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The Vortex Merger Factor in Aircraft Wake Turbulence

Published online by Cambridge University Press:  03 February 2016

Miroslav Mokry
Miroslav Mokry*
Affiliation:
Institute for Aerospace Research, NRC, Ottawa, Canada
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Abstract

Vortex merger is studied within the context of two-dimensional discrete vortex sheets and demonstrated on two equally oriented circular vortices and aircraft tip and flap vortices. It is confirmed that, depending on the wing load distribution, the latter may or may not coalesce into a single counter-rotating pair. The interaction of a vortex with an equally oriented shear layer, governed by the same physical principle, suggests a possible intensification of an aircraft vortex in cross-wind shear.

Type
Research Article
Information
The Aeronautical Journal , Volume 109 , Issue 1091 , January 2005 , pp. 1 - 13
Copyright
Copyright © Royal Aeronautical Society 2005 

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References

[1] Meunier, P. and Leweke, T.. Merging of a pair of corotating vortices, Album of Visualization, The Visualization Society of Japan, No. 16, 1999, pp. 1–2.Google Scholar
[2] Leith, C.E.. Minimum enstrophy vortices, Phys. Fluids, Vol. 27, No. 6, 1984, pp. 1386–1395.Google Scholar
[3] Chorin, A., Vorticity and turbulence, Springer-Verlag, New York, 1994, pp. 84–89.Google Scholar
[4] McWilliams, J.C.. The vortices of two-dimensional turbulence, J. Fluid Mech., Vol. 219, 1990, pp. 361–385.Google Scholar
[5] Dritschel, D.G.. Vortex properties of two-dimensional turbulence, Phys. Fluids A, Vol. 5, 1993, pp. 984–997.Google Scholar
[6] Lander, M. and Holland, G.J.. On the interaction of tropical-cyclone-scale vortices. I: Observations, Quart. J. Roy. Met. Society, Vol. 119, 1993, pp. 1347–1361.Google Scholar
[7] Pavia, E.G. and Cushman-Roisin, B.. Merging of frontal eddies, J. Phys. Oceanography, Vol. 20, 1990, pp. 1886–1906.Google Scholar
[8] Driscoll, C.F., Fine, K.S.. Experiments on vortex dynamics in pure electron plasmas, Phys. Fluids B, Vol. 2, 1990, pp. 1359–1368.Google Scholar
[9] Fine, K.S., Driscoll, C.F., Malmberg, J.H., and Mitchell, T.B.. Measurements of symmetric vortex merger, Phys. Rev. Letters, Vol. 67, No. 5, 1991, pp. 588–591.Google Scholar
[10] Amoretti, M., Durkin, D., Fajans, J., Pozzoli, R., and Romé, M.. Asymmetric vortex merger: experiments and simulations, Physics of Plasmas, Vol. 8, No. 9, 2001, pp. 3865–3868. Vol. 67, No. 5, 1991, pp. 588–591.Google Scholar
[11] Mitchell, T.B. and Driscoll, C.F.. Electron vortex orbits and merger, Phys. Fluids, Vol. 8, 1996, pp. 1828–1841.Google Scholar
[12] Driscoll, C.F., Jin, D.Z., Schecter, D.A., and Dubin, D.H.E., Vortex dynamics of 2D electron plasmas, Physica C 369, 2002, pp. 21–27.Google Scholar
[13] Mokry, M.. Numerical simulation of aircraft trailing vortices interacting with ambient shear or ground, J. Aircraft, Vol. 38, No. 4, 2001, pp. 636–643.Google Scholar
[14] Muskhelishvili, N.I., Singular integral equations, Noordhoff-Groningen, 1953, pp. 42–43.Google Scholar
[15] Raffel, M., Willert, C.E., and Kompenhans, J., Particle image velocimetry – A practical guide, Springer-Verlag 1998, p. 162.Google Scholar
[16] Melander, M.V, Zabusky, N.J., and McWilliams, J.C.. Symmetric vortex merger in two di-ll mensions: Causes and conditions, J. Fluid Mech., Vol. 195, 1988, pp. 303–340.Google Scholar
[17] Waugh, D.W.. The efficiency of symmetric vortex merger, Phys. Fluids A Vol. 4, No. 8, 1992, pp. 1745–1758.Google Scholar
