0
Research Papers: Heat and Mass Transfer

Heat Transfer Modeling of Spent Nuclear Fuel Using Uncertainty Quantification and Polynomial Chaos Expansion

[+] Author and Article Information
Imane Khalil, Quinn Pratt, Harrison Schmachtenberger

Shiley-Marcos Department of
Mechanical Engineering,
University of San Diego,
5998 Alcala Park,
San Diego, CA 92110

Roger Ghanem

Sonny Astani Department of Civil
and Environmental Engineering,
3610 S. Vermont Street,
University of Southern California,
Los Angeles, CA 90089

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received March 27, 2017; final manuscript received June 7, 2017; published online September 6, 2017. Editor: Portonovo S. Ayyaswamy.

J. Heat Transfer 140(2), 022001 (Sep 06, 2017) (9 pages) Paper No: HT-17-1171; doi: 10.1115/1.4037501 History: Received March 27, 2017; Revised June 07, 2017

A novel method that incorporates uncertainty quantification (UQ) into numerical simulations of heat transfer for a 9 × 9 square array of spent nuclear fuel (SNF) assemblies in a boiling water reactor (BWR) is presented in this paper. The results predict the maximum mean temperature at the center of the 9 × 9 BWR fuel assembly to be 462 K using a range of fuel burn-up power. Current related modeling techniques used to predict the heat transfer and the maximum temperature inside SNF assemblies rely on commercial codes and address the uncertainty in the input parameters by running separate simulations for different input parameters. The utility of leveraging polynomial chaos expansion (PCE) to develop a surrogate model that permits the efficient evaluation of the distribution of temperature and heat transfer while accounting for all uncertain input parameters to the model is explored and validated for a complex case of heat transfer that could be substituted with other problems of intricacy. UQ computational methods generated results that are encompassing continuous ranges of variable parameters that also served to conduct sensitivity analysis on heat transfer simulations of SNF assemblies with respect to physically relevant parameters. A two-dimensional (2D) model is used to describe the physical processes within the fuel assembly, and a second-order PCE is used to characterize the dependence of center temperature on ten input parameters.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

