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THERMAL MODELING OF A STORAGE CASK SYSTEM: CAPABILITY DEVELOPMENT
Prepared for
U.S. Nuclear Regulatory CommissionContract NRC–02–02–012
Prepared by
P.K. Shukla1
B. Dasgupta1
S. Chocron2
W. Li2S. Green2
1Center for Nuclear Waste Regulatory Analyses2Southwest Research Institute®
San Antonio, Texas
May 2007
ii
ABSTRACT
The objective of the numerical simulations documented in this report was to develop a capabilityto conduct thermal analyses of a cask system loaded with spent nuclear fuel. At the time theseanalyses began, the U.S. Department of Energy (DOE) surface facility design at the potentialhigh-level waste repository at Yucca Mountain included the option of dry transfer of spentnuclear fuel from transportation casks to the waste packages (DOE, 2005; Bechtel SAICCompany, LLC, 2005). Because the temperature of the fuel and cladding during dry handlingoperations could affect their long-term performance, CNWRA staff focused on developing acapability to conduct thermal simulations. These numerical simulations were meant to developstaff expertise using complex heat transfer models to review DOE assessment of fuel claddingtemperature. As this study progressed, DOE changed its design concept to include handling ofspent nuclear fuel in transportation, aging, and disposal canisters (Harrington, 2006). This newdesign concept could eliminate the exposure of spent nuclear fuel to the atmosphere at therepository surface facilities. However, the basic objective of developing staff expertise forthermal analysis remains valid because evaluation of cladding performance, which depends onthermal history, may be needed during a review of the potential license application. Based onexperience gained in this study, appropriate heat transfer models for the transport, aging, anddisposal canister can be developed, if needed.
Two computational fluid dynamics software packages, FLUENT® (Fluent, Inc., 2005) andFLOW-3D® (Flow Science, Inc., 2005) were evaluated for modeling the cask system. The HI-STAR 100 cask system (Holtec International, 2002) is used as the representative casksystem for developing numerical models in this study. At the time of these analyses, the designof a transportation, aging, and disposal canister was not available; however, it was expectedthat the design of the proposed canister would be analogous to a dry storage cask system suchas HI-STAR 100. The results in this report are not a definitive thermal analysis of the fuelassemblies in the cask system; they are used only to understand the simulation tools andmechanisms of heat transfer in a cask system. Three cases were simulated: (i) the closed-cask model, (ii) the open-cask model, and (iii) the fuel-assembly model. The FLUENT code in atwo-dimensional axisymmetric mode was used for the first two cases, and the FLOW-3D codewas used for thermal analysis of the fuel-assembly model.
Results from the closed-cask simulation compared well with those reported by Holtec (HoltecInternational, 2002), suggesting that the model in FLUENT (Fluent, Inc., 2005) was properlyconstructed. In the open-cask simulation, the results indicated that internal convection stronglyinfluences heat transfer from fuel assemblies. However, these results remain to be verified bydeveloping a three-dimensional heat transfer model of the HI-STAR 100 cask system. Naturalconvection was also a significant heat transfer mechanism in the fuel-assembly model,indicating that natural convection must be included in the heat transfer model for determiningthe thermal history fuel and cladding in a transportation, aging, and disposal canister.
References:
Bechtel SAIC Company, LLC. “Commercial Spent Nuclear Fuel Handling in Air Study.” 000–30R–MGRO–00700–000–000. Las Vegas, Nevada: Bechtel SAIC Company, LLC. 2005.
iii
DOE. “Categorization of Event Sequences for License Application.” 000–00C–MGRO–00800–000–00B. Rev. 00B ICN00. Las Vegas, Nevada: Office of CivilianRadioactive Waste Management. 2005.
Flow Science, Inc. “FLOW-3D® Version 9.0.” Santa Fe, New Mexico: Flow Science, Inc. 2005.
Fluent, Inc. “FLUENT® Version 6.2.16.” Lebanon, New Hampshire: Fluent, Inc. 2005.
Harrington, P. “Design and Engineering Update.” Presented to the U.S. Department of Energy,Nuclear Waste Technical Review Board. McLean, Virginia. May 2006.
Holtec International. “Final Safety Analysis Report for the HI-STAR 100 Dry Spent Fuel StorageSystem.” Marlton, New Jersey: Holtec International. 2002.
iv
CONTENTS
Section Page
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiFIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viTABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-11.2 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-21.3 Scope and Organization of the Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-21.4 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-3
2 DESCRIPTION OF THE CASK SYSTEM AND MODEL PARAMETERS . . . . . . . . . . 2-12.1 Geometric Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-1
2.1.1 Inner Canister . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-12.1.1.1 Fuel Basket . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-12.1.1.2 Fuel Assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-2
2.1.2 Overpack . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-32.2 Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-4
2.2.1 Thermal Conductivities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-42.2.2 Surface Emissivities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-52.2.3 Fluid Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5
2.2.3.1 Thermal Conductivity, Viscosity, and Heat Capacity . . . . 2-52.2.3.2 Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-7
2.3 Concrete Pad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-82.4 Thermal Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-8
2.4.1 Heat Load of the Cask . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-82.4.2 Ambient Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-8
3 MODELING APPROACH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-13.1 Description of Computational Fluid Dynamics Codes . . . . . . . . . . . . . . . . . . . 3-1
3.1.1 FLUENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-13.1.2 FLOW-3D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-1
3.2 Model Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-23.3 Model Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-2
3.3.1 Closed-Cask Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-23.3.2 Open-Cask Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-43.3.3 Fuel-Assembly Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-4
3.4 Model Simplifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-43.5 Effective Thermal Conductivity of Fuel Region . . . . . . . . . . . . . . . . . . . . . . . . 3-4
4 MODEL DESCRIPTION AND RESULTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-14.1 Closed-Cask Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1
4.1.1 Model Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-24.1.2 Model Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-3
v
CONTENTS (continued)
4.2 Open-Cask Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-54.2.1 Model Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-94.2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-10
4.3 Fuel-Assembly Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-144.3.1 Model Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-164.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-17
5 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-1
6 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-1
vi
FIGURES
Figure Page
2-1 (a) Two-Dimensional and (b) Three-Dimensional View of the HI-STAR 100Cask System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-2
4-1 (a) Schematic Representation of the Closed-Cask Model Physical Domain and(b) Axisymmetry Model of the Cask System in FLUENT . . . . . . . . . . . . . . . . . . . . . . 4-2
4-2 Temperature Distribution Inside the HI-STAR 100 Casket System (a) WithoutInsolation and (b) With Insolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-4
4-3 Normalized Fuel Burnup Rate Along the Length of a Pressurized Water ReactorFuel Assembly. The Figure Shows the Burnup Data Listed in Table 2.1.8 . . . . . . . . 4-5
4-4 (a) The Physical Domain of the Open-Cask Model and (b) The ComputationalDomain of the Open-Cask Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-6
4-5 A Schematic Representation of an MPC–24 Fuel Basket (Holtec International,2002) and Its Equivalent Representation in Open-Cask Model . . . . . . . . . . . . . . . . . 4-7
4-6 The HI-STAR 100 Cask System With Three Concentric Cylindrical Fuel Regions . . 4-94-7 Temperature Distribution Inside an Open HI-STAR 100 Cask System (a) No Flow
Condition (i.e., Only Radiation and Conduction Heat Transfer) . . . . . . . . . . . . . . . . 4-104-8 Temperature Distribution Inside an Open HI-STAR 100 Cask System
(a) K-Epsilon Turbulent Flow Model and (b) K-Omega Turbulent Flow Model . . . . . 4-114-9 Temperature Distribution Inside an Open HI-STAR 100 Cask System With
Radiation and Conduction Heat Transfer (a) Without Flow . . . . . . . . . . . . . . . . . . . 4-134-10 Temperature Distribution Inside an Open HI-STAR 100 Cask System With the
(a) K-Epsilon Turbulent Flow Model and (b) K-Omega Turbulent Flow Model . . . . . 4-134-11 Cross Section of the Inner Canister Containing the Pressurized Water Reactor
Fuel Basket With 24 Inserts (Holtec International, 2002) . . . . . . . . . . . . . . . . . . . . . 4-154-12 Schematic Diagram of the Fuel-Assembly Model (a) Represents a Fuel
Assembly and (b) Its Model Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-154-13 Steady-State Temperature Distribution of the Fuel Assembly in the
Fuel-Assembly Model For Air Entering At 350 K [170.33 °F]. . . . . . . . . . . . . . . . . . . 4-174-14 Steady-State Temperature Distribution of the Fuel Assembly in the
Fuel-Assembly Model For Air Entering at 400K [266.33 °F] . . . . . . . . . . . . . . . . . . . 4-18
vii
TABLES
Table Page
2-1 Dimensions of HI-STAR 100 Cask System Components . . . . . . . . . . . . . . . . . . . . . . 2-22-2 Thermal Conductivity of HI-STAR 100 Cask System Materials . . . . . . . . . . . . . . . . . 2-42-3 Parameter Values Used to Calculate Effective Intermediate Shell Thermal
Conductivity of Overpack . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-62-4 Calculated Values [Using Eq. (2-1)] of Effective Intermediate Shells
(Overpack-Carbon) Thermal Conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-62-5 Surface Emissivity of Components Used in HI-STAR 100 Cask System . . . . . . . . . . 2-62-6 Thermal Conductivity of Helium and Air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-72-7 Properties of Helium and Air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-7
4-1 Dimensions of the Fuel Regions in the Open-Cask Model With Flow Channels . . . . 4-84-2 Summary of Calculated Results for the Open HI-STAR Cask System With a
Cylindrical Solid Homogeneous Fuel Region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-114-3 Summary of Calculated Results for the Open HI-STAR Cask System With Three
Concentric Cylindrical Fuel Regions and Flow Channels In Between . . . . . . . . . . . 4-14
viii
ACKNOWLEDGMENTS
This report was prepared to document work performed by the Center for Nuclear WasteRegulatory Analyses (CNWRA) for the U.S. Nuclear Regulatory Commission (NRC) underContract No. NRC–02–02–012. The activities reported here were performed on behalf of theNRC Office of Nuclear Material Safety and Safeguards, Division of High-Level WasteRepository Safety. The report is an independent product of CNWRA and does not necessarilyreflect the views or regulatory position of NRC.
The authors would like to thank S. Stothoff for the technical review, K. Das for the concurrencereview, and B. Sagar for the programmatic review of this report. The authors also appreciateB. Street for providing word processing support and P. Mackin for editorial support inpreparation of this document.
