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Global frequency selection in the observed time-mean wakes of circular cylinders

Published online by Cambridge University Press:  25 April 2008

MOSES KHOR
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, Victoria 3800, Australia
JOHN SHERIDAN
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, Victoria 3800, Australia Division of Biological Engineering, Monash University, Melbourne, Victoria 3800, Australia
MARK C. THOMPSON
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, Victoria 3800, Australia Division of Biological Engineering, Monash University, Melbourne, Victoria 3800, Australia
KERRY HOURIGAN
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, Victoria 3800, Australia Division of Biological Engineering, Monash University, Melbourne, Victoria 3800, Australia

Abstract

Observations have been made of the time-mean velocity profile at midspan in the near-wake of circular cylinders at moderate Reynolds numbers between 600 and 4600, well beyond the Reynolds number of approximately 200 at which the wake becomes three-dimensional. The measured profiles are found to be represented quite accurately by a family of function profiles with known linear instability characteristics. The complex instability frequency is then determined as a function of wake position, using the function profiles. In general, the near wake undergoes a transition from convective to absolute instability; the distance downstream to the point of transition is found to increase over the Reynolds number range investigated. The emergence of a significant region of convective instability is consistent with the known appearance of Bloor–Gerrard vortices. The selected frequency of the wake instability is determined by the saddle-point criterion; the Strouhal numbers for Bénard–von Kármán vortex shedding are found to compare well with the values in the literature.

