Reduced-order modeling and vibration transfer analysis of a fluid-delivering branch pipeline that consider fluid–solid interactions

Abstract

The efficient dynamic modeling and vibration transfer analysis of a fluid-delivering branch pipeline (FDBP) are essential for analyzing vibration coupling effects and implementing vibration reduction optimization. Therefore, this study proposes a reduced-order dynamic modeling method suitable for FDBPs and then analyzes the vibration transfer characteristics. For the modeling method, the finite element method and absorbing transfer matrix method (ATMM) are integrated, considering the fluid–structure coupling effect and fluid disturbances. The dual-domain dynamic substructure method is developed to perform the reduced-order modeling of FDBP, and ATMM is adopted to reduce the matrix order when solving fluid disturbances. Furthermore, the modeling method is validated by experiments on an H-shaped branch pipeline. Finally, transient and steady-state vibration transfer analyses of FDBP are performed, and the effects of branch locations on natural characteristics and vibration transfer behavior are analyzed. Results show that transient vibration transfer represents the transfer and conversion of the kinematic, strain, and damping energies, while steady-state vibration transfer characteristics are related to the vibration mode. In addition, multiple-order mode exchanges are triggered when branch locations vary in frequency-shift regions, and the mode-exchange regions are also the transformation ones for vibration transfer patterns.

Graphical abstract

Keywords

fluid-delivering branch pipeline / vibration transfer analysis / reduced-order modeling / fluid–solid interactions / finite element method / absorbing transfer matrix method

References

[1] Myeong M S, Kim Y J, Budden P J. Plastic limit loads for cracked large bore branch junction. Engineering Fracture Mechanics, 2011, 78(11): 2298–2309

[2] Zheng J Y, Zhang Y, Hou D S, Qin Y K, Guo W C, Zhang C, Shi J F. A review of nondestructive examination technology for polyethylene pipe in nuclear power plant. Frontiers of Mechanical Engineering, 2018, 13(4): 535–545

[3] Miyoshi K, Utanohara Y, Kamaya M. Penetration flow into a branch pipe causing thermal fatigue at a mixing tee. Nuclear Engineering and Design, 2020, 360: 110496

[4] Païdoussis M P. Pipes conveying fluid: a fertile dynamics problem. Journal of Fluids and Structures, 2022, 114: 103664

[5] Sui H T, Niu W T. Branch-pipe-routing approach for ships using improved genetic algorithm. Frontiers of Mechanical Engineering, 2016, 11(3): 316–323

[6] Kim S W, Jeon B G, Hahm D G, Kim M K. Failure criteria evaluation of steel pipe elbows in nuclear power plant piping systems using cumulative damage models. Thin-Walled Structures, 2023, 182: 110250

[7] Yuan H X, Yu J P, Jia D, Liu Q, Ma H. Group-based multiple pipe routing method for aero-engine focusing on parallel layout. Frontiers of Mechanical Engineering, 2021, 16(4): 798–813

[8] Li B, Qiang L, Lu T, Geng X, Li M H. A stoneley wave method to detect interlaminar damage of metal layer composite pipe. Frontiers of Mechanical Engineering, 2015, 10(1): 89–94

[9] Xuan F Z, Li P N, Tu S T. Limit load analysis for the piping branch junctions under in-plane moment. International Journal of Mechanical Sciences, 2006, 48(4): 460–467

[10] Huang J L, Xiang J H, Chu X Y, Sun W J, Liu R L, Ling W S, Zhou W, Tao S L. Thermal performance of flexible branch heat pipe. Applied Thermal Engineering, 2021, 186: 116532

[11] Walker C, Manera A, Niceno B, Simiano M, Prasser H M. Steady-state RANS-simulations of the mixing in a T-junction. Nuclear Engineering and Design, 2010, 240(9): 2107–2115

[12] Pérez-García J, Sanmiguel-Rojas E, Hernández-Grau J, Viedma A. Numerical and experimental investigations on internal compressible flow at T-type junctions. Experimental Thermal and Fluid Science, 2006, 31(1): 61–74

