On the onset of bifurcation and nonlinear characterization of vortex-induced vibrations under varying initial conditions. (English) Zbl 1430.37100
Summary: We perform numerical simulations to investigate the hysteresis phenomenon near the bifurcation points of the synchronization region leading to vortex-induced vibrations. We characterize the response using nonlinear dynamics tools. We find an unstable region at both ends of the synchronization regime where the response depends on initial conditions. Unlike previous studies, the focus of the current research is to analyze the effect of the structure’s initial condition on the VIV response. We vary the initial velocity of the cylinder and observe the response of transverse displacement and lift coefficient as a function of Reynolds number. We observe that in the pre-synchronous and synchronous regimes, the cylinder response is always period-1 at cylinder’s natural frequency. However, in the post-synchronous regime, the response is period-n where \(n>1\). Thus, bifurcation diagrams depicts the variation of the onset of synchronization and its spectrum over the range of Reynolds number.
MSC:
| 37M20 | Computational methods for bifurcation problems in dynamical systems |
| 34D06 | Synchronization of solutions to ordinary differential equations |
| 76M23 | Vortex methods applied to problems in fluid mechanics |
Keywords:
numerical simulations; bifurcation point; vortex-induced vibrations; synchronization; initial conditionsReferences:
| [1] | Williamson, Chk, Vortex dynamics in the cylinder wake, Annu. Rev. Fluid Mech., 28, 477-539 (1996) · doi:10.1146/annurev.fl.28.010196.002401 |
| [2] | Bearman, Pw, Vortex shedding from oscillating bluff bodies, Annu. Rev. Fluid Mech., 16, 195-222 (1984) · Zbl 0605.76045 · doi:10.1146/annurev.fl.16.010184.001211 |
| [3] | Williamson, Chk; Govardhan, R., Vortex-induced vibrations, Annu. Rev. Fluid Mech., 36, 413-455 (2004) · Zbl 1125.74323 · doi:10.1146/annurev.fluid.36.050802.122128 |
| [4] | Gabbai, Rd; Benaroya, H., An overview of modeling and experiments of vortex-induced vibration of circular cylinders, J. Sound Vib., 282, 575-616 (2005) · doi:10.1016/j.jsv.2004.04.017 |
| [5] | Prasanth, Tk; Mittal, S., Vortex-induced vibrations of a circular cylinder at low Reynolds numbers, J. Fluid Mech., 594, 463-491 (2008) · Zbl 1159.76316 · doi:10.1017/S0022112007009202 |
| [6] | Singh, Sp; Mittal, S., Flow past a cylinder: shear layer instability and drag crisis, Int. J. Numer. Methods Fluids, 47, 75-98 (2005) · Zbl 1141.76375 · doi:10.1002/fld.807 |
| [7] | Leonard, A.; Roshko, A., Aspects of Flow-induced vibration, J. Fluids Struct., 15, 415-425 (2001) · doi:10.1006/jfls.2000.0360 |
| [8] | Gad-El-Hak, M., Flow Control: Passive, Active and Reactive Flow Management (2000), Cambridge: Cambridge University Press, Cambridge · Zbl 0968.76001 |
| [9] | Choi, H.; Jeon, W-P; Kim, J., Control of flow over a bluff body, Annu. Rev. Fluid Mech., 40, 113-139 (2008) · Zbl 1136.76022 · doi:10.1146/annurev.fluid.39.050905.110149 |
| [10] | Zdravkovich, Mm, Review and classification of various aerodynamic and hydrodynamic means for suppressing vortex shedding, J. Wind Eng. Ind. Aerodyn., 7, 145-189 (1981) · doi:10.1016/0167-6105(81)90036-2 |
