Journal of Applied Science and Engineering

Published by Tamkang University Press


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Wei Ma This email address is being protected from spambots. You need JavaScript enabled to view it.1, Weidong Song1 and Linbin Qiu2

1School of Civil and Resource Engineering, University of Science and Technology Beijing, Beijing 100083, P.R. China
2School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, P.R. China 


Received: February 22, 2019
Accepted: March 6, 2019
Publication Date: June 1, 2019

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To improve the stability of pressure relief valve, a physical model of relief valve was proposed in this research by considering fluid compressibility, tubes elasticity and energy loss when valve core collides with its seat. A dimensionless dynamic mathematic model of the relief valve was established to perform the analysis of linear stability and Lyapunov exponent. Phase and vector field diagrams were drawn with four dimensionless pre-compressed parameters. The stable equilibrium states of a pipeline system were obtained. One-parameter and two-parameter bifurcation diagrams were drawn using the non-smooth dynamic system theory and XPPAUT software. The results showed that there were Hopf bifurcation, generalized Hopf bifurcation and cusp bifurcation in the pipeline system.

Keywords: Pressure Relief Valve, Dynamic Instability, Lyapunov Exponent, Bifurcation


  1. [1] Yonezawa, K., R. Ogawa, K. Ogi, et al. (2012) Flow induced vibration of a steam control valve, Journal of Fluids & Structures 35(776), 7688. doi: 10.1016/j. jfluidstructs.2012.06.003
  2. [2] Galbally, D., G. García, J. Hernando, et al. (2015) Analysis of pressure oscillations and safety relief valve vibrations in the main steam system of a boiling water reactor, Nuclear Engineering & Design 293(3), 258271. doi: 10.1016/j.nucengdes.2015.08.005
  3. [3] Bolin, C., and A. Engeda (2015) Analysis of flow-induced instability in a redesigned steam control valve, Applied Thermal Engineering 83, 4047. doi: 10. 1016/j.applthermaleng.2015.02.043
  4. [4] Wu, D., S. Li, and P. Wu (2015) CFD simulation of flow-pressure characteristics of a pressure control valve for automotive fuel supply system, Energy Conversion and Management 101, 658665. doi: 10.1016/ j.enconman.2015.06.025
  5. [5] Mehrzad, S., I. Javanshir, A. R. Ranji, et al. (2015) Modeling of fluid-induced vibrations and identification of hydrodynamic forces on flow control valves, Journal of Central South University 22(7), 25962603. doi: 10.1007/s11771-015-2789-y
  6. [6] Izuchi, H. (2010) Stability analysis of safety valve, 10th Topical Conference on Gas Utilization, pp.
  7. [7] Wu, S., C. Li, and Y. Deng (2017) Stability analysis of a direct-operated seawater hydraulic relief valve under deep sea, Mathematical Problems in Engineering 2017, 1-11. doi: 10.1155/2017/5676317
  8. [8] Song, X., L. Cui, M. Cao, et al. (2014) ACFD analysis of the dynamics of a direct-operated safety relief valve mounted on a pressure vessel, Energy Conversionand Management 81, 407419. doi: 10.1016/j.enconman. 2014.02.021
  9. [9] Song, X. G., L. T. Wang, Y. C. Park, et al. (2015) A fluid-structure interaction analysis of the spring-loaded pressure safety valve during popping off, Procedia Engineering 130, 87-94. doi: 10.1016/j.proeng.2015. 12.178
  10. [10] Vallet, C., J. Ferrari, J. F. Rit, et al. (2010) Single phase CFD inside a water safety valve, Proceedings of the Asme Pressure Vessels and Piping Conference, 335 342. doi: 10.1115/PVP2010-25619
  11. [11] Beune, A., J. G. M. Kuerten, M. P. C. Van Heumen (2012) CFDanalysiswithfluid-structure interactionof opening high-pressure safety valves, Computers & Fluids 64, 108116. doi: 10.1016/j.compfluid.2012. 05.010
  12. [12] Gabor, L., C. Alan, and H. Csaba (2009) Nonlinear analysis of a single stage pressure relief valve, IAENG International Journal of Applied Mathematics 39(4), 286299.
  13. [13] Dechert, W. D., and R. Gencay (2010) Lyapunov exponents as a nonparametric diagnostic for stability analysis, Journal of Applied Econometrics 7(S1), S41 S60.
  14. [14] Zamani, N., M. Ataei, and M. Niroomand (2015) Analysis and control of chaotic behavior in boost converter by ramp compensation based on Lyapunov exponents assignment: theoretical and experimental investigation, Chaos, Solitons &Fractals 81, 2029. doi: 10.1016/j.chaos.2015.08.010
  15. [15] Di Bernardo, M., C. Budd, A. Champneys, et al. (2008) Bifurcations in nonsmooth dynamical systems, SIAM Review 50(4), 629701. doi: 10.1137/050625060
  16. [16] Mason, J. F., P. T. Piiroinen, R. E. Wilson, et al. (2009) Basins of attraction in nonsmooth models of gear rattle, International Journal of Bifurcation and Chaos 19(1), 203224. doi: 10.1142/S021812740902283X
  17. [17] Athanasios, I. M. (2012) Simulation and visualization ofchaoticsystems,Computer and Information Science 5(4), 2552.
  18. [18] Bernardo, M. D. (2008) Piecewise-smooth Dynamical Systems: Theory and Applications, London: Springer.
  19. [19] Strogatz, S. H. (2014) Nonlinear Dynamics and Chaos with Applications to Physics, Biology, Chemistry, and Engineering.
  20. [20] Ermentrout, B., and A. Simulating (2002) A guide to XPPAUT for researchers and students, Music & Letters 128(1), 309313.
  21. [21] Liu, X. L., and D. O. Mathematics (2014) Application of XPPAUT software in the teaching of ‘ordinary differential equations’, College Mathematics 30(4), 117 122.
  22. [22] Kong, W., and Q. Yi (2015) The application of XPPAUT in systems biology, Computers & Applied Chemistry 32(8), 938944.
  23. [23] Lynch, S. (2014) Dynamical Systems with Applications Using Matlab, Switzerland: Birkhäuser Basel. doi: 10.1007/978-3-319-06820-6