[13] Tijsseling A S, Vardy A E. Fluid–structure interaction and transient cavitation tests in a T-piece pipe. Journal of Fluids and Structures, 2005, 20(6): 753–762

[14] Vardy A E, Fan D, Tijsseling A S. Fluid–structure interaction in a T-piece pipe. Journal of Fluids and Structures, 1996, 10(7): 763–786

[15] TijsselingA SVaugranteP. FSI in L-shaped and T-shaped pipe systems. In: Proceedings of the 10th International Meeting of the IAHR Work Group on the Behaviour of Hydraulic Machinery under Steady Oscillatory Conditions. Trondheim: IAHR, 2001

[16] Xu Y Z, Johnston D N, Jiao Z X, Plummer A R. Frequency modelling and solution of fluid–structure interaction in complex pipelines. Journal of Sound and Vibration, 2014, 333(10): 2800–2822

[17] Liu G M, Li S J, Li Y H, Chen H. Vibration analysis of pipelines with arbitrary branches by absorbing transfer matrix method. Journal of Sound and Vibration, 2013, 332(24): 6519–6536

[18] Ji W H, Sun W, Du D X, Cao Y H. Dynamic modeling and stress response solution for liquid-filled pipe system considering both fluid velocity and pressure fluctuations. Thin-Walled Structures, 2023, 188: 110831

[19] Boiangiu M, Ceausu V, Untaroiu C D. A transfer matrix method for free vibration analysis of Euler-Bernoulli beams with variable cross section. Journal of Vibration and Control, 2016, 22(11): 2591–2602

[20] Ma H W, Sun W, Ji W H, Liu X F, Liu H H, Du D X. Nonlinear vibration analysis of Z-shaped pipes with CLD considering amplitude-dependent characteristics of clamps. International Journal of Mechanical Sciences, 2024, 262: 108739

[21] Ma H W, Sun W, Ji W H, Zhang Y, Liu X F, Liu H H. Dynamic modeling and vibration analysis of planar pipeline with partial constrained layer damping treatment: theoretical and experimental studies. Composite Structures, 2023, 323: 117476

[22] Askarian A R, Permoon M R, Zahedi M, Shakouri M. Stability analysis of viscoelastic pipes conveying fluid with different boundary conditions described by fractional Zener model. Applied Mathematical Modelling, 2022, 103: 750–763

[23] Askarian A R, Permoon M R, Shakouri M. Vibration analysis of pipes conveying fluid resting on a fractional Kelvin-Voigt viscoelastic foundation with general boundary conditions. International Journal of Mechanical Sciences, 2020, 179: 105702

[24] Deng T C, Ding H, Chen L Q. Critical velocity and supercritical natural frequencies of fluid-conveying pipes with retaining clips. International Journal of Mechanical Sciences, 2022, 222: 107254

[25] Dou B, Ding H, Mao X Y, Feng H R, Chen L Q. Modeling and parametric studies of retaining clips on pipes. Mechanical Systems and Signal Processing, 2023, 186: 109912

[26] Zhen Y X, Gong Y F, Tang Y. Nonlinear vibration analysis of a supercritical fluid-conveying pipe made of functionally graded material with initial curvature. Composite Structures, 2021, 268: 113980

[27] Kheiri M. Nonlinear dynamics of imperfectly-supported pipes conveying fluid. Journal of Fluids and Structures, 2020, 93: 102850

[28] Zhang Y, Sun W, Ma H W, Ji W H, Ma H. Semi-analytical modeling and vibration analysis for U-shaped, Z-shaped and regular spatial pipelines supported by multiple clamps. European Journal of Mechanics—A/Solids, 2023, 97: 104797

[29] Kheiri M, Païdoussis M P, Del Pozo G C, Amabili M. Dynamics of a pipe conveying fluid flexibly restrained at the ends. Journal of Fluids and Structures, 2014, 49: 360–385

[30] Gao Y, Sun W. Inverse identification of the mechanical parameters of a pipeline hoop and analysis of the effect of preload. Frontiers of Mechanical Engineering, 2019, 14(3): 358–368

