THERMAL MODELING OF A STORAGE CASK SYSTEM: CAPABILITY DEVELOPMENT

Prepared for

U.S. Nuclear Regulatory Commission Contract NRC–02–02–012

Prepared by

P.K. Shukla1 B. Dasgupta1 S. Chocron2 W. Li2 S. Green2

1Center for Nuclear Waste Regulatory Analyses 2Southwest Research Institute® San Antonio, Texas

May 2007 ABSTRACT

The objective of the numerical simulations documented in this report was to develop a capability to conduct thermal analyses of a cask system loaded with spent nuclear fuel. At the time these analyses began, the U.S. Department of Energy (DOE) surface facility design at the potential high-level waste repository at Yucca Mountain included the option of dry transfer of spent nuclear fuel from transportation casks to the waste packages (DOE, 2005; Bechtel SAIC Company, LLC, 2005). Because the temperature of the fuel and cladding during dry handling operations could affect their long-term performance, CNWRA staff focused on developing a capability to conduct thermal simulations. These numerical simulations were meant to develop staff expertise using complex heat transfer models to review DOE assessment of fuel cladding temperature. As this study progressed, DOE changed its design concept to include handling of spent nuclear fuel in transportation, aging, and disposal canisters (Harrington, 2006). This new design concept could eliminate the exposure of spent nuclear fuel to the atmosphere at the repository surface facilities. However, the basic objective of developing staff expertise for thermal analysis remains valid because evaluation of cladding performance, which depends on thermal history, may be needed during a review of the potential license application. Based on experience gained in this study, appropriate heat transfer models for the transport, aging, and disposal canister can be developed, if needed.

Two computational fluid dynamics software packages, FLUENT® (Fluent, Inc., 2005) and FLOW-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 cask system for developing numerical models in this study. At the time of these analyses, the design of a transportation, aging, and disposal canister was not available; however, it was expected that the design of the proposed canister would be analogous to a dry storage cask system such as HI-STAR 100. The results in this report are not a definitive thermal analysis of the fuel assemblies in the cask system; they are used only to understand the simulation tools and mechanisms 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 a two-dimensional axisymmetric mode was used for the first two cases, and the FLOW-3D code was used for thermal analysis of the fuel-assembly model.

Results from the closed-cask simulation compared well with those reported by Holtec (Holtec International, 2002), suggesting that the model in FLUENT (Fluent, Inc., 2005) was properly constructed. In the open-cask simulation, the results indicated that internal convection strongly influences heat transfer from fuel assemblies. However, these results remain to be verified by developing a three-dimensional heat transfer model of the HI-STAR 100 cask system. Natural convection 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 determining the 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.

ii DOE. “Categorization of Event Sequences for License Application.” 000–00C–MGRO–00800–000–00B. Rev. 00B ICN00. Las Vegas, Nevada: Office of Civilian Radioactive 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 Storage System.” Marlton, New Jersey: Holtec International. 2002.

iii CONTENTS

Section Page

ABSTRACT ...... ii FIGURES...... vi TABLES...... vii ACKNOWLEDGMENTS ...... viii

1 INTRODUCTION ...... 1-1 1.1 Background ...... 1-1 1.2 Objective...... 1-2 1.3 Scope and Organization of the Report ...... 1-2 1.4 Assumptions...... 1-3

2 DESCRIPTION OF THE CASK SYSTEM AND MODEL PARAMETERS ...... 2-1 2.1 Geometric Description ...... 2-1 2.1.1 Inner Canister ...... 2-1 2.1.1.1 Fuel Basket ...... 2-1 2.1.1.2 Fuel Assembly ...... 2-2 2.1.2 Overpack...... 2-3 2.2 Material Properties ...... 2-4 2.2.1 Thermal Conductivities ...... 2-4 2.2.2 Surface Emissivities ...... 2-5 2.2.3 Fluid Properties ...... 2-5 2.2.3.1 Thermal Conductivity, Viscosity, and Heat Capacity .... 2-5 2.2.3.2 Density...... 2-7 2.3 Concrete Pad ...... 2-8 2.4 Thermal Conditions ...... 2-8 2.4.1 Heat Load of the Cask ...... 2-8 2.4.2 Ambient Condition ...... 2-8

3 MODELING APPROACH ...... 3-1 3.1 Description of Computational Fluid Dynamics Codes ...... 3-1 3.1.1 FLUENT ...... 3-1 3.1.2 FLOW-3D ...... 3-1 3.2 Model Setup ...... 3-2 3.3 Model Boundary Conditions ...... 3-2 3.3.1 Closed-Cask Model ...... 3-2 3.3.2 Open-Cask Model ...... 3-4 3.3.3 Fuel-Assembly Model ...... 3-4 3.4 Model Simplifications ...... 3-4 3.5 Effective Thermal Conductivity of Fuel Region ...... 3-4

4 MODEL DESCRIPTION AND RESULTS...... 4-1 4.1 Closed-Cask Model ...... 4-1 4.1.1 Model Parameters ...... 4-2 4.1.2 Model Results ...... 4-3

iv CONTENTS (continued)

4.2 Open-Cask Model ...... 4-5 4.2.1 Model Parameters ...... 4-9 4.2.2 Results ...... 4-10 4.3 Fuel-Assembly Model ...... 4-14 4.3.1 Model Parameters ...... 4-16 4.3.2 Results ...... 4-17

5 SUMMARY...... 5-1

6 REFERENCES...... 6-1

v FIGURES

Figure Page

2-1 (a) Two-Dimensional and (b) Three-Dimensional View of the HI-STAR 100 Cask 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) Without Insolation and (b) With Insolation ...... 4-4 4-3 Normalized Fuel Burnup Rate Along the Length of a Pressurized Water Reactor Fuel 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 Computational Domain 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 . . 4-9 4-7 Temperature Distribution Inside an Open HI-STAR 100 Cask System (a) No Flow Condition (i.e., Only Radiation and Conduction Heat Transfer) ...... 4-10 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 ..... 4-11 4-9 Temperature Distribution Inside an Open HI-STAR 100 Cask System With Radiation and Conduction Heat Transfer (a) Without Flow ...... 4-13 4-10 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 ..... 4-13 4-11 Cross Section of the Inner Canister Containing the Pressurized Water Reactor Fuel Basket With 24 Inserts (Holtec International, 2002) ...... 4-15 4-12 Schematic Diagram of the Fuel-Assembly Model (a) Represents a Fuel Assembly and (b) Its Model Representation ...... 4-15 4-13 Steady-State Temperature Distribution of the Fuel Assembly in the Fuel-Assembly Model For Air Entering At 350 K [170.33 °F]...... 4-17 4-14 Steady-State Temperature Distribution of the Fuel Assembly in the Fuel-Assembly Model For Air Entering at 400K [266.33 °F] ...... 4-18

vi TABLES

Table Page

2-1 Dimensions of HI-STAR 100 Cask System Components ...... 2-2 2-2 Thermal Conductivity of HI-STAR 100 Cask System Materials ...... 2-4 2-3 Parameter Values Used to Calculate Effective Intermediate Shell Thermal Conductivity of Overpack ...... 2-6 2-4 Calculated Values [Using Eq. (2-1)] of Effective Intermediate Shells (Overpack-Carbon) Thermal Conductivity ...... 2-6 2-5 Surface Emissivity of Components Used in HI-STAR 100 Cask System ...... 2-6 2-6 Thermal Conductivity of Helium and Air ...... 2-7 2-7 Properties of Helium and Air ...... 2-7

