Wake-Induced Vibrations of a Circular Cylinder behind a Stationary Square Cylinder Using a Semi-Implicit Characteristic-Based Split Scheme
Publication: Journal of Engineering Mechanics
Volume 140, Issue 8
Abstract
This study develops a semi-implicit characteristic-based-split (SI-CBS) finite-element algorithm under the framework of the fractional step method to cope with the vortex-induced vibration (VIV) problem. The authors present a modified linear spring analogy algorithm for successful updating of the grid deformation. They verify the computational code against two benchmark problems. One is the VIV of an elastically mounted cylinder with transverse oscillation at . The other is the transversely wake-induced vibration (WIV) of a circular cylinder by a stationary one. The authors conduct a two-dimensional (2D) numerical investigation on the problem of laminar flow over a two-cylinder system, which consists of a front stationary square cylinder and a rear two-degree-of-freedom (2-DOF) circular cylinder in a tandem arrangement. They find that the Reynolds number and reduced velocities play key roles in the WIVs of the circular cylinder. In addition to the wake patterns 2S, 2P, and , the authors observe a steady-state wake pattern. They observe performances of dual-resonance, which means synchronization in both the in-line and transverse directions. For the trajectories of the circular cylinder, they obtain figures in the shape of an egg, a figure-8, and a point.
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Acknowledgments
Support from the National Natural Science Foundation of China (Nos. 11172174, 51278297, and 51078230) and the Program of Shanghai Subject Chief Scientist (No. 13XD1402100) is acknowledged.
References
Ahn, H. T., and Kallinderis, Y. (2006). “Strongly coupled flow/structure interactions with a geometrically conservative ALE scheme on general hybrid meshes.” J. Comput. Phys., 219(2), 671–696.
Allen, D. W., and Henning, D. L. (2003). “Vortex-induced vibration current tanktests of two equal-diameter cylinders in tandem.” J. Fluids Struct., 17(6), 767–781.
Assi, G. R. S., Bearman, P. W., and Meneghini, J. R. (2010). “On the wake-induced vibration of tandem circular cylinders: The vortex interaction excitation mechanism.” J. Fluid Mech., 661(1), 365–401.
Assi, G. R. S., Meneghini, J. R., Aranha, J. A. P., Bearman, P. W., and Casaprima, E. (2006). “Experimental investigation of flow-induced vibration interference between two circular cylinders.” J. Fluids Struct., 22(6–7), 819–827.
Bao, Y., Zhou, D., and Huang, C. (2010a). “Numerical simulation of flow over three circular cylinders in equilateral arrangements at low Reynolds number by a second-order characteristic-based split finite element method.” Comput. Fluids, 39(5), 882–899.
Bao, Y., Zhou, D., and Tu, J. (2011). “Flow interference between a stationary cylinder and an elastically mounted cylinder arranged in proximity.” J. Fluids Struct., 27(8), 1425–1446.
Bao, Y., Zhou, D., and Zhao, Y. (2010b). “A two-step Taylor-characteristic-based Garlerkin method for incompressible flows and its application to flow over triangular cylinder with different incidence angles.” Int. J. Numer. Methods Fluids, 62(11), 1181–1208.
Bearman, P. W. (2011). “Circular cylinder wakes and vortex-induced vibrations.” J. Fluids Struct., 27(5–6), 648–658.
Borazjani, I., and Sotiropoulos, F. (2009). “Vortex-induced vibrations of two cylinders in tandem arrangement in the proximity–wake interference region.” J. Fluid Mech., 621(2), 321–364.
Brika, D., and Laneville, A. (1999). “The flow interaction between a stationary cylinder and a downstream flexible cylinder.” J. Fluids Struct., 13(5), 579–606.
Brooks, A. N., and Hughes, T. J. R. (1982). “Streamline upwind /Petrov–Galerkin formulations for convective dominated flows with particular emphasis on the incompressible Navier–Stokes equations.” Comput. Methods Appl. Mech. Eng., 32(1–3), 199–259.
Carmo, B. S., Sherwin, S. J., Bearman, P. W., and Willden, R. H. J. (2011). “Flow-induced vibration of a circular cylinder subjected to wake interference at low Reynolds number.” J. Fluids Struct., 27(4), 503–522.
Donea, J. (1984). “A Taylor–Galerkin method for convection transport problems.” Int. J. Numer. Methods Eng., 20(1), 101–119.
Donea, J., Guiliani, S., and Halleux, J. P. (1982). “An arbitrary Lagrangian–Eulerian finite element method for transient dynamic fluid–structure interactions.” Comput. Methods Appl. Mech. Eng., 33(1–3), 689–723.
