DOI QR코드

DOI QR Code

Stability and nonlinear vibration of a fuel rod in axial flow with geometric nonlinearity and thermal expansion

  • Received : 2023.04.27
  • Accepted : 2023.08.04
  • Published : 2023.11.25

Abstract

The vibration of fuel rods in axial flow is a universally recognized issue within both engineering and academic communities due to its significant importance in ensuring structural safety. This paper aims to thoroughly investigate the stability and nonlinear vibration of a fuel rod subjected to axial flow in a newly designed high temperature gas cooled reactor. Considering the possible presence of thermal expansion and large deformation in practical scenarios, the thermal effect and geometric nonlinearity are modeled using the von Karman equation. By applying Hamilton's principle, we derive the comprehensive governing equation for this fluid-structure interaction system, which incorporates the quadratic nonlinear stiffness. To establish a connection between the fluid and structure aspects, we utilize the Galerkin method to solve the perturbation potential function, while employing mode expansion techniques associated with the structural analysis. Following convergence and validation analyses, we examine the stability of the structure under various conditions in detail, and also investigate the bifurcation behavior concerning the buckling amplitude and flow velocity. The findings from this research enhance the understanding of the underlying physics governing fuel rod behavior in axial flow under severe yet practical conditions, while providing valuable guidance for reactor design.

Keywords

References

  1. M.A. Christon, R. Lu, J. Bakosi, B.T. Nadiga, Z. Karoutas, M. Berndt, Large-eddy simulation, fuel rod vibration and grid-to-rod fretting in pressurized water reactors, J. Comput. Phys. 322 (2016) 142-161. 
  2. K.T. Kim, The effect of fuel rod supporting conditions on fuel rod vibration characteristics and grid-to-rod fretting wear, Nucl. Eng. Des. 240 (2010) 1886-1891. 
  3. S.S. Chen, Vibration of nuclear fuel bundles, Nucl. Eng. Des. 35 (1975) 399-422. 
  4. M.P. Paidoussis, Dynamics of cylindrical structures subjected to axial flow, J. Sound Vib. 29 (3) (1973) 365-385. 
  5. M.J. Lighthill, Note on the swimming of slender fish, J. Fluid Mech. 9 (1960) 305-317. 
  6. G.I. Taylor, Analysis of the swimming of long and narrow animals, in: Proceeding of the Royal Society (London) vol. 214, 1952, pp. 158-183. A. 
  7. M.P. Paidoussis, Dynamics of flexible slender cylinders in axial flow. Part 2: experiments, J. Fluid Mech. 26 (1966) 737-751. 
  8. L. Divaret, O. Cadot, P. Moussou, O. Doar'e, Normal forces exerted upon a long cylinder oscillating in an axial flow, J. Fluid Mech. 752 (2014) 649-669. 
  9. J.L. Lopes, M.P. Paidoussis, C. Semler, Linear and nonlinear dynamics of cantilevered cylinders in axial flow. Part 2: the equation of motion, J. Fluid Struct. 16 (2002) 715-737. 
  10. Y. Modarres-Sadeghi, M.P. Paidoussis, C. Semler, A nonlinear model for an extensible slender flexible cylinder subjected to axial flow, J. Fluid Struct. 21 (2005) 609-627. 
  11. A.R. Abdelbaki, M.P. Paidoussis, A.K. Misra, A nonlinear model for a free-clamped cylinder subjected to confined axial flow, J. Fluid Struct. 80 (2018) 390-404. 
  12. S. Rinaldi, M.P. Paidoussis, An improved theoretical model for the dynamics of a free-clamped cylinder in axial flow, J. Fluid Struct. 94 (2020), 102903. 
  13. M.P. Paidoussis, Dynamcis of cylindrical structures in axial flow: a review, J. Fluid Struct. 107 (2021), 103374. 
  14. M.P. Paidoussis, Fluid-structure Interactions: Slender Structures and Axial Flow, Academic Press, 2016. 
  15. G. Ferrari, G. Franchini, P. Balasubramanian, F. Giovanniello, S.L. Guisquet, K. Karazis, M. Amabili, Nonlinear vibrations of a nuclear fuel rod supported by spacer grids, Nucl. Eng. Des. 361 (2020), 110503. 
  16. H. Huang, P. Li, Y. Yang, Towards modeling of Grid to Rod and the effect of its nonlinear dynamic behaviors on grid-to-rod fretting wear, Ann. Nucl. Energy 180 (2023), 109481. 
  17. P. Balasubramanian, G. Franchini, G. Ferrari, et al., Nonlinear vibrations of beams with bilinear hysteresis at supports: interpretation of experimental results, J. Sound Vib. 499 (2021), 115998. 
  18. B. Painter, G. Ferrari, M. Amabili, Nonlinear vibrations of beams with Bouc-Wen hysteretic boundary conditions, Nonlinear Dynam. 108 (2022) 2903-2916. 
  19. G. Ferrari, K. Karazis, M. Amabili, Experiments on the localized interaction at the interface fuel rod/spacer grid in pressurized water reactors, Nucl. Eng. Des. 399 (2022), 111998. 
  20. P. Wang, C.W. Wong, Y. Zhou, Turbulent intensity effect on axial-flow-induced cylinder vibration in the presence of a neighboring cylinder, J. Fluid Struct. 85 (2019) 77-93. 
  21. Z.G. Liu, Y. Liu, J. Lu, Fluid structure interaction of single flexible cylinder in axial flow, Comput. Fluid 56 (2012) 143-151. 
  22. J. De Ridder, O. Doare, J. Degroote, K. Van Tichelen, P. Schuurmans, J. Vierendeels, Simulating the fluid forces and fuid-elastic instabilities of a clamped-clamped cylinder in turbulent axial flow, J. Fluid Struct. 55 (2015) 139-154. 
  23. J. Salachna, A. Cioncolini, H. Iacovides, Benchmark simulation of the flow-induced vibrations for nuclear applications, Ann. Nucl. Energy 180 (2023), 109425. 
  24. Y. Ren, R. Huo, D. Zhou, Buckling and post-buckling analysis of restrained nonuniform columns in fire, Eng. Struct. 272 (2022), 114947. 
  25. L. Kloda, S. Lenci, J. Warminski, Hardening vs. softening dichotomy of a hinged-simply supported beam with one end axial linear spring: experimental and numerical studies, Int. J. Mech. Sci. 178 (2020), 105588. 
  26. L. Kloda, S. Lenci, J. Warminski, Nonlinear dynamics of a planar beam-spring system: analytical and numerical approaches, Nonlinear Dynam. 94 (2018) 1721-1738. 
  27. Y. Zhang, C. He, L. Sun, Mathematical model for predicting the vibration performance of a core barrel considering the interaction of seismic load and fluid force, Nucl. Eng. Des. 383 (2021), 111429. 
  28. C. Cruz, E. Miranda, Evaluation of the Rayleigh damping model for buildings, Eng. Struct. 138 (2017) 324-336. 
  29. H. Choi, R.W. Schleicher, The energy multiplier Module (EM2 ): status of conceptual design, Nucl. Technol. 200 (2) (2017) 106-124. 
  30. H. Choi, R.W. Schleicher, J. Bolin, Performance analysis of silicon carbide composite clad uranium carbide fuel for a long-life gas-cooled fast reactor under normal operation-Part I: design criteria and material data, Nucl. Technol. 206 (7) (2020) 993-1009.