4-1 Dimensions of the Fuel Regions in the Open-Cask Model With Flow Channels .... 4-8 4-2 Summary of Calculated Results for the Open HI-STAR Cask System With a Cylindrical Solid Homogeneous Fuel Region ...... 4-11 4-3 Summary of Calculated Results for the Open HI-STAR Cask System With Three Concentric Cylindrical Fuel Regions and Flow Channels In Between ...... 4-14

vii ACKNOWLEDGMENTS

This report was prepared to document work performed by the Center for Nuclear Waste Regulatory Analyses (CNWRA) for the U.S. Nuclear Regulatory Commission (NRC) under Contract No. NRC–02–02–012. The activities reported here were performed on behalf of the NRC Office of Nuclear Material Safety and Safeguards, Division of High-Level Waste Repository Safety. The report is an independent product of CNWRA and does not necessarily reflect the views or regulatory position of NRC.

The authors would like to thank S. Stothoff for the technical review, K. Das for the concurrence review, and B. Sagar for the programmatic review of this report. The authors also appreciate B. Street for providing word processing support and P. Mackin for editorial support in preparation of this document.

QUALITY OF DATA, ANALYSES, AND CODE DEVELOPMENT

DATA: All CNWRA-generated original data contained in this report meet the quality assurance requirements described in the Quality Assurance Manual. Data used in this report are primarily derived from other publicly available sources. Each data source is cited in this report and should be consulted for determining the level of quality for those cited data. The modeling work is documented in CNWRA scientific notebook number 704E.

ANALYSES AND CODES: The computational fluid dynamics analyses presented in this report were conducted using FLUENT®, Version 6.2.16 (Fluent, Inc., 2005). This version of the software has been validated and is under CNWRA configuration control. The computational fluid 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 is under CNWRA configuration control. Spreadsheet calculations were accomplished using Microsoft® Excel® 97 SR–2 (Microsoft Corporation, 1997). Additional calculations were performed 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: Microsoft Corporation. 1997.

viii 1 INTRODUCTION

1.1 Background

The operations at the surface facilities of the proposed repository at Yucca Mountain may include transfer of commercial spent nuclear fuel and high-level nuclear waste from transportation casks to the waste packages. Handling of spent nuclear fuel at the geologic repository operations area in the preclosure period may cause the fuel cladding temperature to rise. Fuel cladding temperature exceeding the allowable limit may potentially affect cladding performance. In addition, there may also be preclosure safety concerns if bare fuel assemblies are handled under dry conditions. Thus, evaluating the stability of cladding, which depends on its thermal history, may be important in the licensing review. The objective of this study is to develop staff capabilities and expertise in thermal modeling for evaluating fuel cladding performance.

This preclosure prelicensing activity began in fiscal year 2005 at the Center for Nuclear Waste Regulatory 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 operations included dry transfer of fuel assemblies and surface aging of nuclear waste at the Yucca Mountain site (DOE, 2005). According to this plan, spent nuclear fuel assemblies would arrive at the surface facilities in transportation casks and would be transferred to waste packages or aging casks in the transfer cells (Bechtel SAIC Company, LLC, 2005). The fuel transfer cells were to be located inside the fuel handling facility. During transport, the transportation casks or canisters would be filled with helium to enhance the passive heat dissipation and to maintain the peak cladding temperature below the allowable limit. The cask was to be opened during the dry transfer 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 rise due to inadequate heat dissipation, potentially affecting fuel cladding integrity. During review of a Yucca Mountain license application, staff might need to conduct an independent confirmatory analysis to evaluate the thermal condition of fuel during anticipated events, such as loss of the heating, ventilation, and air conditioning system. The thermal models of the cask system developed in this report are for the handling of closed casks and bare fuel assemblies in cask opened to ambient temperature.

The DOE changes to the design and operations at the proposed Yucca Mountain surface facilities (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 the surface facilities in sealed transport, aging, and disposal canisters inside transportation casks. After receipt and inspection, the transport, aging, and disposal canisters would be transferred to waste packages or aging casks. The proposed use of a transport, aging, and disposal canister system essentially eliminates the likelihood of exposing the bare fuel assemblies to the atmosphere. Although dry handling operations are no longer anticipated, the experience and capability gained from this activity will be useful for evaluating fuel cladding performance in the new proposed surface facility design. This experience may also be used to review the ability of the DOE facility design to maintain fuel cladding temperature below allowable limits during normal operations.

1-1 1.2 Objective

The overall objective of this study is to prepare NRC and CNWRA staffs to review and independently verify DOE thermal analyses in a potential license application for the high-level waste repository at Yucca Mountain. The specific objectives of this study, conducted using the DOE 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 and to 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 (Holtec International, 2002). This cask system has been approved by NRC for transportation and dry storage of spent fuel (NRC, 2004; 2001). In this report, thermal modeling was performed using two computational fluid dynamics software packages: FLUENT® (Fluent, Inc., 2005) and FLOW-3D® (Flow Science, Inc., 2005). The following two-dimensional models were analyzed for capability development.

• Closed-Cask Model: A thermal model of a closed HI-STAR 100 cask system with 24 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 filled with helium during a dry storage condition. FLUENT is used to analyze this model. The objective is to compare the results from this analysis with the results in the HI-STAR 100 final safety analysis report (Holtec International, 2002). In this model, the fuel assemblies and fuel basket are represented as a cylindrical solid homogeneous fuel region.

• Open-Cask Model: A thermal model of an open HI-STAR 100 cask system with 24 pressurized water reactor fuel assemblies is developed. The cask is assumed to be open to the ambient air and active exchange of heat generated by the fuel assemblies takes place via natural convection, conduction, and radiation heat transfer. In this model, the fuel assemblies and supporting structure are represented in two ways: (i) a cylindrical solid homogeneous fuel region and (ii) three concentric cylindrical solid homogeneous fuel regions. FLUENT is used to simulate the open-cask model. The model simulates the steady-state temperature distribution in the open cask under ambient conditions.

