Effect of mass ratio on hydrodynamic response of a flexible cylinder

Abstract

The effect of the mass ratio on the flow-induced vibration (FIV) of a flexible circular cylinder is experimentally investigated in a towing tank. A Tygon tube with outer and inner diameters of 7.9 mm and 4.8 mm, respectively, was employed for the study. The tube was connected to a carriage and towed from rest to a steady speed up to 1.6 m/s before slowing down to rest again over a distance of 1.6 m in still water. Reynolds number based on the cylinder’s outer diameter was 800–13,000, and the reduced velocity (velocity normalized by the cylinder’s natural frequency and outer diameter) spanned from 2 to 25. When connected, the cylinder was elongated from 420 mm to 460 mm under an axial pre-tension of 11 N. Based on the cylinder’s elongated length, the aspect ratio (ratio of the cylinder’s length to outer diameter) was calculated as 58. Three mass ratios (ratio of the cylinder’s structural mass to displaced fluid mass, m*) of 0.7, 1.0, and 3.4 were determined by filling the cylinder’s interior with air, water, and alloy powder (nickel-chromium-boron matrix alloy), respectively. An optical method was adopted for response measurements. Multi-frequency vibrations were observed in both in-line (IL) and cross-flow (CF) responses; at high Reynolds number, vibration modes up to the 3^rd one were identified in the CF response. The mode transition was found to occur at a lower reduced velocity for the highest tested mass ratio. The vibration amplitude and frequency were quantified and expressed with respect to the reduced velocity. A significant reduced vibration amplitude was found in the IL response with increasing mass ratios, and only initial and upper branches existed in the IL and CF response amplitudes. The normalized response frequencies were revealed to linearly increase with respect to the reduced velocity, and slopes for linear relations were found to be identical for the three cases tested.

Keywords

flow-induced vibration / low mass ratio / flexible cylinder / multi-frequency response / hydrodynamic response

References

[1] Bearman PW. Vortex shedding from oscillating bluff bodies. Annual Review of Fluid Mechanics, 1984, 16: 195-222

[2] Bearman PW. Circular cylinder wakes and vortex-induced vibrations. Journal of Fluids and Structures, 2010, 27: 648-658

[3] Blevins RD. Flow-induced vibration, Second ed. Krieger Publishing, 2001

[4] Brika D, Laneville A. Vortex-induced vibrations of a long flexible circular cylinder. Journal of Fluid Mechanics, 1993, 250: 481-508

[5] Chaplin JR, Bearman PW, Cheng Y, Fontaine E, Graham JMR, Herfjord K, Huera-Huarte FJ, Isherwood M, Lambrakos K, Larsen CM, Meneghini JR, Moe G, Pattenden RJ, Triantafyllou MS, Willden RHJ. Blind predictions of laboratory measurements of vortex induced vibrations of a tension riser. Journal of Fluids and Structures, 2005, 21: 25-40

[6] Chaplin JR, Bearman PW, Huera-Huarte FJ, Pattenden R. Laboratory measurements of vortex-induced vibrations of a vertical tension riser in a stepped current. Journal of Fluids and Structures, 2005, 21: 3-24

[7] Chung TY. Vortex-induced vibration of flexible cylinders in sheared flows. Ph.D. thesis, 1987

[8] Chung TY. Vortex-induced vibration of flexible cylinders having different mass ratios. Korea Research Institute of Ships and Ocean Engineering, 1989

[9] Farrant T, Tan M, Price WG. A cell boundary element method applied to laminar vortex shedding from circular cylinders. Computers & Fluids, 2001, 30: 211-236

[10] Feng CC. The measurements of vortex-induced effects in flow past stationary and oscillating circular and D-section cylinders. Master thesis, 1968

[11] Gabbai RD, Benaroya H. An overview of modeling and experiments of vortex-induced vibration of circular cylinders. Journal of Sound and Vibration, 2005, 282: 575-616

[12] Govardhan R, Williamson CHK. Modes of vortex formation and frequency response for a freely-vibrating cylinder. Journal of Fluid Mechanics, 2000, 420: 85-110