QUALITY OF DATA, ANALYSES, AND CODE DEVELOPMENT
DATA: All CNWRA-generated original data contained in this report meet the quality assurancerequirements described in the Quality Assurance Manual. Data used in this report are primarilyderived from other publicly available sources. Each data source is cited in this report andshould be consulted for determining the level of quality for those cited data. The modeling workis documented in CNWRA scientific notebook number 704E.
ANALYSES AND CODES: The computational fluid dynamics analyses presented in this reportwere conducted using FLUENT®, Version 6.2.16 (Fluent, Inc., 2005). This version of thesoftware has been validated and is under CNWRA configuration control. The computationalfluid dynamics analyses presented in this report were also conducted using FLOW-3D®,Version 9.0 (Flow Science, Inc., 2005). This version of the software has been validated and isunder CNWRA configuration control. Spreadsheet calculations were accomplished usingMicrosoft® Excel® 97 SR–2 (Microsoft Corporation, 1997). Additional calculations wereperformed using Mathcad® 2000 Professional (Mathsoft Engineering and Education, Inc., 1999).
References:
Fluent, Inc. “FLUENT® Version 6.2.16.” Lebanon, New Hampshire: Fluent, Inc. 2005.
Flow Science, Inc. “FLOW-3D® Version 9.0.” Santa Fe, New Mexico: Flow Science, Inc. 2005.
Mathsoft Engineering and Education, Inc. “Mathcad® 2000 Professional.” Cambridge,Massachusetts: Mathsoft Engineering and Education, Inc. 1999.
Microsoft Corporation. “Microsoft® Excel® 97 SR–2.” Redmond, Washington: MicrosoftCorporation. 1997.
1-1
1 INTRODUCTION
1.1 Background
The operations at the surface facilities of the proposed repository at Yucca Mountain mayinclude transfer of commercial spent nuclear fuel and high-level nuclear waste fromtransportation casks to the waste packages. Handling of spent nuclear fuel at the geologicrepository operations area in the preclosure period may cause the fuel cladding temperature torise. Fuel cladding temperature exceeding the allowable limit may potentially affect claddingperformance. In addition, there may also be preclosure safety concerns if bare fuel assembliesare handled under dry conditions. Thus, evaluating the stability of cladding, which depends onits thermal history, may be important in the licensing review. The objective of this study is todevelop staff capabilities and expertise in thermal modeling for evaluating fuelcladding performance.
This preclosure prelicensing activity began in fiscal year 2005 at the Center for Nuclear WasteRegulatory Analyses (CNWRA) at the request of the U.S. Nuclear Regulatory Commission(NRC). At that time, the U.S. Department of Energy (DOE) plan for surface facility operationsincluded dry transfer of fuel assemblies and surface aging of nuclear waste at the YuccaMountain site (DOE, 2005). According to this plan, spent nuclear fuel assemblies would arriveat the surface facilities in transportation casks and would be transferred to waste packages oraging casks in the transfer cells (Bechtel SAIC Company, LLC, 2005). The fuel transfer cellswere to be located inside the fuel handling facility. During transport, the transportation casks orcanisters would be filled with helium to enhance the passive heat dissipation and to maintain thepeak cladding temperature below the allowable limit. The cask was to be opened during the drytransfer operation inside the transfer cell when helium would escape and be replaced by air. Because air has lower thermal conductivity than helium, the fuel cladding temperature could risedue to inadequate heat dissipation, potentially affecting fuel cladding integrity. During review ofa Yucca Mountain license application, staff might need to conduct an independent confirmatoryanalysis to evaluate the thermal condition of fuel during anticipated events, such as loss of theheating, ventilation, and air conditioning system. The thermal models of the cask systemdeveloped in this report are for the handling of closed casks and bare fuel assemblies in caskopened to ambient temperature. The DOE changes to the design and operations at the proposed Yucca Mountain surfacefacilities (Harrington, 2006) include use of the transport, aging, and disposal canister system. According to this modified DOE plan, commercial spent fuel assemblies would arrive at thesurface facilities in sealed transport, aging, and disposal canisters inside transportation casks. After receipt and inspection, the transport, aging, and disposal canisters would be transferred towaste packages or aging casks. The proposed use of a transport, aging, and disposal canistersystem essentially eliminates the likelihood of exposing the bare fuel assemblies to theatmosphere. Although dry handling operations are no longer anticipated, the experience andcapability gained from this activity will be useful for evaluating fuel cladding performance in thenew proposed surface facility design. This experience may also be used to review the ability ofthe DOE facility design to maintain fuel cladding temperature below allowable limits duringnormal operations.
1-2
1.2 Objective
The overall objective of this study is to prepare NRC and CNWRA staffs to review andindependently verify DOE thermal analyses in a potential license application for the high-levelwaste repository at Yucca Mountain. The specific objectives of this study, conducted using theDOE concept of dry transfer of fuel assemblies (DOE, 2005; Bechtel SAIC Company, LLC,2005) are
• Develop computational fluid dynamics modeling capabilities to review DOE analyses andto conduct independent analyses to assess thermal conditions inside the containers
• Assess the capabilities of commercially available computational fluid dynamics software
• Explore the effects of heat transfer mechanisms (i.e., conduction, natural convection,and radiation) from fuel assemblies inside a storage canister under ambient conditions
1.3 Scope and Organization of the Report
Available data on the HI-STAR 100 cask system are used for exercising the simulators (HoltecInternational, 2002). This cask system has been approved by NRC for transportation and drystorage of spent fuel (NRC, 2004; 2001). In this report, thermal modeling was performed usingtwo computational fluid dynamics software packages: FLUENT® (Fluent, Inc., 2005) andFLOW-3D® (Flow Science, Inc., 2005). The following two-dimensional models were analyzedfor capability development.
• Closed-Cask Model: A thermal model of a closed HI-STAR 100 cask system with24 pressurized water reactor fuel assemblies in the ambient environment is developed. The model simulates the steady-state thermal behavior of a closed-cask when it is filledwith helium during a dry storage condition. FLUENT is used to analyze this model. Theobjective is to compare the results from this analysis with the results in the HI-STAR 100final safety analysis report (Holtec International, 2002). In this model, the fuelassemblies and fuel basket are represented as a cylindrical solid homogeneousfuel region.
• Open-Cask Model: A thermal model of an open HI-STAR 100 cask system with24 pressurized water reactor fuel assemblies is developed. The cask is assumed to beopen to the ambient air and active exchange of heat generated by the fuel assembliestakes place via natural convection, conduction, and radiation heat transfer. In thismodel, the fuel assemblies and supporting structure are represented in two ways:(i) a cylindrical solid homogeneous fuel region and (ii) three concentric cylindrical solidhomogeneous fuel regions. FLUENT is used to simulate the open-cask model. The model simulates the steady-state temperature distribution in the open cask underambient conditions.
• Fuel-Assembly Model: This model simulates the steady-state thermal behavior of a barefuel assembly inside an open cask. In this model, the fuel assembly directly contactswith ambient air, and active dissipation of heat takes place by conduction and naturalconvection heat transfer. FLOW-3D is used to simulate the model.
1-3
This report is presented in six chapters, including this introduction as Chapter 1. Modelparameters for all simulations are discussed in Chapter 2. Details of modeling approaches areprovided in Chapter 3. Chapter 4 provides the details of three models and discusses theunderstanding gained from the simulations. Chapter 5 summarizes the experience gained fromthis modeling work, and Chapter 6 contains references used in preparing this report.
1.4 Assumptions
The following assumptions are used in the models:
• Heat transfer from fuel assemblies in an open-cask system is a complex process thatrequires a three-dimensional model to accurately predict the temperature and flow field;however, as a first step, two-dimensional models are developed to gain apreliminary understanding of modes of heat dissipation (e.g., the internal flow field,radiative heat transfer patterns, and the effect of temperature-dependent thermalconductivities of component materials).
• Storage cask system components for both the closed-cask and open-caskmodels are modeled in the two-dimensional plane using axisymmetry.
• In the open-cask and closed-cask models, the fuel assemblies and fuel basket are
represented as cylindrical solid homogeneous fuel regions with an effectivethermal conductivity.
• For the two-dimensional model of the fuel assembly, fluid between fuel rods is stagnant. Therefore, a fuel assembly can be represented as a solid homogeneous power sourcewith an effective thermal conductivity.
• In the open-cask model, the ambient environment extends to infinity and is an infiniteheat sink. Processes such as changes in air temperature inside the fuel transfer cellare neglected.
2-1
2 DESCRIPTION OF THE CASK SYSTEM AND MODEL PARAMETERS
In this report, the HI-STAR 100 cask system was selected for developing heat transfer modelsusing FLUENT and FLOW-3D. The cask system is designed for both transportation and drystorage of spent nuclear fuel and has been certified by NRC (NRC, 2004; 2001). Theinformation required for modeling (e.g., detailed geometric parameters and thermal properties ofcomponent materials) was obtained from the HI-STAR 100 Final Safety Analysis Report (HoltecInternational, 2002).
The cylindrical HI-STAR 100 cask system consists of two discrete components: the innercanister, referred to as the multipurpose canister in Holtec International (2002) and theoverpack. The inner canister shell is placed inside the overpack. A three-dimensional view andcorresponding two-dimensional cross section of the cask system are presented in Figure 2-1. The figure shows components of the cask and canister systems. The closed-cask andopen-cask models in this report are based on the materials and shape of the cask as shown inFigure 2-1.
The geometric descriptions of cask system subcomponents are given in Section 2.1. The casksystem is backfilled with helium gas when closed, and ambient air replaces the helium when thecask system is opened. The material properties of helium, air, and cask subcomponents areprovided in Section 2.2. The thermal properties of the concrete pad are described in Section2.3. The thermal heat load of the cask and ambient conditions are discussed in Section 2.4.
2.1 Geometric Description
2.1.1 Inner Canister
Fuel assemblies and the fuel basket are placed inside the inner canister. The canister is awelded structure consisting of a base plate, canister shell, and a cover lid, as shown inFigure 2-1. The canister is filled with helium under sealed conditions. The dimensions of thecask system components, including that of the inner canister, are provided in Table 2-1. The thicknesses of the shell wall and base plates are 1.27 cm [0.5 in] and 6.35 cm [2.5 in],respectively. The shell material is made of stainless steel (Holtec International, 2002).
