Hostname: page-component-8448b6f56d-42gr6 Total loading time: 0 Render date: 2024-04-24T17:40:15.684Z Has data issue: false hasContentIssue false
  • English
  • Français

Viscous and inviscid simulations of the start-up vortex

Published online by Cambridge University Press:  17 January 2017

Paolo Luchini  and
Renato Tognaccini
Paolo Luchini
Affiliation:
Dipartimento di Ingegneria Industriale, Università di Salerno, Fisciano (SA), 84084, Italia
Renato Tognaccini*
Affiliation:
Dipartimento di Ingegneria Industriale, Università di Napoli Federico II, Napoli, 80125, Italia
*
†Email address for correspondence: renato.tognaccini@unina.it
Get access Rights & Permissions [Opens in a new window]

Abstract

Inviscid, unsteady simulations of the roll up of the start-up vortex issuing from a semi-infinite plate are compared with previous simulations of the viscous flow. The inviscid equations were solved by a lumped-vortex method, the two-dimensional, incompressible Navier–Stokes equations in the vorticity–streamfunction formulation modelled the viscous problem. The purpose is to verify whether the irregular behaviour found by the inviscid solution well approximates the unstable evolution of the viscous spiral vortex in the limit of infinitely large time (or equivalently Reynolds number).

JFM classification

Vortex Flows: Vortex Flows Vortex Flows: Vortex shedding
Type
Papers
Information
Journal of Fluid Mechanics , Volume 813 , 25 February 2017 , pp. 53 - 69
Check for updates
Copyright
© 2017 Cambridge University Press 

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

Koumoutsakos, P. & Shiels, D. 1996 Simulations of the viscous flow normal to an impulsively started and uniformly accelerated flat plate. J. Fluid Mech. 328, 177–227.Google Scholar
Krasny, R. 1986 A study of singularity formation in a vortex sheet by the point vortex approximation. J. Fluid Mech. 167, 65–93.Google Scholar
Krasny, R. 1991 Vortex sheet computations: roll-up, wakes, separation. Lectures Appl. Math. 28, 385–401.Google Scholar
Krasny, R. & Nitsche, M. 2002 The onset of chaos in vortex sheet flow. J. Fluid Mech. 454, 47–69.Google Scholar
Lepage, C., Leweke, T. & Verga, A. 2005 Spiral shear layers: roll-up and incipient instability. Phys. Fluids 17 (3), 031705.Google Scholar
Luchini, P. & Tognaccini, R. 2002 The start-up vortex issuing from a semi-infinite flat plate. J. Fluid Mech. 455, 175–193.Google Scholar
Moore, D. 1976 The stability of an evolving two-dimensional vortex sheet. Mathematika 23, 35–44.Google Scholar
Pierce, D. 1961 Photographic evidence of the formation and growth of vorticity behind plates accelerated from rest in still air. J. Fluid Mech. 11, 460–464.Google Scholar
Pullin, D. I. 1978 The large-scale structure of unsteady self-similar rolled-up vortex sheets. J. Fluid Mech. 88, 401–430.Google Scholar
Pullin, D. I. & Perry, A. E. 1980 Some flow visualization experiments on the starting vortex. J. Fluid Mech. 97, 239–255.CrossRefGoogle Scholar
Saffman, P. G. 1992 Vortex Dynamics. Cambridge University Press.Google Scholar
Sarpkaya, T. 1989 Computational methods with vortices – the 1988 freeman scholar lecture. Trans. ASME J. Fluids Engng 111, 5–52.Google Scholar
Schneider, K., Paget-Goy, M., Verga, A. & Farge, M. 2014 Numerical simulation of flows past flat plates using volume penalization. Comput. Appl. Math. 33 (2), 481–495.Google Scholar
Tryggvason, G., Dahm, W. J. A. & Sbeih, K. 1991 Fine structure of vortex sheet roll up by viscous and inviscid simulation. Trans. ASME J. Fluids Engng 113, 31–36.CrossRefGoogle Scholar
Wang, Z. J., Liu, J. G. & Childress, S. 1999 Connection between corner vortices and shear layer instability in flow past an ellipse. Phys. Fluids 11, 2446–2448.Google Scholar
Xu, L. & Nitsche, M. 2014 Scaling behaviour in impulsively started viscous flow past a finite flat plate. J. Fluid Mech. 756 (4), 689–715.Google Scholar
Xu, L. & Nitsche, M. 2015 Start-up vortex flow past an accelerated flat plate. Phys. Fluids 27 (3), 033602.Google Scholar