Hostname: page-component-8448b6f56d-mp689 Total loading time: 0 Render date: 2024-04-18T12:20:51.268Z Has data issue: false hasContentIssue false
  • English
  • Français

Direct numerical simulation of vortex ring evolution from the laminar to the early turbulent regime

Published online by Cambridge University Press:  25 February 2008

P. J. ARCHER ,
T. G. THOMAS  and
G. N. COLEMAN
P. J. ARCHER
Affiliation:
University of Southampton – Aerospace Engineering, Highfield Campus, University Road Southampton, SO17 1BJ, UKpja@soton.ac.uk
T. G. THOMAS
Affiliation:
University of Southampton – Aerospace Engineering, Highfield Campus, University Road Southampton, SO17 1BJ, UKpja@soton.ac.uk
G. N. COLEMAN
Affiliation:
University of Southampton – Aerospace Engineering, Highfield Campus, University Road Southampton, SO17 1BJ, UKpja@soton.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

Direct numerical simulation is used to study the temporal development of single vortex rings at various Reynolds numbers and core thicknesses. Qualitative differences between the evolution of thin- and thick-core rings are observed leading to a correction factor to the classical equation for the ring translational velocity. We compare the obtained linear modal growth rates with previous work, highlighting the role of the wake in triply periodic numerical simulations. The transition from a laminar to a turbulent ring is marked by the rearrangement of the outer core vorticity into a clearly defined secondary structure. The onset of the fully turbulent state is associated with shedding of the structure in a series of hairpin vortices. A Lagrangian particle analysis was performed to determine the ring entrainment and detrainment properties and to investigate the possibility of an axial flow being generated around the circumference of the core region prior to the onset of turbulence.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 598 , 10 March 2008 , pp. 201 - 226
Copyright
Copyright © Cambridge University Press 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Bergdorf, M., Koumoutsakos, P. & Leonard, A. 2007 Direct numerical simulation of vortex rings at Re γ = 7500. J. Fluid Mech 581, 495–505.CrossRefGoogle Scholar
Crow, S. 1970 Stability theory for a pair of trailing vortices. AAIA J 8, 2172–2179.CrossRefGoogle Scholar
Dabiri, J. & Gharib, M. 2004 Fluid entrainment by isolated vortex rings. J. Fluid Mech. 511, 311–331.CrossRefGoogle Scholar
Dazin, A., Dupont, P. & Stanislas, M. 2006 a Experimental characterization of the instability of the vortex ring. PartI: Linear phase. Exps. Fluids 40, 383–399.CrossRefGoogle Scholar
Dazin, A., Dupont, P. & Stanislas, M. 2006 b Experimental characterization of the instability of the vortex ring. PartII: Non-linear phase. Exps. Fluids 41, 401–413.CrossRefGoogle Scholar
Glezer, A. & Coles, D. 1990 An experimental study of a turbulent vortex ring. J. Fluid Mech. 211, 243–283.CrossRefGoogle Scholar
Kerswell, R. 2002 Elliptical instability. Annu. Rev. Fluid Mech 34, 83–113.CrossRefGoogle Scholar
Krutzsch, C. 1939 Über eine experimentell beobachtete erscheining an werbelringen bei ehrer translatorischen beivegung in weklechin, flussigheiter. Annln Phys 5, 497–523.CrossRefGoogle Scholar
Kumar, M., Arakeri, J. & Shankar, P. 1995 Translational velocity oscillations of piston generated vortex rings. Phys. Fluids 7, 2751–2756.CrossRefGoogle Scholar
Lamb, H. 1932 Hydrodynamics, 6th edn. Dover.Google Scholar
Maxworthy, T. 1972 The structure and stability of vortex rings. J. Fluid Mech. 51, 15–32.CrossRefGoogle Scholar
Maxworthy, T. 1974 Turbulent vortex rings. J. Fluid Mech. 64, 227–239.CrossRefGoogle Scholar
Maxworthy, T. 1977 Some experimental studies of vortex rings. J. Fluid Mech. 81, 465–495.CrossRefGoogle Scholar
Naitoh, T., Fukuda, N., Gotoh, T., Yamada, H. & Nakajima, K. 2002 Experimental study of axial flow in a vortex ring. Phys. Fluids 14, 143–149.CrossRefGoogle Scholar
Rom-Kedar, V., Leonard, A. & Wiggins, S. 1990 An analytical study of transport, mixing and chaos in an unsteady vortical flow. J. Fluid Mech 214, 347–394.CrossRefGoogle Scholar
Saffman, P. 1970 The velocity of viscous vortex rings. Stud. Appl. Maths 49, 371–380.CrossRefGoogle Scholar
Saffman, P. 1978 The number of waves on unstable vortex rings. J. Fluid Mech 84, 625–639.CrossRefGoogle Scholar
Schneider, P. 1980 Sekundärwirbelbildung bei ringwirbeln und in freistrahlen. Z. Flugwiss. Weltraumforschung 4, 307–318.Google Scholar
Shadden, S., Dabiri, J. & Marsden, J. 2006 Lagrangian analysis of fluid transport in empirical vortex ring flows. Phys. Fluids 18, 047105.CrossRefGoogle Scholar
Shariff, K., Verzicco, R. & Orlandi, P. 1994 A numerical study of three-dimensional vortex ring instabilities: viscous corrections and early nonlinear stage. J. Fluid Mech. 279, 351–375.CrossRefGoogle Scholar
Shariff, K., Leonard, A. & Ferziger, J. 2006 Dynamical systems analysis of fluid transport in time-periodic vortex ring flows. Phys. Fluids 18, 047104.CrossRefGoogle Scholar
Widnall, S. 1975 The structure and dynamics of vortex filaments. Annu. Rev. Fluid Mech 7, 141–165.CrossRefGoogle Scholar
Widnall, S. & Sullivan, J. 1973 On the stability of vortex rings. Proc. R. Soc. Lond. A 332, 335–353.Google Scholar
Widnall, S. & Tsai, C.-Y. 1977 The instability of the thin vortex ring of constant vorticity. Phil. Trans. R. Soc. Lond 287, 273–305.Google Scholar
Wiegand, A. & Gharib, M. 1994 On the decay of a turbulent vortex ring. Phys. Fluids 38, 3806–3808.CrossRefGoogle Scholar
Yao, Y., Thomas, T., Sandham, N. & Williams, J. 2001 Direct numerical simulation of turbulent flow over a rectangular trailing edge. Theoret. Comput. Fluid Dyn 14, 337–358.CrossRefGoogle Scholar