Hostname: page-component-7c8c6479df-5xszh Total loading time: 0 Render date: 2024-03-28T19:39:16.407Z Has data issue: false hasContentIssue false

Vortex suppression and drag reduction in the wake of counter-rotating cylinders

Published online by Cambridge University Press:  12 May 2011

ANDRE S. CHAN
Affiliation:
Department of Aeronautics and Astronautics, Stanford University, Stanford, CA 94305, USA Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA
PETER A. DEWEY
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
ANTONY JAMESON*
Affiliation:
Department of Aeronautics and Astronautics, Stanford University, Stanford, CA 94305, USA
CHUNLEI LIANG
Affiliation:
Department of Aeronautics and Astronautics, Stanford University, Stanford, CA 94305, USA Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA
ALEXANDER J. SMITS
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
*
Email address for correspondence: jameson@baboon.stanford.edu
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 flow over a pair of counter-rotating cylinders is investigated numerically and experimentally. It is demonstrated that it is possible to suppress unsteady vortex shedding for gap sizes from one to five cylinder diameters, at Reynolds numbers from 100 to 200, expanding on the more limited work by Chan & Jameson (Intl J. Numer. Meth. Fluids, vol. 63, 2010, p. 22). The degree of unsteady wake suppression is proportional to the speed and the direction of rotation, and there is a critical rotation rate where a complete suppression of flow unsteadiness can be achieved. In the doublet-like configuration at higher rotational speeds, a virtual elliptic body that resembles a potential doublet is formed, and the drag is reduced to zero. The shape of the elliptic body primarily depends on the gap between the two cylinders and the speed of rotation. Prior to the formation of the elliptic body, a second instability region is observed, similar to that seen in studies of single rotating cylinders. It is also shown that the unsteady wake suppression can be achieved by rotating each cylinder in the opposite direction, that is, in a reverse doublet-like configuration. This tends to minimize the wake interaction of the cylinder pair and the second instability does not make an appearance over the range of speeds investigated here.

Type
Papers
Copyright
Copyright © Cambridge University Press 2011. 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 <http://creativecommons.org/licenses/by-nc-sa/2.5/>. The written permission of Cambridge University Press must be obtained for commercial re-use.

Footnotes

Present address: Hitachi Global Storage Technologies, San Jose, CA 95119, USA.

Present address: Department of Mechanical and Aerospace Engineering, George Washington University, Washington, DC 20052, USA.