• Fuel-Assembly Model: This model simulates the steady-state thermal behavior of a bare fuel assembly inside an open cask. In this model, the fuel assembly directly contacts with ambient air, and active dissipation of heat takes place by conduction and natural convection heat transfer. FLOW-3D is used to simulate the model.

1-2 This report is presented in six chapters, including this introduction as Chapter 1. Model parameters for all simulations are discussed in Chapter 2. Details of modeling approaches are provided in Chapter 3. Chapter 4 provides the details of three models and discusses the understanding gained from the simulations. Chapter 5 summarizes the experience gained from this 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 that requires a three-dimensional model to accurately predict the temperature and flow field; however, as a first step, two-dimensional models are developed to gain a preliminary understanding of modes of heat dissipation (e.g., the internal flow field, radiative heat transfer patterns, and the effect of temperature-dependent thermal conductivities of component materials).

• Storage cask system components for both the closed-cask and open-cask models 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 effective thermal 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 source with an effective thermal conductivity.

• In the open-cask model, the ambient environment extends to infinity and is an infinite heat sink. Processes such as changes in air temperature inside the fuel transfer cell are neglected.

1-3 2 DESCRIPTION OF THE CASK SYSTEM AND MODEL PARAMETERS

In this report, the HI-STAR 100 cask system was selected for developing heat transfer models using FLUENT and FLOW-3D. The cask system is designed for both transportation and dry storage of spent nuclear fuel and has been certified by NRC (NRC, 2004; 2001). The information required for modeling (e.g., detailed geometric parameters and thermal properties of component materials) was obtained from the HI-STAR 100 Final Safety Analysis Report (Holtec International, 2002).

The cylindrical HI-STAR 100 cask system consists of two discrete components: the inner canister, referred to as the multipurpose canister in Holtec International (2002) and the overpack. The inner canister shell is placed inside the overpack. A three-dimensional view and corresponding 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 and open-cask models in this report are based on the materials and shape of the cask as shown in Figure 2-1.

The geometric descriptions of cask system subcomponents are given in Section 2.1. The cask system is backfilled with helium gas when closed, and ambient air replaces the helium when the cask system is opened. The material properties of helium, air, and cask subcomponents are provided in Section 2.2. The thermal properties of the concrete pad are described in Section 2.3. 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 a welded structure consisting of a base plate, canister shell, and a cover lid, as shown in Figure 2-1. The canister is filled with helium under sealed conditions. The dimensions of the cask 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. The fuel basket has square fuel compartments where fuel assemblies are inserted prior to closing the inner canister shell. Each fuel compartment panel has a Boral neutron absorber sandwiched between a sheathing plate and the box panel, and covering the entire length of the active fuel region. A fuel basket holding 24 pressurized water reactor fuel assemblies is called an MPC–24. In Figure 2-1, the green panels represent Boral neutron absorbers. At the bottom and 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 stainless steel were used in the model for the fuel basket in thermal analyses.

2-1 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 and lower end fittings. The fuel rods are typically arranged in a 17 × 17 square matrix, with the spacer grids separating the individual rods and keeping them in place. The fittings and spacer grids 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 solid fuel 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 one cylindrical solid homogeneous fuel region, and open-cask fuel assemblies and fuel basket are modeled as three concentric cylindrical solid homogeneous fuel regions separated by annular gaps.

Table 2-1. Dimensions of HI-STAR 100 Cask System Components* Inner Radius Outer Radius Height Component of HI-STAR 100 System {m [in]} {m [in]} {m [in]} Multipurpose Canister Base Plate 0.0 0.8683625 0.0635 [0.0] [34.1875] [2.5] Multipurpose Canister Shell 0.8556625 0.8683625 4.5212 [33.6875] [34.1875] [178.0] Multipurpose Canister Lid 0.0 0.8683625 0.2413 [0.0] [34.1875] [9.5]

2-2 Table 2-1. Dimensions of HI-STAR 100 Cask System Components* (continued) Inner Radius Outer Radius Height Component of HI-STAR 100 System {m [in]} {m [in]} {m [in]} Overpack Base Plate 0.0 1.057275 0.1524 [0.0] [41.625] [6.0] Overpack-Ni layer 0.873125 0.936625 4.854575 [34.375] [36.875] [191.125] Overpack-Carbon Layer 0.936625 1.069975 4.854575 [36.875] [42.125] [191.125] Overpack Lid 0.0 1.069975 0.1524 [0.0] [42.125] [6.0] Carbon Steel Radial Connector (Holtite) 1.069975 1.2192 4.397375 [42.125] [48.0] [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 a base plate and a closure lid. The inner radius of the overpack is slightly larger than the outer radius 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 when the 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 Holtec International (2002).

The innermost shell of the overpack is made of 6.35 cm [2.5 in] Ni-Steel and is labeled overpack-Ni in Figure 2-1. The overpack-Ni layer is surrounded by an intermediate shell of five layers of carbon steel. The first of the five layers is 3.175 cm [1.25 in] thick and is called the gamma shell. The next four layers are each 2.54 cm [1.0 in] thick. These five layers of carbon steel are modeled as a composite shell 13.335 cm [5.25 in] thick, called the overpack-carbon in Figure 2-1.

To reduce doses from neutron radiation emitted by spent nuclear fuel, the overpack is surrounded by neutron shielding material. This material is placed inside radial channels that are vertically welded to the outermost surface of the overpack intermediate shell. These radial channels also act as thermal fins for improved heat transfer between the overpack and its surroundings. The cavities of radial channel segments also contain silicone sponge. The neutron shielding material Holtite-A (Holtec International, 2002) is made of boron carbide (a neutron poison material) and aluminum. The outer modeled layer, representing carbon steel radial connections and material inside, is a composite material labeled Holtite in Figure 2-1.

2-3 2.2 Material Properties

2.2.1 Thermal Conductivities

The value of thermal conductivity used to model each cask subsystem depends on whether the subsystem 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; the corresponding 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 carbon steel. This subsystem is modeled as one 13.335 cm [5.25 in] wall with an effective thermal conductivity that is in part determined by contact resistance due to minute pockets of air entrapped between shells in the fabrication process.

