Skip to main content Accessibility help
×
Home

Formation, growth and instability of vortex pairs in an axisymmetric stagnation flow

  • Jinjun Wang (a1), Chong Pan (a1), Kwing-So Choi (a2), Lei Gao (a3) and Qi-Xiang Lian (a1)...

Abstract

The formation, growth and instability of a pair of counter-rotating vortices over a circular plate in the downstream of a thin fishing line were studied using particle image velocimetry and flow visualization. Initially, the vortex pair in an axisymmetric stagnation flow was small, but it grew steadily by accumulating the shear-layer vorticity of the wake before going through vortical instability. Two types of vortical development were observed in the present experiment. Type I was a common type of vortical development in an axisymmetric stagnation flow over a circular plate. Here, the circulation of the vortex pair increased linearly with time reflecting a constant flux of vorticity impinging on the plate wall. After the growth, the counter-rotating pair of vortices went through an antisymmetric deformation in the wall-normal direction while the vortex deformation was symmetric in the wall-parallel direction. This was remarkably similar to the short-wavelength elliptic instability of counter-rotating vortices in an open system. On the other hand, type II development of a vortex pair was a rare case, where the vortices grew for much longer duration than in type I cases. This initiated a breakdown of vortices before the residual vorticity moved away from the centre of the plate. It is considered that the disturbance due to vortical instability could be partially responsible for the unexpectedly high heat transfer rate in the stagnation region of bluff bodies that has been reported in the last half-century.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Formation, growth and instability of vortex pairs in an axisymmetric stagnation flow
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Formation, growth and instability of vortex pairs in an axisymmetric stagnation flow
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Formation, growth and instability of vortex pairs in an axisymmetric stagnation flow
      Available formats
      ×

Copyright

The online version of this article is published within an Open Access environment subject to the conditions of the Creative Commons Attribution-NonCommercial-ShareAlike licence . The written permission of Cambridge University Press must be obtained for commercial re-use.

