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Symmetry breaking and instabilities of conical vortex pairs over slender delta wings

  • Bao-Feng Ma (a1), Zhijin Wang (a2) and Ismet Gursul (a2)

Abstract

An investigation of symmetry breaking and naturally occurring instabilities over thin slender delta wings with sharp leading edges was carried out in a water tunnel using particle image velocimetry (PIV) measurements. Time-averaged location, strength and core radius of conical vortices vary almost linearly with chordwise distance for three delta wings with $75^{\circ }$ , $80^{\circ }$ and $85^{\circ }$ sweep angles over a wide range of angles of attack. Properties of the time-averaged vortex pairs depend only on the similarity parameter, which is a function of the angle of attack and the sweep angle. It is shown that time-averaged vortex pairs develop asymmetry gradually with increasing values of the similarity parameter. Vortex asymmetry can develop in the absence of vortex breakdown on the wing. Instantaneous PIV snapshots were analysed using proper orthogonal decomposition and dynamic mode decomposition, revealing the shear layer and vortex instabilities. The shear layer mode is the most periodic and more dominant for lower values of the similarity parameter. The Strouhal number based on the free stream velocity component in the cross-flow plane is a function of only the similarity parameter. The dominant frequency of the shear layer mode decreases with the increasing similarity parameter. The vortex modes reveal the fluctuations of the vorticity magnitude and helical displacement of the cores, but with little periodicity. There is little correlation between the fluctuations in the cores of the vortices.