The entrapped air has a lower thermal conductivity than the metal in the overpack and reduces the radial thermal conductivity of the composite. However, axial conductivity will be essentially unchanged, so the overpack thermal conductivity is anisotropic. Radial heat conduction is expected 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 the following expression (Holtec International, 2002)

−1 ⎡ r ⎤ rlog 5 ⎛ r ⎞ ⎢ 5 δ r 0 r ⎥ = 5 0 + 0 (2-1) Krlogeff 0 ⎜ ⎟ ⎢∑ ⎥ ⎝ rK0air⎠ ⎢ i1= ri rKicst⎥ ⎣⎢ ⎦⎥

Table 2-2. Thermal Conductivity of HI-STAR 100 Cask System Materials* Thermal Conductivity (W/m-K) [Btu/ft-hr-°F] @ 93.33 °C @ 232.2 °C @ 371.1 °C Components of the HI-STAR 100 System [200 °F] [450 °F] [700 °F] Multipurpose Canister Shell and Base Plate 14.54 16.96 19.04 (Alloy X) [8.4] [9.8] [11.0] Overpack Inner Shell (Overpack-Ni) and Base Plate 42.23 41.36 38.77 [24.4] [23.9] [22.4] Overpack Holtite-A and Carbon Steel Radial 3.38 3.14 2.85 Connector System (Holtite) [1.95] [1.81] [1.64]

2-4 Table 2-2. Thermal Conductivity of HI-STAR 100 Cask System Materials* (continued) Thermal Conductivity (W/m-K) [Btu/ft-hr-°F]

@ 93.33 °C @ 232.2 °C @ 371.1 °C Components of the HI-STAR 100 System [200 °F] [450 °F] [700 °F] Cylindrical Solid Fuel Region (homogeneous 1.92 2.59, 3.382 representation of MPC–24 fuel basket with [1.108] [1.495] [1.954] 24 pressurized water reactor fuel assemblies)

*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 conductivity r0 —inner radius of the inner intermediate shell th ri —outer radius of i intermediate shell * — interlayer air gap

Kair — thermal conductivity of the air Kcst — carbon steel thermal conductivity

The values for r0, ri, and * are provided in Table 2-3. The calculated values of the effective thermal 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 assigned as 0.85. The surface emissivity of the fuel basket, inner canister shell, base plate, and inner canister lid are assumed to be that of stainless steel. The surface emissivity of the overpack base 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 pressurized helium, which acts as a nonreacting gas medium for passive rejection of heat generated by fuel assemblies. The thermal conductivity of helium and air at different temperatures are listed in Table 2-6. The viscosity, heat capacity, and molecular weight of helium and air are listed in Table 2-7.

2-5 Table 2-3. Parameter Values Used to Calculate Effective Intermediate Shell Thermal 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 0.36 Multipurpose Canister Shell, Base Plate, and Lid 0.36 Overpack Base Plate, Inner Shell, and Lid 0.66 Painted 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.

2-6 Table 2-6. Thermal Conductivity of Helium and Air*

Helium Khelium (W/m-K) Air Kair (W/m-K) Temperature [Btu/ft-hr-°F] [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* Heat Capacity Cp Viscosity : Molecular Weight (J/kg-K) (Pa-sec) (kg/mol) Material [Btu/lbm-°F] [lb/ft-s] [lb/mol] Helium 5193 1.8 × 10!5 4.0026 × 10!3 [1.24] [1.21 × 10!5] [8.8242] Air 1006.43 1.9 × 10!5 28.996 × 10!3 [0.24] [1.28 × 10!5] [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 cask system, the density variations are caused by the temperature gradients in the fluid region. The fluid is modeled as an incompressible ideal gas to account for temperature variation (Holtec International, 2002). The density of gas D can be represented by

PM (2-2) ρ = RT where

P — specified pressure of the gas (pascal) = 1.01325 × 105 pascal M — 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 is neglected by maintaining pressure at the ambient value throughout the model domain.

2-7 2.3 Concrete Pad

The cask system is placed on a concrete pad for both closed- and open-cask models. The pad is modeled as a 0.9144 m [36 in] high concrete cylinder with a radius equal to the overpack base plate. The upper surface of the concrete surface contacts the overpack base plate, and its bottom surface is assumed to be at 288.7 K [60 °F] (Holtec International, 2002). The thermal conductivity 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 sidewalls of 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 assemblies and the age of the spent nuclear fuel. The MPC–24 fuel basket, with 24 pressurized water reactor fuel assemblies, was selected for this modeling.

Each pressurized water reactor fuel assembly has a design basis decay heat generation rate of 792 watts, so the maximum heat load of an MPC–24 fuel basket is 19,008 watts (Holtec International, 2002). Holtec International (2002) distributed the heat generation rate nonuniformly over the length of the fuel. The precise distribution of the heat generation rate is not of primary importance for gaining insight into heat transfer processes, so for simplicity in modeling, 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-cask thermal models (Holtec International, 2002). The atmospheric pressure is assumed to be 1.01 × 105 pascal [14.7 lb/in2].

2-8 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 fluid system in a specified geometry. FLUENT and FLOW-3D have been validated for the features and 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 (Holtec International, 2002).

3.1 Description of Computational Fluid Dynamics Codes

3.1.1 FLUENT

FLUENT is a computational fluid dynamics computer code that numerically solves governing equations for momentum, mass, and energy balance for a system. The software is ISO–9001 certified, and it is routinely used by the automobile, aircraft manufacturing, oil and gas, and microprocessor manufacturing industries. FLUENT uses a control volume formulation to solve the governing equations, simulating laminar and turbulent flow fields and buoyancy-driven natural convection of fluids. The software can also model conductive, convective, and radiative heat transfer in a system. In this report, the closed- and open-cask thermal analyses are performed using FLUENT Version 6.2.1.

FLUENT uses the Semi-Implicit Method for Pressure Linked Equations (SIMPLE) method and its variations to solve momentum, convective heat transfer, and radiation transport equations within a finite volume. The SIMPLE method is described in detail by Patankar (1980). For the open-cask model, the laminar and turbulent flow models are used to simulate buoyancy-driven natural convection fluid flow inside and outside the cask. In case of turbulent flow, the standard k-epsilon and k-omega models are used inside the computational domain. The details of these turbulent flow models can be found in the FLUENT User’s Manual (Fluent, Inc., 2006). For the standard k-epsilon turbulent flow model, the enhanced wall treatment and full buoyancy effects are 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 discrete ordinate method. In FLUENT, the radiative transport equation is discretized into a finite number of solid angles in each volume. The resulting radiative transport equation is then solved for radiation intensities after solving the convective heat transfer and fluid flow equations for several iterations. This process is repeated until radiation intensities, temperature, and fluid flow field converge. The thermal conductivities of component materials and fluid in open- and closed-cask models are defined as piecewise-linear functions of the temperature using the data in 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 finite difference 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 with second-order formulations for spatial and temporal derivatives. The software has a suite of modules for single and multiphase fluids and can consider both compressible and

3-1 incompressible fluids. A set of turbulent flow models are available, ranging from the standard k-epsilon model to a Large Eddy Simulation model, and each model includes supplementary terms to account for heat transfer effects near solid walls. Turbulence effects are considered to be of secondary importance for building insight into heat transfer processes and are computationally demanding. Thus, for simplicity in modeling, it is assumed that the fluid flow field is reasonably well described as laminar flow in the fuel-assembly model. FLOW-3D uses a constant 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 cylindrical coordinates. The cask analyses are simplified by neglecting small subcomponents that are expected to only minimally affect the thermal profile inside the cask. Neglected subcomponents include overpack lifting trunnions and drainage ports, heat conduction elements, and basket supports inside the inner canister shell.