[13] Huera-Huarte FJ, Bangash ZA, Gonzalez LM. Towing tank experiments on the vortex-induced vibrations of low mass ratio long flexible cylinders. Journal of Fluids and Structures, 2014, 48: 81-92

[14] Huera-Huarte FJ, Bearman PW. Wake structures and vortex-induced vibration of a long flexible cylinder–Part 1: Dynamic response. Journal of Fluids and Structures, 2009, 25: 969-990

[15] Jauvtis N, Williamson CHK. Vortex-induced vibration of a cylinder with two degrees of freedom. Journal of Fluids and Structures, 2003, 17: 1035-1042

[16] Jauvtis N, Williamson CHK. The effect of two degrees of freedom on vortex-induced vibration at low mass and damping. Journal of Fluid Mechanics, 2004, 509: 23-62

[17] Khalak A, Williamson CHK. Dynamics of a hydroelastic cylinder with very low mass and damping. Journal of Fluids and Structures, 1996, 10: 455-472

[18] Khalak A, Williamson CHK. Fluid forces and dynamics of a hydroelastic structure with very low mass and damping. Journal of Fluids and Structures, 1997, 11: 973-982

[19] Khalak A, Williamson CHK. Motions, forces and mode transitions in vortex-induced vibrations at low mass-damping. Journal of Fluids and Structures, 1999, 13: 813-851

[20] Kim YH, Vandiver JK, Holler R. Vortex-induced vibration and drag coefficients of long cables subjected to sheared flows. Journal of Energy Resources Technology, 1986, 108: 77-83

[21] Lee L, Allen D. Vibration frequency and lock-in bandwidth of tensioned, flexible cylinders experiencing vortex shedding. Journal of Fluids and Structures, 2010, 26: 602-610

[22] Li XC, Wang YX, Wang GY, Jiang MR, Sun Y. Mode transitions in vortex-induced vibrations of a flexible pipe near plane boundary. Journal of Marine Science and Application, 2013, 12: 334-343

[23] Sarpkaya T. Transverse oscillations of a circular cylinder in uniform flow, 1977

[24] Sarpkaya T. Vortex-induced oscillations. Journal of Applied Mechanics-ASME, 1979, 46: 241-258

[25] Sarpkaya T. A critical review of the intrinsic nature of vortex-induced vibrations. Journal of Fluids and Structures, 2004, 19: 389-447

[26] Song JN, Lu L, Teng B, Park HI, Tang GQ, Wu H. Laboratory tests of vortex-induced vibrations of a long flexible riser pipe subjected to uniform flow. Ocean Engineering, 2011, 38: 1308-1322

[27] Sumer BM, Fredsoe J. Hydrodynamics around cylindrical structures. World Scientific Publishing Co. Pte. Ltd., 1997

[28] Vandiver JK. Drag coefficients of long flexible cylinders. Offshore Technology Conference, 1983

[29] Vandiver JK. Dimensionless parameters important to the prediction of vortex-induced vibration of long, flexible cylinders in ocean currents. Journal of Fluids and Structures, 1993, 7: 423-455

[30] Vandiver JK, Jaiswal V, Jhingran V. Insights on vortex-induced, traveling waves on long risers. Journal of Fluids and Structures, 2009, 25: 641-653

[31] Williamson CHK, Govardhan R. Vortex-induced vibrations. Annual Review of Fluid Mechanics, 2004, 36: 413-455

[32] Williamson CHK, Govardhan R. A brief review of recent results in vortex-induced vibrations. Journal of Wind Engineering and Industrial Aerodynamics, 2008, 96: 713-735

[33] Williamson CHK, Jauvtis N. A high-amplitude 2T mode of vortex-induced vibration for a light body in XY motion. European Journal of Mechanics B/Fluids, 2004, 23: 107-114

[34] Williamson CHK, Roshko A. Vortex formation in the wake of an oscillating cylinder. Journal of Fluids and Structures, 1988, 2: 355-381