Transient Encounters of a NACA0012 Wing with a Streamwise-Oriented Vortex

Abstract

A high-fidelity numerical study has been conducted to examine the unsteady interactions resulting from a finite wing maneuvering into a streamwise-oriented vortex as a representative problem of wake encounters. A NACA0012 wing at an angle of α = 4 • and operating at a Reynolds number of Re = 2.0 × 10 5 is dynamically maneuvered into the path of a stationary vortex, and the transient encounter is analyzed for three side-slip velocities corresponding to 10%, 20%, and 40% of the free stream. The wing is shown to traverse a range of flow regimes, including instances of vortex pairing of the tip and incident vortices that lead to mutual induction and attenuation of the pair, tip vortex suppression as the impingement passes inboard of the wingtip, and induced separation that precipitates an abrupt transition at the leading edge. The overall flow structure is mostly consistent among the wing speeds examined, indicating an almost quasi-stationary response with relative vortex position. However, a notable lag is observed in the development of a spiraling instability in the incident vortex just upstream of the wing. With slower encounter speeds, the vortex core exhibits a pronounced spiraling undulation that persists farther upstream earlier in the motion. The advanced development is attributed to prolonged exposure to the adverse pressure gradient from stagnation on the underside of the wing that decelerates the core axial flow below known stability bounds of the vortex. Additionally, a dynamic loading effect is identified prior to the vortex crossing inboard of the wingtip, whereby the incident structure's relative position at peak loading shifts outboard with increased wing speed. The peak magnitudes of lift, pitching moment, and rolling moment coefficients are also shown to scale proportionally with the wing's side-slip speed as they are predicated upon an enhanced tip vortex development. In all cases as the wing approaches the vortex, an upstream progression of separation, transition, and reattachment over the leading edge leads, which forward tilts the force vector and reduces the drag. Once the vortex is brought inboard, however, the drag saturates, and the other quantities exhibit a nearly quasi-stationary response with vortex position as the wingtip unloads.

Further Investigations of the Tip Vortex on an Oscillating NACA0012 Wing

“…The wing is fixed at a geometric angle of α = 8 • and operates at a chord-based Reynolds number of Re c = 2 × 10 5 following previous work by the current authors. 28,29 The free-stream Mach number is set to M ∞ = 0.1 to largely avoid effects of compressibility for this stage of the analysis. The flow is assumed to be symmetric about the midspan, which makes the problem more computationally tractable for LES by allowing only half of the wing to be modeled.…”