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This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced ...
This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced ...
This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced ...
This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced ...
This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced ...
This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced ...
This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced ...
This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced ...
This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced ...
This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced ...
This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced ...
This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced ...
This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced ...
This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced ...
This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced ...
This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced ...
This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced ...
This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced ...
This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced ...
This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced ...
This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced ...
This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced ...
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"Parametric analysis of modelling governing the seismic response of free-standing spent fuel racks" presented at ESREL2017 by Alberto Gonzalez Merino

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Abstract: Spent fuel racks are steel structures designed to store the spent fuel assemblies removed from the nuclear power reactor. They rest in free-standing conditions submerged in the depths of the spent fuel pool. During a strong-motion earthquake, racks undergo large displacements subjected to inertial forces. An accurate estimation of their response is essential to achieve a safe pool layout and a reliable structural design. A transient analysis with direct integration of the equation of motion throughout the whole earthquake duration becomes therefore unavoidable. The computational cost associated to this analysis leads to the use of simplified finite element models giving rise to a certain dose of uncertainty. This paper carries out a parametric analysis of the key modelling properties for a two-rack system. This technique examines the behavior of the main transient outputs as a modelling parameter is systematically varied. Numerical results provide a source of insight into the general behavior of the rack system and an effective tool to propose an efficient and reliable modeling and meshing. The trade-off between outputs and computational cost and is also discussed.

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"Parametric analysis of modelling governing the seismic response of free-standing spent fuel racks" presented at ESREL2017 by Alberto Gonzalez Merino

  1. 1. This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced without written authorization of Ensa. ENSA (Grupo SEPI) ESREL 2017 Portoroz, Slovenia Alberto GONZALEZ MERINO Parametric analysis of modelling properties governing the seismic response of free-standing spent fuel racks HORIZON 2020 Marie Skłodowska-Curie Actions Training in Reducing Uncertainty in Structural Safety
  2. 2. This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced without written authorization of Ensa. Outline • Spent Fuel Rack o Introduction o Challenges of their seismic analysis • Current analysis methodology • Sources of uncertainty • Parametric analysis of modelling properties (OFAT) • Sensitivity analysis of modelling properties o Scatter plots o Sobol order indices o PCE metamodelling • Conclusion
  3. 3. This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced without written authorization of Ensa. Steel structures designed to store nuclear spent fuel assemblies removed from the nuclear power reactor. • Slightly spaced by only a few centimeters, • free-standing conditions, • submerged in water. Spent Fuel Racks Spent Fuel Pool 6x4 racks Fuel storage rack unit ~4m ~12m Nuclear Fuel assemblies
  4. 4. This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced without written authorization of Ensa. Highly nonlinear behavior o Contacts are changing-status singularities affecting the stiffness matrix o Friction hysteresis and damping bring energy-dissipative effects. Transient Dynamic response o Input time-history acceleration loading and time-depending variables, o Inertial and damping effects, o Direct integration of the equation of motion (superposition principle), o Numerical integration through iterative algorithms: Newmark and alpha method. Fluid-Structure Interaction o Water coupling between pool & racks, racks & racks → ‘in-phase’ motion, o Dynamic fluid and fuel assemblies inside the storage cells. Challenges of the rack seismic analysis
  5. 5. This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced without written authorization of Ensa. RACK SYSTEM STRUCTURAL MODEL SEISMIC MODEL Soler, A.I., & Singh, K.O. (1982) FLUID MODEL Loads and displacements to • Calculate local stresses • Check instabilities Current analysis methodology SHELL63 MASS21
  6. 6. This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced without written authorization of Ensa.