2.1.1.1 Fuel Basket
The fuel basket is a honeycombed structure that is placed inside the inner canister shell. Thefuel basket has square fuel compartments where fuel assemblies are inserted prior to closingthe inner canister shell. Each fuel compartment panel has a Boral neutron absorbersandwiched between a sheathing plate and the box panel, and covering the entire length of theactive fuel region. A fuel basket holding 24 pressurized water reactor fuel assemblies is calledan MPC–24. In Figure 2-1, the green panels represent Boral neutron absorbers. At the bottomand top of the fuel basket panels are circular undercuts that provide a passage for fluid flow. Thermal analysis of only the MPC–24 fuel baskets is conducted. Holtec International (2002)has not specified the material of construction for the fuel basket, but the properties of stainlesssteel were used in the model for the fuel basket in thermal analyses.
2-2
Figure 2-1. (a) Two-Dimensional and (b) Three-Dimensional View of the HI-STAR 100 Cask System
2.1.1.2 Fuel Assembly
Each pressurized water reactor fuel assembly consists of fuel rods, spacer grids, and upper andlower end fittings. The fuel rods are typically arranged in a 17 × 17 square matrix, with thespacer grids separating the individual rods and keeping them in place. The fittings and spacergrids have holes for the coolant flow that are small relative to the gaps between the fuel rods. The fuel-assembly model represents the geometry of a fuel assembly and the surrounding gaps,while the cask system models represent the fuel assemblies and fuel basket as equivalent solidfuel regions, with effective thermal conductivities that depend on the gas in the gaps. As discussed in Section 3.5, closed-cask fuel assemblies and fuel basket are modeled as onecylindrical solid homogeneous fuel region, and open-cask fuel assemblies and fuel basket aremodeled as three concentric cylindrical solid homogeneous fuel regions separated byannular gaps.
Table 2-1. Dimensions of HI-STAR 100 Cask System Components*
Component of HI-STAR 100 SystemInner Radius
{m [in]} Outer Radius
{m [in]}Height {m [in]}
Multipurpose Canister Base Plate 0.0[0.0]
0.8683625[34.1875]
0.0635[2.5]
Multipurpose Canister Shell 0.8556625[33.6875]
0.8683625[34.1875]
4.5212[178.0]
Multipurpose Canister Lid 0.0[0.0]
0.8683625[34.1875]
0.2413[9.5]
2-3
Table 2-1. Dimensions of HI-STAR 100 Cask System Components* (continued)
Component of HI-STAR 100 SystemInner Radius
{m [in]} Outer Radius
{m [in]}Height {m [in]}
Overpack Base Plate 0.0[0.0]
1.057275[41.625]
0.1524[6.0]
Overpack-Ni layer 0.873125[34.375]
0.936625[36.875]
4.854575[191.125]
Overpack-Carbon Layer 0.936625[36.875]
1.069975[42.125]
4.854575[191.125]
Overpack Lid 0.0[0.0]
1.069975[42.125]
0.1524[6.0]
Carbon Steel Radial Connector (Holtite) 1.069975[42.125]
1.2192[48.0]
4.397375[173.125]
*Holtec International. “Final Safety Analysis Report for the HI-STAR 100 Dry Spent Fuel Storage System.” Marlton, New Jersey: Holtec International. 2002.
2.1.2 Overpack
The overpack is the container for the inner canister. It is a multiwalled cylindrical vessel with abase plate and a closure lid. The inner radius of the overpack is slightly larger than the outerradius of the inner canister shell. The difference between these two radii is 0.47625 cm[0.1875 in]. The space between the overpack and the inner canister is filled with helium whenthe cask is closed, and is replaced by air when the overpack closure lid is opened. A detailed schematic diagram of the cross section of the overpack can be found in HoltecInternational (2002).
The innermost shell of the overpack is made of 6.35 cm [2.5 in] Ni-Steel and is labeledoverpack-Ni in Figure 2-1. The overpack-Ni layer is surrounded by an intermediate shell of fivelayers of carbon steel. The first of the five layers is 3.175 cm [1.25 in] thick and is called thegamma shell. The next four layers are each 2.54 cm [1.0 in] thick. These five layers of carbonsteel are modeled as a composite shell 13.335 cm [5.25 in] thick, called the overpack-carbonin Figure 2-1.
To reduce doses from neutron radiation emitted by spent nuclear fuel, the overpack issurrounded by neutron shielding material. This material is placed inside radial channels that arevertically welded to the outermost surface of the overpack intermediate shell. These radialchannels also act as thermal fins for improved heat transfer between the overpack and itssurroundings. The cavities of radial channel segments also contain silicone sponge. Theneutron shielding material Holtite-A (Holtec International, 2002) is made of boron carbide(a neutron poison material) and aluminum. The outer modeled layer, representing carbon steelradial connections and material inside, is a composite material labeled Holtite in Figure 2-1.
2-4
K r logrr K
rr
r logrr
r Keff 05
0 airi 1
50
i
05
0
i cst
1
=⎛⎝⎜
⎞⎠⎟ +
⎡
⎣
⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥
=
−
∑ δ
2.2 Material Properties
2.2.1 Thermal Conductivities
The value of thermal conductivity used to model each cask subsystem depends on whether thesubsystem contains void spaces. The inner canister shell, overpack inner shell (Overpack-Ni)and base plate, and carbon steel radial connector (Holtite) region do not contain voids; thecorresponding properties used by Holtec (Holtec International, 2002) are provided in Table 2-2.
The intermediate overpack-carbon shell is a multilayered region consisting of a 3.175 cm[1.25 in] gamma layer (made of Ni-steel) and four 2.54 cm [1.0 in] outer layers made of carbonsteel. This subsystem is modeled as one 13.335 cm [5.25 in] wall with an effective thermalconductivity that is in part determined by contact resistance due to minute pockets of airentrapped between shells in the fabrication process.
The entrapped air has a lower thermal conductivity than the metal in the overpack and reducesthe radial thermal conductivity of the composite. However, axial conductivity will be essentiallyunchanged, so the overpack thermal conductivity is anisotropic. Radial heat conduction isexpected to dominate axial heat conduction due to a much steeper thermal gradient. Thus,an isotropic thermal conductivity is used with properties characteristic of the radial direction.
The effective thermal conductivity of the multilayered overpack-carbon is estimated by thefollowing expression (Holtec International, 2002)
(2-1)
Table 2-2. Thermal Conductivity of HI-STAR 100 Cask System Materials*
Components of the HI-STAR 100 System
Thermal Conductivity (W/m-K) [Btu/ft-hr-°F]
@ 93.33 °C[200 °F]
@ 232.2 °C[450 °F]
@ 371.1 °C[700 °F]
Multipurpose Canister Shell and Base Plate(Alloy X)
14.54[8.4]
16.96[9.8]
19.04[11.0]
Overpack Inner Shell (Overpack-Ni) and Base Plate 42.23[24.4]
41.36[23.9]
38.77[22.4]
Overpack Holtite-A and Carbon Steel RadialConnector System (Holtite)
3.38[1.95]
3.14[1.81]
2.85[1.64]
2-5
Table 2-2. Thermal Conductivity of HI-STAR 100 Cask System Materials* (continued)
Components of the HI-STAR 100 System
Thermal Conductivity (W/m-K) [Btu/ft-hr-°F]
@ 93.33 °C[200 °F]
@ 232.2 °C[450 °F]
@ 371.1 °C[700 °F]
Cylindrical Solid Fuel Region (homogeneousrepresentation of MPC–24 fuel basket with24 pressurized water reactor fuel assemblies)
1.92 [1.108]
2.59,[1.495]
3.382[1.954]
*Holtec International. “Final Safety Analysis Report for the HI-STAR 100 Dry Spent Fuel Storage System.” Marlton, New Jersey: Holtec International. 2002.
where
Keff — effective intermediate shell region conductivityr0 — inner radius of the inner intermediate shellri — outer radius of ith intermediate shell* — interlayer air gap Kair — thermal conductivity of the airKcst — carbon steel thermal conductivity
The values for r0, ri, and * are provided in Table 2-3. The calculated values of the effectivethermal conductivity Keff for the overpack carbon shell are given in Table 2-4.
2.2.2 Surface Emissivities
The outer surface of the cask system is painted white. Its surface emissivity is assignedas 0.85. The surface emissivity of the fuel basket, inner canister shell, base plate, and innercanister lid are assumed to be that of stainless steel. The surface emissivity of the overpackbase plate, overpack cylindrical shell, and overpack lid are assumed to be that of carbon-steel. The surface emissivities of materials used in the cask models are given in Table 2-5.
2.2.3 Fluid Properties
2.2.3.1 Thermal Conductivity, Viscosity, and Heat Capacity
When the cask is closed, the inner canister shell and overpack are filled with pressurizedhelium, which acts as a nonreacting gas medium for passive rejection of heat generated by fuelassemblies. The thermal conductivity of helium and air at different temperatures are listed inTable 2-6. The viscosity, heat capacity, and molecular weight of helium and air are listedin Table 2-7.
2-6
Table 2-3. Parameter Values Used to Calculate Effective Intermediate ShellThermal Conductivity of Overpack*
Parameter Value {m [in]}r0 0.934339 [36.785]
r1 0.974725 [38.375]
r2 1.000125 [39.375]
r3 1.025525 [40.375]
r4 1.050925 [41.375]
r5 1.076325 [42.375]
* 787.4 : [2,000 :]*Holtec International. “Final Safety Analysis Report for the HI-STAR 100 Dry Spent Fuel Storage System.” Marlton, New Jersey: Holtec International. 2002.
Table 2-4. Calculated Values [Using Eq. (2-1)] of Effective Intermediate Shells(Overpack-Carbon) Thermal Conductivity*
Temperature Keff (W/m-K) [Btu/ft-hr-°F]
93.33 °C [200 °F] 11.58 [6.69]
232.2 °C [450 °F] 13.82 [7.98]
371.1 °C [700 °F] 15.24 [8.81]
*Holtec International. “Final Safety Analysis Report for the HI-STAR 100 Dry Spent Fuel Storage System.” Marlton, New Jersey: Holtec International. 2002.
Table 2-5. Surface Emissivity of Components Used in HI-STAR 100 Cask System*
Component Emissivity
Fuel Basket 0.36Multipurpose Canister Shell, Base Plate, and Lid 0.36Overpack Base Plate, Inner Shell, and Lid 0.66Painted Surfaces (Overpack External Surface) 0.85*Holtec International. “Final Safety Analysis Report for the HI-STAR 100 Dry Spent Fuel Storage System.” Marlton, New Jersey: Holtec International. 2002.