[31] JiW HSun WMaH WZhangYWangD. A high-precision super element used for the parametric finite element modeling and vibration reduction optimization of the pipeline system. Journal of Vibration Engineering and Technologies, 2024, 12: 1177–1193

[32] Gao P X, Zhang Y L, Liu X F, Yu T, Wang J. Vibration analysis of aero parallel-pipeline systems based on a novel reduced order modeling method. Journal of Mechanical Science and Technology, 2020, 34(8): 3137–3146

[33] Ji W H, Sun W, Wang D H, Liu Z H. Optimization of aero-engine pipeline for avoiding vibration based on length adjustment of straight-line segment. Frontiers of Mechanical Engineering, 2022, 17(1): 11

[34] Maess M, Gaul L. Substructuring and model reduction of pipe components interacting with acoustic fluids. Mechanical Systems and Signal Processing, 2006, 20(1): 45–64

[35] Herrmann J, Maess M, Gaul L. Substructuring including interface reduction for the efficient vibro-acoustic simulation of fluid-filled piping systems. Mechanical Systems and Signal Processing, 2010, 24(1): 153–163

[36] Krishna R K, Kochupillai J. A new formulation for fluid–structure interaction in pipes conveying fluids using Mindlin shell element and 3-D acoustic fluid element. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2020, 42(7): 388

[37] Zhang Y L, Gorman D G, Reese J M. A finite element method for modelling the vibration of initially tensioned thin-walled orthotropic cylindrical tubes conveying fluid. Journal of Sound and Vibration, 2001, 245(1): 93–112

[38] Schardt R. Generalized beam theory—an adequate method for coupled stability problems. Thin-Walled Structures, 1994, 19(2–4): 161–180

[39] Duan L P, Zhao J C, Liu S. A b-splines based nonlinear GBT formulation for elastoplastic analysis of prismatic thin-walled members. Engineering Structures, 2016, 110: 325–346

[40] Duan W H, Koh C G. Axisymmetric transverse vibrations of circular cylindrical shells with variable thickness. Journal of Sound and Vibration, 2008, 317(3–5): 1035–1041

[41] Païdoussis M P. Dynamic of cylindrical structures in axial flow: a review. Journal of Fluids and Structures, 2021, 107: 103374

[42] Hong J N, Kim J W, Lee D Y, Lee J M, Kim Y J. Very low-cycle fatigue failure behaviours of pipe elbows under displacement-controlled cyclic loading. Thin-Walled Structures, 2023, 193: 111261

[43] Antoniou K, Stamou A G, Karamanos S A, Palagas C, Tazedakis A, Dourdounis E. Finite element modeling of the JCO-E line pipe fabrication process; material properties and collapse pressure prediction. Thin-Walled Structures, 2023, 192: 111120

[44] Tijsseling A S, Vardy A E, Fan D. Fluid-structure interaction and cavitation in a single-elbow pipe system. Journal of Fluids and Structures, 1996, 10(4): 395–420

[45] Andrade D M, de Freitas Rachid F B, Tijsseling A S. A new model for fluid transients in piping systems taking into account the fluid–structure interaction. Journal of Fluids and Structures, 2022, 114: 103720

[46] Norton M P, Bull M K. Mechanisms of the generation of external acoustic radiation from pipes due to internal flow disturbances. Journal of Sound and Vibration, 1984, 94(1): 105–146

[47] Langley R S. Analysis of power flow in beams and frameworks using the direct-dynamic stiffness method. Journal of Sound and Vibration, 1990, 136(3): 439–452

[48] Xiong Y P, Xing J T, Price W G. Power flow analysis of complex coupled systems by progressive approaches. Journal of Sound and Vibration, 2001, 239(2): 275–295

[49] Mace B R, Shorter P J. Energy flow models from finite element analysis. Journal of Sound and Vibration, 2000, 233(3): 369–389

[50] Wang Z H, Xing J T, Price W G. Power flow analysis of indeterminate rod/beam systems using a substructure method. Journal of Sound and Vibration, 2002, 249(1): 3–22

[51] Zhu C D, Yang J, Rudd C. Vibration transmission and power flow of laminated composite plates with inerter-based suppression configurations. International Journal of Mechanical Sciences, 2021, 190: 106012

