Abstract
An experimental investigation on vortex breakdown dynamics is performed. An adverse pressure gradient is created along the axis of a wing-tip vortex by introducing a sphere downstream of an elliptical hydrofoil. The instrumentation involves high-speed visualizations with air bubbles used as tracers and 2D Laser Doppler Velocimeter (LDV). Two key parameters are identified and varied to control the onset of vortex breakdown: the swirl number, defined as the maximum azimuthal velocity divided by the free-stream velocity, and the adverse pressure gradient. They were controlled through the incidence angle of the elliptical hydrofoil, the free-stream velocity and the sphere diameter. A single helical breakdown of the vortex was systematically observed over a wide range of experimental parameters. The helical breakdown coiled around the sphere in the direction opposite to the vortex but rotated along the vortex direction. We have observed that the location of vortex breakdown moved upstream as the swirl number or the sphere diameter was increased. LDV measurements were corrected using a reconstruction procedure taking into account the so-called vortex wandering and the size of the LDV measurement volume. This allows us to investigate the spatio-temporal linear stability properties of the flow and demonstrate that the flow transition from columnar to single helical shape is due to a transition from convective to absolute instability.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Alekseenko S, Bilsky A, Dublin V, Markovich D (2007) Experimental study of an impinging jet with different swirl rates. Int J Heat Fluid Flow 28:1340
Antkowiak A, Brancher P (2004) Transient energy growth for the lamb-oseen vortex. Phys Fluids 16(1):L1–L4
Avellan F, Herre P, Ryhming IL (1987) A new high speed cavitation tunnel. ASME 57:49–60
Billant P, Chomaz JM, Huerre P (1998) Experimental study of vortex breakdown in swirling jets. J Fluid Mech 376:183–219
Cooper D, Jackson D, Launder B, Liao G (1993) Impinging jet studies for turbulence model assessment–I. Flow field experiments. Int J Heat Mass Transfer 36(10):2675–2684
Deissler RJ (1987) The convective nature of instability in plane poiseuille flow. Phys Fluids 30:2303–2305
Devenport WJ, Rife MC, Liapis SI, Follin GJ (1996) The structure and development of a wing-tip vortex. J Fluid Mech 312:67–106
Escudier M, Bornstein J, Maxworthy T (1982) The dynamics of confined vortices. Proc R Soc Lond Ser A 382:335–360
Escudier MP (1988) Vortex breakdown: observations and explanations. Prog Aerospace Sci 25:189–229
Fabre D, Jacquin L (2004) Short-wave cooperative instabilities in representative aircraft vortices. Phys Fluids 16:1366
Gallaire F, Ruith M, Meiburg E, Chomaz JM, Huerre P (2006) Spiral vortex breakdown as global mode. J Fluid Mech 549:71–80
Grabowski W, Berger S (1976) Solutions of the navier-stokes equations for vortex breakdown as a global mode. J Fluid Mech 75:71–80
Hall M (1972) Vortex breakdown. Ann Rev Fluid Mech 4:195–218
Herrada MA, Fernandez-Feria R (2006) On the development of three-dimensional vortex breakdown in cylindrical regions. Phys Fluid 18(084105):1–15
Herrada MA, Pino CD, Ortega-Casanova J (2009) Confined swirling jet impingement on a flat plate at moderate Reynolds numbers. Phys Fluids 21(013601):1–9
Heyes A, Hubbard S, Marquis A, DS, (2003) On the roll-up of a trailing vortex sheet in the very near field. Proc Inst Mech Eng G J Aerospace Eng 217:217–269
Huerre P, Rossi M, Godreche C, Manneville P (1998) Hydrodynamic instabilities in open flows. Cambridge University Press, In Hydrodynamic and Nonlinear Instabilities
Huerre P, Batchelor G, Moffat H, Worster M (2000) Open shear flow instabilities. In Perspectives in fluid dynamics, Cambridge University Press
Iungo GV, Skinner P, Buresti G (2009) Correction of wandering smoothing effects on static measurements of a wing-tip vortex. Exp Fluids 46:435–452
Lambourne NC, Bryer DW (1961) The bursting of leading-edge vortices: some observations and discussion of the phenomenon. Aeronautical Research Council, Report & Memoranda R & M 3282:1–35
Leibovich S (1978) The structure of vortex breakdown. Ann Rev Fluid Mech 10:221–246
Lopez J (1994) On the bifurcation structure of axisymmetric vortex breakdown in a constricted pipe. Phys Fluids 6:3683–3693
Meliga P, Gallaire F (2011) Control of axisymmetric vortex breakdown in a constricted pipe: nonlinear steady states and weakly nonlinear asymptotic expansions. Phys Fluids 23:1–23
Meliga P, Gallaire F, Chomaz JM (2012) A weakly nonlinear mechanism for mode selection in swirling jets. J Fluid Mech 699:216–262
Ortega-Casanova J, Fernandez-Feria R (2009) Three-dimensional transitions in a swirling jet impinging against a solid wall at moderate reynolds numbers. J Fluid Mech 21(034107):1–9
Pier B, Huerre P, Chomaz JM (2001) Nonlinear self-sustained structures and fronts in spatially developing wake flows. J Fluid Mech 435:147–174
Qadri UA, Mistry D, Juniper MP (2013) Structural sensitivity of spiral vortex breakdown. J Fluid Mech 720:558–581
Ruith MR, Chen P, Meiburg E, Maxworthy T (2003) Three-dimensional vortex breakdown in swirling jets and wakes: direct numerical simulation. J Fluid Mech 486:331–378
Prothin S, Djeridi H, Billard J-Y (2014) Coherent and turbulent process analysis of the effects of a longitudinal vortex on boundary layer detachment on a NACA0015 foil. J Fluids Struct 47:2–20
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Pasche, S., Gallaire, F., Dreyer, M. et al. Obstacle-induced spiral vortex breakdown. Exp Fluids 55, 1784 (2014). https://doi.org/10.1007/s00348-014-1784-7
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00348-014-1784-7