2-7
ρ =PMRT
Table 2-6. Thermal Conductivity of Helium and Air*
TemperatureHelium Khelium (W/m-K)
[Btu/ft-hr-°F]Air Kair (W/m-K)
[Btu/ft-hr-°F]
93.33 °C [200 °F] 1.689 × 10!1 [9.76 × 10!2] 2.994 × 10!2 [1.731 × 10!2]
232.2 °C [450 °F] 2.231 × 10!1 [1.289 × 10!1] 3.894 × 10!2 [2.251 × 10!2]
371.1 °C [700 °F] 2.762 × 10!1 [1.575 × 10!1] 4.707 × 10!2 [2.270 × 10!2]
*Holtec International. “Final Safety Analysis Report for the HI-STAR 100 Dry Spent Fuel Storage System.” Marlton, New Jersey: Holtec International. 2002.
Table 2-7. Properties of Helium and Air*
Material
Heat Capacity Cp (J/kg-K)
[Btu/lbm-°F]
Viscosity :(Pa-sec)[lb/ft-s]
Molecular Weight(kg/mol)[lb/mol]
Helium 5193[1.24]
1.8 × 10!5
[1.21 × 10!5] 4.0026 × 10!3
[8.8242]
Air 1006.43[0.24]
1.9 × 10!5
[1.28 × 10!5]28.996 × 10!3
[63.9256]*Holtec International. “Final Safety Analysis Report for the HI-STAR 100 Dry Spent Fuel Storage System.” Marlton, New Jersey: Holtec International. 2002.
2.2.3.2 Density
The spatial variation in fluid density causes fluid to convect due to buoyancy forces. In a casksystem, the density variations are caused by the temperature gradients in the fluid region. Thefluid is modeled as an incompressible ideal gas to account for temperature variation (HoltecInternational, 2002). The density of gas D can be represented by
(2-2)
where
P — specified pressure of the gas (pascal) = 1.01325 × 105 pascalM — molecular weight of the gas (mol/kg) (see Table 2-5)R — universal gas constant, 8.3144 J/mol-K T — temperature of the gas (K)
Because of the incompressible ideal gas approximation, the pressure variation for fluid isneglected by maintaining pressure at the ambient value throughout the model domain.
2-8
2.3 Concrete Pad
The cask system is placed on a concrete pad for both closed- and open-cask models. The padis modeled as a 0.9144 m [36 in] high concrete cylinder with a radius equal to the overpackbase plate. The upper surface of the concrete surface contacts the overpack base plate, and itsbottom surface is assumed to be at 288.7 K [60 °F] (Holtec International, 2002). The thermalconductivity of concrete, which is in the range of 0.6 to 1.0 watts/m-K [0.35 to 0.58 Btu/ft-hr-°F](Incropera and Dewitt, 1996), is assumed to be 0.8 watts/m-K [0.46 Btu/ft-hr-°F]. The sidewallsof the concrete pad are conservatively assumed to be adiabatic.
2.4 Thermal Conditions
2.4.1 Heat Load of the Cask
The thermal load of the cask system is dependent upon the type and number of fuel assembliesand the age of the spent nuclear fuel. The MPC–24 fuel basket, with 24 pressurized waterreactor fuel assemblies, was selected for this modeling. Each pressurized water reactor fuel assembly has a design basis decay heat generation rate of792 watts, so the maximum heat load of an MPC–24 fuel basket is 19,008 watts (HoltecInternational, 2002). Holtec International (2002) distributed the heat generation ratenonuniformly over the length of the fuel. The precise distribution of the heat generation rate isnot of primary importance for gaining insight into heat transfer processes, so for simplicity inmodeling, it was assumed that the heat generation rate is uniformly distributed.
2.4.2 Ambient Condition
The ambient air temperature is assumed to be 299.82 K [80 °F] in the closed- and open-caskthermal models (Holtec International, 2002). The atmospheric pressure is assumed to be 1.01× 105 pascal [14.7 lb/in2].
3-1
3 MODELING APPROACH
The thermal models are developed using FLUENT and FLOW-3D commercially available codes
that numerically solve fluid dynamics and heat transfer governing equations for a given fluidsystem in a specified geometry. FLUENT and FLOW-3D have been validated for the featuresand functions used in the models analyzed in this report (Green, et al, 2005; Shukla, 2006). FLUENT was used to perform thermal analyses of the HI-STAR 100 cask system (HoltecInternational, 2002).
3.1 Description of Computational Fluid Dynamics Codes
3.1.1 FLUENT
FLUENT is a computational fluid dynamics computer code that numerically solves governingequations for momentum, mass, and energy balance for a system. The software is ISO–9001certified, and it is routinely used by the automobile, aircraft manufacturing, oil and gas, andmicroprocessor manufacturing industries. FLUENT uses a control volume formulation to solvethe governing equations, simulating laminar and turbulent flow fields and buoyancy-drivennatural convection of fluids. The software can also model conductive, convective, and radiativeheat transfer in a system. In this report, the closed- and open-cask thermal analyses areperformed using FLUENT Version 6.2.1.
FLUENT uses the Semi-Implicit Method for Pressure Linked Equations (SIMPLE) method andits variations to solve momentum, convective heat transfer, and radiation transport equationswithin a finite volume. The SIMPLE method is described in detail by Patankar (1980). For theopen-cask model, the laminar and turbulent flow models are used to simulate buoyancy-drivennatural convection fluid flow inside and outside the cask. In case of turbulent flow, the standardk-epsilon and k-omega models are used inside the computational domain. The details of theseturbulent flow models can be found in the FLUENT User’s Manual (Fluent, Inc., 2006). For thestandard k-epsilon turbulent flow model, the enhanced wall treatment and full buoyancy effectsare activated, and for the standard k-omega model, the transitional flow option is used.
Radiation heat transfer in the closed- and open-cask models is solved using the discreteordinate method. In FLUENT, the radiative transport equation is discretized into a finite numberof solid angles in each volume. The resulting radiative transport equation is then solved forradiation intensities after solving the convective heat transfer and fluid flow equations for severaliterations. This process is repeated until radiation intensities, temperature, and fluid flow fieldconverge. The thermal conductivities of component materials and fluid in open- andclosed-cask models are defined as piecewise-linear functions of the temperature using the datain Tables 2-2, 2-4, and 2-6.
3.1.2 FLOW-3D
FLOW-3D Version 9.0 is used to analyze the fuel-assembly model. FLOW-3D is a finitedifference code based on the volume-of-fluid formulation for modeling two-fluid systems. FLOW-3D solves time-dependent flow of fluids using a semi-implicit formulation withsecond-order formulations for spatial and temporal derivatives. The software has a suite ofmodules for single and multiphase fluids and can consider both compressible and
3-2
incompressible fluids. A set of turbulent flow models are available, ranging from the standardk-epsilon model to a Large Eddy Simulation model, and each model includes supplementaryterms to account for heat transfer effects near solid walls. Turbulence effects are considered tobe of secondary importance for building insight into heat transfer processes and arecomputationally demanding. Thus, for simplicity in modeling, it is assumed that the fluid flowfield is reasonably well described as laminar flow in the fuel-assembly model. FLOW-3D uses aconstant value of thermal conductivity for each component material in heat transfer calculations.
3.2 Model Setup
Both cask systems are simulated as two-dimensional axisymmetric models in cylindricalcoordinates. The cask analyses are simplified by neglecting small subcomponents that areexpected to only minimally affect the thermal profile inside the cask. Neglected subcomponentsinclude overpack lifting trunnions and drainage ports, heat conduction elements, and basketsupports inside the inner canister shell.
The computational domain of the closed-cask model is divided into rectangular structuredelements. The fluid region between the cylindrical solid homogeneous fuel region and innercanister, and the fluid region between the inner canister shell and the overpack interior surfaceare divided into a finer rectangular mesh. In the open-cask model, the computational domain is modeled with a hybrid mesh. The computational domain of the open-cask model contains an open-cask system and ahemispherical dome of air outside the cask. The overpack and inner canister lids are removedin the open-cask model. The open-cask system computational domain is divided intorectangular elements, and the computational domain of air existing outside the cask is dividedinto unstructured quadrilateral elements. The mesh on the air side is clustered at the boundaryof the cask system and ambient air. The mesh is similarly clustered near the boundary ofcomputational domain. The fluid regions inside the cask are divided into a finerrectangular mesh.
The fuel-assembly model is developed in the rectangular coordinate system. The fuel assemblyis modeled as one planar surface. The side panels of the fuel basket structure, adjacent to thefuel assembly inside the cask, are assumed to be part of the fuel-assembly model. Thecomputational domain is discretized into rectangular elements.
3.3 Model Boundary Conditions
3.3.1 Closed-Cask Model
Heat transfer from the overpack exterior surface to the atmosphere takes place by naturalconvection and radiation when the cask is closed. The large temperature difference betweenthe overpack surface and ambient air causes the air in the vicinity of the cask to convect,transferring heat to the atmosphere. Heat will also be dissipated by radiation heat transferbecause the cask surface temperature is higher than the surrounding temperature.
3-3
RaC g L T
kLp
2 3
=ρ β
μΔ
h 1.25(T T ) (Horizontal)S A1/ 3= −
h 1.08(T T ) (Vertical)S A1/ 3= −
The total rate of heat loss from the exterior surface can be expressed by the followingrelationship (Holtec International, 2002)
q h(T T ) F (T T )S A 1A S4
A4= − + −σε (3-1)
where
q — heat flux (W/m2)h — heat transfer coefficient (W/m2-K)TS, TA — surface, ambient temperatures (K)F — Stefan-Boltzmann constant = 5.67×10-8 W/m2-K4
g — surface emissivityF1A — view factor between cask surface and air (assumed to be unity)
The fluid flow regime can be characterized by the value of Rayleigh number, RaL, defined as
(3-2)
where
Cp — heat capacity of the gasD — gas densityg — acceleration due to gravity$ — thermal expansion coefficient of gasL — height of the vertical plate)T — temperature difference between cask and atmosphere: — dynamic viscosity6 — gas thermal conductivity
The fluid flow is expected to be turbulent if RaL is greater than 109 for a vertical surface and 107
for a horizontal surface (Holtec International, 2002). The Rayleigh number RaL as a function ofcask height and temperature difference is 2.27 × 108L3 )T. The Rayleigh number along theheight of the cask surface will exceed the critical value of 109 even for a small value of )T. Therefore, a turbulent flow field near the cask surface is expected.
The following correlations were suggested by Jacob and Hawkins (1957) for the naturalconvection heat transfer coefficient h from the heated horizontal and vertical surfaces in theturbulent fluid flow regime
(3-3)
and
(3-4)
where h has unit of W/m2!K. The heat transfer coefficient for a vertical surface is less than that
3-4
for a horizontal surface. In the closed-cask model, the heat transfer coefficient for a verticalsurface [given by (Eq. 3-4)] is also applied to horizontal surfaces of the cask system, asimplification that will conservatively reduce the heat transfer rate. This approach is consistentwith the approach adopted by Holtec International (2002).