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Corresponding author

Email address for correspondence: ensiag@bath.ac.uk

References

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Antkowiak, A. & Brancher, P. 2004 Transient energy growth for the Lamb–Oseen vortex. Phys. Fluids 16, 14.
Ayoub, A. & McLachlan, B. G 1987 Slender delta wing at high angles of attack – a flow visualization study. In AIAA 19th Fluid Dynamics, Plasma Dynamics and Lasers Conference, June 8–10, Honolulu, Hawaii, AIAA Paper 87-1230, American Institute of Aeronautics and Astronautics.
Birds, J. D.1969 Tuft-grid surveys at low speeds for delta wings. NASA Technical Note 5045.
Brown, C. E. & Michael, W. H. 1954 Effect of leading-edge separation on the lift of a delta wing. J. Aerosp. Sci. 21, 690694.
Bulathsinghala, D., Jackson, R., Wang, Z. & Gursul, I. 2017 Afterbody vortices of axisymmetric cylinders with a slanted base. Exp. Fluids 58, 60;doi:10.1007/s00348-017-2343-9.
Cai, J., Liu, F. & Luo, S.2001 Stability of symmetric vortices over slender conical bodies at high angles of attack. AIAA Paper 2001-2845.
Cai, J., Liu, F. & Luo, S. 2003 Stability of symmetric vortices in two dimensions and over three-dimensional slender conical bodies. J. Fluid Mech. 480, 6594.
Cerretelli, C. & Williamson, C. H. K. 2003 The physical mechanism for vortex merging. J. Fluid Mech. 475, 4177.
Chen, C., Wang, Z., Cleaver, D. J. & Gursul, I.2016 Interaction of trailing vortices with downstream wings. AIAA Paper 2016-1848.
Cipolla, K. M. & Rockwell, D. 1998 Small-scale vortical structures in crossflow plane of a rolling delta wing. AIAA J. 36, 22762278.
Degani, D. 1991 Effect of geometrical disturbances on vortex asymmetry. AIAA J. 29, 560566.
Degani, D. & Tobak, M. 1992 Experimental study of controlled tip disturbance effect on flow asymmetry. Phys. Fluids. 4, 28252832.
Del Pino, C., Lopez-Alonso, J. M., Parras, L. & Fernandez-Feria, R. 2011 Dynamics of the wing-tip vortex in the near field of a NACA0012 aerofoil. Aeronaut. J. 111, 229239.
Delery, J. M. 1994 Aspects of vortex breakdown. Prog. Aerosp. Sci. 30, 159.
Devenport, W. J., Rife, M. C., Liapis, S. I. & Follin, G. J. 1996 The structure and development of a wing-tip vortex. J. Fluid Mech. 312, 67106.
Edstrand, A. M., Davis, T. B., Schmid, P. J., Taira, K. & Cattafesta, L. N. 2016 On the mechanism of trailing vortex wandering. J. Fluid Mech. 801, R1-1R1-11.
Fabre, D., Sipp, D. & Jacquin, L. 2006 Kelvin waves and the singular modes of the Lamb–Oseen vortex. J. Fluid Mech. 551, 235274.
Gad-el-Hak, M. & Blackwelder, R. F. 1985 The discrete vortices from a delta wing. AIAA J. 23, 961962.
Gordnier, R. & Visbal, M. R. 1994 Unsteady vortex structure over a delta wing. J. Aircraft 31, 243248.
Gursul, I. 1994 Unsteady flow phenomena over delta wings at high angle of attack. AIAA J. 32, 225231.
Gursul, I. 2005 Review of unsteady vortex flows over slender delta wings. J. Aircraft 42, 299319.
Gursul, I. & Yang, H. 1995 On fluctuations of vortex breakdown location. Phys. Fluids 7, 229231.
Hall, M. G. 1961 A theory for the core of a leading-edge vortex. J. Fluid Mech. 11, 209228.
Heaton, C. J. & Peake, N. 2007 Transient growth in vortices with axial flow. J. Fluid Mech. 587, 271301.
Heiland, R. W.1992 KLTOOL: a mathematical tool for analyzing spatiotemporal data, Master thesis, Arizona State University, Dept of Mathematics.
Huang, M. K. & Chow, C. Y. 1996 Stability of leading-edge vortex pair on a slender delta wing. AIAA J. 34, 11821187.
Keener, E. R. & Chapman, G. T. 1977 Similarity in vortex asymmetries over slender bodies and wings. AIAA J. 15, 13701372.
Lee, M. & Ho, C.-M. 1990 Lift force of delta wings. Appl. Mech. Rev. 43, 209221.
Leibovich, S. 1984 Vortex stability and breakdown – survey and extension. AIAA J. 22, 11921206.
Leweke, T., Le Dizés, S. & Williamson, C. H. K. 2016 Dynamics and instabilities of vortex pairs. Annu. Rev. Fluid Mech. 48, 507541.
Lim, T. T., Lua, K. B. & Luo, S. C. 2001 Role of tip and edge geometry on vortex asymmetry. AIAA J. 39, 539543.
Lowson, M. V. & Ponton, A. J. C. 1992 Symmetry breaking in vortex flows on conical bodies. AIAA J. 30, 15761583.
Lumley, J. L. 1970 Stochastic tools in turbulence. Applied Mathematics and Mechanics, vol. 12. Academic.
Menke, M. & Gursul, I. 1997 Unsteady nature of leading edge vortices. Phys. Fluids 9, 17.
Menke, M., Yang, H. & Gursul, I. 1999 Experiments on the unsteady nature of vortex breakdown over delta wings. Exp. Fluids 27, 262272.
Polhamus, E. C. 1971 Predictions of vortex-lift characteristics by a leading-edge suction analogy. J. Aircraft 8, 193199.
Pradeep, D. S. & Hussain, F. 2006 Transient growth of perturbations in a vortex column. J. Fluid Mech. 550, 251288.
Raffel, M., Willert, C. E., Wereley, S. & Kompenhans, J. 2007 Particle Image Velocimetry – A Practical Guide, 2nd edn. Springer.
Renac, F. & Jacquin, L. 2007 Linear stability properties of lifting vortices over delta wings. AIAA J. 45, 19421951.
Roy, C. & Leweke, T.2008 Experiments on vortex meandering. FARWake Technical Report AST4-CT-2005-012238, CNRS-IRPHE, also presented in International Workshop on Fundamental Issues Related to Aircraft Trailing Wakes 27–29 May 2008, Marseille, France.
Schmid, P. J. 2010 Dynamic mode decomposition of numerical and experimental data. J. Fluid Mech. 656, 528.
Sirovich, L. 1987 Turbulence and the dynamics of coherent structures. Parts I–III. Q. Appl. Maths 45, 561590.
Smith, J. H. B. 1968 Improved calculations of leading-edge separation from slender, thin, delta wings. Proc. R. Soc. Lond. A 306, 6790.
Stahl, W. H., Mahmood, M. & Asghar, A. 1992 Experimental investigations of the vortex flow on delta wings at high incidence. AIAA J. 30, 10271032.
Theofilis, V. 2011 Global linear instability. Annu. Rev. Fluid Mech. 43, 319352.
Towfighi, J. & Rockwell, D. 1993 Instantaneous structure of vortex breakdown on a pitching delta wing. AIAA J. 31, 11601162.
Tobak, M. & Peake, D. J. 1982 Topology of three-dimensional separated flows. Annu. Rev. Fluid Mech. 14, 6185.
Tu, J. H., Rowley, C. W., Luchtenburg, M., Brunton, S. L. & Kutz, J. N. 2014 On dynamic mode decomposition: theory and applications. J. Comput. Dyn. 1, 391421.
Wang, Z. & Gursul, I. 2012 Unsteady characteristics of inlet vortices. Exp. Fluids 53, 10151032.
Wu, G. X., Deng, X. Y. & Wang, Y. K. 2014 Effects of tip perturbation on asymmetric vortex flow over slender delta wings. AIAA J. 52, 886890.
Wu, J.-Z., Ma, H.-Y. & Zhou, M.-D. 2006 Vorticity and Vortex Dynamics. p. 73. Springer.
Zhang, X., Wang, Z. & Gursul, I. 2016 Interaction of multiple vortices over a double delta wing. Aerosp. Sci. Technol. 48, 291307.
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Symmetry breaking and instabilities of conical vortex pairs over slender delta wings

  • Bao-Feng Ma (a1), Zhijin Wang (a2) and Ismet Gursul (a2)

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