The computational domain of the closed-cask model is divided into rectangular structured elements. The fluid region between the cylindrical solid homogeneous fuel region and inner canister, and the fluid region between the inner canister shell and the overpack interior surface are 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 a hemispherical dome of air outside the cask. The overpack and inner canister lids are removed in the open-cask model. The open-cask system computational domain is divided into rectangular elements, and the computational domain of air existing outside the cask is divided into unstructured quadrilateral elements. The mesh on the air side is clustered at the boundary of the cask system and ambient air. The mesh is similarly clustered near the boundary of computational domain. The fluid regions inside the cask are divided into a finer rectangular mesh.

The fuel-assembly model is developed in the rectangular coordinate system. The fuel assembly is modeled as one planar surface. The side panels of the fuel basket structure, adjacent to the fuel assembly inside the cask, are assumed to be part of the fuel-assembly model. The computational 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 natural convection and radiation when the cask is closed. The large temperature difference between the 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 transfer because the cask surface temperature is higher than the surrounding temperature.

3-2 The total rate of heat loss from the exterior surface can be expressed by the following relationship (Holtec International, 2002)

=−+σε 4 −4 (3-1) qh(TT)FSA 1AS (TT)A 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 emissivity

F1A — 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

CgLTρβ23Δ (3-2) Ra = p L kμ where

Cp — heat capacity of the gas D — gas density g — acceleration due to gravity $ — thermal expansion coefficient of gas L — height of the vertical plate )T — temperature difference between cask and atmosphere : — dynamic viscosity 6 — gas thermal conductivity

9 7 The fluid flow is expected to be turbulent if RaL is greater than 10 for a vertical surface and 10 for a horizontal surface (Holtec International, 2002). The Rayleigh number RaL as a function of cask height and temperature difference is 2.27 × 108L3 )T. The Rayleigh number along the height 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 natural convection heat transfer coefficient h from the heated horizontal and vertical surfaces in the turbulent fluid flow regime

(3-3) =−1/3 h 1.25(TSA T ) (Horizontal) and =−1/3 (3-4) h 1.08(TSA T ) (Vertical) where h has unit of W/m2!K. The heat transfer coefficient for a vertical surface is less than that

3-3 for a horizontal surface. In the closed-cask model, the heat transfer coefficient for a vertical surface [given by (Eq. 3-4)] is also applied to horizontal surfaces of the cask system, a simplification that will conservatively reduce the heat transfer rate. This approach is consistent with the approach adopted by Holtec International (2002).

The heat transfer coefficient h [Eq. (3-4)] is used to model the natural convection and radiation heat transfer from the overpack exterior surface in the closed-cask model. The approach obviates 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 cask system. 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 active exchange of air. This model is described in detail in Section 4.2. The heat transfer from the overpack exterior surface to ambient air is determined by the solution of the governing equation for 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. The computational 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-cask model are represented as three concentric cylinders. The total decay heat from the fuel assemblies is divided between the three cylinders based on their volume. For both models, the effective 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 from Holtec International (2002). For the open-cask model, the effective thermal conductivity of the fuel 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 basket panels, and there is little or no room for backfill gas to enter easily from the side. Although there are holes in the spacer grids and the upper and lower fittings, permitting some fluid flow through the fuel assembly, flow resistance through fuel assemblies is expected to be much higher than within the channels located between fuel assemblies in the fuel basket. Therefore, it is conservatively assumed that fluid inside the fuel assembly remains stagnant, and a fuel assembly is modeled as one solid object with an effective thermal conductivity in the fuel-assembly model.

3.5 Effective Thermal Conductivity of Fuel Region

In the closed- and open-cask models, the fuel assemblies, space between fuel assemblies, and fuel basket walls are modeled as homogeneous solid fuel regions with an effective thermal conductivity. When the cask system is closed, the fuel basket and fuel assemblies are filled

3-4 with helium. Holtec International (2002) used a finite volume method to calculate the effective thermal conductivity of the fuel region representing the fuel assemblies and fuel basket as a function 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 conductivity of the equivalent fuel region changes because the thermal conductivity of air is different from that of helium. The following method is adopted to estimate the effective thermal conductivity of 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 can be estimated with several mathematical models for composite materials. Methods for calculating the effective thermal conductivity (for example, the geometric mean, harmonic mean, and arithmetic mean methods) are described by Beck (1988). The effective thermal conductivity of the fuel region calculated using geometric mean, harmonic mean, and arithmetic mean methods are 0.69 W/m-K [1.19 BTU/ft-hr-°F], 0.79 W/m-K [1.373 BTU/ft-hr-°F], and 1.965 watts/m-K [1.138 Btu/ft-hr-°F], respectively. The reported value of the effective thermal conductivity is 2.59 watts/m-K [1.5 Btu/ft-hr-°F] at 450 °F (Holtec International, 2002). The calculated effective thermal conductivity is closest to the reported value for the geometric mean method, and it is 24 percent less than the reported value.

Holtec International (2002) developed a two-dimensional model of the fuel assembly and fuel basket structure using ANSYS® (Swanson Analysis Systems, Inc., 1993) to calculate the effective thermal conductivity of the helium-filled structure. This approach assumes that fluid within the fuel basket is stagnant. Since the geometric mean method under predicts the effective thermal conductivity for a helium-filled basket, it is assumed that geometric mean method also under predicts the effective thermal conductivity of an air-filled basket. The scope of this work precludes the estimation of effective thermal conductivity for the fuel basket and fuel assembly system using a model similar to the Holtec International (2002) model.

