Stability characteristics of counter-rotating vortex pairs in the wakes of triangular-flapped airfoils.

摘要

A rapidly growing instability is observed to develop between unequal strength, counter-rotating vortex pairs in the wakes of airfoils with outboard triangular flaps. To investigate the physical mechanisms for this instability, a linear stability analysis is performed on a single vortex pair. This analytical model reveals that the instability is driven by the strain rate field from one vortex acting on the perturbations of its neighboring vortex. Another linear stability analysis is conducted to include the effects of the other counter-rotating vortex pair. The qualitative features of the instability, such as its wavelength and non-linear evolution, are examined by flow visualization measurements that are made in a towing tank facility at a chord-based Reynolds number of O(105). From these observations, a sinuous instability is seen to develop on the weaker flap vortices and have a wavelength of order one wingspan. The instability wavelengths that are observed in the flow visualization data compare favorably with those predicted by the two- and four-vortex linear stability analyses, demonstrating that the analytical models capture the essential physics of the instability growth. Quantitative measurements of the vortex wakes are made with a PIV technique, allowing the vortex structure, trajectories, kinetic energy, and distribution to be assessed up to several hundred wingspans downstream of the airfoils. Additionally, the circulation-based Reynolds number is seen to be of O(105). The PIV data indicate that the wake's two-dimensional kinetic energy decreases substantially as the instability transforms the two-dimensional nature of the wake into a three-dimensional one. Finally, the wake alleviation properties of this instability are measured by computing the maximum rolling moment and downwash that a following wing might experience if it were placed in the wakes of these airfoils. These calculations show that by 75 wingspans, the wakes of the triangular-flapped airfoils have rolling moments and downwash that are always less than those of a conventional rectangular airfoil. This rapid reduction in the rolling moment and downwash leads to the conclusion that this instability between unequal strength, counter-rotating vortex pairs has the potential to solve the wake hazard problem.