DOE, 1987, “ Characteristics of Spent Fuel, High-Level Waste, and Other Radioactive Wastes Which May Require Long-Term Isolation,” Office of Civilian Radioactive Waste Management, Oak Ridge National Laboratory, Oak Ridge, TN, Technical Report No. DOE RW-0184. https://curie.ornl.gov/content/characteristics-spent-fuel-high-level-waste-and-other-radioactive-wastes-which-may-require
Saling, J. H. , and Fentiman, W. A. , 2002, Radioactive Waste Management, 2nd ed., Taylor and Francis, New York.
Greiner, M. , Araya, P. , Chalasani, N. R. , Li, J. , and Liu, Y. , 2013, “ Two-Dimensional CFD Simulations of a Square 8x8 Heater Rod Array in an Isothermal Enclosure Filled With Rarified Air,” International High-Level Radioactive Waste Management Conference (IHLRWMC), Albuquerque, NM, April 28–May 2, pp. 831–840. http://wolfweb.unr.edu/homepage/greiner/pubs/Fires/2013.IHLRWM.Conference.6857.pdf
Greene, S. , Medford, J. S. , and Macy, S. A. , 2013, “ Storage and Transport Cask Data for Used Commercial Nuclear Fuel,” Advanced Technology Insights LLC, Oak Ridge, TN, Technical Report No. ATI-TR-13047. https://curie.ornl.gov/content/storage-and-transport-cask-data-used-commercial-nuclear-fuel-2013-us-edition
Kessler, J. , 2010, “ Industry Spent Fuel Storage Handbook,” Electric Power Research Institute, Palo Alto, CA, Technical Report No. 1021048 https://curie.ornl.gov/content/industry-spent-fuel-storage-handbook-2.
Saidi, M. , and Hosseini Abardeh, R. , 2010, “ Air Pressure Dependence of Natural-Convection Heat Transfer,” World Congress on Engineering (WCE), London, June 30–July 2, pp. 1444–1447. http://www.iaeng.org/publication/WCE2010/WCE2010_pp1444-1447.pdf
NRC, 2003, “ Cladding Considerations for the Transportation and Storage of Spent Fuel,” Spent Fuel Project Office Interim Staff Guidance-11, Revision 3, Nuclear Regulatory Commission, Washington, DC, Technical Report No. ISG-11 R3. https://www.nrc.gov/reading-rm/doc-collections/isg/isg-11R3.pdf
Canaan, R. E. , and Klein, D. E. , 1998, “ A Numerical Investigation of Natural Convection Heat Transfer Within Horizontal Spent-Fuel Assemblies,” Nucl. Technol., 123(2), pp. 193–208. [CrossRef]
Araya, P. E. , and Greiner, M. , 2009, “ Benchmark of Natural Convection/Radiation Simulations Within an Enclosed Array of Horizontal Heated Rods,” Nucl. Technol., 167(3), pp. 384–394. [CrossRef]
Najm, H. , 2009, “ Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics,” Annu. Rev. Fluid Mech., 41(1), pp. 35–52. [CrossRef]
Cuta, J. M. , Suffield, S. R. , Fort, J. A. , and Adkins, H. E. , 2013, “ Thermal Performance Sensitivity Studies in Support of Material Modeling for Extended Storage of Used Nuclear Fuel,” TRW Environmental Safety Systems, Inc., Las Vegas, NV, Report No. PNNL-22646. https://curie.ornl.gov/system/files/documents/not%20yet%20assigned/FCRD-UFD-2013-000257.pdf
Bahney, R. , and Lotz, L. T. , 1996, “ Spent Nuclear Fuel Effective Thermal Conductivity Report,” U.S. Department of Energy, Las Vegas, NV, Technical Report No. BBA000000-01717-5705-00010 Rev 00. https://www.osti.gov/scitech/servlets/purl/778872
Moore, R. S. , and Notz, K. J. , 1989, “ Physical Characteristics of GE [General Electric] BWR [Boiling-Water Reactor] Fuel Assemblies,” Oak Ridge National Laboratory, Oak Ridge, TN, Techncial Report No. ORNL/TM-10902 https://inis.iaea.org/search/search.aspx?orig_q=RN:21011100.
Ade, B. J. , and Gauld, I. C. , 2011, “ Decay Heat Calculations for PWR and BWR Assemblies Fueled With Uranium and Plutonium Mixed Oxide Fuel Using Scale,” Oak Ridge National Laboratory, Oak Ridge, TN, Technical Report No. ORNL/TM-2011/290 https://info.ornl.gov/sites/publications/Files/Pub31857.pdf.
Manzo, T. , Nacer, M.-H. , and Greiner, M. , 2015, “ Geometrically-Accurate-Three-Dimensional Simulations of a Used Nuclear Fuel Canister Filled With Helium,” ASME Paper No. PVP2015-45851.
Hyungjin, K. , Kwon, O. H. , Kang, G.-U. , and Lee, D.-G. , 2014, “ Comparisons of Prediction Methods for Peak Cladding Temperature and Effective Thermal Conductivity in Spent Fuel Assemblies of Transportation/Storage Casks,” Ann. Nucl. Energy, 71, pp. 427–435. [CrossRef]
ANSYS, 2016, “ ANSYS Commercial Release 16.2 User-Manual,” ANSYS Inc., Canonsburg, PA.
Ghanem, R. , and Spanos, P. , 1991, Stochastic Finite Elements: A Spectral Approach. Springer-Verlag, New York. [CrossRef]
Salloum, M. , and Gharagozloo, P. E. , 2014, “ Empirical and Physics-Based Mathematical Models of Uranium Hydride Decomposition Kinetics With Quantified Uncertainty,” Chem. Eng. Sci., 116, pp. 452–464. [CrossRef]
Debusschere, B. , Safta, C. , Sargsyan, K. , Chowdhary, K. , Alexanderian, A. , Salloum, M. , Najm, H. , Knio, O. , Ghanem, R. , and Adalsteinsson, H. , 2015, The Uncertainty Quantification Toolkit (UQTk), 1st ed., Sandia National Laboratory, Albuquerque, NM.
Debusschere, B. , Najm, H. N. , Pebay, P. P. , Knio, O. M. , Ghanem, R. G. , and Le Maitre, O. P. , 2005, “ Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes,” SIAM J. Sci. Comput., 26(2), pp. 698–719. [CrossRef]
Ghanem, R. , and Higdon, D. O. H. , 2017, Handbook of Uncertainty Quantification, Vol. 1, Springer-Verlag, Cham, Switzerland.
Araya, P. E. , and Greiner, M. , 2008, “ CFD Simulations of an 8x8 Rod Array Inside of an Isothermal Enclosure Filled With a Rarefied Gas,” ASME Paper No. PVP2008-61582.
Greiner, M. , and Araya, P. , 2007, “ Two-Dimensional Simulations of Natural Convection/Radiation Heat Transfer for BWR Assembly Within Isothermal Enclosure,” Packag. Transp. Storage Secur. Radioact. Mater., 18(3), pp. 171–179. [CrossRef]
Hadj-Nacer, M. , Manzo, T. , Ho, M. , Graur, I. , and Greiner, M. , 2015, “ Phenomena Affecting Used Nuclear Fuel Cladding Temperatures During Vacuum Drying Operations,” International High-Level Radioactive Waste Management Conference (IHLRWM), Charleston, SC, Apr. 12–16, pp. 501–508. http://cc.greydenpress.com/gp/CloudConferencing/CloudConferencingTemplate/Data/pdfs/12591.pdf

