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The structure and development of a wing-tip vortex

Published online by Cambridge University Press:  26 April 2006

William J. Devenport ,
Michael C. Rife ,
Stergios I. Liapis  and
Gordon J. Follin
William J. Devenport
Affiliation:
Department of Aerospace and Ocean Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA
Michael C. Rife
Affiliation:
Department of Aerospace and Ocean Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA
Stergios I. Liapis
Affiliation:
Department of Aerospace and Ocean Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA
Gordon J. Follin
Affiliation:
Department of Aerospace and Ocean Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA
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Abstract

Experiments have been performed on the tip vortex trailing from a rectangular NACA 0012 half-wing. Preliminary studies showed the vortex to be insensitive to the introduction of a probe and subject only to small wandering motions. Meaningful velocity measurements could therefore be made using hot-wire probes.

Detailed analysis of the effects of wandering was performed to properly reveal the flow structure in the core region and to give confidence in measurements made outside the core. A theory has been developed to correct mean-velocity profiles for the effects of wandering and to provide complete quantitative estimates of its amplitude and contributions to Reynolds stress fields. Spectral decomposition was found to be the most effective method of separating these contributions from velocity fluctuations due to turbulence.

Outside the core the flow structure is dominated by the remainder of the wing wake which winds into an ever-increasing spiral. There is no large region of axisymmetric turbulence surrounding the core and little sign of turbulence generated by the rotational motion of the vortex. Turbulence stress levels vary along the wake spiral in response to the varying rates of strain imposed by the vortex. Despite this complexity, the shape of the wake spiral and its turbulent structure reach an approximately self-similar form.

On moving from the spiral wake to the core the overall level of velocity fluctuations greatly increases, but none of this increase is directly produced by turbulence. Velocity spectra measured at the vortex centre scale in a manner that implies that the core is laminar and that velocity fluctuations here are a consequence of inactive motion produced as the core is buffeted by turbulence in the surrounding spiral wake. Mean-velocity profiles through the core show evidence of a two-layered structure that dies away with distance downstream.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 312 , 10 April 1996 , pp. 67 - 106
Copyright
© 1996 Cambridge University Press