Corresponding author

Email address for correspondence: kwing-so.choi@nottingham.ac.uk

References

Hide All
Adrian, R. J. 2007 Hairpin vortex organization in wall turbulence. Phys. Fluids 19, 041301.
Adrian, R. J., Meinhart, C. D. & Tomkins, C. D. 2000 Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech. 422, 1.
Ames, F. E. & Moffat, R. J. 1990 Heat transfer with high intensity, large-scale turbulence: the flat plate turbulent boundary layer and the cylindrical stagnation point. Technical Report HMT-43, Thermoscience Division, Mechanical Engineering Department, Stanford University, Stanford, CA.
Bae, S., Lele, S. K. & Sung, H. J. 2000 Influence of inflow disturbances on stagnation-region heat transfer. J. Heat Transfer 122, 258.
Bae, S., Lele, S. K. & Sung, H. J. 2003 Direct numerical simulation of stagnation region flow and heat transfer. Phys. Fluids 15, 1462.
Barrett, M. J. & Hollingworth, D. K. 2001 On the calculation of length scales for turbulent heat transfer correlation. J. Heat Transfer 123, 878.
Böttcher, J. & Wedemeyer, E. 1989 The flow downstream of screens and its influence on the stagnation region of cylindrical bodies. J. Fluid Mech. 204, 501.
Carlier, J. & Stanislas, M. 2005 Experimental study of eddy structures in a turbulent boundary layer using particle image velocimetry. J. Fluid Mech. 535, 143.
Chong, M. S., Perry, A. E. & Cantwell, B. J. 1990 A general classification of three-dimensional flow fields. Phys. Fluids A 2, 765.
Coleman, T. F. & Li, Y. 1996 An interior, trust region approach for nonlinear minimization subject to bounds. SIAM J. Optim. 6, 418.
Crow, S. C. 1970 Stability theory for a pair of trailing vortices. AIAA J. 8, 2172.
Danaila, I. 2004 Vortex dipoles impinging on finite aspect ratio rectangular obstacles. Flow Turbul. Combust. 72, 391.
Dhanak, M. R. & Stuart, J. T. 1995 Distortion of the stagnation-point flow due to cross-stream vorticity in the external flow. Phil. Trans. R. Soc. Lond. A 352, 443.
Hodson, P. R. & Nagib, H. M. 1977 Vortices induced in a stagnation region by wakes–their incipient formation and effect on heat transfer. AIAA-Paper 77-790.
Homman, F. 1936 Der einfluss grosser zahigkeit bei der stomung um den zylinder und um die kugel. Z. Angew. Math. Mech. 16, 153.
Hunt, J. C. R., Wray, A. A. & Moin, P. 1988 Eddies, stream and convergence zones in turbulent flows. In Proceedngs of Summer Program 1988, pp. 193208. Center for Turbulence Research, Stanford Univesity.
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69.
Kerswell, R. R. 2002 Elliptic instability. Annu. Rev. Fluid Mech. 34, 83.
Kestin, J. 1966 The effect of free stream turbulence on heat transfer rates. Adv. Heat Transfer 3, 1.
Kestin, J., Maeder, P. F. & Sogin, H. H. 1961 The influence of turbulence on the transfer of heat to cylinders near the stagnation point. Z. Angew. Math. Phys. 12, 115.
Kestin, J. & Wood, R. T. 1970 On the instability of two-dimensional stagnation flow. J. Fluid Mech. 44, 461.
Laporte, F. & Corjon, A. 2000 Direct numerical simulations of the elliptic instability of a vortex pair. Phys. Fluids 12, 1016.
Le Dizes, S., Rossi, M. & Moffatt, H. K. 1996 On the three-dimensional instability of elliptical vortex subjected to stretching. Phys. Fluids 8 (8), 2084.
Leweke, T. & Williamson, C. H. K. 1998 Cooperative elliptic instability of a vortex pair. J. Fluid Mech. 360, 85.
Lian, Q. X. & Su, T. C. 1994 Large vortex in front of stagnation region of a square plate induced by a fine vortex generating wire. Sci. China (Ser. A) 37, 469.
Lian, Q. X. & Zhou, M. X 1989 Experimental investigation on rigid hollow hemi-spherical parachute model in accelerating and steady flows (in Chinese). Acta Aeronaut. Astronaut. Sin. 9, 84.
Moore, D. W. & Saffman, P. G. 1975 The instability of a straight vortex filament in a strain field. Proc. R. Soc. Lond. Ser. A 346, 413.
Morkovin, M. V. 1979 On the question of instabilities upstream of cylindrical bodies. NASA Report 3231.
Oo, A. N. & Ching, C. Y. 2001 Effect of turbulence with different vortical structures on stagnation region heat transfer. J. Heat Transfer 123, 665.
Oo, A. N. & Ching, C. Y. 2002 Stagnation line heat transfer augmentation due to free stream vortical structures and vorticity. J. Heat Transfer 124, 583.
Orlandi, P. 1990 Vortex dipole rebound from a wall. Phys. Fluids A 2, 1429.
Pierrehumbert, R. T. 1986 Universal short wave instability of two-dimensional eddies in an inviscid fluid. Phys. Rev. Lett. 57, 2157.
Pirozzoli, S., Bernardini, M. & Grasso, F. 2008 Characterization of coherent vortical structures in a supersonic turbulent boundary layer. J. Fluid Mech. 613, 205.
Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23, 601.
Sadeh, W. Z. & Brauer, H. J. 1980 A visual investigation of turbulence in stagnation flow about a circular cylinder. J. Fluid Mech. 99, 53.
Scarano, F., Benocci, C. & Riethmuller, M. L. 1999 Pattern recognition analysis of the turbulent flow past a backward facing step. Phys. Fluids 11 (12), 3808.
Scarano, F. & Riethmuller, M. L. 2000 Advances in iterative multigrid PIV image processing. Exp. Fluids 29, S51S60.
Shenoy, A. R. & Kleinstreuer, C. 2008 Flow over a thin circular disk at low to moderate Reynolds numbers. J. Fluid Mech. 605, 253.
Stanislas, M., Perret, L. & Foucaut, J.-M. 2008 Vortical structures in the turbulent boundary layer: a possible route to a universal representation. J. Fluid Mech. 602, 327.
Sutera, S. P. 1965 Vorticity amplification in stagnation point flow and its effect on heat transfer. J. Fluid Mech. 21, 513.
Sutera, S. P., Maeder, P. F. & Kestin, J. 1963 On the sensitivity of heat transfer in the stagnation-point boundary layer to free stream vorticity. J. Fluid Mech. 16, 32.
Tomkins, C. D. & Adrian, R. J. 2003 Spanwise structure and scale growth in turbulent boundary layers. J. Fluid Mech. 490, 37.
Xiong, Z. & Lele, S. 2004 Distortion of upstream disturbances in a Hiemenz boundary layer. J. Fluid Mech. 519, 201.
Xiong, Z. & Lele, S. 2007 Stagnation-point flow under free stream turbulence. J. Fluid Mech. 590, 1.
Zhou, J., Adrian, R. J., Balachandar, S. & Kendall, T. M. 1999 Mechanism for generating coherent packets of hairpin vortices in channel flow. J. Fluid Mech. 387, 353.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Related content

Powered by UNSILO

Formation, growth and instability of vortex pairs in an axisymmetric stagnation flow

  • Jinjun Wang (a1), Chong Pan (a1), Kwing-So Choi (a2), Lei Gao (a3) and Qi-Xiang Lian (a1)...

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.