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Vortex Filament and Global Instability Analysis of the Crow Mode

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Part of the book series: Fluid Mechanics and Its Applications ((FMIA,volume 107))

Abstract

Aircraft trailing vortices and their wakes are important to understand in order to shorten the minimum aircraft distances for safe operation in commercial flights. The mechanisms of wake destruction are studied by predictions by both inviscid vortex filament and viscous BiGlobal instability analyses. The two methods have already been applied to the wake problem, but a more detailed comparison is carried out here. The results show excellent agreement between the two methodologies predicting the long wave symmetric instability of a counter-rotating pair of vortices, namely the Crow instability, even at low Reynolds numbers.

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Notes

  1. 1.

    There exist several cases where viscosity is added to filament methods applied to evolution problems, but its introduction to eigenvalue problems is still an open issue.

References

  1. Brion V, Sipp D, Jacquin L (2007) Optimal amplification of the crow instability. Phys Fluids 19(11):111703

    Article  Google Scholar 

  2. Crouch JD (1997) Instability and transient growth for two trailing-vortex pairs. J Fluid Mech 350:311–330

    Article  MathSciNet  MATH  Google Scholar 

  3. Crow SC (1970) Stability theory for a pair of trailing vortices. AIAA J 8:2172–2179

    Article  Google Scholar 

  4. Fabre D, Jacquin L (2000) Stability of a four-vortex aircraft wake model. Phys Fluids 12(10):2438–2443

    Article  MathSciNet  Google Scholar 

  5. Gómez F, Gómez R, Theofilis V (2014) On three-dimensional global linear instability analysis of flows with standard aerodynamics codes. Aerosp Sci Technol 32(1):223–234

    Article  Google Scholar 

  6. Gonzalez LM, Gomez-Blanco R, Theofilis V (2008) Eigenmodes of a counter-rotating vortex dipole. AIAA J 46(11):2796–2805

    Article  Google Scholar 

  7. Hein S, Theofilis V (2004) On instability characteristics of isolated vortices and models of trailing-vortex systems. Comp Fluids 33(5–6):741–753

    Article  MATH  Google Scholar 

  8. Jiménez J (1970) Stability of a pair of co-rotating vortices. Phys Fluids 18(11):1580–1581

    Article  Google Scholar 

  9. Kármán TV (1912) Über den mechanismus des widerstandes, den ein bewegter Körper in einer Flüssigkeit erfährt. Nachr Ges Wissenschaft Göttingen, pp 547–556

    Google Scholar 

  10. Paredes P, Hermanns M, Le Clainche S, Theofilis V (2013) Order \(10^4\) speedup in global linear instability analysis using matrix formation. Comput Method Appl M 253:287–304

    Article  MATH  Google Scholar 

  11. Rodríguez D, Theofilis V (2009) Massively parallel solution of the BiGlobal eigenvalue problem using dense linear algebra. AIAA J 47(10):2449–2459

    Article  Google Scholar 

  12. Sipp D, Jacquin L, Cossu C (2000) Self-adaptation and viscous selection in concentrated two-dimensional vortex dipoles. Phys Fluids 12(2):245–248

    Article  MATH  Google Scholar 

  13. Spalart P (1998) Airplane trailing vortices. Annu Rev Fluid Mech 30:107–138

    Article  MathSciNet  Google Scholar 

  14. Tendero JA, Paredes P, Roura M, Govindarajan R, Theofilis V (2013) Biglobal and point vortex methods for the instability analysis of wakes. AIAA Paper 2013–2820

    Google Scholar 

  15. Theofilis V (2003) Advances in global linear instability analysis of nonparallel and three-dimensional flows. Prog Aerosp Sci 39(4):249–315

    Article  Google Scholar 

  16. Theofilis V (2011) Global linear instability. Annu Rev Fluid Mech 43:319–352

    Article  MathSciNet  Google Scholar 

  17. Widnall SE (1975) Structure and dynamics of vortex filaments. Annu Rev Fluid Mech 7:141–165

    Article  Google Scholar 

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Acknowledgments

Discussions with Dr. J. D. Crouch and Mr. S. Benton regarding the role of the cutoff distance and other aspects are gratefully acknowledged. Support of the Marie Curie Grant PIRSES-GA-2009-247651 “FP7-PEOPLE-IRSES: ICOMASEF—Instability and Control of Massively Separated Flows” as well as from the Plan Nacional Grant TRA2009-13648 “Metodologías Computacionales para la Predicción de Inestabilidades Globales Hidrodinámicas y Aeroacústicas en Flujos Complejos” are gratefully acknowledged.

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Correspondence to Juan Ángel Tendero .

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Tendero, J.Á., Paredes, P., Roura, M., Govindarajan, R., Theofilis, V. (2015). Vortex Filament and Global Instability Analysis of the Crow Mode. In: Theofilis, V., Soria, J. (eds) Instability and Control of Massively Separated Flows. Fluid Mechanics and Its Applications, vol 107. Springer, Cham. https://doi.org/10.1007/978-3-319-06260-0_34

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  • DOI: https://doi.org/10.1007/978-3-319-06260-0_34

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-06259-4

  • Online ISBN: 978-3-319-06260-0

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