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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 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
Brion V, Sipp D, Jacquin L (2007) Optimal amplification of the crow instability. Phys Fluids 19(11):111703
Crouch JD (1997) Instability and transient growth for two trailing-vortex pairs. J Fluid Mech 350:311–330
Crow SC (1970) Stability theory for a pair of trailing vortices. AIAA J 8:2172–2179
Fabre D, Jacquin L (2000) Stability of a four-vortex aircraft wake model. Phys Fluids 12(10):2438–2443
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
Gonzalez LM, Gomez-Blanco R, Theofilis V (2008) Eigenmodes of a counter-rotating vortex dipole. AIAA J 46(11):2796–2805
Hein S, Theofilis V (2004) On instability characteristics of isolated vortices and models of trailing-vortex systems. Comp Fluids 33(5–6):741–753
Jiménez J (1970) Stability of a pair of co-rotating vortices. Phys Fluids 18(11):1580–1581
Kármán TV (1912) Über den mechanismus des widerstandes, den ein bewegter Körper in einer Flüssigkeit erfährt. Nachr Ges Wissenschaft Göttingen, pp 547–556
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
Rodríguez D, Theofilis V (2009) Massively parallel solution of the BiGlobal eigenvalue problem using dense linear algebra. AIAA J 47(10):2449–2459
Sipp D, Jacquin L, Cossu C (2000) Self-adaptation and viscous selection in concentrated two-dimensional vortex dipoles. Phys Fluids 12(2):245–248
Spalart P (1998) Airplane trailing vortices. Annu Rev Fluid Mech 30:107–138
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
Theofilis V (2003) Advances in global linear instability analysis of nonparallel and three-dimensional flows. Prog Aerosp Sci 39(4):249–315
Theofilis V (2011) Global linear instability. Annu Rev Fluid Mech 43:319–352
Widnall SE (1975) Structure and dynamics of vortex filaments. Annu Rev Fluid Mech 7:141–165
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.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/978-3-319-06260-0_34
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-06259-4
Online ISBN: 978-3-319-06260-0
eBook Packages: EngineeringEngineering (R0)