| [11] | Walshe, De; Wootton, Lr, Preventing wind-induced oscillations of structures of circular section, Proc. Inst. Civ. Eng., 47, 1-24 (1979) |
| [12] | Abdelkefi, A.; Hajj, Mr; Nayfeh, Ah, Phenomena and modeling of piezoelectric energy harvesting from freely oscillating cylinders, Nonlinear Dyn., 70, 1377-1388 (2012) · doi:10.1007/s11071-012-0540-x |
| [13] | Mehmood, A.; Abdelkefi, A.; Hajj, Mr; Akhtar, I.; Nuhait, Ao, Piezoelectric Energy Harvesting from Vortex-Induced Vibrations of Circular Cylinder, J. Sound Vib., 332, 19, 4656-4667 (2013) · doi:10.1016/j.jsv.2013.03.033 |
| [14] | Javed, U.; Abdelkefi, A., Characteristics and comparative analysis of piezoelectric-electromagnetic energy harvesters from vortex-induced oscillations, Nonlinear Dyn., 95, 3309-3333 (2019) · doi:10.1007/s11071-018-04757-x |
| [15] | Ahsan, N., Akhtar, I.: Computational analysis of vortex-induced vibration and its potential in energy harvesting. In: 12th International Bhurban Conference on Applied Sciences and Technology (IBCAST), pp. 437-443 (2015) |
| [16] | Javed, U., Abdelkefi, A., Akhtar, I.: Enhanced stability identification and global response prediction of galloping energy harvesters. In: 57th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 0211 (2016) |
| [17] | Sarfaraz, S., Shahid, M. H., Akhtar, I.: Energy harvesting potentials of flow-induced vibrations for trapezoid and square bodies: numerical simulations and analyses. In: 16th International Bhurban Conference on Applied Sciences and Technology (IBCAST), pp. 725-731 (2019) |
| [18] | Navrose; Mittal, S., The critical mass phenomenon in vortex-induced vibration at low Re, J. Fluid Mech., 820, 59-186 (2017) · Zbl 1383.76108 · doi:10.1017/jfm.2017.199 |
| [19] | Williamson, Chk; Roshko, A., Vortex formation in the wake of an oscillating cylinder, J. Fluids Struct., 2, 355-381 (1988) · doi:10.1016/S0889-9746(88)90058-8 |
| [20] | Jauvtis, N.; Williamson, Chk, The effect of two degrees of freedom on vortex-induced vibration at low mass and damping, J. Fluid Mech., 509, 23-62 (2004) · Zbl 1163.76348 · doi:10.1017/S0022112004008778 |
| [21] | Anagnostopoulos, P.; Bearman, Pw, Response characteristics of a vortex-excited cylinder at low Reynolds numbers, J. Fluids Struct., 6, 39-50 (1992) · doi:10.1016/0889-9746(92)90054-7 |
| [22] | Yang, J.; Preidikman, S.; Balaras, E., A strongly coupled, embedded-boundary method for fluid-structure interactions of elastically mounted rigid bodies, J. Fluids Struct., 24, 167-182 (2008) · doi:10.1016/j.jfluidstructs.2007.08.002 |
| [23] | Schulz, Kw; Kallinderis, Y., Unsteady flow structure interaction for incompressible flows using deformable hybrid grids, J. Comput. Phys., 143, 569-597 (1998) · Zbl 0935.76052 · doi:10.1006/jcph.1998.5969 |
| [24] | Anagnostopoulos, P., Numerical investigation of response and wake characteristics of a vortex-excited cylinder in a uniform stream, J. Fluids Struct., 8, 367-390 (1994) · doi:10.1006/jfls.1994.1018 |
| [25] | Feng, C.C.: The measurement of vortex-induced effects in flow past stationary and oscillating circular and D-section cylinders, MSc thesis. The University of British Columbia, Vancouver (1968) |
| [26] | Blackburn, Hm; Henderson, R., Lock-in behavior in simulated vortex-induced vibration, Exp. Therm. Fluid Sci., 12, 184-189 (1996) · doi:10.1016/0894-1777(95)00093-3 |