The heat transfer coefficient h [Eq. (3-4)] is used to model the natural convection and radiationheat transfer from the overpack exterior surface in the closed-cask model. The approachobviates the need to model natural convection of air outside the cask.
3.3.2 Open-Cask Model
The computational domain for the open-cask model includes ambient air outside the casksystem. The heat is transferred by active exchange of air between the cask and ambient air. Therefore, the model setup includes an extended domain to explicitly model the activeexchange of air. This model is described in detail in Section 4.2. The heat transfer from theoverpack exterior surface to ambient air is determined by the solution of the governing equationfor convective and radiation heat transfer.
3.3.3 Fuel-Assembly Model
The detailed description of the fuel assembly model is provided in Section 4.3. Thecomputational domain in the model does not require a specification of heat transfer coefficient.
3.4 Model Simplifications
In the closed-cask model, the fuel assemblies and fuel basket are represented as a cylindrical solid homogeneous solid fuel region. The fuel assemblies and fuel baskets in the open-caskmodel are represented as three concentric cylinders. The total decay heat from the fuelassemblies is divided between the three cylinders based on their volume. For both models, theeffective thermal conductivities of the cylindrical solid fuel regions are specified. In the closed-cask model, the effective thermal conductivity values, given in Table 2-3, are obtained fromHoltec International (2002). For the open-cask model, the effective thermal conductivity of thefuel region is estimated using the geometric mean method, as described in the Section 3.5.
When fuel assemblies are placed in the fuel basket, the sides are covered by Alloy X basketpanels, and there is little or no room for backfill gas to enter easily from the side. Although thereare holes in the spacer grids and the upper and lower fittings, permitting some fluid flow throughthe fuel assembly, flow resistance through fuel assemblies is expected to be much higher thanwithin the channels located between fuel assemblies in the fuel basket. Therefore, it isconservatively assumed that fluid inside the fuel assembly remains stagnant, and a fuelassembly is modeled as one solid object with an effective thermal conductivity in thefuel-assembly model.
3.5 Effective Thermal Conductivity of Fuel Region
In the closed- and open-cask models, the fuel assemblies, space between fuel assemblies, andfuel basket walls are modeled as homogeneous solid fuel regions with an effective thermalconductivity. When the cask system is closed, the fuel basket and fuel assemblies are filled
3-5
k (adjusted)effair
k (estimated)effair
with helium. Holtec International (2002) used a finite volume method to calculate the effectivethermal conductivity of the fuel region representing the fuel assemblies and fuel basket as afunction of temperature. The reported values are given in Table 2-2.
When the cask is open, helium is replaced by ambient air, and the effective thermal conductivityof the equivalent fuel region changes because the thermal conductivity of air is different fromthat of helium. The following method is adopted to estimate the effective thermal conductivityof the fuel assemblies and fuel basket system filled with ambient air for the thermal simulations. The effective thermal conductivity of a helium-filled fuel assemblies and fuel basket system canbe estimated with several mathematical models for composite materials. Methods forcalculating the effective thermal conductivity (for example, the geometric mean, harmonic mean,and arithmetic mean methods) are described by Beck (1988). The effective thermal conductivityof the fuel region calculated using geometric mean, harmonic mean, and arithmetic meanmethods are 0.69 W/m-K [1.19 BTU/ft-hr-°F], 0.79 W/m-K [1.373 BTU/ft-hr-°F], and1.965 watts/m-K [1.138 Btu/ft-hr-°F], respectively. The reported value of the effective thermalconductivity is 2.59 watts/m-K [1.5 Btu/ft-hr-°F] at 450 °F (Holtec International, 2002). Thecalculated effective thermal conductivity is closest to the reported value for the geometric meanmethod, and it is 24 percent less than the reported value.
Holtec International (2002) developed a two-dimensional model of the fuel assembly and fuelbasket structure using ANSYS® (Swanson Analysis Systems, Inc., 1993) to calculate theeffective thermal conductivity of the helium-filled structure. This approach assumes that fluidwithin the fuel basket is stagnant. Since the geometric mean method under predicts theeffective thermal conductivity for a helium-filled basket, it is assumed that geometric meanmethod also under predicts the effective thermal conductivity of an air-filled basket. The scopeof this work precludes the estimation of effective thermal conductivity for the fuel basket and fuelassembly system using a model similar to the Holtec International (2002) model.
The geometric mean method estimates the effective thermal conductivity of an air-filled basketwith fuel assemblies at 505.37 K [450 °F]. Since the estimated value of the air-filled fuel basketis expected to be under predicted, its value is adjusted by multiplying and dividing with theknown and the estimated value thermal conductivity of the helium-filled fuel assemblies and fuelbasket system, respectively. Thus, the effective thermal conductivity of the fuel basket with24 pressurized water reactor fuel assemblies is estimated by the following expression
k (adjusted) k (estimated)k (known)k (estimated)eff
air effair
effHe
efffHe
=(3-5)
where
— adjusted thermal conductivity of the fuel assemblies and fuelbasket filled with air
— estimated thermal conductivity of the fuel assemblies and fuel
3-6
k (known)effHe
k (estimated)effHe
— thermal conductivity of the fuel assemblies and fuel basket filledwith helium from Holtec International (2002), listed in Table 2-2
— estimated thermal conductivity of the fuel assemblies and fuelbasket filled with helium using the geometric mean method
The estimated thermal conductivity of the fuel region is 1.286 watts/m-K [0.743k (estimated)effair
Btu/ft-hr-°F], and the corresponding adjusted effective thermal conductivity is 1.692 watts/m-K[watts/m-K (0.977 Btu/ft-hr-°F)]. The adjusted effective thermal conductivity isk (adjusted)eff
air
used in the open-cask model for the fuel regions.
4-1
4 MODEL DESCRIPTION AND RESULTS
Model descriptions and results of thermal analysis are presented in this chapter. As describedin Chapter 1, closed-cask, open-cask, and fuel-assembly model are analyzed. The closed- andopen-cask models are simulated using FLUENT, and the fuel-assembly model is simulated withFLOW-3D. The heat source for all three models is consistent with pressurized water reactorfuel assemblies. The model parameters and material properties are given in Chapter 2. A briefoverview of the models follows:
• Closed-Cask Model: A two-dimensional axisymmetric model of a closed HI-STAR 100cask system is used to calculate the temperature profile inside a closed cask. Theresults are compared to the results presented by Holtec International (2002).
• Open-Cask Model: A two-dimensional axisymmetric model of a HI-STAR 100cask system with equivalent fuel region open to the ambient air is used toexamine the effect of fluid flow and the active heat exchange process insidea cask.
• Fuel-Assembly Model: A two-dimensional model simulating the thermal behavior of afuel assembly in contact with ambient air is used to understand fluid flow and activedissipation of heat by conduction and natural convection. The fuel-assembly modelresults are studied for different values of inlet air temperature.
4.1 Closed-Cask Model
The closed-cask model of the HI-STAR 100 system is developed using FLUENT Version 6.2.16. The cask is placed on a concrete pad and exposed to the ambient environment, as shown inFigure 4-1(a). The computational domain of the closed-cask model is presented inFigure 4-1(b), which shows the model setup in FLUENT. The cask centerline is aligned alongthe X axis with the bottom of the concrete pad at X = 0, and the cask radius is aligned in theY direction. As seen in the figure, the X axis is the axis of symmetry in the model, andgravitational acceleration acts along the !X direction. In this model, heat transfer from the fuelbasket to the inner canister shell and from the inner canister shell to the overpack inner wall,takes place via radiation and conduction through helium gas. Heat transfer from the caskexterior surface to ambient air is modeled using the natural convection and radiation boundarycondition defined by Eq. (3-1).
A cask system is filled with pressurized helium. Helium assists in passive rejection of heat fromthe fuel assemblies and also maintains an inert environment. A closed-cask system loaded withspent nuclear fuel is normally placed in the open environment, where the cask may be insolatedduring daylight. The peak temperature and the temperature distribution inside the cask arecalculated with and without insolation. The peak temperature is also compared to thetemperature calculated by Holtec International (2002). The model does not takecredit for internal convection of helium, consistent with the approach adopted by HoltecInternational (2002).
4-2
(a) (b)
Figure 4-1. (a) Schematic Representation of the Closed-Cask Model Physical Domainand (b) Axisymmetry Model of the Cask System in FLUENT
4.1.1 Model Parameters
The geometric model of the closed cask and concrete pad is developed using the preprocessorGAMBIT, which is a part of the FLUENT software package. The preprocessor is used togenerate and mesh the geometric model. The geometric parameters and thermal properties ofthe component materials are provided in Chapter 2. The thermal conductivity of materials isdefined as a piecewise-linear function of temperature, using the data in Tables 2.2 and 2.3. Thethermal conductivities of the component materials at the intermediate temperature (between99.3 °C [200 °F] and 232 °C [450 °F], and between 232 °C [450 °F] and 371.1 °C [700 °F]) isobtained by linear interpolation. In the model, the emissivities of the fuel region and innercanister shell, overpack material, and exposed overpack surface are 0.36, 0.66, and 0.85,respectively. The natural convection heat transfer coefficient for the vertical surface [given byEq. (3-4)] is applied at the interface of the overpack exterior surface and ambient air when thecask is not insolated.
The solar heat input to the exposed surface is determined based on 12-hour insolation. Thesolar heat flux of 775 watts/m2 [800 Cal/cm2] for flat horizontal surfaces and 388 watts/m2
[400 Cal/cm2] for cylindrical curved vertical surfaces of the cask system are consistent with therequirements in 10 CFR 71.71. The insolation on the exposed cask surface is applied by adding a thin layer (one grid-cell thick)of a semitransparent material to the top of the cask exterior surface. It is assumed that the cask
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exterior surface receives the solar insolation from all directions. The cell temperature isspecified as ambient temperature (299.82 K [80 °F]). The thermal conductivity, k, of the layeradjacent to the cask exterior wall is defined as
k htwall= (4-1)
where h is the heat transfer coefficient of the overpack exposed surface [Eq. (3-4)]. The thickness of the transparent wall twall is specified as 0.635 cm [0.25 in]. This approachallows all convection from the overpack exterior surface to be modeled by conduction asspecified by Eq. (3-1).