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References

Accardo, L., Cenedese, A. & Cioffi, F. 1984 Experimental analysis of tip vortex by laser Doppler anemometry. 2nd Int Symp. on Applications of Laser Anemometry to Fluid Mechanics, Lisbon Portugal, July 2–5.
Antonia, R. A. & Britz, D. 1989 Phase-averaging in the turbulent far wake. Exps. Fluids 7, 138–142.Google Scholar
Baker, G. R., Barker, S. J., Bofah, K. K. & Saffman, P. G. 1974 Laser anemometer measurements of trailing vortices in water. J. Fluid Mech. 65, 325–336.Google Scholar
Baldwin, B. S., Chigier, N. A. & Sheaffer, Y. S. 1973 Decay of far-flowfield in trailing vortices. AIAA J. 11, 1601–1602.Google Scholar
Bandyopadhyay, P. R., Stead, D. J. & Ash, R. L. 1991 Organized nature of a turbulent trailing vortex. AIAA J. 29, 1627–1633.Google Scholar
Batchelor, G. K. 1964 Axial flow in trailing line vortices. J. Fluid Mech. 12, 645–658.Google Scholar
Bechner, W. 1975 Inequalities in Fourier Analysis. Annl Maths 102, 159–182.Google Scholar
Betz, A. 1933 Behavior of vortex systems. NACA Tech. Note 713, pp. 237–253.Google Scholar
Bilanin, A. J., Teske, M. E. & Williamson, G. G. 1977 Vortex interactions and decay in aircraft wakes. AIAA J. 15, 250–260.Google Scholar
Bisgood, P. L., Maltby, R. L. & Dee, F. W. 1971 Some work at the Royal Aircraft Establishment on the behavior of vortex wakes. In Aircraft Wake Turbulence and its Detection (ed.J. H. Olsen, A. Goldberg & M. Rogers), pp. 171–206. Plenum.
Brandt, S. A. & Iversen, J. D. 1977 Merging of aircraft trailing vortices. J. Aircraft 14, 1212–1220.Google Scholar
Browne, L. B. W., Antonia, R. A. & Chua, L. P. 1989 Calibration of X-probes for turbulent flow measurement. Exps. Fluids 7, 201–208.Google Scholar
Chigier, N. A. & Corsiglia, V. R. 1971 Tip vortices – velocity distributions. NASA TM-62,087.
Choi, K. & Simpson, R. L. 1987 Some mean-velocity, turbulence and unsteadiness characteristics of the VPI Stability Wind Tunnel. Rep. VPI-AOE-161. VPI, Blacksburg VA.
Chow, J. S., Zilliac, G. G. & Bradshaw, P. 1994 Turbulence measurements in the near-field of a wingtip vortex. ASME Forum on Turbulence in Complex Flows, Chicago IL, Nov. 6–11.
Ciffone, D. L. 1974 Correlation for estimating vortex rotational velocity downstream dependence. J. Aircraft 11, 716–717.Google Scholar
Ciffone, D. L. & Orloff, K. L. 1975 Far-field wake-vortex characteristics of wings. J. Aircraft 12, 464–470.Google Scholar
Corsiglia, V. R., Iversen, V. J. & Ciffone, D. L. 1976 Experimental study of the effect of span loading on aircraft wakes. J. Aircraft 13, 968–973.Google Scholar
Corsiglia, V. R., Schwind, R. G. & Chigier, N. A. 1973 Rapid scanning, three-dimensional hotwire anemometer surveys of wing-tip vortices. J. Aircraft 10, 752–757.Google Scholar
Devenport, W. J., Glegg, S. A. L. & Sharma, G. 1992 Turbulence measurements in trailing vortices for BWI noise prediction. Rep. VPI-AOE-192. VPI, Blacksburg VA.
Devenport, W. J. & Sharma, G. 1990 Flow visualizations of a wing-tip vortex in the presence of a probe. Rep. VPI-AOE-177. VPI, Blacksburg VA.
Döbbeling, K., Lenze, B. & Leuckel, W. 1990 Computer-aided calibration with a quadruple hotwire probe. Exps. Fluids 8, 257–262.Google Scholar
Donaldson, C.duP. 1972 Calculation of turbulent shear flows for atmospheric and vortex motions. AIAA J. 10, 4–12.Google Scholar
Donaldson, C.duP., Snedeker, R. S. & Sullivan, R. D. 1974 Calculation of aircraft wake velocity profiles and comparison with experimental measurements. J. Aircraft 11, 547–555.Google Scholar
Dosanjh, D. S., Gasparek, E. P. & Eskinazi, S. 1962 Decay of a viscous vortex. Aero. Q. 13, 167–188.Google Scholar
Engel, M. 1995 A wind-tunnel investigation of a wing-tip trailing vortex. 1 thesis, AOE Dept, VPI, Blacksburg, VA.
Francis, T. B. & Katz, J. 1988 Observations on the development of a tip vortex on a rectangular hydrofoil. Trans. ASME I: J. Fluids Engng 110, 208–215.Google Scholar
Garodz, L. J. 1971 Federal Aviation Administration full-scale aircraft vortex wake turbulence flight test investigations: past, present, and future. AIAA Paper 71–97.Google Scholar
Gasparek, E. P. 1957 Viscous decay of a vortex. 1 thesis, Syracuse University, NY.
Green, S.I. & Acosta, A. J. 1991 Unsteady flow in trailing vortices. J. Fluid Mech. 227, 107–134.Google Scholar
Hoffman, E. R. & Joubert, P. N. 1963 Turbulent line vortices. J. Fluid Mech. 16, 395–411.Google Scholar
Huffaker, R. M., Jelalian, A. V. & Thompson, J. A. L. 1970 Laser Doppler system for detection of aircraft trailing vortices. Proc. IEEE 58, 322–326.Google Scholar
Iversen, J. D. 1976 Correlation of turbulent trailing vortex decay data. J. Aircraft 13, 338–342.Google Scholar
Iversen, J. D., Corsiglia, V. R., Park, S., Backhus, D. R. & Brickman, R. A. 1979 Hot-wire, laser-anemometer, and force measurements of interacting trailing vortices. J. Aircraft 16, 448–454.Google Scholar
Katz, J. & Bueno Galdo, J. 1989 Effect of roughness on rollup of tip vortices on a rectangular hydrofoil. J. Aircraft 26, 247–253.Google Scholar
Kovasznay, L. S. G. 1954 Physical Measurements in Gas Dynamics and Combustion, p. 227. Princeton University Press.