[52] Guo X M, Ge H, Xiao C L, Ma H, Sun W, Li H. Vibration transmission characteristics analysis of the parallel fluid-conveying pipes system: numerical and experimental studies. Mechanical Systems and Signal Processing, 2022, 177: 109180

[53] Ji W H, Sun W, Du D X, Cao Y H. Dynamics modeling and vibration transmission visualization of fluid-conveying series pipe system based on FEM-TMM. Ocean Engineering, 2023, 280: 114693

[54] Ji W H, Sun W, Zhang Y, Wang D, Wang B. Parametric model order reduction and vibration analysis of pipeline system based on adaptive dynamic substructure method. Structures, 2023, 50: 689–706

[55] Zeng J, Zhao C G, Ma H, Cui X L, Sun W, Luo Z. Dynamic response characteristics of the shaft-blisk-casing system with blade-tip rubbing fault. Engineering Failure Analysis, 2021, 125: 105406

[56] Huangfu Y F, Zeng J, Ma H, Dong X J, Han H Z, Zhao Z F. A flexible-helical-geared rotor dynamic model based on hybrid beam-shell elements. Journal of Sound and Vibration, 2021, 511: 116361

[57] Yue J G, Fafitis A, Qian J, Lei T. Application of 1D/3D finite elements coupling for structural nonlinear analysis. Journal of Central South University, 2011, 18(3): 889–897

[58] Shim K W, Monaghan D J, Armstrong C G. Mixed dimensional coupling in finite element stress analysis. Engineering with Computers, 2002, 18(3): 241–252

[59] Liu G M, Li Y H. Vibration analysis of liquid-filled pipelines with elastic constraints. Journal of Sound and Vibration, 2011, 330(13): 3166–3181

[60] Li S J, Liu G M, Kong W T. Vibration analysis of pipes conveying fluid by transfer matrix method. Nuclear Engineering and Design, 2014, 266: 78–88

[61] Adhikari S. An iterative approach for nonproportionally damped systems. Mechanics Research Communications, 2011, 38(3): 226–230

[62] Udwadia F E, Esfandiari R S. Nonclassically damped dynamic systems: an iterative approach. Journal of Applied Mechanics, 1990, 57(2): 423–433

[63] Zienkiewicz O C, Zhu J Z. The superconvergent patch recovery and a posteriori error estimates. Part 1: the recovery technique. International Journal for Numerical Methods in Engineering, 1992, 33(7): 1331–1364

[64] Zhang Z M, Naga A. A new finite element gradient recovery method: superconvergence property. SIAM Journal on Scientific Computing, 2005, 26(4): 1192–1213

[65] Ma Y Q, Zhao Q J, Zhang K, Xu M, Zhao W. Analysis of instantaneous vibrational energy flow for an aero-engine dual-rotor–support–casing coupling system. Journal of Engineering for Gas Turbines and Power, 2020, 142(5): 051011

[66] Ma Y Q, Zhao Q J, Zhang K, Xu M, Zhao W. Effects of mount positions on vibrational energy flow transmission characteristics in aero-engine casing structures. Journal of Low Frequency Noise, Vibration and Active Control, 2020, 39(2): 313–326

[67] Ji W H, Sun W, Ma H W, Li J X. Dynamic modeling and analysis of fluid-delivering cracked pipeline considering breathing effect. International Journal of Mechanical Sciences, 2024, 264: 108805

[68] Egner F S, Sangiuliano L, Boukadia R F, van Ophem S, Desmet W, Deckers E. Polynomial filters for camera-based structural intensity analysis on curved plates. Mechanical Systems and Signal Processing, 2023, 193: 110245

Acknowledgements

This work was supported by the Fundamental Research Funds for the Central Universities (Grant No. N2403006) and the National Science and Technology Major Project, China (Grant No. J2019-I-0008-0008).

Electronic Supplementary Material

The supplementary material can be found in the online version of this article at https://doi.org/10.1007/s11465-024-0781-7 and is accessible to authorized users.

Conflict of Interest

The authors declare that they have no conflict of interest.

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