The thin layer is defined as a semitransparent wall. The absorptivity of the thin layer is specifiedto be zero in the model. Therefore, insolation is not absorbed by the thin layer. The insolationis assumed to be incident on the wall from all directions; therefore, the diffuse fraction of solarinflux is specified as unity in the model. Due to the addition of the thin layer, the cask exteriorsurface becomes an internal surface in the model. The internal emissivity of the exterior surfaceis specified as 0.85 in the model. This approach accounts for radiation heat transfer from caskexterior surface to ambient, as specified by Eq. (3-1).
The cask exterior surface is assumed to be gray for radiation and is assumed to be opaque, soinsolation will be absorbed, emitted, and reflected from the surface. For a gray surface, theabsorptivity is equal to the emissivity. Since the emissivity of the painted surface is 0.85 in themodel, the absorptivity is also 0.85. The reflectivity of the exterior surface is 0.15 (radiation isnot transmitted by the overpack wall), so 15 percent of the incident radiation is reflected.
It is conservatively assumed that all incident solar radiation on the cask surface is absorbed,which requires adjustment of the radiation flux to compensate for reflectivity in the model. Bydividing the incident solar radiation by 0.85, the net input radiation is compensated for the15 percent loss due to reflection.
4.1.2 Model Results
The calculated temperature contours for the cask system, with and without solar radiation, areshown in Figures 4-2(a) and 4-2(b), respectively. The calculated maximum temperature of thecylindrical solid homogeneous fuel region representing the fuel assemblies and fuel basket is619.3 K [655.1 °F] when the cask system is not insolated, with the peak temperature locatedslightly above of the middle of the fuel region. Similarly, the maximum temperature of the fuelregion is 634.4 K [682.2 °F] when the cask system is insolated, again with the peak temperaturelocated slightly above the middle of the fuel region. The calculated peak temperature of the fuelincreases by 15 K [27 °F] in the presence of insolation, and the region above 612 K [641.93 °F]is larger inside an insolated cask.
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(a) (b)
Figure 4-2. Temperature Distribution Inside the HI-STAR 100 Cask System(a) Without Insolation and (b) With Insolation
Holtec International (2002) reported the maximum temperature of the equivalent fuel source tobe 649.1 K [708.7 °F] when the cask is insolated, which is 14.7 K [26.46 °F] higher thanpredicted by this closed-cask model. Holtec International (2002) specified a nonuniform heatgeneration rate along the length of the fuel region in their closed-cask model. The burnupprofile of a pressurized reactor fuel assembly is presented in Figure 4-3. As seen in this figure,the maximum decay heat is emitted at an axial distance of 16.66 to 33.33 percent of the activefuel length from the bottom of the fuel assembly. The temperature contours presented byHoltec International (2002) for the closed-cask model show that the predicted maximumtemperature is located in the lower part of the fuel region {see Figure 4.4.17 in the HI-STAR 100Final Safety Analyses Report, Holtec International (2002)}. The calculated maximumtemperature is only 2.26 percent less than the maximum temperature predicted by HoltecInternational (2002) (the relative difference with respect to ambient temperature is 4.2 percent),suggesting that the models are in reasonable agreement. Therefore, the uniform heatgeneration rate is also applied in the open-cask and fuel-assembly models.
Holtec International (2002) developed a closed-cask model for a cask system that is placed onan independent spent fuel storage installation pad and is surrounded by other casks. Theneighboring cask systems will block the radiation heat transfer from the modeled cask system. The value of the dimensionless view factor, denoted by F1A in Eq. (3-1), represents the extent ofradiation blockage due to neighboring cask systems. Holtec International (2002) used ANSYSto determine the view factor of the most adversely located cask system placed on anindependent spent fuel storage installation pad. Therefore, the difference in predictedmaximum temperature may also be attributed to the view factor, but it is not clear what value ofview factor was used by Holtec International (2002) in the boundary condition [Eq. (3-1)]. However, the view factor is not likely to significantly change the fuel temperature cask becausethe cask surface temperatures are not high enough to affect the radiation heat loss.
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Figure 4-3. Normalized Fuel Burnup Rate Along the Length of a Pressurized WaterReactor Fuel Assembly. The Figure Shows the Burnup Data Listed in Table 2.1.8 in the
HI-STAR 100 Final Safety Analysis Report (Holtec International, 2002).
4.2 Open-Cask Model
A two-dimensional axisymmetric model of an open HI-STAR 100 cask system is described inthis section. The overpack and inner canister lids are removed in the open-cask model and fuelassemblies are in contact with ambient air. An active exchange of air between the cask andsurrounding atmosphere would take place for an open cask. The ambient air would enter thecask through colder regions and exit from hotter regions, with the temperature of entering andexiting air determined by thermal conditions inside the cask. To represent air exchangebetween cask and its surroundings, the model consists of an open cask and an hemisphericaldome of air. A schematic diagram of the open-cask model physical domain is presented inFigure 4-4(a). The diameter of the dome is chosen to be large enough so that the ambient aircan enter or leave the computational domain at atmospheric pressure. The computationaldomain and mesh of the open-cask model are presented in Figure 4-4(b). The computationaldomain is only half of the physical domain because of axisymmetry. In the model, the cask axisis aligned along the X axis, and the radius is aligned in the Y direction. As seen in the figure,the X axis is the axis of symmetry in the model, and gravitational acceleration acts along the !Xdirection. In the model, the boundary of the dome is specified as a constant-pressure boundarycondition. The temperature of the air entering the dome is 299.82 K [80 °F], and thetemperature of the air leaving the dome is determined by the model. The radius of thehemispherical dome is 25.4 m [1,000 in], which is approximately five times the height ofthe cask.
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(a)
(b)
Figure 4-4. (a) The Physical Domain of the Open-Cask Model and(b) The Computational Domain of the Open-Cask Model
In this model, the 24 pressurized water reactor fuel assemblies and fuel basket are grouped andrepresented in two ways:
(A) A cylindrical solid homogeneous fuel region with an effective thermal conductivity.
(B) Three concentric cylindrical solid homogeneous fuel regions with annular gaps betweencylinders. The annular gap provides channels for fluid flow.
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In representation (A), the effective thermal conductivity of the fuel medium is calculatedby replacing the helium with air in the fuel basket as described in Section 3.5, but is otherwiseidentical to the closed-cask model. The effective thermal conductivity fuel basket and fuelassemblies with air is lower than the effective thermal conductivity with helium.
In representation (B), the fuel assemblies and fuel basket are represented as three cylindricalsolid homogeneous fuel regions. These three fuel regions represent segments of the fuelbasket with 4, 8, and 12 fuel assemblies, respectively. A schematic diagram of thisrepresentation is shown in Figure 4-5. The inner and outer radii of the fuel regions are givenin Table 4-1.
The following method is adopted to calculate the inner and outer radii of the fuel regions inrepresentation (B). The cross-sectional length and width of a fuel assembly is 22.66 cm[8.92 in], and the assembly is covered by 0.79 cm [5/16 in] thick side panels. Only two sidepanels are considered part of the fuel assembly and the other two panels are replaced byambient air. This is a reasonable approximation because side panels only conduct heat, andtheir thermal conductivity is much higher than that of air. The cross-sectional area occupied byfour fuel assemblies and side panels (denoted by numbers 9, 10, 15, and 16 in Figure 4-5)located at the center of the fuel basket is 2199.71 cm2 [340.96 in2]. Therefore, the radius of thefirst equivalent cylindrical fuel region R1 is 26.46 cm [10.4177 in].
Figure 4-5. A Schematic Representation of an MPC–24 Fuel Basket (On the Left)(Holtec International, 2002) and Its Equivalent Representation in Open-Cask Model(On the Right). The Fuel Assemblies and Fuel Basket Are Represented As Three
Cylindrical Homogeneous Solid Fuel Regions. The Innermost Cylinder On the RightRepresents Fuel Assemblies 9, 10, 15, and 16. The Next Cylinder Represents FuelAssemblies 4, 5, 8, 11, 14, 17, 20, and 21. The Outermost Cylinder Represents the
Remaining Fuel Assemblies.
4-8
R (23.8 10 / 16)2
2
=−
π
R R 8 (8.92 5 / 16)3 2
2
= + × +π
R R 12 (8.92 5 / 16)4 5
2
= − × +π
Table 4-1. Dimensions of the Fuel Regions in the Open-Cask Model With Flow Channels
ComponentInner Radius
{m [in]}Outer Radius
{m [in]}
First Fuel Region 0.0 [0.0] 0.2646172 [10.418]
Second Fuel Region 0.332105 [13.075] 0.5003292 [19.698]
Third Fuel Region 0.637794 [25.11] 0.785368 [30.92]
These four fuel assemblies are encased inside the 60.45 cm [23.8 in] basket structure (seedrawing #3926 in the HI-STAR 100 Final Safety Analysis Report, Holtec International, 2002). The outer radius of the annular space R2 is determined by
R2 is equal to 33.2 cm [13.1 in]. This is also the inner radius of the second fuel region.
The cross-sectional surface area of the next eight fuel assemblies (marked as 4, 5, 8, 11, 14,17, 20, and 21 in Figure 4-5) is 4399.43 cm2 [681.91 in2]. Therefore, the outer radius, R3, of thesecond fuel region is determined by the following expression
R3 is equal to 50.0334 cm [19.6982 in].
The outer radius of the third fuel region R5 is equal to 78.5368 cm [30.92 in], the same as theradius of the single equivalent fuel region in representation (A). The inner radius of this fuelsource, R4, is determined by subtracting the cross-sectional the area of 12 fuel assemblies fromthe area of the single fuel region. Thus, R4 is calculated using the following expression
R4 is equal to 63.7766 cm [25.1089 in]. The second fuel region has twice the volume of the firstfuel region, and the third region is three times larger than the first one. The power density of allthree fuel regions is the same.
The fuel basket for 24 pressurized water reactor fuel assemblies has 7.1 cm [2.8 in] undercutsto provide for airflow. Therefore, in the concentric-cylindrical representation, the fuel regions
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are raised by 7.1 cm [2.8 in] to provide passage of air underneath them. The verticalcross-sectional schematic diagram of the cask system placed on the concrete pad is presentedin Figure 4-6. As seen in the figure, the fuel basket and fuel assemblies are represented asthree concentric solid cylindrical fuel regions placed 7.1 cm [2.8 in] above the inner canistershell base plate. The height of these fuel regions is identical.
