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Suppression of vortex shedding behind a circular cylinder by another control cylinder at low Reynolds numbers

Published online by Cambridge University Press:  05 February 2007

A. DIPANKAR ,
T. K. SENGUPTA  and
S. B. TALLA
A. DIPANKAR
Affiliation:
Department of Aerospace Engineering, IIT Kanpur 208 016, India
T. K. SENGUPTA
Affiliation:
Department of Aerospace Engineering, IIT Kanpur 208 016, India
S. B. TALLA
Affiliation:
Department of Aerospace Engineering, IIT Kanpur 208 016, India
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Abstract

Vortex shedding behind a cylinder can be controlled by placing another small cylinder behind it, at low Reynolds numbers. This has been demonstrated experimentally by Strykowski & Sreenivasan (J. Fluid Mech. vol. 218, 1990, p. 74). These authors also provided preliminary numerical results, modelling the control cylinder by the innovative application of boundary conditions on some selective nodes. There are no other computational and theoretical studies that have explored the physical mechanism. In the present work, using an over-set grid method, we report and verify numerically the experimental results for flow past a pair of cylinders. Apart from providing an accurate solution of the Navier–Stokes equation, we also employ an energy-based receptivity analysis method to discuss some aspects of the physical mechanism behind vortex shedding and its control. These results are compared with the flow picture developed using a dynamical system approach based on the proper orthogonal decomposition (POD) technique.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 573 , February 2007 , pp. 171 - 190
Copyright
Copyright © Cambridge University Press 2007

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References

Braza, M., Chassaing, P. & Ha Minh, H. 1986 Numerical study and physical analysis of the pressure and velocity fields in the near wake of a circular cylinder. J. Fluid Mech. 165, 79–130.CrossRefGoogle Scholar
Chesshire, G. & Henshaw, W. D. 1990 Composite overlapping meshes for the solution of partial differential equations. J. Comput. Phys. 90, 1–64.CrossRefGoogle Scholar
Coutanceau, M. & Defaye, J. R. 1991 Circular cylinder wake configuration: a flow visualization survey. Appl. Mech. Rev. 44, 225–305.CrossRefGoogle Scholar
Deane, A. E. & Mavriplis, C. 1994 Low-dimensional description of the dynamics in separated flow past thick airfoils. AIAA J. 32, 1222–1227.CrossRefGoogle Scholar
Deane, A. E., Kevrekidis, I. G., Karniadakis, G. E. & Orszag, S. A. 1991 Low-dimensional models for complex geometry flows: application to grooved channels and circular cylinders. Phys. Fluids A 3, 2337–2354.CrossRefGoogle Scholar
Esposito, P. G., Verzicco, R. & Orlandi, P. 1993 Boundary condition influence on the flow around a circular cylinder. In the Proc. IUTAM Symp. on Bluff-body Wakes, Dynamics and Instabilities (ed. Eckelmann, H., Graham, G., Huerre, P. & Monkewitz, P. A.). Springer.Google Scholar
Hankey, W. L. & Shang, J. S. 1984 Numerical simulation of self-excited oscillations in fluid flows. In Computational Methods in Viscous Flows (ed. W. G. Habashi), vol. 3. Pineridge, Swansea.Google Scholar
Henshaw, W. D. 1994 A fourth order accurate method for the incompressible Navier–Stokes equations on overlapping grids. J. Comput. Phys. 113, 13–25.CrossRefGoogle Scholar
Holmes, P., Lumley, J. L. & Berkooz, G. 1996 Turbulence, Coherent Structures, Dynamical Systems and Symmetry. Cambridge University Press.CrossRefGoogle Scholar
Honji, H. & Taneda, S. 1969 Unsteady flow past a circular cylinder. J. Phys. Soc. Japan 27, 1668–1677.CrossRefGoogle Scholar
Jackson, C. P. 1987 A finite element study of the onset of vortex shedding in flow past variously shaped bodies. J. Fluid Mech. 182, 23–45.CrossRefGoogle Scholar
Nair, M. T. & Sengupta, T. K. 1996 Onset of asymmetry: flow past circular and elliptic cylinders. Intl J. Numer. Meth. Fluids 23, 1327–1345.3.0.CO;2-Q>CrossRefGoogle Scholar
Orlanski, I. 1976 A simple boundary condition for unbounded hyperbolic flows. J. Comput. Phys. 21, 251–259.CrossRefGoogle Scholar
Sengupta, T. K. 2004 Fundamentals of Computational Fluid Dynamics. Universities Press, Hyderabad, India.Google Scholar
Sengupta, T. K. & Dipankar, A. 2005 Subcritical instability on the attachment-line of an infinite swept wing. J. Fluid Mech. 529, 147–171.CrossRefGoogle Scholar
Sengupta, T. K., De, S. & Sarkar, S. 2003a Vortex-induced instability of an incompressible wall-bounded shear layer. J. Fluid Mech. 493, 277–286.CrossRefGoogle Scholar
Sengupta, T. K., Ganeriwal, G. & De, S. 2003b Analysis of central and upwind compact schemes. J. Comput. Phys. 192, 677–694.CrossRefGoogle Scholar
Sengupta, T. K., Kasliwal, A., De, S. & Nair, M. 2003c Temporal flow instability for Magnus–Robins effect at high rotation rates. J. Fluids Struct. 17, 941–953.CrossRefGoogle Scholar
Sengupta, T. K., Talla, S. B. & Pradhan, S. C. 2005 Galerkin finite element methods for wave problems. Sadhana 30, 611–623.CrossRefGoogle Scholar
Sengupta, T. K., Vikas, V. & Johri, A. 2006 An improved method for calculating flow past flapping and hovering airfoils. Theoret. Comput. Fluid Dyn. 19, 417–440.CrossRefGoogle Scholar
Sirovich, S. 1987 Turbulence and the dynamics of coherent structures. Parts I, II and III. Q. Appl. Maths 45, 561–590.CrossRefGoogle Scholar
Sreenivasan, K. R., Strykowski, P. J. & Olinger, D. J. 1987 Hopf bifurcation, Landau equation and vortex ‘shedding’ behind circular cylinders. In Forum on Unsteady Flow Separation (ed. Ghia, K. N.), pp. 1–13. ASME.Google Scholar
Steger, J. L. & Benek, J. A. 1987 On the use of composite grid schemes in computational aerodynamics. Comput. Meth. Appl. Mech. Engng 64, 301–320.CrossRefGoogle Scholar
Strykowski, P. J. 1986 The control of absolutely and convectively unstable shear flows. PhD dissertation, Yale University.Google Scholar
Strykowski, P. J. & Sreenivasan, K. R. 1990 On the formation and suppression of vortex ‘shedding’ at low Reynolds numbers. J. Fluid Mech. 218, 74–107.CrossRefGoogle Scholar