Instability of Unequal Strength, Counter-Rotating Vortex Pairs*


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.

 

Animation of dye flow visualization in the wake of an airfoil with unequal strength, counter-rotating vortex pairs: (Click on the image to watch the movie.)

Dye flow visualization




Animation axial vorticity measurement in the wake of an airfoil with unequal strength, counter-rotating vortex pairs: (Click on the image to watch the movie.)

Animation axial vorticity measurement


Links

Triangular-flapped aircraft wing designed by UC Berkeley researchers significantly reduces wake turbulence
http://www.berkeley.edu/news/media/releases/2001/11/20_wings.html

Flow Visualization of Unequal Strength, Counter-Rotating Vortex Pairs (Wake Vortex Instability)
http://www.me.berkeley.edu/ME260A_B/

U.C. Berkeley Fluid Mechanics Laboratory
http://www.me.berkeley.edu/fml/

 

Publications

Stability Characteristics of Counter-Rotating Vortex Pairs in the Wakes of Triangular-Flapped Airfoils (View this document as a PDF)

Rapidly Growing Instability Mode in Trailing Multiple Vortex Wakes, Ortega, J.M. & Savas, O., AIAA Journal, 39, No. 4, 750–754

Wake Alleviation Properties of Triangular-Flapped Wings (View this document as a PDF), Ortega, J.M., Bristol, R.L. & Savas, AIAA Journal, 40, No. 4, 2002, 709-721.

*This work was done by Jason Ortega as his dissertation topic at the University of California Berkeley.


For more information, contact Jason Ortega at:

Lawrence Livermore National Laboratory
P.O. Box 808, L-206
Livermore, CA 94551

Phone: (925) 423-0958
Fax: (925) 422-3389
ortega17@llnl.gov

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