References

REFERENCES

Belov, A., Martinelli, L. & Jameson, A. 1995 A new implicit algorithm with multigrid for unsteady incompressible flow calculations. AIAA Paper 1995-0049, 33rd Aerospace Sciences Meeting and Exhibit, 9–12 January 1995, Reno, NV.Google Scholar
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, 79130.Google Scholar
Chan, A. S. & Jameson, A. 2010 Suppression of the unsteady vortex wakes of a circular cylinder pair by a doublet-like counter-rotation. Intl J. Numer. Meth. Fluids 63, 2239.CrossRefGoogle Scholar
Cockburn, B., Hou, S. & Shu, C. W. 1990 TVB Runge–Kutta local projection discontinuous Galerkin finite element method for conservation laws. Part IV: The multidimensional case. Math. Comput. 54, 545581.Google Scholar
Cockburn, B., Lin, S. Y. & Shu, C. W. 1989 TVB Runge–Kutta local projection discontinuous Galerkin finite element method for conservation laws. Part III: One-dimensional systems. J. Comput. Phys. 84, 90113.CrossRefGoogle Scholar
Cockburn, B. & Shu, C. W. 1989 TVB Runge–Kutta local projection discontinuous Galerkin finite element method for conservation laws. Part II: General framework. Math. Comput. 52, 411435.Google Scholar
Cockburn, B. & Shu, C. W. 1998 TVB Runge–Kutta local projection discontinuous Galerkin finite element method for conservation laws. Part V: Multidimensional system. J. Comput. Phys. 141, 199224.CrossRefGoogle Scholar
Ding, H., Shu, C., Yeo, K. S. & Xu, D. 2007 Numerical simulation of flows around two circular cylinders by mesh-free least square-based finite difference methods. Intl J. Numer. Meth. Fluids 53, 305332.CrossRefGoogle Scholar
Harten, A. & Hyman, J. M. 1983 Self-adjusting grid methods for one-dimensional hyperbolic conservation laws. J. Comput. Phys. 50, 235269.CrossRefGoogle Scholar
Henderson, R. D. 1994 Unstructured spectral element methods: Parallel algorithms and simulations. PhD thesis, Princeton University.Google Scholar
Henderson, R. D. 1995 Details of the drag curve near the onset of vortex shedding. Phys. Fluids 7, 21022104.CrossRefGoogle Scholar
Hesthaven, J. S. & Warburton, T. 2008 Nodal Discontinuous Galerkin Methods – Algorithms, Analysis, and Applications. Springer.Google Scholar
Huynh, H. T. 2007 A flux reconstruction approach to high-order schemes including discontinuous Galerkin methods. AIAA Paper 2007-4079, 18th AIAA CFD Conference, 25–28 June 2007, Miami, FL.CrossRefGoogle Scholar
Jameson, A. 2010 A proof of the stability of the spectral difference method for all orders of accuracy. J. Sci. Comput. 45, 348358CrossRefGoogle Scholar
Jiménez, J. M. 2002 Low Reynolds number studies in the wake of a submarine model using particle image velocimetry. MSE thesis, Princeton University.Google Scholar
Kang, S. 2003 Characteristics of flow over two circular cylinders in a side-by-side arrangement at low Reynolds numbers. Phys. Fluids 15, 24862498.CrossRefGoogle Scholar
Kang, S., Choi, H. & Lee, S. 1999 Laminar flow past a rotating circular cylinder. Phys. Fluids 11, 33123321.Google Scholar
Kim, H. J. & Durbin, P. A. 1988 Investigation of the flow between a pair of circular cylinders in the flopping regime. J. Fluid Mech. 196, 431448.CrossRefGoogle Scholar
Kopriva, D. A. & Kolias, J. H. 1996 A conservative staggered-grid Chebyshev multidomain method for compressible flows. J. Comput. Phys. 125 (1), 244261.CrossRefGoogle Scholar
Kovasznay, L. S. G. 1949 Hot-wire investigation of the wake behind cylinders at low Reynolds numbers. Proc. R. Soc. Lond. A 198, 174190.Google Scholar
Lecointe, Y. & Piquet, J. 1984 On the use of several compact methods for the study of unsteady incompressible viscous flow round a circular cylinder. Comput Fluids 12, 255280.Google Scholar
Liang, C., Jameson, A. & Wang, Z. J. 2009 a Spectral difference method for two-dimensional compressible flow on unstructured grids with mixed elements. J. Comput. Phys. 228, 28472858.CrossRefGoogle Scholar
Liang, C., Premasuthan, S. & Jameson, A. 2009 b High-order accurate simulation of flow past two side-by-side cylinders with spectral difference method. J. Comput. Struct. 87, 812817.CrossRefGoogle Scholar
