Abstract
Pipe-in-pipe (PIP) structures are widely used in offshore oil and gas pipelines to settle thermal insulation issues. A PIP structure system usually consists of two concentric pipes and one softer layer for thermal insulation consideration. The total response of the system is related to the dynamics of both pipes and the interactions between these two concentric pipes. In the current work, a theoretical model for flow-induced vibrations of a PIP structure system is proposed and analyzed in the presence of an internal axial flow and an external cross flow. The interactions between the two pipes are modeled by a linear distributed damper, a linear distributed spring and a nonlinear distributed spring along the pipe length. The unsteady hydrodynamic forces due to cross flow are modeled by two distributed van der Pol wake oscillators. The nonlinear partial differential equations for the two pipes and the wake are further discretized by the aid of Galerkin’s technique, resulting in a set of ordinary differential equations. These ordinary differential equations are further numerically solved by using a fourth-order Runge–Kutta integration algorithm. Phase portraits, bifurcation diagrams, an Argand diagram and oscillation shape diagrams are plotted, showing the existence of a lock-in phenomenon and figure-of-eight trajectory. The PIP system subjected to cross flow displays some interesting dynamical behaviors different from that of a single-pipe structure.
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References
Yettou, E., Derradji-Aouat, A., Williams, C.: Fluid-Structure Interactions Modelling of PIP Riser Systems Operating in Ocean Environments. National Research Council Canada, Institute for Ocean Technology, St. John’s (2008)
Sun, J., Jukes P.: From installation to operation: a full-scale finite element modeling of deep-water PIP system. In: Third ISOPE International Deep-Ocean Technology Symposium. International Society of Offshore and Polar Engineers, Beijing, May 31–June 5 (2009)
Sun, J., Jukes, P., Eltaher, A.: Exploring the challenges of pipe-in-pipe (PIP) flowline installation in deepwater. In: Third ISOPE International Deep-Ocean Technology Symposium. International Society of Offshore and Polar Engineers, Beijing, June 28–July 1 (2009)
Wang, Z., Chen, Z., Liu, H.: Numerical study on upheaval buckling of pipe-in-pipe systems with full contact imperfections. Eng. Struct. 99, 264–271 (2015)
Karampour, H., Alrsai, M., Albermani, F., Guan, H., Jeng, D.S.: Propagation buckling in subsea pipe-in-pipe systems. J. Eng. Mech. 143, 04017113 (2017)
Kyriakides, S.: Buckle propagation in pipe-in-pipe systems: part I. Experiments. Int. J. Solids Struct. 39, 351–366 (2002)
Kyriakides, S., Vogler, T.J.: Buckle propagation in pipe-in-pipe systems: part II. Analysis. Int. J. Solids Struct. 39, 367–392 (2002)
Kyriakides, S., Netto, T.A.: On the dynamic propagation and arrest of buckles in pipe-in-pipe systems. Int. J. Solids Struct. 41, 5463–5482 (2004)
Gong, S.F., Li, G.: Buckle propagation of pipe-in-pipe systems under external pressure. Eng. Struct. 84, 207–222 (2015)
Skop, R.A., Balasubramanian, S.: A new twist on an old model for vortex-excited vibrations. J. Fluids Struct. 11, 395–412 (1997)
Evangelinos, C., Karniadakis, G.E.: Dynamics and flow structures in the turbulent wake of rigid and flexible cylinders subject to vortex-induced vibrations. J. Fluid Mech. 400, 91–124 (1999)
Balasubramanian, S., Haan, F.L., Szewczyk, A.A., et al.: An experimental investigation of the vortex-excited vibrations of pivoted tapered circular cylinders in uniform and shear flow. J. Wind Eng. Ind. Aerodyn. 89, 757–784 (2001)
Lin, L.M., Ling, G.C., Wu, Y.X., et al.: Nonlinear fluid damping in structure-wake oscillators in modeling vortex-induced vibrations. J. Hydrodyn. Ser. B 21, 1–11 (2009)
Srinil, N.: Analysis and prediction of vortex-induced vibrations of variable-tension vertical risers in linearly sheared currents. Appl. Ocean Res. 33, 41–53 (2011)
Dai, H.L., Wang, L., Qian, Q., et al.: Vortex-induced vibrations of pipes conveying pulsating fluid. Ocean Eng. 77, 12–22 (2014)
Gu, J.J., Duan, M.L.: Integral transform solution for fluid force investigation of a flexible circular cylinder subject to vortex-induced vibrations. J. Mar. Sci. Technol. 21, 663–678 (2016)
Wang, L., Jiang, T.L., Dai, H.L.: Three-dimensional dynamics of supported pipes conveying fluid. Acta. Mech. Sin. 33, 1065–1074 (2017)
Nishi, Y., Motoyoshi, M., Ueda, T.: Growth and coexistence of structural and lift force modes in vortex-induced vibration of a flexible riser. J. Mar. Sci. Technol. 23, 899–914 (2018)
Bi, K., Hao, H.: Using PIP systems for subsea pipeline vibration control. Eng. Struct. 109, 75–84 (2016)