  7. 7. This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced without written authorization of Ensa. Sources of uncertainty Modelling features Hydrodynamic mass approach Numerical integration algorithms FE meshing Dynamic frictional contactsStochastic input data Spent Fuel Pool 6x4 racks Fuel storage rack unit ~4m ~12m Nuclear Fuel assemblies
  8. 8. This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced without written authorization of Ensa. Parametric analysis One-factor-at-a-time (OFAT) A. Data Input ••Seism time-history ••Rack mass & submerged weight ••Fuel mass & submerged weight ••Eigen-frequency X ••Eigen-frequency Z ••Hydrodynamic mass matrix B. Modelling properties ••FE mesh discretization ••Rack-to-Pool friction coefficient ••Rack-to-Pool contact stiffness ••Fuel-to-cell contact stiffness ••Fuel-cell gap ••Fuel flexural rigidity C. Analysis parameters ••Integration parameter (INTPARA) ••Convergence criteria (CNVTOL) ••Equilibrium iterations (NEQIT) ••Stiffness proportional damping (ALPHAD) ••Mass proportional damping (BETAD) ••Time marching (DELTIM)
  9. 9. This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced without written authorization of Ensa. • Mesh discretisation B: Parametric analysis of modelling properties 0.0E+00 2.0E+04 4.0E+04 6.0E+04 8.0E+04 1.0E+05 1.2E+05 1.4E+05 -0.04 -0.03 -0.02 -0.01 0.00 0.01 0.02 0.03 0 10 20 30 40 50 Max vertical force on support (N) Relative sliding displacement R1-Pool (m) Max. Sliding disp. Min. Sliding disp. Max. Vertical force
  10. 10. This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced without written authorization of Ensa. • Rack-to-pool friction coefficient B: Parametric analysis of modelling properties 0.0E+00 2.0E+04 4.0E+04 6.0E+04 8.0E+04 1.0E+05 1.2E+05 -0.10 -0.08 -0.06 -0.04 -0.02 0.00 0.02 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Max vertical force on support (N) Relative sliding displacement R1-Pool (m) Max. Sliding disp. Min. Sliding disp. Max. Vertical force
  11. 11. This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced without written authorization of Ensa. • Rack-to-pool contact stiffness B: Parametric analysis of modelling properties 0.0E+00 3.0E+04 6.0E+04 9.0E+04 1.2E+05 1.5E+05 1.8E+05 2.1E+05 2.4E+05 -0.12 -0.10 -0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 1.E+06 1.E+07 1.E+08 1.E+09 1.E+10 1.E+11 1.E+12 Max. Vertical force on support (N) Relative sliding displacement R1-Pool (m) Max. Sliding disp. Min. Sliding disp. Max. Vertical force
  12. 12. This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced without written authorization of Ensa. • Fuel-to-cell contact stiffness B: Parametric analysis of modelling properties -3.0E+04 0.0E+00 3.0E+04 6.0E+04 9.0E+04 1.2E+05 1.5E+05 1.8E+05 2.1E+05 2.4E+05 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 1.E+09 1.E+10 Max. Vertical force on support (N) Relative sliding displacement R1-Pool (m) Max. Sliding disp. Min. Sliding disp. Max. Vertical force
  13. 13. This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced without written authorization of Ensa. • Fuel-cell inner gap B: Parametric analysis of modelling properties 0.0E+00 2.5E+04 5.0E+04 7.5E+04 1.0E+05 1.3E+05 1.5E+05 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08 2 4 6 8 10 12 14 Max vertical force on support (N) Relative sliding displacement R1-Pool (m) Max. Sliding disp. Min. Sliding disp. Max. Vertical force
  14. 14. This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced without written authorization of Ensa. • Fuel beam flexural rigidity B: Parametric analysis of modelling properties 0.0E+00 3.0E+04 6.0E+04 9.0E+04 1.2E+05 1.5E+05 1.8E+05 2.1E+05 2.4E+05 -0.04 -0.03 -0.02 -0.01 0.00 0.01 0.02 0.03 0.04 2.E+00 2.E+01 2.E+02 2.E+03 2.E+04 2.E+05 2.E+06 Max. Vertical force on support (N) Relative sliding displacement R1-Pool (m) Max. Sliding disp. Min. Sliding disp. Max. Vertical force
  15. 15. This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced without written authorization of Ensa. Sensitivity analysis : Monte Carlo