[18] Shashikanth, B.N. and Newton, P.K.. Geometric phases for corotating vortex patches, J. Math. Phys., Vol. 41, 2000, pp. 8148–8162.Google Scholar
[19] Marshall, J.S., Inviscid incompressible flow, J. Wiley, New York, 2001, pp. 186–191.Google Scholar
[20] Roberts, K.V. and Christiansen, J.P.. Topics in computational fluid mechanics, Comput. Phys. Commun., Vol. 3, 1972, pp. 14–32.Google Scholar
[21] Christiansen, J.P. and Zabusky, N.J.. Instability, coalescence and fission of finite-area vortex structures, J. Fluid Mech., Vol. 61, 1973, pp. 219–243.Google Scholar
[22] Zabusky, N.J., Hughes, M.H., Roberts, K.V.. Contour dynamics for the Euler equations in two dimensions, J. Comp. Phys., 1979, Vol. 30, pp. 96–106.Google Scholar
[23] Dritschel, D.G.. Contour dynamics and contour surgery, Computer Physics Reports, 1989, Vol. 10, pp. 77–146.Google Scholar
[24] Pullin, D.I.. Contour dynamics methods, Annu. Rev. Fluid Mech, Vol. 24, 1992, pp. 89–115.Google Scholar
[25] Rossow, V.J.. Convective merging of vortex cores in lift-generated wakes, J. Aircraft, Vol. 14, No. 3, 1977, pp. 283–290.Google Scholar
[26] Moore, D.W.. The stability of an evolving two-dimensional vortex sheet, Mathematika, Vol. 23, 1976, pp. 35–44.Google Scholar
[27] Dritschel, D.G.. On the stabilization of a two-dimensional vortex strip in adverse shear, J. Fluid. Mech., Vol 206, 1989, pp. 193–221.Google Scholar
[28] Crow, S.. Stability theory for a pair of trailing vortices, AIAA J. Aircraft, Vol. 8, No. 12, 1970, pp. 2172–2179.Google Scholar
[29] Leweke, T. and Williamson, C.H.K.. Cooperative elliptic instability of a vortex pair, J.Fluid Mech., Vol. 360, 1998, pp. 85–119.Google Scholar
[30] Meleshko, V.V. and Van Heijst, G.J.F.. Interacting two-dimensional vortex structures: point vortices, contour kinematics and stirring properties, Chaos, Solitons & Fractals, Vol. 4, 1994, pp. 977–1010.Google Scholar
[31] Dritschel, D.G.. The nonlinear evolution of rotating configurations of uniform vorticity, J.Fluid Mech., Vol. 172, 157–182.Google Scholar
[32] Griffiths, R.W. and Hopfinger, E.J.. Coalescing of geostropic vortices, J. Fluid Mech., Vol. 178, 1987, pp. 73–97.Google Scholar
[33] Chen, A.L., Jacob, J.D., and Savas, O¨. Dynamics of corotating vortex pairs in the wakes of flapped airfoils, J. Fluid Mech., Vol. 382, 1999, pp. 155–193.Google Scholar
[34] Li, X. and Jacob, J.D.. Initial spacing effects on co-rotating tip vortex formation and merger, AIAA 2000-2219, Fluids 2000.Google Scholar
[35] Dritschel, D.G. and Waugh, D.W.. Quantification of the inelastic interaction of unequal vortices in two-dimensional vortex dynamics, Phys. Fluids A Vol. 4, No. 8, 1992, pp. 1737–1744.Google Scholar
[36] Melander, M.V., Zabusky, N.J., and McWilliams, J.C., Asymmetric vortex merger in two dimensions: Which vortex is victorious? Phys. Fluids, Vol. 30, 1987, pp. 2610–2612.Google Scholar
[37] Dritschel, D.G.. A general theory for two-dimensional vortex interactions, J. Fluid Mech., Vol. 293, 1995, pp. 269–303.Google Scholar
[38] Huenecke, K. and Huenecke, C.. Flowfield visualization in aircraft wake vortex research, 9th International Symp. on Flow Visualization, Paper 139, Edinburgh, UK, 2000.Google Scholar
[39] Jacquin, L., Fabre, D., and Geffroy, P.. The properties of a transport aircraft wake in the extended near field: an experimental study, AIAA 2001-1038, 39th AIAA Aero. Sci. Meeting, Reno, NV, 2001.Google Scholar
