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Direct numerical simulation of vortex synchronization due to small perturbations

Published online by Cambridge University Press:  26 August 2009

S. H. KIM ,
J. Y. PARK ,
N. PARK ,
J. H. BAE  and
J. Y. YOO
S. H. KIM
Affiliation:
School of Mechanical and Aerospace Engineering, Seoul National University, Seoul 151-744, Korea
J. Y. PARK
Affiliation:
Halla Climate Control Corporation, Daejeon 306-230, Korea
N. PARK
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455, USA
J. H. BAE
Affiliation:
Mechanical and Aerospace Engineering Department, University of California, Los Angeles, CA 90095-1597, USA
J. Y. YOO*
Affiliation:
School of Mechanical and Aerospace Engineering, Seoul National University, Seoul 151-744, Korea Institute of Advanced Machinery and Design, Seoul National University, Seoul 151-744, Korea
*
†Email address for correspondence: [email protected]
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Abstract

Direct numerical simulation (DNS) is performed to investigate the vortex synchronization phenomena in the wake behind a circular cylinder at the Reynolds numbers, Re = 220 (mode-A regime) and 360 (mode-B regime). To generate vortex synchronization, a sinusoidal streamwise velocity perturbation, the frequency of which is about twice the natural shedding frequency, is superimposed on the free stream velocity. At Re = 360, vortex synchronization occurs when the perturbation frequency is exactly twice the natural shedding frequency. However, at Re = 220, it does not occur when the same perturbation frequency condition is imposed. Instead, it occurs when the perturbation frequency is near twice the hypothetical two-dimensional laminar vortex shedding frequency as if there were no wake transition at Re = 220.

