Numerical study of laminar flow past one and two circular cylinders. (English) Zbl 0721.76049

Summary: A finite element program was developed in order to simulate the vortex shedding behind one or two circular cylinders. The velocity-pressure formulation was used to solve the unsteady, two-dimensional, incompressible Navier-Stokes equations. The characteristics of the time integration schemes (implicit-Euler and Crank-Nicolson) were studied. Using the Crank-Nicolson scheme, the classical von Kármán vortex street was found in the solution of the Navier-Stokes equations. The drag lift coefficients as well as the Strouhal number calculated from our numerical data for Re\(\leq 500\) were compared both with experimental and numerical results and good agreement was observed. The critical Reynolds number \(Re_ c\) found in the present study was well within the range of experimental measurements. Flow past two circular cylinders arranged behind one another at different intervals was also studied for \(Re=100\). The pressure distributions around the upstream and downstream cylinders together with their vortex shedding frequencies as a function of cylinder interval were determined and compared with the experimental values. Discontinuity changes in the flow pattern, the Strouhal number and the pressure distribution were detected.


76M10 Finite element methods applied to problems in fluid mechanics
76D10 Boundary-layer theory, separation and reattachment, higher-order effects
Full Text: DOI


[1] Blevins, R. D., Flow Induced Vibration (1977), Van Nostrand-Reinhold: Van Nostrand-Reinhold New York · Zbl 0385.73001
[2] Roshko, A., On the drag and shedding frequency of two-dimensional bluff bodies, NACA TN 3169 (1954)
[3] Tritton, D. J., Experiments on the flow past a circular cylinder at low Reynolds numbers, J. Fluid Mech., 6, 547 (1959) · Zbl 0092.19502
[4] Coutanceau, M.; Bouard, R., Experimental determination of the main features of the viscous flow in the wake of a circular cylinder in uniform translation, J. Fluid Mech., 79, 237 (1977)
[5] Friehe, C. A., Vortex shedding from cylinders at low Reynolds numbers, J. Fluid Mech., 100, 237-241 (1980), part 2
[6] Nishioka, M.; Sato, H., Mechanism of determination of the shedding frequency of vortices behind a cylinder at low Reynolds numbers, J. Fluid Mech., 89, 49-60 (1978), part 1
[7] Nishioka, M.; Sato, H., Measurements of velocity distributions in the wake of a circular cylinder at low Reynolds numbers, J. Fluid Mech., 65, 97-112 (1974), part 1
[8] Berger, E.; Wille, R., Periodic flow phenomena, Ann. Rev. Fluid Mech., 4, 313-340 (1972)
[9] Peyret, R.; Taylor, T. D., Computational methods for fluid flow, (Springer Physics in Computational Physics (1983), Springer: Springer New York) · Zbl 0514.76001
[10] Jordan, S. K.; Fromm, J. E., Oscillatory drag, lift, and torque on a circular cylinder in a uniform flow, Phys. Fluids, 15, 371-376 (1972) · Zbl 0255.76036
[11] Lecointe, Y.; Piquet, J., On the use of several compact methods for the study of unsteady incompressible viscous flow around a circular cylinder, Comput. Fluids, 12, 255-280 (1984) · Zbl 0619.76023
[12] Braza, M.; Chassaing, P.; Ha Minh, H., A numerical study of the dynamics of different scale structures in the near wake of a circular cylinder in laminar to turbulent transition, J. Fluid Mech., 165, 79 (1986) · Zbl 0596.76047
[13] Gresho, P. M.; Lee, R. L.; Sani, R. L., On the time dependent solution of the incompressible Navier-Stokes equations, (Taylor, C.; Morgan, K., Recent Advances in Numerical Methods in Fluids (1980), Pineridge Press: Pineridge Press Swansea) · Zbl 0446.76034
[14] Gresho, P. M.; Chan, S. T.; Lee, R. L.; Upson, C. D., A modified finite element method for solving the time-dependent, incompressible Navier-Stokes equations. Part 2: Applications, Int. J. Num. Meth. Fluids, 4, 619-640 (1984) · Zbl 0559.76031
[15] Van de Vosse, F. N.; Segal, A.; Van Steenhoven, A. A.; Janssen, J. D., A finite element approximation of the unsteady two-dimensional Navier-Stokes equations, Int. J. Num. Meth. Fluids, 6 (1986) · Zbl 0613.76025
[16] Eaton, B. E., Analysis of laminar vortex shedding behind a circular cylinder by computer-aided flow visualization, J. Fluid Mech., 180, 117-145 (1987)
[17] Jackson, C. P., A finite element study of the onset of vortex shedding in flow past variously shaped bodies, J. Fluid Mech., 182, 23-45 (1987) · Zbl 0639.76041
[18] Hori, E., Experiments on flow around a pair of parallel circular cylinders, (Proc. 9th Japan National Congress for Applied Mech.. Proc. 9th Japan National Congress for Applied Mech., Tokyo (1959)), 231-234
[19] Zdravkovich, M. M., Review of flow interference between two cylinders in various arrangements, Trans. ASME J. Fluids Engng, 618-633 (1977)
[20] Stansby, P. K., A numerical study of vortex shedding frome one and two circular cylinders, Aero. Q., 48-71 (1981)
[21] Chen, C. K.; Wong, K. L.; Cleaver, J. W., Finite element solution of laminar and heat transfer of air in a staggered and in-line tube bank, Int. Heat Fluid Flow, 4, 291 (1986)
[22] Li, J., Simulation numérique d’un écoulement bidimensionnel autour d’un et de deux cylindres en ligne par la méthode des éléments finis, (PhD. Dissertation (1989), University de Provence)
[23] Ziemniak, E. M.; Mitra, N. K.; Fiebig, M., Numerical study of two-dimensional vortex structure in a channel behind a circular cylinder, (Numerical Methods in Laminar and Turbulent Flow, Vol. 6 (1989), Pineridge Press: Pineridge Press Swansea), part 1
[24] Lecointe, Y.; Piquet, J., Flow structure in the wake of an oscillating cylinder, J. Fluids Engng Trans ASME, 111, 139 (1989)
[25] Mathis, C.; Provansal, M.; Boyer, L., The Bénard-von Karman instability: an experimental study near the threshold, J. Phys. Lett., Paris, 45, 483-491 (1984)
[26] Landau, L. D.; Lifshitz, E. M., Mécanique des Fluides (1971), Mir: Mir Moscou · Zbl 0216.25801
[27] Provansal, M., Etude expérimentale de l’instabilité de Bénard-von Karman, (Thesis (1988), Université de Provence)
[28] Zdravkovich, M. M., Smoke observations of wakes of tandem cylinders at low Reynolds numbers, Aero. J., 76, 108-114 (1972)
[29] Ishigai, S.; Nishikawa, E.; Nishimura, K.; Cho, K., Experimental study on structure of gas flow in tube banks with tube axes normal to flow (part 1, Karman vortex flow around two tubes at various spacings), Bull. Jap. Soc. mech. Engrs, 15, 949-956 (1972)
[30] Wieselsberger, V. C., Neuere festellungen über die Gesetze des Flüssigkeits und Luftwiderstands, Physik. Z., 22, 231 (1921)
[31] Oka, S.; Kostic, Z. G.; Sikmanovic, S., Investigation of the heat transfer processes in tube banks in cross flow, (Int. Seminar on Recent Developments in Heat Exchangers. Int. Seminar on Recent Developments in Heat Exchangers, Trogir, Yugoslavia (1972))
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.