Leuptow, R. M., Breuer, K. S. & Haritonidis, J.H. 1988 Computer-aided calibration of X-probes using a look-up table. Exps Fluids 7, 201–208.Google Scholar
Lezius, D. K. 1974 Water tank study of the decay of trailing vortices. AIAA J. 12, 1065–1071.Google Scholar
Lundgren T. S. & Ashurst, W. T. 1989 Area-varying waves on curved vortex tubes with application to vortex breakdown. J. Fluid Mech. 200, 283–307.Google Scholar
Marshall, J. S. 1993 The effect of axial pressure gradient on axisymmetrical and helical vortex waves. Phys. Fluids A 5, 588–599.Google Scholar
Mason, W. H. & Marchman, J. F. 1972 Far-field structure of an aircraft trailing vortex. NASA CR 62078.
Mason, W. H. & Marchman, J. F. 1973 Far-field structure of aircraft wake turbulence. J. Aircraft 10, 86–92.Google Scholar
Mathioudakis, K. & Breugelmans, F. A. E. 1985 Use of triple hot wires to measure unsteady flows with large direction changes. J. Phys. E: Sci. Instrum. 18, 414–419.Google Scholar
Maxworthy, T. 1988 Waves on vortex cores. Fluid Dyn. Res. 3, 52–62.Google Scholar
Maxworthy, T., Hopfinger, E. J. & Redekopp, L. G. 1985 Wave motions on vortex cores. J. Fluid Mech. 151, 141–165.Google Scholar
Mayer, E. W. & Powell, K. G. 1992 Similarity solutions for viscous vortex cores. J. Fluid Mech. 238, 487–507.Google Scholar
McCormick, B. W., Tangler, J. L. & Sherrieb, H. E. 1968 Structure of trailing vortices. J. Aircraft 5, 260–267.Google Scholar
Melander, M. V. & Hussain, F. 1991 Coherent structure dynamics: Interaction between large and fine scales. 8th Symp. on Turbulent Shear Flows, Munich, Sept. 9–11, Paper 28–5.
Mertaugh, L. J., Damania, R. B. & Paillet, F. L. 1977 An investigation of the near-field wake behind a full-scale test aircraft. J. Aircraft 14, 894–902.Google Scholar
Monaghan, J. J. & Humble, R. J. 1993 Vortex particle methods for periodic channel flow. J. Comput. Phys. 107, 152–159.Google Scholar
Orloff, K. L. 1974 Trailing vortex wind-tunnel diagnostics with a laser velocimeter. J. Aircraft 11, 477–482.Google Scholar
Panton, R. L., Oberkampf, W. L. & Soskic, N. 1980 Flight measurements of a wing tip vortex. J. Aircraft 17, 250–259.Google Scholar
Phillips, W. R. C. & Graham, J. A. H. 1984 Reynolds stress measurements in a turbulent trailing vortex. J. Fluid Mech. 147, 353–371.Google Scholar
Ragab, S. 1995 Direct numerical simulation of instability waves in a trailing vortex. AIAA Paper 95-0591.
Ragab, S. & Sreedhar, M. 1995 Numerical simulation of vortices with axial velocity deficits. Phys. Fluids 7, 549–558.Google Scholar
Reed, R. E. 1973 Properties of the lateral random oscillations of trailing vortices observed in wind-tunnel tests. Nielsen Engineering, NEAR TR-47, January.
Rossow, V. J. 1973 On the inviscid rolled-up structure of lift-generated vortices. J. Aircraft 10, 647–650.Google Scholar
Sarpkaya, T. 1992 Three-dimensional interactions of vortices with a free surface. AIAA Paper 92-0059.
Shekarriz, A., Fu, T. C., Katz, J. & Huang, T. T. 1993 Near-field behavior of a tip vortex. AIAA J. 31, 112–118.Google Scholar
Singh, P. I. & Uberoi, M. S. 1976 Experiments on vortex stability. Phys. Fluids 19 1858–1863 1858–1863.Google Scholar
Smits, A. J. & Kummer, R. P. 1985 The interaction and merger of two turbulent line vortices. AIAA Paper 85-0046.
Steger, J. L. & Cutler, P. 1976 Implicit finite-difference procedures for the computation of vortex wakes. AIAA Paper 76-385.
Stifle, K. E. & Panton, R. L. 1991 Experiments concerning the theories of vortex breakdown. AIAA Paper 91-0736.
Stinebring, D. R., Farell, K. J. & Billet, M. L. 1991 The structure of a three-dimensional tip vortex at high Reynolds numbers. Trans. ASME Fluids Engng 113, 496–503.Google Scholar
Thompson, D. H. 1975 Experimental study of axial flow in wing tip vortices. J. Aircraft 8, 910–911.Google Scholar
Tutu, N. K. & Chevray, R. 1975 Cross-wire anemometry in high-intensity turbulence. J. Fluid Mech. 71, 785–800.Google Scholar
Vogel, C. M., Devenport, W. J. & Zsoldos, J. S. 1995 Turbulence structure of a pair of merging tip vortices. 10th Symp. on Turbulent Shear Flows, Pennsylvania State University, August 14–16.
Vukoslavčević, P. & Wallace, J. M. 1981 Influence of velocity gradients on measurements of velocity and streamwise vorticity with hot-wire X-array probes. Rev. Sci. Instrum. 52, 869–879.Google Scholar
Wood, N. B. 1975 A method for the determination and control of the frequency response of a constant-temperature hot-wire anemometer. J. Fluid Mech. 67, 769–786.Google Scholar
Wygnanski, I., Champagne, F. & Marasli, B. 1986 On the large scale structures in two-dimensional small-deficit turbulent wakes. J. Fluid Mech. 168, 31–71.Google Scholar
Zeman, O. 1995 The persistence of trailing vortices: a modelling study. Phys. Fluids 7, 135–143.Google Scholar
Zheng, Y. 1992 An experimental study of wing-tip vortex in the near wake of a rectangular wing. PhD dissertation, Washington State University.
Zsoldos, J. S. & Devenport, W. J. 1991 Flow visualizations of interacting wing-tip vortex pairs. Rep. VPI-AOE-188. VPI, Blacksburg VA.
Zsoldos, J. S. & Devenport, W. J. 1992 An experimental investigation of interacting trailing vortex pairs. Proc. 19th Symp. on Naval Hydrodynamics, Seoul, South Korea, August.