  16. 16. This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced without written authorization of Ensa. Sensitivity analysis: Distribution of variables Type Name Distribution Min Max 1 Data input Acceleration time-history Uniform 90% 100% 2 Data input Rack mass and submerged weight Uniform 90% 100% 3 Data input Fuel mass and submerged weight Uniform 90% 100% 4 Data input Eigen-frequencies in X Uniform 5Hz 17.6Hz 5 Data input Eigen-frequencies in Z Uniform 80Hz 88.8Hz 6 Data input Hydrodynamic mass Uniform 90% 100% 7 Model properties Rack-to-Pool friction coefficient Normal 0.20 0.80 8 Model properties Rack-to-Pool contact stiffness Uniform 1E6 1E12 9 Model properties Fuel-to-Cell contact stiffness Uniform 1E4 1E10 10 Model properties Fuel-cell gap Uniform 2mm 14mm 11 Model properties Fuel beam flexural rigidity Uniform 2E0 2E6 12 Analysis parameter Integration parameter (INTPARA) Uniform 0 0,05 13 Analysis parameter Convergence parameter (CNVTOL) Uniform 1E-7 1E-2 14 Analysis parameter Number of equilibrium iterations (NEQIT) Uniform 2 22 15 Analysis parameter Rayleigh stiffness proportional damping (ALPHAD) Uniform 0% 10% 16 Analysis parameter Rayleigh mass proportional damping (BETAD) Uniform 0% 10% 17 Analysis parameter Maximum allowed time step (DELTIM) Uniform 3E-3 1.5E-4
  17. 17. This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced without written authorization of Ensa. Sensitivity analysis: Scatter plots modelling properties Vs sliding displacement Displ.base.R1_Max_ Fbeaminertia Displ.base.R1_Max_ Fgap Displ.base.R1_Max_ FC Displ.base.R1_Max_ Rcontastiff Displ.base.R1_Max_ Fcontastiff Displ.base.R1_Max_
  18. 18. This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced without written authorization of Ensa. Fz.feet.R1_Max_ Fbeaminertia Fz.feet.R1_Max_ Fgap Fz.feet.R1_Max_ FC Fz.feet.R1_Max_ Rcontastiff Fz.feet.R1_Max_ Fcontastiff Fz.feet.R1_Max_ HydroMass Sensitivity analysis: Scatter plots modelling properties Vs vertical force on support
  19. 19. This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced without written authorization of Ensa. Sensitivity analysis: Sobol index and PCE modelling properties Vs sliding displacement
  20. 20. This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced without written authorization of Ensa. Sensitivity analysis: Sobol index and PCE modelling properties Vs vertical force on support
  21. 21. This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced without written authorization of Ensa. Conclusions Minor variations in the modelling parameters lead to a wide deviations in final results due to the iterative process of the transient analysis. • a 10 levels mesh discretization provides stable results within a limited computation time so it is considered cost effective, • sliding displacements are strongly influenced by the friction coefficient, especially in the range of 0.2 to 0.6, • assuming stiff rack-to-poll contacts lead to a safe structural design since the peaks of vertical force on supports are maximized, • a resonance effect can happen in the fuel rattling and the rack rocking in function of fuel-to-cell contact stiffness, • an influence of fuel gaps in the sliding displacements is only visible for gaps larger than 8 mm, • flexural rigidity has slight influence in the general behavior of the rack unit.
  22. 22. This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced without written authorization of Ensa. ENSA (Grupo SEPI) Thanks for your attention! HORIZON 2020 Marie Skłodowska-Curie Actions Training in Reducing Uncertainty in Structural Safety Equipos Nucleares, S.A.
  23. 23. ENSA (Grupo SEPI) Oficina Central / Head Office: José Ortega y Gasset 20-5º 28006 Madrid, Spain Phone: +34 91 555 36 17 Fax: +34 91 556 31 49 commercial@ensa.es Instalaciones / Facility: Avda. Juan Carlos I, 8 39600 Maliaño, Cantabria, Spain Phone: +34 942 20 01 01 Fax: +34 942 20 01 48 commercial@ensa.es www.ensa.es This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 642453. trussitn.eu/alberto-gonzalez-merino/
  24. 24. This document contains information proprietary to Equipos Nucleares, S.A. (Ensa) and shall not be disclosed or reproduced without written authorization of Ensa. Impact of the research • better understanding of the rack seismic behaviour, • reduction of the current safety margins (nuclear authorities), • reduction of the nominal gap between units (designers), • increase the storage capacity of the existing fuel storage pools (NPP operator), • increase in the operation span of nuclear power plants without fuel reprocessing or dry cask storage (electric company), Also applicable to the dynamic analysis of any other submerged sliding structure. (Engineering)

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