It is elucidated that, as a result of vortex synchronization, the trajectory of the Kármán vortices and the vortex structure are changed. The Kármán vortices are formed along the mean separating streamline slightly inside the mean wake bubble at Re = 220, but slightly outside at Re = 360. Thus, the Reynolds shear stress force has different contribution to the streamwise force balance of the mean wake bubble depending on the Reynolds numbers: its magnitude is negligible at Re = 220, compared to other force components, while it reverses its sign at Re = 360. More importantly, at Re = 220, the mode-A instability is suppressed into two-dimensional laminar flow with strong Kármań vortices. At Re = 360, the dominant instability mode changes from mode B to mode A.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 634 , 10 September 2009 , pp. 61 - 90
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Armstrong, B. J., Barnes, F. H. & Grant, I. 1986 The effect of a perturbation on the flow over a bluff cylinder. Phys. Fluids 29, 2095–2102.CrossRefGoogle Scholar
Balachandar, S., Mittal, R. & Najjar, F. M. 1997 Properties of the mean recirculation region in the wakes of two-dimensional bluff bodies. J. Fluid Mech. 351, 167–199.CrossRefGoogle Scholar
Barbi, C., Favier, D. P., Maresca, C. A. & Telionis, D. P. 1986 Vortex shedding and lock-on of a circular cylinder in oscillatory flow. J. Fluid Mech. 170, 527–544.CrossRefGoogle Scholar
Beaudan, P. & Moin, P. 1994 Numerical experiments on the flow past a circular cylinder at subcritical Reynolds number. Tech. Rep. TF-62. Thermosciences Division. Department of Mechanical Engineering, Stanford University.Google Scholar
Blaisdell, A., Mansour, N. N. & Reynolds, W. C. 1991 Numerical simulations of compressible homogeneous turbulence. Tech. Rep. TF-50. Thermosciences Division. Dept. of Mechanical Engineering, Stanford University.Google Scholar
Brede, M., Eckelmann, H. & Rockwell, D. 1996 On secondary vortices in the cylinder wake. Phys. Fluids 8, 2117–2124.CrossRefGoogle Scholar
Ekaterinaris, J. A. 1999 Implicit, high-resolution, compact schemes for gas dynamics and aeroacoustics. J. Comput. Phys. 156, 272–299.CrossRefGoogle Scholar
Fey, U., König, M. & Eckelmann, H. 1998 A new Strouhal–Reynolds-number relationship for the circular cylinder in the range 47 < Re < 2 × 105. Phys. Fluids 10, 1547.CrossRefGoogle Scholar
Griffin, O. M. & Hall, M. S. 1991 Review - vortex shedding lock-on and flow control in bluff body wakes. ASME J. Fluids Engng 113, 526–537.CrossRefGoogle Scholar
Griffin, O. M. & Ramberg, S. E. 1976 Vortex shedding from a cylinder vibrating in line with an incident uniform flow. J. Fluid Mech. 75, 257–271.CrossRefGoogle Scholar
Henderson, R. D. 1997 Nonlinear dynamics and pattern formation in turbulent wake transition. J. Fluid Mech. 352, 65–112.CrossRefGoogle Scholar
Jin, B. J., Park, N. & Yoo, J. Y. 2001 Large eddy simulation of boundary layer transition on the axial turbine blade by rotor induced wake. In Proceedings of 2001 ASME Fluids Engineering Division Summer Meeting, FEDSM2001-18195, New Orleans.Google Scholar
Kim, J. & Choi, H. 2005 Distributed forcing of flow over a circular cylinder. Phys. Fulids 17, 033103.CrossRefGoogle Scholar
Kim, W., Yoo, J. Y. & Sung, J. 2006 Dynamics of vortex lock-on in a perturbed cylinder wake. Phys. Fluids 18, 074103.CrossRefGoogle Scholar
Konstantinidis, E., Balabani, S. & Yianneskis, M. 2003 The effect of flow perturbations on the near wake characteristics of a circular cylinder. J. Fluids Struct. 18, 367–386.CrossRefGoogle Scholar
Kravchenko, A. G. & Moin, P. 1997 On the effect of numerical errors in large eddy simulations of turbulent flows. J. Comput. Phys. 131, 310–322.CrossRefGoogle Scholar
Kwon, K. & Choi, H. 1996 Control of laminar vortex shedding behind a circular cylinder using splitter plates. Phys. Fluids 8, 479–486.CrossRefGoogle Scholar
Lele, S. K. 1992 Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103, 16–42.CrossRefGoogle Scholar
Miller, G. D. & Williamson, C. H. K. 1994 Control of three-dimensional phase dynamics in a cylinder wake. Exp. Fluids 18, 26–35.CrossRefGoogle Scholar
Mittal, R. & Balachandar, S. 1997 On the inclusion of three-dimensional effects in simulations of two-dimensional bluff body wake flows. In Proceedings of ASME Fluids Engineering Division Summer Meeting, Vancouver, British Columbia, Canada. Available on CD-ROM only.Google Scholar
Nagarajan, S., Lele, S. K. & Ferziger, J. H. 2003 A robust high-order compact method for large eddy simulation. J. Comput. Phys. 191, 392–419.CrossRefGoogle Scholar
Park, N. & Mahesh, K. 2007 Analysis of numerical errors in large eddy simulation using statistical closure theory. J. Comput. Phys. 222, 194–216.CrossRefGoogle Scholar
Park, N., Yoo, J. Y. & Choi, H. 2004 Discretization errors in large eddy simulation: on the suitability of centred and upwind-biased compact difference schemes. J. Comput. Phys. 198, 580–616.CrossRefGoogle Scholar
Persillon, H. & Braza, M. 1998 Physical analysis of the transition to turbulence in the wake of a circular cylinder by three-dimensional Navier–Stokes simulation. J. Fluid Mech. 365, 23–88.CrossRefGoogle Scholar
Poncet, P. 2002 Vanishing of mode B in the wake behind a rotationally oscillating circular cylinder. Phys. Fluids 14, 2021–2024.CrossRefGoogle Scholar
Poncet, P. 2004 Topological aspects of three-dimensional wakes behind rotary oscillating cylinders. J. Fluid Mech. 517, 27–53.CrossRefGoogle Scholar
Posdziech, O. & Grundmann, R. 2001 Numerical simulation of the flow around an infinitely long circular cylinder in the transition regime. Theor. Comput. Fluid Dyn. 15, 121–141.Google Scholar
Roshko, A. 1993 Perspectives on bluff body aerodynamics. J. Wind Engng Ind. Aerodyn. 49, 79–100.CrossRefGoogle Scholar
Sung, J. & Yoo, J. Y. 2003 Near-wake vortex motions behind a circular cylinder at low Reynolds number. J. Fluids Struct. 17, 261–274.CrossRefGoogle Scholar
Tanida, Y., Okajima, A. & Watanabe, Y. 1973 Stability of a circular cylinder oscillating in uniform flow or in a wake. J. Fluid Mech. 61, 769–784.CrossRefGoogle Scholar
Visbal, M. R. & Gaitonde, D. V. 1999 High-order-accurate methods for complex unsteady subsonic flows. AIAA J. 37, 1231–1239.CrossRefGoogle Scholar
Visbal, M. R. & Rizzetta, D. P. 2002 Large-eddy simulation on curvilinear grids using compact differencing and filtering schemes. ASME J. Fluids Engng 124, 836–847.CrossRefGoogle Scholar
Williamson, C. H. K. 1987 Three-dimensional transition in the near wake of a cylinder. Bull. Am. Phys. Soc. 32, 2098.Google Scholar
Williamson, C. H. K. 1992 The natural and forced formation of spot-like ‘vortex dislocations’ in the transition of a wake. J. Fluid Mech. 243, 393–441.CrossRefGoogle Scholar
Williamson, C. H. K. 1996 a Mode A secondary instability in wake transition. Phys. Fulids 8, 1680–1682.CrossRefGoogle Scholar
Williamson, C. H. K. 1996 b Three-dimensional wake transition. J. Fluid Mech. 328, 345–407.CrossRefGoogle Scholar
Williamson, C. H. K. 1996 c Vortex dynamics in the cylinder wake. Annu. Rev. Fluid Mech. 28, 477–539.CrossRefGoogle Scholar
Williamson, C. H. K. & Roshko, A. 1990 Measurements of base pressure in the wake of a cylinder at low Reynolds numbers. Z. Flugwiss. Weltraumforsch. 14, 38–46.Google Scholar
Yoo, J. Y., Kim, S. H. & Bae, J. H. 2006 Suppressed wake transition and vortex lock-on phenomena in a perturbed flow past a circular cylinder. Bull. Am. Phys. Soc. 51 (9), 127.Google Scholar
Yoo, J. Y., Park, J. Y. & Park, N. 2005 Direct numerical simulation of lock-on phenomenon in the wake of a circular cylinder. Bull. Am. Phys. Soc. 50 (9), 235.Google Scholar
You, D., Mittal, R., Wang, M. & Moin, P. 2006 Analysis of stability and accuracy of finite-differencing schemes on a skewed mesh. J. Comput. Phys. 213, 184–204.CrossRefGoogle Scholar
Zhang, H.-Q., Fey, U. & Noack, B. R. 1995 On the transition of the cylinder wake. Phys. Fluids 7, 779–794.CrossRefGoogle Scholar