Type
Papers
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Barkley, D. 2006 Linear analysis of the cylinder wake mean flow. Europhys. Lett. 75, 750756.CrossRefGoogle Scholar
Barkley, D. & Henderson, R. D. 1996 Three-dimensional Floquet stability analysis of the wake of a circular cylinder. J. Fluid Mech. 322, 215241.CrossRefGoogle Scholar
Bearman, P. W. 1969 On vortex shedding from a circular cylinder in the critical Reynolds number regime. J. Fluid Mech. 37, 577585.CrossRefGoogle Scholar
Bers, A. 1975 Linear waves and instabilities. In Physique des Plasmas (ed. DeWitt, C. & Peyraud, J.), pp. 117213. Springer.Google Scholar
Betchov, R. & Criminale, W. 1966 Spatial instability of the inviscid jet and wake. Phys. Fluids 9, 359362.CrossRefGoogle Scholar
Bloor, M. 1964 The transition to turbulence in the wake of a circular cylinder. J. Fluid Mech. 19, 290304.CrossRefGoogle Scholar
Briggs, R. J. 1964 Electron-Stream Interaction with Plasmas. MIT Press.CrossRefGoogle Scholar
Chomaz, J. M. 2003 Fully nonlinear dynamics of parallel wakes. J. Fluid Mech. 495, 5775.CrossRefGoogle Scholar
Chomaz, J. M., Huerre, P. & Redekopp, L. 1988 Bifurcations to local and global modes in spatially developing flows. Phys. Rev. Lett. 60, 2528.CrossRefGoogle ScholarPubMed
Chomaz, J. M., Huerre, P. & Redekopp, L. 1991 A frequency selection criterion in spatially developing flows. Stud. Appl. Maths 84, 119144.CrossRefGoogle Scholar
Dimopoulos, H. & Hanratty, T. 1968 Velocity gradients at the wall for flow around a cylinder for Reynolds numbers between 60 and 360. J. Fluid Mech. 33, 303319.CrossRefGoogle Scholar
Fornberg, B. 1980 A numerical study of steady viscous flow past a circular cylinder. J. Fluid Mech. 98, 819855.CrossRefGoogle Scholar
Fouras, A., Dusting, J. & Hourigan, K. 2007 a A simple calibration technique for Stereoscopic Particle Image Velocimetry. Exps. Fluids 42, 799810.CrossRefGoogle Scholar
Fouras, A., Jacono, D. L. & Hourigan, K. 2008 Target-free Stereo PIV: a novel technique with inherent error estimation and improved accuracy. Exps. Fluids 44, 317329.CrossRefGoogle Scholar
Fouras, A., Jacono, D. L., Sheard, G. J. & Hourigan, K. 2007 b Measurement of instantaneous velocity and surface topography of a cylinder at low Reynolds number. In Proc. IUTAM Symp. on Unsteady Separated Flows and Their Control (ed. Braza, E. M. & Hourigan, K.), Corfu, Greece, 18–22 June.Google Scholar
Freymuth, P. 1966 On transition in a separated laminar boundary layer. J. Fluid Mech. 25, 683704.CrossRefGoogle Scholar
Gallaire, F., Ruith, M., Meiburg, E., Chomaz, J. M. & Huerre, P. 2006 Spiral vortex breakdown as a global mode. J. Fluid Mech. 549, 7180.CrossRefGoogle Scholar
Gerich, D. & Ecklemann, H. 1982 Influence of end plates and free ends on the shedding frequency of circular cylinders. J. Fluid Mech. 122, 109121.CrossRefGoogle Scholar
Hammond, D. & Redekopp, L. 1997 Global dynamics of symmetric and asymmetric wakes. J. Fluid Mech. 331, 231260.CrossRefGoogle Scholar
Hannemann, K. & Oertel, H. 1989 Numerical simulation of the absolutely and convectively unstable wake. J. Fluid Mech. 199, 5588.CrossRefGoogle Scholar
Ho, C. M. & Huerre, P. 1984 Perturbed free shear layers. Annu. Rev. Fluid Mech. 16, 365424.CrossRefGoogle Scholar
Huerre, P. & Monkewitz, P. A. 1985 Absolute and convective instabilities in free shear layers. J. Fluid Mech. 159, 151168.CrossRefGoogle Scholar
Huerre, P. & Monkewitz, P. A. 1990 Local and global instabilities in spatially developing flows. Annu. Rev. Fluid Mech. 22, 473537.CrossRefGoogle Scholar
Huerre, P. & Rossi, M. 1998 Hydrodynamic instabilities in open flows. In Hydrodynamics and Nonlinear Instabilities (ed. Godrèche, C. & Manneville, P.), pp. 81294. Cambridge University Press.CrossRefGoogle Scholar
Karniadakis, G. E. & Triantafyllou, G. S. 1989 Frequency selection and asymptotic states in laminar wakes. J. Fluid Mech. 199, 441469.CrossRefGoogle Scholar
Khor, M. 1998 The character of the near-wake instability of the circular cylinder. PhD thesis, Department of Mechanical Engineering, Monash University.Google Scholar
Koch, W. 1985 Local instability characteristics and frequency determination of self-excited wake flows. J. Sound Vib. 99, 5383.CrossRefGoogle Scholar
Kourta, A., Boisson, H., Chassaing, P. & Ha Minh, H. 1987 Nonlinear interaction and the transition to turbulence in the wake of a circular cylinder. J. Fluid Mech. 181, 141.CrossRefGoogle Scholar
Le Dizès, S., Huerre, P., Chomaz, J.-M. & Monkewitz, P. 1996 Linear global modes in spatially developing media. Phil. Trans. R. Soc. Lond. A 354, 168212.Google Scholar
Leontini, J., Thompson, M. C. & Hourigan, K. 2007 Three-dimensional transition in the wake of a transversely oscillating cylinder. J. Fluid Mech. 577, 79104.CrossRefGoogle Scholar
Lesshafft, L., Huerre, P., Sagaut, P. & Terracol, M. 2006 Nonlinear global modes in hot jets. J. Fluid Mech. 554, 393409.CrossRefGoogle Scholar
