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Stability of flows past a pair of circular cylinders in a side-by-side arrangement

Published online by Cambridge University Press:  08 January 2008

J. MIZUSHIMA  and
Y. INO
J. MIZUSHIMA
Affiliation:
Department of Mechanical Engineering, Doshisha University, Kyotanabe, Kyoto 610-0321, Japan
Y. INO
Affiliation:
Department of Mechanical Engineering, Doshisha University, Kyotanabe, Kyoto 610-0321, Japan
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Abstract

The stability and transition of flow past a pair of circular cylinders in a side-by-side arrangement are investigated by numerical simulations and linear stability analyses. Various flow patterns around the cylinders have been reported to appear due to an instability of the steady symmetric flow that is realized at small Reynolds numbers, among which deflected oscillatory flow is particularly noticeable. The physical origin of the flow is explored by bifurcation analyses of the numerical data. We found that the deflected oscillatory flow arises from the steady symmetric flow through sequential instabilities due to stationary and oscillatory unstable modes. Steady asymmetric flow with respect to the streamwise centreline between the two cylinders was also found to be induced by the instability due to a stationary mode in a very narrow range of the gap width between the two cylinders. We classify the instability modes of the steady symmetric flow into four groups in the parameter space of the gap width, and evaluate the critical Reynolds number for each mode of instability.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 595 , 25 January 2008 , pp. 491 - 507
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Agrawal, A., Djenidi, L. & Antonia, R. A. 2005 Investigation of flow around a pair of side-by-side square cylinders using the lattice Boltzmann method. Comput. Fluids 35, 1093–1107.CrossRefGoogle Scholar
Akinaga, T. & Mizushima, J. 2005 Linear stability of flow past two circular cylinders in a side-by-side arrangement. J. Phys. Soc. Japan 74, 1366–1369.CrossRefGoogle Scholar
Bearman, P. W. & Wadcock, A. J. 1973 The interaction between a pair of circular cylinders normal to a stream. J. Fluid Mech. 61, 499–511.CrossRefGoogle Scholar
Ishigai, S., Nishikawa, E. & Cho, K. 1972 Experimental study on structure of gas flow in tube banks with tube axes normal to flow. Bull. JSME 15, 949–956.CrossRefGoogle Scholar
Kang, S. 2003 Characteristics of flow over two circular cylinders in a side-by-side arrangement at low Reynolds numbers. Phys. Fluids 15, 2486–2498.CrossRefGoogle 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, 431–448.CrossRefGoogle Scholar
Le Gal, P., Chauve, M. P., Lima, R. & Rezende, R. 1990 Coupled wakes behind two circular cylinders. Phys. Rev. A 41, 4566–4569.CrossRefGoogle Scholar
Le Gal, P., Peschard, I., Chauve, M. P. & Takeda, Y. 1996 Collective behavior of wakes downstream a row of cylinders. Phys. Fluids 8, 2097–2106.CrossRefGoogle Scholar
Mizushima, J. & Kawaguchi, Y. 2000 Transition of flow past a row of square bars. J. Fluid Mech. 405, 305–323.CrossRefGoogle Scholar
Mizushima, J. & Suehiro, N. 2005 Instability and transition of flow past two tandem circular cylinders. Phys. Fluids. 17 104107-1–11.CrossRefGoogle Scholar
Mizushima, J. & Takemoto, Y. 1996 Stability of the flow past a row of square bars. J. Phys. Soc. Japan 65, 1673–1685.CrossRefGoogle Scholar
Ohya, Y., Okajima, A. & Hayashi, M. 1988 Wake interference and vortex shedding. In Encyclopedia of Fluid Mechanics (ed. Cheremisinoff, N. P.), vol. 8, pp. 323–389. Gulf.Google Scholar
Peschard, I. & Le Gal, P. 1996 Coupled wakes of cylinders. Phys. Rev. Lett. 77, 3122–3125.CrossRefGoogle ScholarPubMed
Ravoux, J. F., Nadim, A. & Haj-Hariri, H. 2003 An embedding method for bluff body flows: interactions of two side-by-side cylinder wakes. Theor. Comput. Fluid Dyn. 16, 433–466.CrossRefGoogle Scholar
Spivack, H. M. 1946 Vortex frequency and flow pattern in the wake of two parallel cylinders at varied spacings normal to the an air stream. J. Aeronaut. Sci. 13, 289–297.CrossRefGoogle Scholar
Steger, J. L. & Sorenson, R. L. 1979 Automatic mesh-point clustering near a boundary in grid generation with elliptic partial differential equation. J. Comput. Phys. 33, 405–410.CrossRefGoogle Scholar
Sumner, D., Wong, S. S. T., Price, S. J. & Païdoussis, M. P. 1999 Fluid behaviour of side-by-side circular cylinders in steady cross-flow. J. Fluids Struct. 13, 309–338.CrossRefGoogle Scholar
Williamson, C. H. K. 1985 Evolution of a single wake behind a pair of bluff bodies. J. Fluid Mech. 159, 1–18.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, 1214–1219.CrossRefGoogle Scholar
Zdravkovich, M. M. 1977 Review of flow intererence between two circular cylinders in various arrangement. Trans. ASMEI: J. Fluids Engng 99, 618–633.Google Scholar
Zdravkovich, M. M. & Pridded, D. L. 1977 Interference between two circular cylinders; series of unexpected discountinuities. J. Ind. Aero. 2, 255–270.CrossRefGoogle Scholar
Zhou, Y., Wang, Z. J., So, R. M. C., Xu, S. J. & Jin, W. 2001 Free vibrations of two side-by-side cylinders in a cross-flow. J. Fluid Mech. 443, 197–229.CrossRefGoogle Scholar
Zhou, Y., Zhang, H. J. & Yiu, M. W. 2002 The turublent wake of two side-by-side circular cylinders. J. Fluid Mech. 458, 303–332.CrossRefGoogle Scholar