The geometric mean method estimates the effective thermal conductivity of an air-filled basket with fuel assemblies at 505.37 K [450 °F]. Since the estimated value of the air-filled fuel basket is expected to be under predicted, its value is adjusted by multiplying and dividing with the known and the estimated value thermal conductivity of the helium-filled fuel assemblies and fuel basket system, respectively. Thus, the effective thermal conductivity of the fuel basket with 24 pressurized water reactor fuel assemblies is estimated by the following expression

kair (estimated)kHe (known) (3-5) air = eff eff keff (adjusted) He kefff (estimated) where

k(adjusted)air — adjusted thermal conductivity of the fuel assemblies and fuel eff basket filled with air

air — estimated thermal conductivity of the fuel assemblies and fuel keff (estimated)

3-5 kHe (known) — thermal conductivity of the fuel assemblies and fuel basket filled eff with helium from Holtec International (2002), listed in Table 2-2

He — estimated thermal conductivity of the fuel assemblies and fuel keff (estimated) basket filled with helium using the geometric mean method

air The estimated thermal conductivity keff (estimated) of the fuel region is 1.286 watts/m-K [0.743 Btu/ft-hr-°F], and the corresponding adjusted effective thermal conductivity is 1.692 watts/m-K air [watts/m-K (0.977 Btu/ft-hr-°F)]. The adjusted effective thermal conductivitykeff (adjusted) is used in the open-cask model for the fuel regions.

3-6 4 MODEL DESCRIPTION AND RESULTS

Model descriptions and results of thermal analysis are presented in this chapter. As described in Chapter 1, closed-cask, open-cask, and fuel-assembly model are analyzed. The closed- and open-cask models are simulated using FLUENT, and the fuel-assembly model is simulated with FLOW-3D. The heat source for all three models is consistent with pressurized water reactor fuel assemblies. The model parameters and material properties are given in Chapter 2. A brief overview of the models follows:

• Closed-Cask Model: A two-dimensional axisymmetric model of a closed HI-STAR 100 cask system is used to calculate the temperature profile inside a closed cask. The results are compared to the results presented by Holtec International (2002).

• Open-Cask Model: A two-dimensional axisymmetric model of a HI-STAR 100 cask system with equivalent fuel region open to the ambient air is used to examine the effect of fluid flow and the active heat exchange process inside a cask.

• Fuel-Assembly Model: A two-dimensional model simulating the thermal behavior of a fuel assembly in contact with ambient air is used to understand fluid flow and active dissipation of heat by conduction and natural convection. The fuel-assembly model results 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 in Figure 4-1(a). The computational domain of the closed-cask model is presented in Figure 4-1(b), which shows the model setup in FLUENT. The cask centerline is aligned along the X axis with the bottom of the concrete pad at X = 0, and the cask 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 !X direction. In this model, heat transfer from the fuel basket 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 cask exterior surface to ambient air is modeled using the natural convection and radiation boundary condition defined by Eq. (3-1).

A cask system is filled with pressurized helium. Helium assists in passive rejection of heat from the fuel assemblies and also maintains an inert environment. A closed-cask system loaded with spent nuclear fuel is normally placed in the open environment, where the cask may be insolated during daylight. The peak temperature and the temperature distribution inside the cask are calculated with and without insolation. The peak temperature is also compared to the temperature calculated by Holtec International (2002). The model does not take credit for internal convection of helium, consistent with the approach adopted by Holtec International (2002).

4-1 (a) (b) Figure 4-1. (a) Schematic Representation of the Closed-Cask Model Physical Domain and (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 preprocessor GAMBIT, which is a part of the FLUENT software package. The preprocessor is used to generate and mesh the geometric model. The geometric parameters and thermal properties of the component materials are provided in Chapter 2. The thermal conductivity of materials is defined as a piecewise-linear function of temperature, using the data in Tables 2.2 and 2.3. The thermal conductivities of the component materials at the intermediate temperature (between 99.3 °C [200 °F] and 232 °C [450 °F], and between 232 °C [450 °F] and 371.1 °C [700 °F]) is obtained by linear interpolation. In the model, the emissivities of the fuel region and inner canister 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 by Eq. (3-4)] is applied at the interface of the overpack exterior surface and ambient air when the cask is not insolated.

The solar heat input to the exposed surface is determined based on 12-hour insolation. The solar 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 the requirements 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

4-2 exterior surface receives the solar insolation from all directions. The cell temperature is specified as ambient temperature (299.82 K [80 °F]). The thermal conductivity, k, of the layer adjacent to the cask exterior wall is defined as

= (4-1) khtwall 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 approach allows all convection from the overpack exterior surface to be modeled by conduction as specified by Eq. (3-1).

The thin layer is defined as a semitransparent wall. The absorptivity of the thin layer is specified to be zero in the model. Therefore, insolation is not absorbed by the thin layer. The insolation is assumed to be incident on the wall from all directions; therefore, the diffuse fraction of solar influx is specified as unity in the model. Due to the addition of the thin layer, the cask exterior surface becomes an internal surface in the model. The internal emissivity of the exterior surface is specified as 0.85 in the model. This approach accounts for radiation heat transfer from cask exterior 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, so insolation will be absorbed, emitted, and reflected from the surface. For a gray surface, the absorptivity is equal to the emissivity. Since the emissivity of the painted surface is 0.85 in the model, the absorptivity is also 0.85. The reflectivity of the exterior surface is 0.15 (radiation is not 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. By dividing the incident solar radiation by 0.85, the net input radiation is compensated for the 15 percent loss due to reflection.

4.1.2 Model Results

The calculated temperature contours for the cask system, with and without solar radiation, are shown in Figures 4-2(a) and 4-2(b), respectively. The calculated maximum temperature of the cylindrical solid homogeneous fuel region representing the fuel assemblies and fuel basket is 619.3 K [655.1 °F] when the cask system is not insolated, with the peak temperature located slightly above of the middle of the fuel region. Similarly, the maximum temperature of the fuel region is 634.4 K [682.2 °F] when the cask system is insolated, again with the peak temperature located slightly above the middle of the fuel region. The calculated peak temperature of the fuel increases 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.

4-3 (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 to be 649.1 K [708.7 °F] when the cask is insolated, which is 14.7 K [26.46 °F] higher than predicted by this closed-cask model. Holtec International (2002) specified a nonuniform heat generation rate along the length of the fuel region in their closed-cask model. The burnup profile 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 active fuel length from the bottom of the fuel assembly. The temperature contours presented by Holtec International (2002) for the closed-cask model show that the predicted maximum temperature is located in the lower part of the fuel region {see Figure 4.4.17 in the HI-STAR 100 Final Safety Analyses Report, Holtec International (2002)}. The calculated maximum temperature is only 2.26 percent less than the maximum temperature predicted by Holtec International (2002) (the relative difference with respect to ambient temperature is 4.2 percent), suggesting that the models are in reasonable agreement. Therefore, the uniform heat generation 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 on an independent spent fuel storage installation pad and is surrounded by other casks. The neighboring 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 of radiation blockage due to neighboring cask systems. Holtec International (2002) used ANSYS to determine the view factor of the most adversely located cask system placed on an independent spent fuel storage installation pad. Therefore, the difference in predicted maximum temperature may also be attributed to the view factor, but it is not clear what value of view 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 because the cask surface temperatures are not high enough to affect the radiation heat loss.