4.2.1 Model Parameters
The effective thermal conductivity of the fuel regions is 1.692 W/m-K [0.977 Btu/ft-hr-°F] in bothrepresentations of the fuel assemblies and fuel basket system. The thermal conductivities ofother component materials are the same as those used in the closed-cask model (Tables 2-2and 2-3). The emissivities of the fuel region and inner canister shell, overpack material, andexposed overpack surface are 0.36, 0.66, and 0.85, respectively. Separate simulations wererun to represent (i) no flow, (ii) laminar flow, and (iii) turbulent flow conditions. Heat transferfrom the overpack exterior surface to the atmosphere is determined by the solution ofconvective and radiation heat transfer equations. The k-epsilon and k-omega turbulent flowmodels are used for simulating turbulent fluid flow inside and outside the cask. Enhanced walltreatment and full buoyancy effects are activated in the k-epsilon turbulent-flow model. Thetransitional flow option was activated for the k-epsilon model. Both turbulent-flow models canbe applied for buoyancy-driven flows with low Reynolds numbers (Fluent, Inc., 2006).
Figure 4-6. The HI-STAR 100 Cask System With Three Concentric Cylindrical Fuel Regions
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4.2.2 Results
The results of the simulations for the open-cask model with a cylindrical solid homogeneous fuelregion {representation (A)} are presented first. The calculated maximum temperature of the fuelsource is 765.9 K [918.9 °F] with radiation and conduction heat transfer without air movement,and the maximum temperature of the fuel source is 737.9 K [868.5 °F] under laminar flowconditions. The temperature distribution inside the cask system for these two conditions ispresented in Figure 4-7. The thermal profile of the cask system under turbulent flow conditionsis presented in Figure 4-8. The maximum temperature of the fuel region is 730.6 K [855.4 °F]for the k-epsilon turbulent model, and 729.9 K [854.1 °F] for the k-omega turbulent model. Thecalculation results are summarized in Table 4-2. The radiation and conduction heat transfer are92.44 and 7.54 percent, respectively, under the no flow condition. When flow is allowed tooccur, heat is removed by convection in addition to the radiation and conduction processes.
(a) (b)
Figure 4-7. Temperature Distribution Inside an Open HI-STAR 100 Cask System (a) No Flow Condition (i.e., Only Radiation and Conduction Heat Transfer)
and (b) Laminar Flow Condition
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(a) (b)
Figure 4-8. Temperature Distribution Inside an Open HI-STAR 100 Cask System (a) K-Epsilon Turbulent Flow Model and (b) K-Omega Turbulent Flow Model
Table 4-2. Summary of Calculated Results for the Open HI-STAR Cask SystemWith a Cylindrical Solid Homogeneous Fuel Region
Flow Model
MaximumTemperature K
[°F]
Percentage HeatDissipation by
Radiation
Percentage HeatDissipation by
Conduction andConvection
No Flow 765.9 K [918.9 °F]
92.44 7.56
Laminar Flow 737.9 K[868.5 °F]
68.08 31.92
K-Epsilon TurbulentFlow
730.6 K [855.4 °F]
66.42 33.58
K-Omega TurbulentFlow
729.9 K [854.1 °F]
64.7
35.3
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As a result, the maximum temperature of the fuel region decreases to 737.9 K [868.5 °F]. Thepercentage of conduction and convection heat transfer increases to 33.58 percent for thek-epsilon turbulent flow model and 35.3 percent for the k-omega turbulent flow model. Theseresults indicate that natural convection aids in heat removal from the fuel region; however, thedrop in peak temperature is only 4.5 percent with respect to the peak temperature of an opencask with conduction and radiation only. These results are expected because a cylindrical solidhomogeneous fuel region representation of the fuel assemblies and fuel basket has a smallsurface area-to-volume ratio for convective heat transfer.
When the fuel basket and fuel assemblies are represented in three fuel regions {representation(B)}, the maximum temperature is 754.5 K [898.4 °F] with radiation and conduction heattransfer. In this case, 92.9 percent of the heat is transferred by radiation under the no-flowcondition, and the maximum temperature is only 10 K [18 °F] less than the single fuel regionrepresentation. The heat source density is higher in the three cylindrical fuel regionsrepresentation due to introduction of a gap between fuel regions. As a result, one would expecthigher peak temperatures compared to the comparable single fuel region. The annular gap aidsin radiation heat transfer between fuel regions, which is not available in the single fuel regionrepresentation. Therefore, the effective thermal conductivity of the annular gap is higher thanthe thermal conductivity of the single fuel region, and the lower value of peak temperature isobserved. The maximum temperature drops to 501.3 K [442.7 °F] when fluid is allowed toconvect as laminar flow. In this case, 74.4 percent of the heat is dissipated by conduction andconvection. The larger surface area enables the fluid to remove heat more effectively from thefuel regions. The temperature distribution inside the open cask for no flow and laminar flow arepresented in Figure 4-9. The maximum temperature of the fuel decreases to 426.7 K [308.4 °F]when the k-epsilon turbulent-flow model is employed. The conduction and convection heat lossis 85.3 percent. However, the maximum temperature of the fuel is 457.1 K [363.1 °F] when thek-omega turbulent model is used. The maximum temperature using the k-epsilon model is 30K[54 °F] less than using the k-omega model. This difference is attributed to the buoyancy effectused in the k-epsilon model, which is not considered in the k-omega model. The k-epsilonbuoyancy effect in the model is responsible for an enhanced heat dissipation rate, so thecalculated maximum temperature is lower. The temperature distribution inside the cask for theturbulent- flow models is presented in Figure 4-10. The calculation results are summarizedin Table 4-3.
The following observations are made regarding the temperature distributions in therepresentation (B) of fuel assemblies and fuel basket:
• The maximum temperature occurs in the central fuel region under no flow, laminar flow,and turbulent flow conditions.
• The location of the maximum temperature is in the middle of the central fuel region forno flow conditions; however, the maximum temperature is located in the upper part ofthe central fuel region for laminar fluid flow.
• The location of maximum temperature is in the upper part of the central fuel region forboth turbulent flow models.
• The other two fuel regions are colder than the central fuel region.
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(a) (b)
Figure 4-9. Temperature Distribution Inside an Open HI-STAR 100 Cask System WithRadiation and Conduction Heat Transfer (a) Without Flow and (b) Under Laminar FlowConditions. The Results Are for the Case When the Fuel Basket and Fuel Assemblies
Are Represented By Three Fuel Regions With Flow Channels in Between.
(a) (b)
Figure 4-10. Temperature Distribution Inside an Open HI-STAR 100 Casket SystemWith the (a) K-Epsilon Turbulent Flow Model and (b) K-Omega Turbulent Flow Model.
These Results Are for the Case When the Fuel Basket and Fuel Assemblies AreRepresented By Three Fuel Regions With Flow Channels In Between.
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Table 4-3. Summary of Calculated Results for the Open HI-STAR Cask System WithThree Concentric Cylindrical Fuel Regions and Flow Channels In Between
Flow Model
MaximumTemperature
[°F]
Percentage HeatDissipation byRadiation Heat
Transfer
Percentage HeatDissipation by
Conduction andConvection
Heat Transfer
No Flow 754.5 K [898.4 °F]
92.9 7.1
Laminar Flow 501.3 K[442.7 °F]
25.6 74.4
K-Epsilon TurbulentFlow
426.7 K[308.4 °F]
14.7 85.3
K-Omega TurbulentFlow
457.1 K[363.1 °F]
25.6 74.4
• For both the laminar and turbulent flow, air enters through the periphery and exitsat the center. This observation agrees with the assumption that air fluid isexpected to enter into the colder regions and exit from the hotter regions ofthe cask.
4.3 Fuel-Assembly Model
The equivalent fuel representation of the fuel basket and fuel assemblies in the open-caskmodel does not provide a temperature distribution at the level of individual fuel assemblies. Moreover, the effect of convective heat transfer cannot be accurately estimated in the open-cask model because the gap between fuel regions is only an approximation of the flow channelwidth in the fuel basket. Accordingly, the fuel-assembly model is developed to simulate thethermal behavior of an individual fuel assembly in the open cask. The model considersconduction within a fuel assembly and the surrounding air, as well as convection by moving air. The model does not consider radiation transfer, which would tend to lower fuel assemblytemperatures through heat loss toward the overpack.
A schematic diagram of a inner fuel canister cross section with an MPC–24 fuel basket is shownin Figure 4-11. The fuel-assembly model consists of a fuel assembly and an adjacent channelfor airflow near the axis of the fuel basket, as shown in Figure 4-12. The fuel-assembly modelrepresents a single cell in an extensive array of identical cells, which is most representative oftwo center fuel assemblies and the channel between them, as indicated in Figure 4-11.
A two-dimensional model can only provide an approximation of the three-dimensionaltemperature profile within a fuel assembly. A single fuel assembly can be represented in twodimensions either as a slab or a cylinder; both approaches distort heat flow and thermal
4-15
Figure 4-11. Cross Section of the Inner Canister Containing the Pressurized WaterReactor Fuel Basket With 24 Inserts (Holtec International, 2002). The Ninth Fuel
Assembly is Simulated in the Two-Dimensional Fuel Assembly Model.
(a) (b)
Figure 4-12. Schematic Diagram of the Fuel-Assembly Model(a) Represents a Fuel Assembly and (b) Its Model Representation
4-16
patterns within the fuel assembly to a certain extent. The temperature at the interface betweenthe fuel assembly and the air gap may be of primary interest, and both approaches can providereasonable approximations near the interface. Without a firm basis for favoring one approachover another, the slab model is adopted with the intent of reasonably representing the air andfuel assembly interface temperatures.
The model is developed in Cartesian coordinates, with the X and Y axes representing thehorizontal and vertical directions, respectively, and with the Z axis perpendicular to the XYplane. The modeled fuel assembly is 3.5 m [137.8 in] high and 0.1135 m [4.47 in] wide. Thechannel for airflow is 1.538 cm [0.60550 in], half the distance between two adjacent fuelassemblies. Symmetry boundary conditions on the right and left, as shown in Figure 4-12,account for the thermal effect of identical adjacent fuel assemblies; periodic boundaryconditions in the Z direction perform the same function.
4.3.1 Model Parameters
The thickness in the Z direction is arbitrary for a two-dimensional model. For consistency withthe cask simulations, the total heat load to the cell is 792 W, representing a pressurized waterreactor fuel assembly that generates a maximum power of 792 W after 5 years of initial wetstorage (Holtec International, 2002). This amount of heat is dissipated to the air across theperimeter of the fuel assembly. To provide the same rate of heat dissipation across theperimeter, the total thickness in the Z direction was equal to the perimeter of the fuel assembly,90.64 cm [35.68 in]. The fuel assembly volume in the model is twice that of an actual one, thusthe power density is half that of an actual fuel assembly, and the temperature field near thecenter of the fuel assembly may be distorted. However, the thermal flux to the air per unit of thefuel assembly surface area is captured, implying that air temperatures and fuel temperatures atthe interface are reasonably well represented with this approximation.
