Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-12-01T04:01:08.355Z Has data issue: false hasContentIssue false
  • English
  • Français

An experimental investigation of the laminar horseshoe vortex around an emerging obstacle

Published online by Cambridge University Press:  29 September 2017

Gaby Launay Open the ORCID record for Gaby Launay [Opens in a new window] ,
E. Mignot ,
N. Riviere  and
R. Perkins
Gaby Launay*
Affiliation:
LMFA, CNRS-Universite de Lyon, INSA de Lyon, Bat. Joseph Jacquard, 20 avenue A. Einstein, 69621 Villeurbanne CEDEX, France
E. Mignot
Affiliation:
LMFA, CNRS-Universite de Lyon, INSA de Lyon, Bat. Joseph Jacquard, 20 avenue A. Einstein, 69621 Villeurbanne CEDEX, France
N. Riviere
Affiliation:
LMFA, CNRS-Universite de Lyon, INSA de Lyon, Bat. Joseph Jacquard, 20 avenue A. Einstein, 69621 Villeurbanne CEDEX, France
R. Perkins
Affiliation:
LMFA, CNRS-Universite de Lyon, ECL de Lyon, 36 avenue Guy de Collongue, 69134 Ecully CEDEX, France
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

An emerging long obstacle placed in a boundary layer developing under a free surface generates a complex horseshoe vortex (HSV) system, which is composed of a set of vortices exhibiting a rich variety of dynamics. The present experimental study examines such flow structure and characterizes precisely, using particle image velocimetry (PIV) measurements, the evolution of the HSV geometrical and dynamical properties over a wide range of dimensionless parameters (Reynolds number $Re_{h}\in [750,8300]$ , boundary layer development ratio $h/\unicode[STIX]{x1D6FF}\in [1.25,4.25]$ and obstacle aspect ratio $W/h\in [0.67,2.33]$ ). The dynamical study of the HSV is based on the categorization of the motions of HSV vortices that result in an enhanced specific bi-dimensional typology, separating a coherent (due to vortex–vortex interactions) and an irregular evolution (due to the appearance of small-scale instabilities). This precise categorization is made possible thanks to the use of vortex tracking methods applied to PIV measurements; a semi-empirical model for the motion of the HSV vortices is then proposed to highlight some important mechanisms of the HSV dynamics, such as (i) the influence of the surrounding vortices on vortex motion and (ii) the presence of a phase shift between the motion of all vortices. Finally, the study of the HSV’s geometrical properties (vortex position and characteristic lengths and frequencies) evolution with the flow parameters shows that strong dependencies exist between the streamwise extension of the HSV and the obstacle width, and between the HSV vortex number and its elongation. Comparison of these data with prior studies for immersed obstacles reveals that emerging obstacles lead to greater adverse pressure gradients and down-flows in front of the obstacle. This implies a precocious separation of the boundary layer, leading to a larger HSV streamwise extension, and a lower vertical extension of the HSV, leading to smaller HSV vortices.

JFM classification

Boundary Layers: Boundary layer separation Waves/Free-surface Flows: Channel flow Vortex Flows: Vortex dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 830 , 10 November 2017 , pp. 257 - 299
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