4-4 Figure 4-3. Normalized Fuel Burnup Rate Along the Length of a Pressurized Water Reactor 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 in this section. The overpack and inner canister lids are removed in the open-cask model and fuel assemblies are in contact with ambient air. An active exchange of air between the cask and surrounding atmosphere would take place for an open cask. The ambient air would enter the cask through colder regions and exit from hotter regions, with the temperature of entering and exiting air determined by thermal conditions inside the cask. To represent air exchange between cask and its surroundings, the model consists of an open cask and an hemispherical dome of air. A schematic diagram of the open-cask model physical domain is presented in Figure 4-4(a). The diameter of the dome is chosen to be large enough so that the ambient air can enter or leave the computational domain at atmospheric pressure. The computational domain and mesh of the open-cask model are presented in Figure 4-4(b). The computational domain is only half of the physical domain because of axisymmetry. In the model, the cask axis is 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 !X direction. In the model, the boundary of the dome is specified as a constant-pressure boundary condition. The temperature of the air entering the dome is 299.82 K [80 °F], and the temperature of the air leaving the dome is determined by the model. The radius of the hemispherical dome is 25.4 m [1,000 in], which is approximately five times the height of the cask.

4-5 (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 and represented 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 between cylinders. The annular gap provides channels for fluid flow.

4-6 In representation (A), the effective thermal conductivity of the fuel medium is calculated by replacing the helium with air in the fuel basket as described in Section 3.5, but is otherwise identical to the closed-cask model. The effective thermal conductivity fuel basket and fuel assemblies with air is lower than the effective thermal conductivity with helium.

In representation (B), the fuel assemblies and fuel basket are represented as three cylindrical solid homogeneous fuel regions. These three fuel regions represent segments of the fuel basket with 4, 8, and 12 fuel assemblies, respectively. A schematic diagram of this representation is shown in Figure 4-5. The inner and outer radii of the fuel regions are given in Table 4-1.

The following method is adopted to calculate the inner and outer radii of the fuel regions in representation (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 side panels are considered part of the fuel assembly and the other two panels are replaced by ambient air. This is a reasonable approximation because side panels only conduct heat, and their thermal conductivity is much higher than that of air. The cross-sectional area occupied by four 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 the first 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 Right Represents Fuel Assemblies 9, 10, 15, and 16. The Next Cylinder Represents Fuel Assemblies 4, 5, 8, 11, 14, 17, 20, and 21. The Outermost Cylinder Represents the Remaining Fuel Assemblies.

4-7 Table 4-1. Dimensions of the Fuel Regions in the Open-Cask Model With Flow Channels Inner Radius Outer Radius Component {m [in]} {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 (see drawing #3926 in the HI-STAR 100 Final Safety Analysis Report, Holtec International, 2002).

The outer radius of the annular space R2 is determined by

(23.8− 10 / 16)2 R = 2 π

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, 2 2 17, 20, and 21 in Figure 4-5) is 4399.43 cm [681.91 in ]. Therefore, the outer radius, R3, of the second fuel region is determined by the following expression

(8.92+ 5 / 16)2 RR=+× 8 32 π

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 the radius of the single equivalent fuel region in representation (A). The inner radius of this fuel source, R4, is determined by subtracting the cross-sectional the area of 12 fuel assemblies from the area of the single fuel region. Thus, R4 is calculated using the following expression

(8.92+ 5 / 16)2 RR=− 12 × 45 π

R4 is equal to 63.7766 cm [25.1089 in]. The second fuel region has twice the volume of the first fuel region, and the third region is three times larger than the first one. The power density of all three fuel regions is the same.

The fuel basket for 24 pressurized water reactor fuel assemblies has 7.1 cm [2.8 in] undercuts to provide for airflow. Therefore, in the concentric-cylindrical representation, the fuel regions

4-8 are raised by 7.1 cm [2.8 in] to provide passage of air underneath them. The vertical cross-sectional schematic diagram of the cask system placed on the concrete pad is presented in Figure 4-6. As seen in the figure, the fuel basket and fuel assemblies are represented as three concentric solid cylindrical fuel regions placed 7.1 cm [2.8 in] above the inner canister shell 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 both representations of the fuel assemblies and fuel basket system. The thermal conductivities of other component materials are the same as those used in the closed-cask model (Tables 2-2 and 2-3). The emissivities of the fuel region and inner canister shell, overpack material, and exposed overpack surface are 0.36, 0.66, and 0.85, respectively. Separate simulations were run to represent (i) no flow, (ii) laminar flow, and (iii) turbulent flow conditions. Heat transfer from the overpack exterior surface to the atmosphere is determined by the solution of convective and radiation heat transfer equations. The k-epsilon and k-omega turbulent flow models are used for simulating turbulent fluid flow inside and outside the cask. Enhanced wall treatment and full buoyancy effects are activated in the k-epsilon turbulent-flow model. The transitional flow option was activated for the k-epsilon model. Both turbulent-flow models can be 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

4-9 4.2.2 Results

The results of the simulations for the open-cask model with a cylindrical solid homogeneous fuel region {representation (A)} are presented first. The calculated maximum temperature of the fuel source 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 flow conditions. The temperature distribution inside the cask system for these two conditions is presented in Figure 4-7. The thermal profile of the cask system under turbulent flow conditions is 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. The calculation results are summarized in Table 4-2. The radiation and conduction heat transfer are 92.44 and 7.54 percent, respectively, under the no flow condition. When flow is allowed to occur, 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

4-10 (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 System With a Cylindrical Solid Homogeneous Fuel Region Percentage Heat Maximum Percentage Heat Dissipation by Temperature K Dissipation by Conduction and Flow Model [°F] Radiation Convection No Flow 765.9 K 92.44 7.56 [918.9 °F] Laminar Flow 737.9 K 68.08 31.92 [868.5 °F] K-Epsilon Turbulent 730.6 K 66.42 33.58 Flow [855.4 °F] K-Omega Turbulent 729.9 K 64.7 35.3 Flow [854.1 °F]

