three-dimensional flow fields proves to be nontrivial. 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 α = 5 • 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.

On the formation of three-dimensional separated flows over wings under tip effects

“…Both factors contribute to the decay of the strength of tip vortices in a linear manner with increasing streamwise distance. Such linear decay of the tip vortices has also been observed in Edstrand et al (2018b). The line associated with smaller contour level |ω x | measures extended length and reduced decay rate.…”

“…Over the years, more detailed investigations have been carried out to reveal the formation, evolution and instability mechanisms of the tip vortices (McCormick, Sherrier & Tangler 1968;Crow 1970;Francis & Kennedy 1979;Katz & Galdo 1989;Green & Acosta 1991;Devenport et al 1996;Birch et al 2004;Duraisamy 2005;Giuni 2013;Edstrand et al 2016Edstrand et al , 2018a. Based on the insights from these studies, various control techniques to alleviate the tip vortices have also been developed to reduce the induced drag and wake vortex hazards (Gursul et al 2007;Greenblatt 2012;Edstrand et al 2018b;Gursul & Wang 2018).…”

Modal Analysis of Fluid Flows: Applications and Outlook

“…Flow over an airfoil is another example that attracts great engineering interests in aerodynamic and turbomachinery applications. Modal analysis has examined various aspects of airfoil wakes, including the wake structures [120,121], body geometry [122,123], tip vortex [124][125][126][127], aeroacoustics [128][129][130], and buffeting [131][132][133][134]. Key efforts have been placed on mitigating flow separation over an airfoil for performance enhancement and improved safety of aircraft.…”

The evolution of wingtip vortex wandering: a stability analysis based on stereo-PIV experiment

“…Previous efforts include studies of the effect of Reynolds number, swirl parameter, and azimuthal wavenumber on the stability of a theoretical Batchelor vortex [12,13]. In Oberleithner's stability analysis of swirling jets, a global resonant frequency was found throughout the wake [14] and Bi-global LSA performed by Edstrand et al tackled the influence of trailing wake on the stability of wingtip vortex solved by DNS computation at Re = 1000 [15] and found the fifth wake mode with optimal attenuation effect on the wingtip vortex [16]. However, the temporal and spatial evolution of the instability of wingtip vortex has not been fully investigated, which limits the knowledge of the underlying mechanism of vortex wandering and its development.…”