Abstract
Wandering is a typical feature of wing-tip vortices and it consists in random fluctuations of the vortex core. Consequently, vortices measured by static measuring techniques appear to be more diffuse than in reality, so that a correction method is needed. In the present paper statistical simulations of the wandering of a Lamb-Oseen vortex are first performed by representing the vortex core locations through bi-variate normal probability density functions. It is found that wandering amplitudes smaller than 60% of the core radius are well predicted by using the ratio between the RMS value of the mean cross-velocity and its slope measured at the mean vortex center. Furthermore, the principal axes of wandering can be accurately evaluated from the opposite of the cross-correlation coefficient between the spanwise and the normal velocities measured at the mean vortex center. The correction of the wandering smoothing effects is then carried out through four different algorithms that perform the deconvolution of the mean velocity field with the probability density function that represents the wandering. The corrections performed are very accurate for the simulations with wandering amplitudes smaller than 60% of the core radius, whereas errors become larger with increasing wandering amplitudes. Subsequently, the whole procedure to evaluate wandering and to correct the mean velocity field is applied to static measurements, carried out with a fast-response five-hole pressure probe, of a tip vortex generated from a NACA 0012 half-wing model. It is found that the wandering is predominantly in the upward-outboard to downward-inboard direction. Furthermore, the wandering amplitude grows with increasing streamwise distance from the wing, whereas it decreases with increasing angle of attack and free-stream velocity.
Similar content being viewed by others
References
Bandyopadhyay P, Stead D, Ash R (1991) Organized nature of a turbulent trailing vortex. AIAA J 29:1627–1633
Batchelor G (1964) Axial flow in trailing line vortices. J Fluid Mech 20:645–658
Beninati M, Marshall J (2005) An experimental study of the effect of free-stream turbulence on a trailing vortex. Exp Fluids 38:244–257
Chigier N, Corsiglia V (1972) Wind-tunnel studies of wing wake turbulence. J Aircraft 9:820–825
Chow J, Zilliac G, Bradshaw P (1997) Mean and turbulence measurements in the near field of a wingtip vortex. AIAA J 35:1561–1567
Corsiglia V, Schwind R, Chigier N (1973) Rapid scanning, three-dimensional hot-wire anemometer surveys of wing-tip vortices. J Aircraft 12:752–757
Devenport W, Rife M, Liapis S, Follin G (1996) The structure and development of a wing-tip vortex. J Fluid Mech 326:67–106
Gerner A, Maurar C (1981) Calibration of seven-hole probes suitable for high angles in subsonic compressible flow. Tech. rep., USAFA-TR-81-4
Green S, Acosta A (1991) Unsteady flow in trailing vortices. J Fluid Mech 227:107–134
Gursul I, Xie W (2000) Origin of vortex wandering over delta wings. J Aircraft 37:348–350
Heyes A, Hubbard S, Marquis A, Smith D (2003) On the roll-up of a trailing vortex sheet in the very near field. Proc Inst Mech Eng G J Aerospace Eng 217:217–269
Heyes A, Jones R, Smith D (2004) Wandering of wing-tip vortices. In: 12th International symposium on application of laser techniques to fluid mechanics, Lisbon, Portugal
Hoffmann E, Joubert P (1963) Turbulent line vortices. J Fluid Mech 16:395–411
Iungo G, Skinner P (2007) Correction of wandering effects on static measurements of a wing tip vortex. Tech. Rep. ADIA 2007-2, Atti del Dipartimento di Ingegneria Aerospaziale dell’Università di Pisa
Jansson PA (1984) Deconvolution with application in spectroscopy. Academic Press, New York
Jaquin J, Fabre D, Geffroy P, Coustols E (2001) The properties of a transport aircraft wake in extended near field: an experimental study. AIAA Paper 1038
Larson J (2002) Two-dimensional and three-dimensional blind deconvolution of fluorescence confocal images. In: Proceedings of SPIE
Richardson WH (1972) Bayesian-based iterative method of image restoration. J Opt Soc Am 62(55):820–825
Ripley B (1987) Stochastic Simulation. ISBN 0 471 81884 4. Wiley, New York
Rokhsaz K, Foster S, Miller L (2000) Exploratory study of aircraft wake vortex filaments in a water tunnel. J Aircraft 37:1022–1027
Shekarriz A, Fu T, Katz J, Liu H, Huang T (1992) Study of junction and tip vortices using particle displacement velocimetry. AIAA J 30:145–152
Yeung A, Lee B (1999) Particle image velocimetry study of wing-tip vortices. J Aircraft 36:482–484
Acknowledgments
The authors would like to thank M. Morelli, who made a useful contribution to the planning of the tests at CSIR, and G. Lombardi for many useful discussions. Thanks are also due to F. Flandoli for his essential suggestions on statistics. Finally, the authors are grateful to G. Barbaro for his contribution in the execution of the tests.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Iungo, G.V., Skinner, P. & Buresti, G. Correction of wandering smoothing effects on static measurements of a wing-tip vortex. Exp Fluids 46, 435–452 (2009). https://doi.org/10.1007/s00348-008-0569-2
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00348-008-0569-2