Figures

Grahic Jump Location
Fig. 1

Fluent computational mesh for the 9 × 9 storage basket

Grahic Jump Location
Fig. 2

Lower right corner of computational model of the 9 × 9 storage basket

Grahic Jump Location
Fig. 3

Schematic of typical dry cask storage

Grahic Jump Location
Fig. 4

Mean temperature (Kelvin) throughout the assembly for high boundary wall temperature

Grahic Jump Location
Fig. 5

Mean temperature (Kelvin) throughout the assembly for low boundary wall temperature

Grahic Jump Location
Fig. 6

PDF for the center temperature in the high boundary wall temperature case

Grahic Jump Location
Fig. 7

PDF for the center temperature in the low boundary wall temperature case

Grahic Jump Location
Fig. 8

Mean velocity streamlines for high boundary wall temperature case

Grahic Jump Location
Fig. 9

Perspective view of the COV at each point in the mesh; predictions about the center of the basket will typically exhibit more variation

Grahic Jump Location
Fig. 10

Spatial dependence of the sensitivity of the temperature with respect to variations in the specific heat of helium

Grahic Jump Location
Fig. 11

Spatial dependence of the sensitivity of the temperature with respect to variations in the thermal conductivity of zircaloy for the high boundary wall temperature case

Grahic Jump Location
Fig. 12

Spatial dependence of the sensitivity of the temperature with respect to variations in the thermal conductivity of zircaloy for the low boundary wall temperature case

Grahic Jump Location
Fig. 13

Spatial dependence of the sensitivity of the temperature with respect to variations in the thermal conductivity of UO2 for the high boundary wall temperature case

Grahic Jump Location
Fig. 14

Spatial dependence of the sensitivity of the temperature with respect to variations in the fuel emissivity for the high boundary wall temperature case

Grahic Jump Location
Fig. 15

Spatial dependence of the sensitivity of the temperature with respect to variations in the specific heat of the UO2 for the high boundary wall temperature case

Grahic Jump Location
Fig. 16

Comparison of the PDFs for the center temperature created from the n = 6, p = 2 and n = 10, p = 1 simulations

Grahic Jump Location
Fig. 17

Comparison between the PDFs for the center temperature, the hotter one being the result of +50% heat generation rate

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In