The equivalent thermal conductivity of the air-filled fuel assembly is 0.16 W/m-K[0.092 Btu/ft-hr-°F], obtained using the geometric mean method described in Section 3.5and assuming that the Alloy X and Boral panels are part of the fuel assembly and have thesame effective thermal conductivities as the fuel assembly.
The open-cask simulations suggest that cool air enters the cask through the colder regions andexits from the hotter regions and show that the fuel basket with multiple fuel assemblies is hotterin the center of the basket and colder toward the periphery. In general, air enters the cask inthe gap between the fuel basket and the inner canister shell, moves down the annular spacebetween basket and shell, passes through undercuts beneath the fuel basket, and returns to theatmosphere via channels between fuel assemblies. Air temperature rises as it moves along thispath. Open-cask simulations with laminar or turbulent air movement shown in Figures 4-9 and4-10 have air temperatures in the undercut region in the approximate range of 330 to 400 K[134 to 260 °F].
The fuel-assembly model neglects detailed consideration of air movement, except in the gapadjacent to the fuel assembly. Both the top and bottom of the assembly are simulated as openboundaries, with a uniform constant pressure fixed at the ambient atmospheric pressure. Thedirection of air movement across an open boundary is a result of conditions within the domain. Air exiting an open boundary leaves at the calculated temperature adjacent to the boundary,whereas incoming air has a specified temperature. Heating within the fuel assembly ensures
4-17
that air moves unidirectionally from bottom to top, so the temperature of incoming air at thebottom boundary must be specified. Two separate simulations were run, with inlet temperaturesof 350 and 400 K [170.33 and 260.33 °F] to represent low and high inlet temperatures.
4.3.2 Results
The steady-state temperature profile of the fuel assembly with air entering at 350 K [170.33 °F]is presented in Figure 4-13, with the upper and lower parts of the fuel assembly shown inFigure 4-13(a) and (b), respectively. Similarly, the temperature profile of the fuel assembly withair entering at 400 K [266.33 °F] is presented in Figure 4-14. The fuel assembly attains amaximum temperature of 530 K [494.33 °F] with air inlet temperature at 350 K [170.33 °F]. Themaximum fuel assembly temperature increases by approximately 30 K [54 °F] when theincoming air is 50 K [90 °F] warmer; increased airflow driven by warmer air compensates tosome degree for the reduced heat removal rate caused by a lower thermal differential betweenthe fuel assembly and air.
The airflow in the gaps between the assemblies is similar to the classical laminar boundary layerin natural convection on a hot vertical flat plate, with a peak in fluid velocity near the hot wall andslower velocities in the cooler center of the gap. The maximum centerline air velocity is 0.8 m/s[1.05 ft/s] for laminar flow in the cool inlet simulation {i.e., air enters at 350 K [170.33 °F]}, and islocated approximately 6 mm [0.24 in] below the top boundary. The minimum velocity,approximately 0.5 m/s [0.66 ft/s], is found in the center of the gap, which is the plane ofsymmetry in the model. Simulations performed with the mixing length turbulence model yieldessentially identical results to the laminar-flow model, presumably because the fluid velocitiesare small. It can be concluded that, due to narrow channel width between fuel assemblies, thefluid flow field is predominately laminar.
(a) (b)
Figure 4-13. Steady-State Temperature Distribution of the Fuel Assembly in theFuel-Assembly Model for Air Entering at 350 K [170.33 °F]. The Figure Represents
Temperature Distribution in (a) the Upper Part of the Fuel Assembly and in (b) The Lower Part of the Fuel Assembly.
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(a) (b)
Figure 4-14. Steady-State Temperature Distribution of the Fuel Assembly in theFuel-Assembly Model for Air Entering at 400 K [266.33 °F]. The Figure RepresentsTemperature Distribution in (a) the Upper Part of the Fuel Assembly, and in (b) the
Lower Part of the Fuel Assembly.
5-1
5 SUMMARY
Staff is developing capabilities and expertise in thermal modeling in preparation for reviewingpotential DOE thermal analyses. Preliminary analyses presented in this report explore heattransfer within a cask system in both open and closed conditions. These analyses provide abasis for assessing the capabilities of commercially available computational fluid dynamicssoftware and enhance understanding of modes of heat transfer (i.e., conduction, naturalconvection, and radiation) from fuel assemblies under ambient conditions.
This activity started in fiscal year 2005, when DOE-planned operations at Yucca Mountainsurface facilities included dry transfer of fuel assemblies (DOE, 2005). The thermal models ofthe cask systems investigated in these preliminary analyses are based on theseDOE-planned activities.
In fiscal year 2006, DOE proposed changes to the design and operations of Yucca Mountainsurface facilities (Harrington, 2006) as a result of the newly proposed transport, aging, anddisposal canister system. In the new approach, fuel would arrive at the repository loaded into atransportation, aging, and disposal canister, and the fuel assemblies would not be exposed toair under normal operations. Even under the new disposal concept, experience and capabilitiesgained during this activity will be useful in future thermal analyses.
Based on studies presented in this report, FLUENT can, without modification, effectivelysimulate the thermal condition of fuel assemblies in a cask system. The off-the-shelf version ofFLUENT is capable of modeling conduction, radiation, and natural-convection heat transfer andcan specify thermal conductivities for a material as a function of temperature. Thesecapabilities are demonstrated in the cask models developed in this report. The off-the-shelfversion of FLOW-3D, on the other hand, does not consider radiation heat transfer and cannotdefine thermal conductivity of a material as a function of temperature. User-defined modulescan be added in FLOW-3D to include radiation heat transfer for simple geometries (Green andManepally, 2006), as can the specification of temperature-dependent thermal conductivities. However, significant effort is required to add these capabilities in FLOW-3D.
The HI-STAR 100 cask system certified by NRC for transportation and interim storage is usedas an example cask system for thermal analyses. Three representative models were analyzedto assess temperature inside the cask: (i) a closed-cask model, (ii) an open-cask model, and(iii) a fuel-assembly model within an open cask.
The helium-filled closed-cask system includes 24 pressurized-water reactor fuel assemblies in acanister. Energy exchange between the cask system and the ambient environment is analyzedfor a dry storage condition using a two-dimensional model in cylindrical coordinates. Theindividual fuel assemblies and gaps between the assemblies are represented by a cylindricalhomogeneous solid fuel region. Model calculations qualitatively match independent calculationsby Holtec International (2002), although a different modeling assumption for the decay heatsource of fuel region yields somewhat different temperature fields in the two models. Simulatedpeak temperatures in the closed-cask model is 14.7 K [26.5 °F] less than calculated by HoltecInternational (2002), in part because the heat source distribution in the fuel region consideredby Holtec International (2002) is nonuniform with peak source rate approximately 10 percenthigher than the average rate, while the example calculation considers a spatially uniform sourcefor simplicity. The calculated deviation between maximum fuel temperature and ambient
5-2
temperature for the two models differs by approximately 4.2 percent with respect to ambienttemperature (299.82 K [80 °F]), suggesting that the models are in reasonable agreement asidefrom the heat source distribution.
The open-cask system is similar to the closed-cask model, except that the overpack and innercanister lids have been removed, and the helium has been replaced with air. Tworepresentations of the fuel assemblies and fuel basket are considered: (i) the fuel region usedfor the closed-cask calculation and (ii) three concentric cylindrical solid homogeneous fuelregions with annular gaps between them. The total void volume in the annular gaps isapproximately equal to the total void space in the fuel assemblies and fuel basket structure,although the gap width is larger than typical gaps between fuel assemblies. Total heatproduction is the same in the two approaches, although the heat source density in the fuelregions is larger in the three separate homogeneous fuel regions to compensate for the annularspace. Several observations can be made from the open-cask system:
• Gaps appear to enhance radial energy transfer, evidenced by comparing theno-flow cases for the two representations. Lower peak temperatures areseen in the three fuel regions model without air flow, despite higherheat-source densities.
• Annular spaces between fuel regions greatly increase the efficiency of heatremoval and also reduce the influence of radiation transfer. Without flow (threeconcentric cylindrical solid homogeneous fuel regions), the maximumtemperature is about 455 K [819 °F] above the ambient temperature, and almost93 percent of heat dissipation is by radiation heat transfer. With flow, themaximum temperature above ambient is between 126 K [226.8 °F] and 201 K[361.8 °F], with radiation heat transfer between 14.7 and 25.6 percent of totalheat dissipation.
• The peak temperature of the fuel regions decreases with turbulent flow modelswhen compared to the laminar-flow model, indicating that turbulence offerssignificantly greater cooling capability.
• The representation of flow in the annular gaps significantly lowers the maximumtemperature of the fuel regions, and neglect of flow in the gaps yields the largerpeak temperatures. The fluid flow in the case of three concentric cylindricalhomogeneous fuel regions representation may yield a lower-bound estimate, asthe annular space imposes unrealistically small amounts of drag and overpredicts volumetric air flow.
The fuel-assembly model considers a fuel assembly near the center of an open-cask as well asthe gap between two assemblies. The gap has the physical dimensions typical of an actualgap, rather than being the result of a volumetric constraint as in the open-cask model. Thusconvection was more closely represented relative to the open-cask model. The fuel-assemblymodel confirms that internal convection is an important mode of heat transfer for removingdecay heat from fuel assemblies, even with apertures representative of the gap betweenadjacent fuel assemblies and high inlet air temperatures. The fuel-assembly model agrees withthe open-cask model in that the location of peak temperature is near the upper part of the fuelassembly. This model indicates that the three separate fuel regions representation in the
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open-cask model may represent a lower bound for fuel temperature. In this model, the narrowgap between assemblies appears to constrain flow velocities sufficiently to make the particularchoice of flow model (i.e., either laminar or turbulent flow) unimportant.
This work helped CNWRA develop an understanding of issues related to thermal analysis of thecask system. If necessary, the capabilities acquired in this work can be extended to develop afull-scale three-dimensional heat transfer model of the proposed transportation, aging, anddisposal canister. A detailed three-dimensional model would require accurate geometricrepresentation of the canister, temperature-dependent thermophysical properties of componentmaterials, and a flow model that adequately describes the fluid motion of backfilled gas insidethe canister. The detailed three-dimentional model could be used to estimate the effect ofinternal convection on heat transfer from fuel assemblies in a transportation, aging, anddisposal canister.
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