[40] Albano, F., De Gregorio, F., and Ragni, A.. Trailing vortex detection and quantitative evaluation of vortex characteristics by PIV technique, Paper 2.2,20th Intern. Congress on Instrum. in Aerospace Simulation Facilities, Goöttingen, Germany, 2003.Google Scholar
[41] Stumpf, E., Hepperle, M., Darracq, D., Meese, E.A., Elphick, G., and Galpin, S.. Benchmark test for Euler calculations of a high lift configuration vortex wake, AIAA-2002-0554, 40th Aerospace Sci. Meeting & Exhibit, Reno, NV, 2002.Google Scholar
[42] Graham, W. R., Park, S.W., and Nickels, T.B.. Trailing vortices from a wing with a notched lift distribution, AIAA J., Vol. 41, No. 9, 2003, pp. 1835–1838.Google Scholar
[43] Corsiglia, V.R., Iversen, J.D., and Orloff, K.L.. Laser-velocimeter surveys of merging vortices in a wind tunnel, J. Aircraft, Vol. 15, 1978, pp. 762–768.Google Scholar
[44] Breitsamter, C., Bellastrada, C., and Laschka, B., Investigations on the turbulent wake vortex flow of large transport aircraft, ICAS Congress, 2002, pp. 382.1–382.13.Google Scholar
[45] Cliffone, D.L.. Vortex interactions in multiple vortex wakes behind aircraft, J. Aircraft, Vol. 14, 1977, pp. 440–446.Google Scholar
[46] Bao, F., Vollmers, H. and Mattner, H.. Experimentala study on controlling wake vortex in water towing tank, ICIASF’03, 2003, pp. 214–223.Google Scholar
[47] Veldhuis, L.L.M., Scarano, F., and Van Wijk, C.. Vortex wake investigation of an Airbus A340 model using PIV and towing tank, AIAA 2003-3814, Appl. Aero. Conference, Orlando, 2003.Google Scholar
[48] Graham, W. R.. Optimising wing lift distribution to minimize wake vortex hazard, Aeronautical J., Vol. 106, 2002, pp. 413–426.Google Scholar
[49] Tombach, I.. Observation of atmospheric effects on vortex wake behavior, J. Aircraft, Vol. 10, 1973, pp. 641–647.Google Scholar
[50] Bilanin, A.J., Teske, M.E., and Hirsch, J.E.. Neutral atmospheric effects on the dissipation of aircraft vortex wakes, AIAA J., Vol. 16, 1978, pp. 956–961.Google Scholar
[51] Robins, R.E. and Delisi, D.P.. Numerical study of vertical shear and stratification effects on the evolution of a vortex pair, AIAA J., Vol. 28, 1990, pp. 661–669.Google Scholar
[52] Lewellen, D.C. and Lewellen, W.S.. Largeeddy simulations of the vortex-pair breakup in aircraft wakes, AIAA J., Vol. 34, 1996, pp. 2337–2345.Google Scholar
[53] Garten, J.F., Arendt, S., Fritts, D.C., and Werne, J.. Dynamics of counter-rotating vortex pairs in stratified and sheared environments, J.Fluid Mech., Vol. 361, 1998, pp. 189–236.Google Scholar
[54] Mokry, M.. Intensification of aircraft wake vortices in crosswind shear, J. Aircraft, Vol. 40, No. 2, 2003, pp. 405–407.Google Scholar
[55] Fichtl, G.H., Camp, D.W., and Frost, W.. Sources of low-level wind shear around airports, J. Aircraft, Vol. 14, No. 1, 1977, pp. 5–14.Google Scholar
[56] Frech, M. and Zinner, T.. Concept of wake vortex behavior classes, J. Aircraft, Vol. 41, No. 3, 2004, pp. 564–570.Google Scholar
[57] Brown, A.P., Politis, E. and Othman, A.. Line vortex modelling of vortices encountered as takeoff windshear by widebody jet transport, AIAA-2003-5384, AIAA Atm. Flight Mech. Conference, Austin, TX, 2003.Google Scholar
[58] Clark, T.L., Hall, W.D., Kerr, R.M., Middleton, D., Radke, L.F., Ralph, F.M., Neiman, P.J., and Levinson, D.. Origins of aircraft-damaging clear-air turbulence during the 9 December 1992 Colorado downslope windstorm: Numerical simulations and comparison with observations, J. Atmospheric Sci., Vol. 57, 2000, pp. 1105–11.Google Scholar
[59] Clark, T.L. and Radke, L.F.. Horizontal vortex tubes, clear air turbulence and implications for aviation safety, to be published in ICAO J.Google Scholar