Adrian, R. J. & Westerweel, J. 2011 Particle Image Velocimetry. Cambridge University Press.Google Scholar
Agui, J. H. & Andreopoulos, J. 1992 Experimental investigation of a three-dimensional boundary layer flow in the vicinity of an upright wall mounted cylinder (data bank contribution). Trans. ASME J. Fluids Engng 114 (4), 566–576.Google Scholar
Ahmed, F. & Rajaratnam, N. 1998 Flow around bridge piers. J. Hydraul. Engng 124 (3), 288–300.Google Scholar
Baker, C. J. 1978 The laminar horseshoe vortex. J. Fluid Mech. 95 (02), 347–367.CrossRefGoogle Scholar
Baker, C. J.1979 Vortex flow around the bases of obstacles. Thesis, University of Cambridge.Google Scholar
Baker, C. J. 1980 The turbulent horseshoe vortex. J. Wind Engng Ind. Aerodyn. 6 (1–2), 9–23.Google Scholar
Baker, C. J. 1985 The position of points of maximum and minimum shear stress upstream of cylinders mounted normal to flat plates. J. Wind Engng Ind. Aerodyn. 18 (3), 263–274.CrossRefGoogle Scholar
Baker, C. J. 1991 The oscillation of horseshoe vortex systems. Trans. ASME J. Fluids Engng 113, 489–495.Google Scholar
Ballio, F., Bettoni, C. & Franzetti, S. 1998 A survey of time-averaged characteristics of laminar and turbulent horseshoe vortices. Trans. ASME J. Fluids Engng 120 (2), 233.CrossRefGoogle Scholar
Belik, L. 1973 The secondary flow about circular cylinders mounted normal to a flat plate. Aeronaut. Q. 24, 47–54.Google Scholar
Bhattacharya, P., Manoharan, M. P., Govindarajan, R. & Narasimha, R. 2006 The critical Reynolds number of a laminar incompressible mixing layer from minimal composite theory. J. Fluid Mech. 565, 105–114.Google Scholar
Dargahi, B. 1989 The turbulent flow field around a circular cylinder. Exp. Fluids 8 (1–2), 1–12.CrossRefGoogle Scholar
Depardon, S., Lasserre, J. J., Brizzi, L. E. & Borée, J. 2007 Automated topology classification method for instantaneous velocity fields. Exp. Fluids 42 (5), 697–710.CrossRefGoogle Scholar
Devenport, W. J. & Simpson, R. L. 1990 Time-dependent and time-averaged turbulence structure near the nose of a wing-body junction. J. Fluid Mech. 210, 23–55.CrossRefGoogle Scholar
Dimotakis, P. E. 2000 The mixing transition in turbulent flows. J. Fluid Mech. 409, 69–98.Google Scholar
Doligalski, T. L., Smith, C. R. & Walker, J. D. A. 1994 Vortex interactions with walls. Annu. Rev. Fluid Mech. 26 (1), 573–616.CrossRefGoogle Scholar
Dritschel, D. G. & Waugh, D. W. 1992 Quantification of the inelastic interaction of unequal vortices in two-dimensional vortex dynamics. Phys. Fluids A 4 (8), 1737.CrossRefGoogle Scholar
Eckerle, W. A. & Awad, J. K. 1991 Effect of freestream velocity on the three-dimensional separated flow region in front of a cylinder. Trans. ASME J. Fluids Engng 113 (1), 37–44.Google Scholar
Eckerle, W. A. & Langston, L. S. 1987 Horseshoe vortex formation around a cylinder. Trans. ASME J. Turbomach. 109 (2), 278.Google Scholar
Effenberger, F. & Weiskopf, D. 2010 Finding and classifying critical points of 2D vector fields: a cell-oriented approach using group theory. Comput. Vis. Sci. 13 (8), 377–396.CrossRefGoogle Scholar
Escauriaza, C. & Sotiropoulos, F. 2011 Reynolds number effects on the coherent dynamics of the turbulent horseshoe vortex system. Flow Turbul. Combust. 86 (2), 231–262.Google Scholar
Euler, T. & Herget, J. 2012 Controls on local scour and deposition induced by obstacles in fluvial environments. CATENA 91, 35–46.Google Scholar
Floryan, J. M. 1986 Görtler instability of boundary layers over concave and convex walls. Phys. Fluids 29 (8), 2380.Google Scholar
Graf, W. H. & Yulistiyanto, B. 1998 Experiments on flow around a cylinder; the velocity and vorticity fields. J. Hydraul Res. 36 (4), 637–654.Google Scholar
Graftieaux, L., Michard, M. & Grosjean, N. 2001 Combining PIV, POD and vortex identification algorithms for the study of unsteady turbulent swirling flows. Meas. Sci. Technol. 12 (9), 1422.Google Scholar
Greco, J. J.1990 The flow structure in the vicinity of a cylinder-flat plate junction: flow regimes, periodicity, and vortex interactions. PhD thesis, Department of Mechanical Engineering and Mechanics, Lehigh University, Lehigh.Google Scholar
Hunt, J. C. R., Abell, C. J., Peterka, J. A. & Woo, H. 1978 Kinematical studies of the flows around free or surface-mounted obstacles; applying topology to flow visualization. J. Fluid Mech. 86 (01), 179.CrossRefGoogle Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.Google Scholar
Johnson, K. & Ting, F. 2003 Measurements of water surface profile and velocity field at a circular pier. J. Engng Mech. 129 (5), 502–513.Google Scholar
Josserand, C. & Rossi, M. 2007 The merging of two co-rotating vortices: a numerical study. Eur. J. Mech. (B/Fluids) 26 (6), 779–794.Google Scholar
Kelso, R. M. & Smits, A. J. 1995 Horseshoe vortex systems resulting from the interaction between a laminar boundary layer and a transverse jet. Phys. Fluids 7 (1), 153.Google Scholar
Kerswell, R. R. 2002 Elliptical instability. Annu. Rev. Fluid Mech. 34 (1), 83–113.Google Scholar