Marquillie, M. & Ehrenstein, U. 2003 On the onset of nonlinear oscillations in a separating boundary-layer flow. J. Fluid Mech. 490, 169188.CrossRefGoogle Scholar
Mattingly, G. E. & Criminale, W. 1972 The stability of an incompressible two-dimensional wake. J. Fluid Mech. 51, 233272.CrossRefGoogle Scholar
Michalke, A. 1964 On the inviscid instability of the hyperbolic tangent velocity profile. J. Fluid Mech. 19, 543556.CrossRefGoogle Scholar
Michalke, A. 1965 a On spatially growing disturbance in an inviscid shear layer. J. Fluid Mech. 23, 521544.CrossRefGoogle Scholar
Michalke, A. 1965 b Vortex formation in a free boundary layer according to stability theory. J. Fluid Mech. 22, 371383.CrossRefGoogle Scholar
Monkewitz, P. A. 1974 Wake control. In IUTAM Symposium: Bluff-Body Wakes, Dynamics and Instabilities, pp. 227–240. Springer.CrossRefGoogle Scholar
Monkewitz, P. A. 1988 The absolute and convective nature of instability in two-dimensional wakes at low Reynolds numbers. Phys. Fluids 31, 9991006.CrossRefGoogle Scholar
Monkewitz, P. A., Huerre, P. & Chomaz, J.-P. 1993 Global instability analysis of weakly non-parallel shear flows. J. Fluid Mech. 251, 120.CrossRefGoogle Scholar
Monkewitz, P. A. & Nguyen, L. N. 1987 Absolute instabilities in the near-wake of two-dimensional bluff bodies. J. Fluids Struct. 1, 165184.CrossRefGoogle Scholar
Nishioka, M. 1973 Hot-wire technique for measuring velocities at extremely low wind-speed. Bull. JSME 16, 18871899.CrossRefGoogle Scholar
Norberg, C. 1987 Effects of Reynolds number and a low-intensity freestream turbulence on the flow around a circular cylinder. PhD thesis, Chalmers Univ. Tech. Pub. No 87/2, S-412-96. Goteborg, Sweden.Google Scholar
Norberg, C. 1994 An experimental investigation of the flow around a circular cylinder: influence of aspect ratio. J. Fluid Mech. 258, 287.CrossRefGoogle Scholar
Pier, B. 2002 On the frequency selection of finite-amplitude vortex shedding in the cylinder wake. J. Fluid Mech. 458, 407417.CrossRefGoogle Scholar
Pier, B. & Huerre, P. 2001 a Nonlinear self-sustained structures and fronts in spatially developing wake flows. J. Fluid Mech. 435, 145174.CrossRefGoogle Scholar
Pier, B. & Huerre, P. 2001 b Nonlinear synchronization in open flows. J. Fluids Struct. 15, 471480.CrossRefGoogle Scholar
Pier, B., Huerre, P. & Chomaz, J.-M. 2001 Bifurcation to fully nonlinear synchronized structures in slowly varying media. Physica D 148, 4996.Google Scholar
Pier, B., Huerre, P., Chomaz, J.-M. & Couairon, A. 1998 Steep nonlinear global modes in spatially developing media. Phys. Fluids 10, 24332435.CrossRefGoogle Scholar
Pierrehumbert, R. T. 1984 Local and global baroclinic instability of zonally varying flow. J. Atmos. Sci. 41, 21412162.2.0.CO;2>CrossRefGoogle Scholar
Prasad, A. & Williamson, C. H. K. 1997 The instability of the shear layer separating from a bluff body. J. Fluid Mech. 333, 375402.CrossRefGoogle Scholar
Provansal, M., Mathis, C. & Boyer, L. 1987 Bénard–von Kármán instability: transient and forced regimes. J. Fluid Mech. 182, 122.CrossRefGoogle Scholar
Sato, H. & Kuriki, K. 1961 The mechanism of transition in the wake of a thin flat plate placed parallel to a uniform flow. J. Fluid Mech. 11, 321352.CrossRefGoogle Scholar
Sipp, D. & Lebedev, A. 2007 Global stability of base and mean-flows: a general approach and its applications to cylinder and open cavity flows. J. Fluid Mech. 593, 333358.CrossRefGoogle Scholar
Strykowski, P. 1986 The control of absolutely and convectively unstable shear flows. PhD thesis, Yale University, New Haven, Connecticut, USA.Google Scholar
Thiria, B. & Wesfreid, J. 2007 Stability properties of forced wakes. J. Fluid Mech. 579, 137161.CrossRefGoogle Scholar
Thompson, M. C. & Hourigan, K. 2005 The shear layer instability of a circular cylinder wake. Phys. Fluids 17, 021702–5.CrossRefGoogle Scholar
Thompson, M. C., Hourigan, K. & Sheridan, J. 1996 Three-dimensional instabilities in the wake of a circular cylinder. Expl Therm. Fluid Sci. 12, 190196.CrossRefGoogle Scholar
Triantafyllou, G. S., Triantafyllou, M. S. & Chryssostomidis, C. 1986 On the formation of vortex streets behind stationary cylinders. J. Fluid Mech. 170, 461477.CrossRefGoogle Scholar
Unal, M. F. & Rockwell, D. 1988 On vortex formation from a cylinder. Part 1. The initial instability. J. Fluid Mech. 190, 491512.CrossRefGoogle Scholar
Wei, T. & Smith, C. R. 1986 Secondary vortices in the wake of circular cylinders. J. Fluid Mech. 169, 513.CrossRefGoogle Scholar
Williamson, C. & Brown, G. 1998 A series in to represent the Strouhal-Reynolds number relationship of the cylinder wake. J. Fluids Struct. 12, 10731085.CrossRefGoogle Scholar
Williamson, C. H. K. 1989 Oblique and parallel modes of Vortex shedding in the wake of a circular cylinder at low Reynolds numbers. J. Fluid Mech. 206, 579627.CrossRefGoogle Scholar
Zdravkovich, M. 1997 Flow around Circular Cylinders Volume 1: Fundamentals, 1st edn. Oxford University Press.CrossRefGoogle Scholar