Hostname: page-component-8448b6f56d-c47g7 Total loading time: 0 Render date: 2024-04-19T11:43:11.161Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  23 May 2013

Jinjun Wang ,
Chong Pan ,
Kwing-So Choi ,
Lei Gao  and
Qi-Xiang Lian
Jinjun Wang
Affiliation:
Fluid Mechanics Key Laboratory of Education Ministry, Beijing University of Aeronautics and Astronautics, 100191 Beijing, PR China
Chong Pan
Affiliation:
Fluid Mechanics Key Laboratory of Education Ministry, Beijing University of Aeronautics and Astronautics, 100191 Beijing, PR China
Kwing-So Choi*
Affiliation:
Faculty of Engineering, University of Nottingham, Nottingham NG7 2RD, UK
Lei Gao
Affiliation:
School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798
Qi-Xiang Lian
Affiliation:
Fluid Mechanics Key Laboratory of Education Ministry, Beijing University of Aeronautics and Astronautics, 100191 Beijing, PR China
*
†Email address for correspondence: kwing-so.choi@nottingham.ac.uk
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

JFM classification

Vortex Flows: Vortex dynamics Vortex Flows: Vortex instability Vortex Flows: Vortex interactions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 725 , 25 June 2013 , pp. 681 - 708
Creative Commons
Creative Common License - CCCreative Common License - BYCreative Common License - NCCreative Common License - SA
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.
Copyright
©2013 Cambridge University Press.

References

Adrian, R. J. 2007 Hairpin vortex organization in wall turbulence. Phys. Fluids 19, 041301.Google Scholar
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.Google Scholar
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.Google Scholar
Bae, S., Lele, S. K. & Sung, H. J. 2000 Influence of inflow disturbances on stagnation-region heat transfer. J. Heat Transfer 122, 258.Google Scholar
Bae, S., Lele, S. K. & Sung, H. J. 2003 Direct numerical simulation of stagnation region flow and heat transfer. Phys. Fluids 15, 1462.Google Scholar
Barrett, M. J. & Hollingworth, D. K. 2001 On the calculation of length scales for turbulent heat transfer correlation. J. Heat Transfer 123, 878.Google Scholar
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.CrossRefGoogle Scholar
Carlier, J. & Stanislas, M. 2005 Experimental study of eddy structures in a turbulent boundary layer using particle image velocimetry. J. Fluid Mech. 535, 143.CrossRefGoogle Scholar
Chong, M. S., Perry, A. E. & Cantwell, B. J. 1990 A general classification of three-dimensional flow fields. Phys. Fluids A 2, 765.Google Scholar
Coleman, T. F. & Li, Y. 1996 An interior, trust region approach for nonlinear minimization subject to bounds. SIAM J. Optim. 6, 418.Google Scholar
Crow, S. C. 1970 Stability theory for a pair of trailing vortices. AIAA J. 8, 2172.Google Scholar
Danaila, I. 2004 Vortex dipoles impinging on finite aspect ratio rectangular obstacles. Flow Turbul. Combust. 72, 391.Google Scholar
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.Google Scholar
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.Google Scholar
Homman, F. 1936 Der einfluss grosser zahigkeit bei der stomung um den zylinder und um die kugel. Z. Angew. Math. Mech. 16, 153.Google Scholar
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. 193–208. Center for Turbulence Research, Stanford Univesity.Google Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69.Google Scholar
Kerswell, R. R. 2002 Elliptic instability. Annu. Rev. Fluid Mech. 34, 83.Google Scholar
Kestin, J. 1966 The effect of free stream turbulence on heat transfer rates. Adv. Heat Transfer 3, 1.Google Scholar
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.Google Scholar
Kestin, J. & Wood, R. T. 1970 On the instability of two-dimensional stagnation flow. J. Fluid Mech. 44, 461.Google Scholar
Laporte, F. & Corjon, A. 2000 Direct numerical simulations of the elliptic instability of a vortex pair. Phys. Fluids 12, 1016.Google Scholar
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.Google Scholar
Leweke, T. & Williamson, C. H. K. 1998 Cooperative elliptic instability of a vortex pair. J. Fluid Mech. 360, 85.Google Scholar
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.Google Scholar
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.Google Scholar
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.Google Scholar
Morkovin, M. V. 1979 On the question of instabilities upstream of cylindrical bodies. NASA Report 3231.Google Scholar
Oo, A. N. & Ching, C. Y. 2001 Effect of turbulence with different vortical structures on stagnation region heat transfer. J. Heat Transfer 123, 665.Google Scholar
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.Google Scholar
Orlandi, P. 1990 Vortex dipole rebound from a wall. Phys. Fluids A 2, 1429.Google Scholar
Pierrehumbert, R. T. 1986 Universal short wave instability of two-dimensional eddies in an inviscid fluid. Phys. Rev. Lett. 57, 2157.Google Scholar
Pirozzoli, S., Bernardini, M. & Grasso, F. 2008 Characterization of coherent vortical structures in a supersonic turbulent boundary layer. J. Fluid Mech. 613, 205.Google Scholar
Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23, 601.Google Scholar
Sadeh, W. Z. & Brauer, H. J. 1980 A visual investigation of turbulence in stagnation flow about a circular cylinder. J. Fluid Mech. 99, 53.Google Scholar
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.Google Scholar
Scarano, F. & Riethmuller, M. L. 2000 Advances in iterative multigrid PIV image processing. Exp. Fluids 29, S51–S60.Google Scholar
Shenoy, A. R. & Kleinstreuer, C. 2008 Flow over a thin circular disk at low to moderate Reynolds numbers. J. Fluid Mech. 605, 253.Google Scholar
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.CrossRefGoogle Scholar
Sutera, S. P. 1965 Vorticity amplification in stagnation point flow and its effect on heat transfer. J. Fluid Mech. 21, 513.Google Scholar
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.CrossRefGoogle Scholar
Tomkins, C. D. & Adrian, R. J. 2003 Spanwise structure and scale growth in turbulent boundary layers. J. Fluid Mech. 490, 37.Google Scholar
Xiong, Z. & Lele, S. 2004 Distortion of upstream disturbances in a Hiemenz boundary layer. J. Fluid Mech. 519, 201.Google Scholar
Xiong, Z. & Lele, S. 2007 Stagnation-point flow under free stream turbulence. J. Fluid Mech. 590, 1.Google Scholar
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.Google Scholar