Liang, C., Premasuthan, S., Jameson, A. & Wang, Z. J. 2009 c Large eddy simulation of compressible turbulent channel flow with spectral difference method. AIAA Paper 2009-402, 47th AIAA Aerospace Sciences Meeting, 5–8 January 2009, Orlando, FL.CrossRefGoogle Scholar
Liu, C., Zheng, X. & Sung, C. H. 1998 Preconditioned multigrid methods for unsteady incompressible flows. J. Comput. Phys. 139, 3557.CrossRefGoogle Scholar
Liu, Y., Vinokur, M. & Wang, Z. J. 2006 Spectral difference method for unstructured grids. Part I: Basic formulation. J. Comput. Phys. 216, 780801.Google Scholar
Miller, G. D. & Williamson, C. H. K. 1994 Control of three-dimensional phase dynamics in a cylinder wake. Exp. Fluids 18, 2635.CrossRefGoogle Scholar
Mittal, S. & Kumar, B. 2003 Flow past a rotating cylinder. J. Fluid Mech. 476, 303334.CrossRefGoogle Scholar
Mohammad, A. H., Wang, Z. J. & Liang, C. 2008 LES of turbulent flow past a cylinder using spectral difference method. AIAA Paper 2008-7184. 26th AIAA Applied Aerodynamics Meeting, 18–21 August 2008, Honolulu, HI.Google Scholar
Ou, K., Liang, C., Premasuthan, S. & Jameson, A. 2009 High-order spectral difference simulation of laminar compressible flow over two counter-rotating cylinders. AIAA Paper 2009-3956, 27th AIAA Applied Aerodynamics Conference, 22–25 June 2009, San Antonio, TXCrossRefGoogle Scholar
Park, J., Kwon, K. & Choi, H. 1998 Numerical solutions of flow past a circular cylinder at Reynolds numbers up to 160. KSME Intl J. 12, 12001205.CrossRefGoogle Scholar
Peschard, I. & Le Gal, P. 1996 Coupled wakes of cylinders. Phys. Rev. Lett. 77, 31223125.CrossRefGoogle ScholarPubMed
Prandtl, L. & Tietjens, O. G. 1934 Applied Hydro- and Aeromechanics, Dover edn. 1957. Dover Publications.Google Scholar
Premasuthan, S., Liang, C., Jameson, A. & Wang, Z. J. 2009 A P-multigrid spectral difference method for viscous flow. AIAA Paper 2009-950, 47th AIAA Aerospace Sciences Meeting, 5–8 January 2009, Orlando, FL.Google Scholar
Raffel, M., Willert, C., Wereley, S. & Kompenhans, J. 1998 Particle Image Velocimetry. Springer.CrossRefGoogle Scholar
Roe, P. L. 1981 Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys. 43, 357372.CrossRefGoogle Scholar
Rogers, S. E. & Kwak, D. 1990 Upwind differencing scheme for the time-accurate incompressible Navier–Stokes equations. AIAA J. 28, 253262.CrossRefGoogle Scholar
Sharman, B., Lien, F. S., Davidson, L. & Norberg, C. 2005 Numerical predictions of low Reynolds number flows over two tandem circular cylinders. Intl J. Numer. Meth. Fluids 47, 423447.CrossRefGoogle Scholar
Spiteri, R. J. & Ruuth, S. J. 2002 A new class of optimal high-order strong-stability-preserving time discretization methods. SIAM J. Numer. Anal. 40, 469491.Google Scholar
Sumner, D., Wong, S. S. T., Price, S. J. & Paidoussis, M. P. 1999 Fluid behaviour of side-by-side circular cylinders in steady cross-flow. J. Fluids Struct. 13, 309338.CrossRefGoogle Scholar
Wang, Z. J., Liu, Y., May, G. & Jameson, A. 2007 Spectral difference method for unstructured grids. Part II: Extension to the Euler equations. J. Sci. Comput. 32 (1), 4571.CrossRefGoogle Scholar
Whittlesey, R. W., Liska, S. & Dabiri, J. O. 2010 Fish schooling as a basis for vertical axis wind turbine farm design Bioinsp. Biomim. 5, 035005(16).CrossRefGoogle ScholarPubMed
Williamson, C. H. K. 1985 Evolution of a single wake behind a pair of bluff bodies. J. Fluid Mech. 159, 118.Google 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.Google 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, 3846.Google Scholar
Williamson, C. H. K. 1996 Vortex dynamics in the cylinder wake. Annu. Rev. Fluid Mech. 28, 477539.CrossRefGoogle Scholar
Xu, S. J., Zhou, Y. & So, R. M. C. 2003 Reynolds number effects on the flow structure behind two side-by-side cylinders. Phys. Fluids 15, 1214.CrossRefGoogle Scholar
Yoon, H. S., Kim, J. H., Chun, H. H. & Choi, H. J. 2007 Laminar flow past two rotating cylinders in a side-by-side arrangement. Phys. Fluids 19, 128103-1-128103-4.CrossRefGoogle Scholar