Zarei, M.S., Kolahchi, R., Hajmohammad, M.H., et al.: Seismic response of underwater fluid-conveying concrete pipes reinforced with SiO2 nanoparticles and fiber reinforced polymer (FRP) layer. Soil Dyn. Earthq. Eng. 103, 76–85 (2017)
Hajmohammad, M.H., Kolahchi, R., Zarei, M.S., et al.: Earthquake induced dynamic deflection of submerged viscoelastic cylindrical shell reinforced by agglomerated CNTs considering thermal and moisture effects. Compos. Struct. 187, 498–508 (2018)
Hajmohammad, M.H., Maleki, M., Kolahchi, R.: Seismic response of underwater concrete pipes conveying fluid covered with nano-fiber reinforced polymer layer. Soil Dyn. Earthq. Eng. 110, 18–27 (2018)
Matin, Nikoo H., Bi, K., Hao, H.: Passive vibration control of cylindrical offshore components using PIP (PIP) concept: an analytical study. Ocean Eng. 142, 39–50 (2017)
Matin, Nikoo H., Bi, K., Hao, H.: Effectiveness of using PIP (PIP) concept to reduce vortex-induced vibrations (VIV): three-dimensional two-way FSI analysis. Ocean Eng. 148, 263–276 (2018)
Yang, Z.M., Thorkildsen, F., Norland, K.: Vortex induced vibrations and fatigue assessment of pipe-in-pipe systems. In: Proceedings of the ASME 2018 37th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, Madrid, 17–22 June (2018)
Williams, D., Kenny, F.: Calculation of VIV fatigue of multi-pipe systems. In: ASME 2017 36th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, Trondheim, 25–30 June (2017)
Wadham-Gagnon, M., Paidoussis, M.P., Semler, C.: Dynamics of cantilevered pipes conveying fluid. Part 1: nonlinear equations of three-dimensional motion. Journal of Fluids and Structures 23, 545–567 (2007)
Liu, Z.Y., Wang, L., Dai, H.L., et al.: Nonplanar vortex-induced vibrations of cantilevered pipes conveying fluid subjected to loose constraints. Ocean Eng. 178, 1–19 (2019)
Wang, L., Jiang, T.L., Dai, H.L., et al.: Three-dimensional vortex-induced vibrations of supported pipes conveying fluid based on wake oscillator models. J. Sound Vib. 422, 590–612 (2018)
Facchinetti, M.L., de Langre, E., Biolley, F.: Coupling of structure and wake oscillators in vortex-induced vibrations. J. Fluids Struct. 19, 123–140 (2004)
Ge, F., Long, X., Wang, L., et al.: Flow-induced vibrations of long circular cylinders modeled by coupled nonlinear oscillators. Sci. China Ser. G Phys. Mech. Astron. 52, 1086–1093 (2009)
Munir, A., Zhao, M., Wu, H., et al.: Numerical investigation of the effect of plane boundary on two-degree-of-freedom of vortex-induced vibration of a circular cylinder in oscillatory flow. Ocean Eng. 148, 17–32 (2018)
Yang, W.W., Ai, Z.J., Zhang, X.D., et al.: Nonlinear three-dimensional dynamics of a marine viscoelastic riser subjected to uniform flow. Ocean Eng. 149, 38–52 (2018)
Paidoussis, M.P., Li, G.X., Moon, F.C.: Chaotic oscillations of the autonomous system of a constrained pipe conveying fluid. J. Sound Vib. 135, 1–19 (1989)
Xu, J., Huang, Y.Y.: Bifurcations of a cantilevered pipe conveying steady fluid with a terminal nozzle. Acta. Mech. Sin. 16, 264–272 (2000)
Ghayesh, M.H., Paidoussis, M.P.: Three-dimensional dynamics of a cantilevered pipe conveying fluid, additionally supported by an intermediate spring array. Int. J. Non-Linear Mech. 45, 507–524 (2010)
Dai, H.L., Abdelkefi, A., Wang, L.: Theoretical modeling and nonlinear analysis of piezoelectric energy harvesting from vortex-induced vibrations. J. Intell. Mater. Syst. Struct. 25, 1861–1874 (2014)
Wang, L., Liu, Z.Y., Abdelkefi, A., et al.: Nonlinear dynamics of cantilevered pipes conveying fluid: towards a further understanding of the effect of loose constraints. Int. J. Non-Linear Mech. 95, 19–29 (2017)
Dai, H.L., Wang, L., Qian, Q.: Vortex-induced vibrations of pipes conveying fluid in the subcritical and supercritical regimes. J. Fluids Struct. 39, 322–334 (2013)
Song, L.J., Fu, S.X., Cao, J., et al.: An investigation into the hydrodynamics of a flexible riser undergoing vortex-induced vibration. J. Fluids Struct. 63, 325–350 (2016)
Bokaian, A.: Thermal expansion of PIP systems. Mar. Struct. 17, 475–500 (2004)
Wang, F.C.: Effective design of submarine PIP using finite element analysis. Ocean Eng. 153, 23–32 (2018)
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The work was supported by the National Natural Science Foundation of China (Grant 11622216).
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Liu, Z.Y., Jiang, T.L., Wang, L. et al. Nonplanar flow-induced vibrations of a cantilevered PIP structure system concurrently subjected to internal and cross flows. Acta Mech. Sin. 35, 1241–1256 (2019). https://doi.org/10.1007/s10409-019-00879-6
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DOI: https://doi.org/10.1007/s10409-019-00879-6