Gabbai, R. D., and Benaroya, H. (2005). “An overview of modeling and experiments of vortex-induced vibration of circular cylinders.” J. Sound Vib., 282(3–5), 575–616.
Han, Z., Zhou, D., and Tu, J. (2013). “Laminar flow patterns around three side-by-side arranged circular cylinders using semi-implicit three-step Taylor-characteristic-based-split (3-TCBS) algorithm.” Eng. Appl. Comput. Fluid Mech., 7(1), 1–12.
Hover, F. S., and Triantafyllou, M. S. (2001). “Galloping response of a cylinder with upstream wake interference.” J. Fluids Struct., 15(3–4), 503–512.
Hughes, T. J. R., Franca, L. P., and Hulbert, G. M. (1989). “A new finite element formulation for computational fluid dynamics: VIII. The Galerkin/least-squares method for advective–diffusive equations.” Comput. Methods Appl. Mech. Eng., 73(2), 173–189.
Jauvtis, N., and Williamson, C. H. K. (2004). “The effect of two degrees of freedom on vortex-induced vibration at low mass and damping.” J. Fluid Mech., 509(6), 23–62.
Kang, S. (2003). “Characteristics of flow over two circular cylinders in a side-by-side arrangement at low Reynolds numbers.” Phys. Fluids, 15(9), 2486–2498.
Meneghini, J. R., Saltara, F., Siqueira, C. L. R., and Ferrari, J. A., Jr. (2001). “Numerical simulation of flow interference between two circular cylinders in tandem and side-by-side arrangements.” J. Fluids Struct., 15(2), 327–350.
Mittal, S., and Kumar, V. (2001). “Flow-induced oscillations of two cylinders in tandem and staggered arrangement.” J. Fluids Struct., 15(5), 717–736.
Nithiarasu, P., and Liu, C. B. (2006). “An artificial compressibility based characteristic based split (CBS) scheme for steady and unsteady turbulent incompressible flows.” Comput. Methods Appl. Mech. Eng., 195(23–24), 2961–2982.
Nithiarasu, P., Mathur, J. S., Weatherill, N. P., and Morgan, K. (2004). “Three-dimensional incompressible flow calculations using the characteristic based split (CBS) scheme.” Int. J. Numer. Methods Fluids, 44(11), 1207–1229.
Papaioannou, G. V., Yue, D. K. P., Triantafyllou, M. S., and Karniadakis, G. E. (2008). “On the effect of spacing on the vortex-induced vibrations of two tandem cylinders.” J. Fluids Struct., 24(6), 833–854.
Placzek, A., Sigrist, J. F., and Hamdouni, A. (2009). “Numerical simulation of an oscillating cylinder in a cross-flow at low Reynolds number: Forced and free oscillations.” Comput. Fluids, 38(1), 80–100.
Prasanth, T. K., and Mittal, S. (2009a). “Flow-induced oscillation of two circular cylinders in tandem arrangement at low Re.” J. Fluids Structures, 25(6), 1029–1048.
Prasanth, T. K., and Mittal, S. (2009b). “Vortex-induced vibration of two circular cylinders at low Reynolds number.” J. Fluids Structures, 25(4), 731–741.
Sarpkaya, T. (2004). “A critical review of the intrinsic nature of vortex-induced vibrations.” J. Fluids Struct., 19(4), 389–447.
Tasaka, Y., Kon, S., Schouveiler, L., and Gal, P. L. (2006). “Hysteretic mode exchange in the wake of two circular cylinders in tandem.” Phys. Fluids, 18(8), 084104.
Williamson, C. H. K., and Govardhan, R. (2004). “Vortex-induced vibrations.” Annu. Rev. Fluid Mech., 36, 413–455.
Zeng, D., and Ethier, C. R. (2005). “A semi-torsional spring analogy model for updating unstructured meshes in 3D moving domains.” Finite Elem. Anal. Des., 41(11–12), 1118–1139.
Zhao, M., Cheng, L., Teng, B., and Dong, G. (2007). “Hydrodynamic forces on dual cylinders of different diameters in steady current.” J. Fluids Struct., 23(1), 59–83.
Zienkiewicz, O. C., and Codina, R. (1995). “A general algorithm for compressible and incompressible flow, part I: The split, characteristic-based scheme.” Int. J. Numer. Methods Fluids, 20(8–9), 869–885.
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Published In
Journal of Engineering Mechanics
Volume 140 • Issue 8 • August 2014
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Jan 16, 2013
Accepted: Oct 11, 2013
Published online: Feb 12, 2014
Discussion open until: Jul 12, 2014
Published in print: Aug 1, 2014
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