| [27] | Blackburn, Hm; Henderson, Rd, A study of two-dimensional flow past an oscillating cylinder, J. Fluid Mech., 385, 255-286 (1999) · Zbl 0938.76022 · doi:10.1017/S0022112099004309 |
| [28] | Blackburn, H. M., Computational Bluff Body Fluid Dynamics and Aeroelasticity, Notes on Numerical Fluid Mechanics and Multidisciplinary Design (NNFM), 10-23 (2003), Berlin, Heidelberg: Springer Berlin Heidelberg, Berlin, Heidelberg |
| [29] | Mittal, R.; Iaccarino, G., Immersed boundary methods, Annu. Rev. Fluid Mech., 37, 239-261 (2005) · Zbl 1117.76049 · doi:10.1146/annurev.fluid.37.061903.175743 |
| [30] | Hirt, Cw; Amsden, Aa; Cook, Jl, An arbitrary Lagrangian-Eulerian computing method for all flow speeds, J. Comput. Phys., 14, 227-253 (1974) · Zbl 0292.76018 · doi:10.1016/0021-9991(74)90051-5 |
| [31] | Zang, Y.; Street, Rl; Koseff, Jr, A non-staggered grid, fractional step method for time-dependent incompressible Navier-Stokes equations in curvilinear coordinates, J. Comput. Phys., 114, 18-33 (1994) · Zbl 0809.76069 · doi:10.1006/jcph.1994.1146 |
| [32] | Leonard, Bp, A stable and accurate convective modeling procedure based on quadratic upstream interpolation, Comput. Methods Appl. Mech. Eng., 19, 59-98 (1979) · Zbl 0423.76070 · doi:10.1016/0045-7825(79)90034-3 |
| [33] | Akhtar, I.; Nayfeh, Ah; Ribbens, Cj, On the stability and extension of reduced-order Galerkin models in incompressible flows: a numerical study of vortex shedding, Theoret. Comput. Fluid Dyn., 23, 3, 213-237 (2009) · Zbl 1234.76040 · doi:10.1007/s00162-009-0112-y |
| [34] | Mehmood, A.; Abdelkefi, A.; Akhtar, I.; Nayfeh, Ah; Nuhait, A.; Hajj, Mr, Linear and nonlinear active feedback controls for vortex-induced vibrations of circular cylinders, J. Vib. Control, 20, 8, 1137-1147 (2014) · doi:10.1177/1077546312469425 |
| [35] | Akhtar, I.: Parallel simulations, reduced-order modeling, and feedback control of vortex shedding using fluidic actuators, Ph.D. Dissertation, Virginia Tech, Blacksburg, VA, USA (2008) |
| [36] | Imtiaz, H.; Akhtar, I., On lift and drag decomposition coefficients in a model reduction framework using pressure-mode decomposition (PMD) analysis, J. Fluids Struct., 75, 174-192 (2017) · doi:10.1016/j.jfluidstructs.2017.09.003 |
| [37] | Carnahan, B.; Luther, Ha; Wilkes, Jo, Applied Numerical Methods (1969), New York: Wiley, New York · Zbl 0195.44701 |
| [38] | Marzouk, Oa; Nayfeh, Ah, Characterization of the flow over a cylinder moving harmonically in the cross-flow direction, Int. J. Non-Linear Mech., 45, 821-833 (2010) · doi:10.1016/j.ijnonlinmec.2010.06.004 |
| [39] | Zeinoddini, M.; Bakhtiari, A.; Asil Gharebaghi, S., Towards an understanding of the marine fouling effects on VIV of circular cylinders: a probe into the chaotic features, Nonlinear Dyn., 94, 575-595 (2018) · doi:10.1007/s11071-018-4378-8 |
| [40] | Xu, S.; Wang, S.; Zhang, J.; Ye, Z., Bifurcations of vortex-induced vibrations of a fixed membrane wing at \(\text{Re} \le 1000\), Nonlinear Dyn., 91, 2097-2112 (2018) · doi:10.1007/s11071-017-3915-1 |
| [41] | Fukuoka, H.; Hirabayashi, S.; Suzuki, H., The effects of free surface and end cell on flow around a finite circular cylinder with low aspect ratio, J. Mar. Sci. Technol., 21, 145-153 (2016) · doi:10.1007/s00773-015-0338-x |
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.