Khan, M. J. & Ahmed, A. 2005 Topological model of flow regimes in the plane of symmetry of a surface-mounted obstacle. Phys. Fluids 17 (4), 045101.Google Scholar
Khan, M. J., Ahmed, A. & Trosper, J. R. 1995 Dynamics of the juncture vortex. AIAA J. 33 (7), 1273–1278.Google Scholar
Kolář, V. 2007 Vortex identification: new requirements and limitations. Intl J. Heat Fluid Flow 28 (4), 638–652.Google Scholar
Larousse, A., Martinuzzi, R. & Tropea, C. 1993 Flow around surface-mounted, three-dimensional obstacles. In Turbulent Shear Flows (ed. Durst, F., Friedrich, R., Launder, B. E., Schmidt, F. W., Schumann, U. & Whitelaw, J. H.), vol. 8, pp. 127–139. Springer.Google Scholar
Launay, G., Mignot, E. & Riviere, N.2017 Laminar free-surface flow around emerging obstacles: role of the obstacle elongation (in review).Google Scholar
Lighthill, M. J. 1963 Boundary Layer Theory. Oxford University Press.Google Scholar
Lin, C., Chiu, P.-H. & Shieh, S.-J. 2002 Characteristics of horseshoe vortex system near a vertical plate–base plate juncture. Exp. Therm. Fluid Sci. 27 (1), 25–46.CrossRefGoogle Scholar
Lin, C., Ho, T. C. & Dey, S. 2008 Characteristics of steady horseshoe vortex system near junction of square cylinder and base plate. J. Engng Mech. 134 (2), 184–197.Google Scholar
Lin, C., Lai, W. & Chang, K. 2003 Simultaneous particle image velocimetry and laser Doppler velocimetry measurements of periodical oscillatory horseshoe vortex system near square cylinder-base plate juncture. J. Engng Mech. 129 (10), 1173–1188.Google Scholar
Loucks, R. B. & Wallace, J. M. 2012 Velocity and velocity gradient based properties of a turbulent plane mixing layer. J. Fluid Mech. 699, 280–319.Google Scholar
Meunier, P., Le Dizès, S. & Leweke, T. 2005 Physics of vortex merging. C. R. Phys. 6 (4–5), 431–450.Google Scholar
Mignot, E., Cai, W., Launay, G., Riviere, N. & Escauriaza, C. 2016 Coherent turbulent structures at the mixing-interface of a square open-channel lateral cavity. Phys. Fluids 28 (4), 045104.Google Scholar
Ozturk, N. A., Akkoca, A. & Sahin, B. 2008 Flow details of a circular cylinder mounted on a flat plate. J. Hydraul Res. 46 (3), 344–355.Google Scholar
Paik, J., Escauriaza, C. & Sotiropoulos, F. 2007 On the bimodal dynamics of the turbulent horseshoe vortex system in a wing-body junction. Phys. Fluids 19 (4), 045107.Google Scholar
Peltier, Y., Erpicum, S., Archambeau, P., Pirotton, M. & Dewals, B. 2014 Meandering jets in shallow rectangular reservoirs: POD analysis and identification of coherent structures. Exp. Fluids 55 (6), 1740.Google Scholar
Riviere, N., Laïly, A. G., Mignot, E. & Doppler, D. 2012 Supercritical flow around and beneath a fixed obstacle. In 2nd IAHR Europe Congress, Lehrstuhl und Versuchsanstalt fur Wasserbau und Wasserwirtschaft, Munchen, Germany. IAHR.Google Scholar
Roulund, A., Sumer, B. M., Fredsoe, J. & Michelsen, J. 2005 Numerical and experimental investigation of flow and scour around a circular pile. J. Fluid Mech. 534, 351–401.Google Scholar
Sabatino, D. R. & Smith, C. R. 2008 Boundary layer influence on the unsteady horseshoe vortex flow and surface heat transfer. Trans. ASME J. Turbomach. 131 (1), 011015.Google Scholar
Sadeque, M., Rajaratnam, N. & Loewen, M. 2008 Flow around cylinders in open channels. J. Engng Mech. 134 (1), 60–71.Google Scholar
Sahin, B., Ozturk, N. A. & Akilli, H. 2007 Horseshoe vortex system in the vicinity of the vertical cylinder mounted on a flat plate. Flow Meas. Instrum. 18 (2), 57–68.Google Scholar
Schwind, R. G. 1962 The Three Dimensional Boundary Layer Near a Strut. Massachusetts Institute of Technology.Google Scholar
Seal, C. V., Smith, C. R., Akin, O. & Rockwell, D. 1995 Quantitative characteristics of a laminar, unsteady necklace vortex system at a rectangular block-flat plate juncture. J. Fluid Mech. 286, 117–135.Google Scholar
Seal, C. V., Smith, C. R. & Rockwell, D. 1997 Dynamics of the vorticity distribution in endwall junctions. AIAA J. 35 (6), 1041–1047.Google Scholar
Shavit, U., Lowe, R. J. & Steinbuck, J. V. 2006 Intensity capping: a simple method to improve cross-correlation PIV results. Exp. Fluids 42 (2), 225–240.Google Scholar
Simpson, R. L. 2001 Junction flows. Annu. Rev. Fluid Mech. 33 (1), 415–443.Google Scholar
Thomas, A. S. W. 1987 The unsteady characteristics of laminar juncture flow. Phys. Fluids 30 (2), 283–285.Google Scholar
Trieling, R. R., Linssen, A. H. & Van Heijst, G. J. F. 1998 Monopolar vortices in an irrotational annular shear flow. J. Fluid Mech. 360, 273–294.Google Scholar
Tropea, C., Yarin, A. L. & Foss, J. F.(Eds) 2007 Springer Handbook of Experimental Fluid Mechanics. Springer.Google Scholar
Wygnanski, I. & Fiedler, H. E. 1970 The two-dimensional mixing region. J. Fluid Mech. 41 (02), 327–361.Google Scholar
Younis, M. Y., Zhang, H., Hu, B. & Mehmood, S. 2014 Topological evolution of laminar juncture flows under different critical parameters. Sci. China Technol. Sci. 57 (7), 1342–1351.Google Scholar