Effect of Transitions on Flow past a Square Cylinder at Low Reynolds Number
Publication: Journal of Engineering Mechanics
Volume 135, Issue 8
Abstract
Numerical simulations have been performed for three-dimensional flow past a square cylinder. The cylinders are placed normal to the incoming uniform flow. The results are based on higher order spatial and temporal discretization. The computations are carried out for a range of Reynolds number (100-325). The flow is found to be two-dimensional at while it becomes three-dimensional at . Both Mode-A and Mode- are observed to be quite prominent and distinct at though they are present in a range of Reynolds number. The spanwise wavelength for Mode-A is higher than at where finer-scale structures are observed called Mode-B. The decay rate for primary vortices in Mode- is the fastest and it is the lowest for Mode-B. The magnitude of secondary vortices of Mode- is quite high compared to Mode-A, but of comparable magnitude to Mode-B. The effect of transitions on the instantaneous flow and root mean square fluctuations are quite significant while the time-averaged flow does not show any noticeable variation.
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References
Bloor, M. S. (1964). “The transition to turbulence in the wake of a circular cylinder.” J. Fluid Mech., 19(2), 290–304.
Brede, M., Eckelmann, H., and Rockwell, D. (1996). “On secondary vortices in the cylinder wake.” Phys. Fluids, 8(8), 2117–2124.
Davis, R. W., Moore, E. F., and Purtell, L. P. (1984). “A numerical-experimental study on confined flow around rectangular cylinders.” Phys. Fluids, 23(1), 46–59.
Franke, R., Rodi, W., and Schonung, B. (1990). “Numerical calculation of laminar vortex-shedding flow past cylinders.” J. Wind. Eng. Ind. Aerodyn., 35(1–3), 237–257.
Harlow, F. H., and Welch, J. E. (1965). “Numerical calculation of time dependent viscous incompressible flow of fluid with free surfaces.” Phys. Fluids, 8(12), 2182–2188.
Henderson, R. D. (1997). “Nonlinear dynamics and pattern formation in turbulent wake transition.” J. Fluid Mech., 352, 65–112.
Henderson, R. D., and Barkley, D. (1996). “Secondary instability in the wake of a circular cylinder.” Phys. Fluids, 8(6), 1683–1685.
Hoffman, G., and Benocci, C. (1994). “Numerical simulation of spatially developing planer jets.” AGARD Conf. Proc., 551, 26.1–26.6.
Luo, S. C., Chew, Y. T., and Ng, Y. T. (2003). “Characteristics of square cylinder wake transition flows.” Phys. Fluids, 15(9), 2549–2559.
Maskell, E. C. (1963). “A theory of the blockage effects on bluff bodies and stalled wings in a closed wind tunnel.” Rep. and Memoranda, 3400, Aeronautical Research Council (ARC).
Okajima, A. (1982). “Strouhal numbers of rectangular cylinders.” J. Fluid Mech., 123, 379–398.
Orlanski, I. (1976). “A simple boundary condition for unbounded flows.” J. Comput. Phys., 21(3), 251–269.
Robichaux, J., Balachandar, S., and Vanka, S. P. (1999). “Three-dimensional Floquet instability of the wake of square cylinder.” Phys. Fluids, 11(3), 560–578.
Roshko, A. (1954). “On the development of turbulent wakes from vortex streets.” NACA Rep. 1191.
Saha, A. K., Biswas, G., and Muralidhar, K. (2003). “Three-dimensional study of flow past a square cylinder at low Reynolds numbers.” Int. J. Heat Fluid Flow, 24(1), 54–66.
Saha, A. K., Muralidhar, K., and Biswas, G. (2000a). “Vortex structures and kinetic energy budget in two-dimensional flow past a square cylinder.” Comput. Fluids, 29(6), 669–694.
Saha, A. K., Muralidhar, K., and Biswas, G. (2000b). “Numerical simulation of transition and chaos in two-dimensional flow past a square cylinder.” J. Eng. Mech., 126(5), 523–532.
Sohankar, A., Norberg, C., and Davidson, L. (1998). “Low-Reynolds-number flow around a square cylinder at incidence: Study of blockage, onset of vortex shedding and outlet boundary condition.” Int. J. Numer. Methods Fluids, 26(1), 39–56.
Sohankar, A., Norberg, C., and Davidson, L. (1999). “Simulation of three-dimensional flow around a square cylinder at moderate Reynolds numbers.” Phys. Fluids, 11(2), 288–306.
Tombazis, N., and Bearman, P. W. (1997). “A study of three-dimensional aspects of vortex shedding from a bluff body with a mild geometric disturbance.” J. Fluid Mech., 330, 85–112.
Williamson, C. H. K. (1988). “The existence of two stages in the transition to three-dimensionality.” Phys. Fluids, 31(11), 3165–3168.
Williamson, C. H. K. (1992). “The natural and forced formation of spotlike vortex dislocations in the transition of a wake.” J. Fluid Mech., 243, 393–441.
Williamson, C. H. K. (1996). “Vortex dynamics in the cylinder wake.” Annu. Rev. Fluid Mech., 28, 477–539.
Wu, M.-H., and Wang, A.-B. (2007). “On the transitional wake behind a heated circular cylinder.” Phys. Fluids, 19(8), 084102.
Zhang, H., Fey, U., Noack, U., Konig, M., and Eckelmann, H. (1995). “On the transition of the cylinder wake.” Phys. Fluids, 7(4), 779–794.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 135 • Issue 8 • August 2009
Pages: 839 - 851
Copyright
© 2009 ASCE.
History
Received: Dec 11, 2007
Accepted: Jan 15, 2009
Published online: Jul 15, 2009
Published in print: Aug 2009
Notes
Note. Associate Editor: Kuang-An Chang
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