4-11 As a result, the maximum temperature of the fuel region decreases to 737.9 K [868.5 °F]. The percentage of conduction and convection heat transfer increases to 33.58 percent for the k-epsilon turbulent flow model and 35.3 percent for the k-omega turbulent flow model. These results indicate that natural convection aids in heat removal from the fuel region; however, the drop in peak temperature is only 4.5 percent with respect to the peak temperature of an open cask with conduction and radiation only. These results are expected because a cylindrical solid homogeneous fuel region representation of the fuel assemblies and fuel basket has a small surface 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 heat transfer. In this case, 92.9 percent of the heat is transferred by radiation under the no-flow condition, and the maximum temperature is only 10 K [18 °F] less than the single fuel region representation. The heat source density is higher in the three cylindrical fuel regions representation due to introduction of a gap between fuel regions. As a result, one would expect higher peak temperatures compared to the comparable single fuel region. The annular gap aids in radiation heat transfer between fuel regions, which is not available in the single fuel region representation. Therefore, the effective thermal conductivity of the annular gap is higher than the thermal conductivity of the single fuel region, and the lower value of peak temperature is observed. The maximum temperature drops to 501.3 K [442.7 °F] when fluid is allowed to convect as laminar flow. In this case, 74.4 percent of the heat is dissipated by conduction and convection. The larger surface area enables the fluid to remove heat more effectively from the fuel regions. The temperature distribution inside the open cask for no flow and laminar flow are presented 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 loss is 85.3 percent. However, the maximum temperature of the fuel is 457.1 K [363.1 °F] when the k-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 effect used in the k-epsilon model, which is not considered in the k-omega model. The k-epsilon buoyancy effect in the model is responsible for an enhanced heat dissipation rate, so the calculated maximum temperature is lower. The temperature distribution inside the cask for the turbulent- flow models is presented in Figure 4-10. The calculation results are summarized in Table 4-3.

The following observations are made regarding the temperature distributions in the representation (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 for no flow conditions; however, the maximum temperature is located in the upper part of the central fuel region for laminar fluid flow.

• The location of maximum temperature is in the upper part of the central fuel region for both turbulent flow models.

• The other two fuel regions are colder than the central fuel region.

4-12 (a) (b) Figure 4-9. Temperature Distribution Inside an Open HI-STAR 100 Cask System With Radiation and Conduction Heat Transfer (a) Without Flow and (b) Under Laminar Flow Conditions. 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 System With 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 Are Represented By Three Fuel Regions With Flow Channels In Between.

4-13 Table 4-3. Summary of Calculated Results for the Open HI-STAR Cask System With Three Concentric Cylindrical Fuel Regions and Flow Channels In Between Percentage Heat Percentage Heat Dissipation by Maximum Dissipation by Conduction and Temperature Radiation Heat Convection Flow Model [°F] Transfer Heat Transfer No Flow 754.5 K 92.9 7.1 [898.4 °F]

Laminar Flow 501.3 K 25.6 74.4 [442.7 °F] K-Epsilon Turbulent 426.7 K 14.7 85.3 Flow [308.4 °F] K-Omega Turbulent 457.1 K 25.6 74.4 Flow [363.1 °F]

• For both the laminar and turbulent flow, air enters through the periphery and exits at the center. This observation agrees with the assumption that air fluid is expected to enter into the colder regions and exit from the hotter regions of the cask.

4.3 Fuel-Assembly Model

The equivalent fuel representation of the fuel basket and fuel assemblies in the open-cask model 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 channel width in the fuel basket. Accordingly, the fuel-assembly model is developed to simulate the thermal behavior of an individual fuel assembly in the open cask. The model considers conduction 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 assembly temperatures through heat loss toward the overpack.

A schematic diagram of a inner fuel canister cross section with an MPC–24 fuel basket is shown in Figure 4-11. The fuel-assembly model consists of a fuel assembly and an adjacent channel for airflow near the axis of the fuel basket, as shown in Figure 4-12. The fuel-assembly model represents a single cell in an extensive array of identical cells, which is most representative of two 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-dimensional temperature profile within a fuel assembly. A single fuel assembly can be represented in two dimensions either as a slab or a cylinder; both approaches distort heat flow and thermal

4-14 Figure 4-11. Cross Section of the Inner Canister Containing the Pressurized Water Reactor 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

4-15 patterns within the fuel assembly to a certain extent. The temperature at the interface between the fuel assembly and the air gap may be of primary interest, and both approaches can provide reasonable approximations near the interface. Without a firm basis for favoring one approach over another, the slab model is adopted with the intent of reasonably representing the air and fuel assembly interface temperatures.

The model is developed in Cartesian coordinates, with the X and Y axes representing the horizontal and vertical directions, respectively, and with the Z axis perpendicular to the XY plane. The modeled fuel assembly is 3.5 m [137.8 in] high and 0.1135 m [4.47 in] wide. The channel for airflow is 1.538 cm [0.60550 in], half the distance between two adjacent fuel assemblies. 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 boundary conditions 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 with the cask simulations, the total heat load to the cell is 792 W, representing a pressurized water reactor fuel assembly that generates a maximum power of 792 W after 5 years of initial wet storage (Holtec International, 2002). This amount of heat is dissipated to the air across the perimeter of the fuel assembly. To provide the same rate of heat dissipation across the perimeter, 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, thus the power density is half that of an actual fuel assembly, and the temperature field near the center of the fuel assembly may be distorted. However, the thermal flux to the air per unit of the fuel assembly surface area is captured, implying that air temperatures and fuel temperatures at the 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 3.5 and assuming that the Alloy X and Boral panels are part of the fuel assembly and have the same effective thermal conductivities as the fuel assembly.

The open-cask simulations suggest that cool air enters the cask through the colder regions and exits from the hotter regions and show that the fuel basket with multiple fuel assemblies is hotter in the center of the basket and colder toward the periphery. In general, air enters the cask in the gap between the fuel basket and the inner canister shell, moves down the annular space between basket and shell, passes through undercuts beneath the fuel basket, and returns to the atmosphere via channels between fuel assemblies. Air temperature rises as it moves along this path. Open-cask simulations with laminar or turbulent air movement shown in Figures 4-9 and 4-10 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 gap adjacent to the fuel assembly. Both the top and bottom of the assembly are simulated as open boundaries, with a uniform constant pressure fixed at the ambient atmospheric pressure. The direction 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

4-16 that air moves unidirectionally from bottom to top, so the temperature of incoming air at the bottom boundary must be specified. Two separate simulations were run, with inlet temperatures of 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 in Figure 4-13(a) and (b), respectively. Similarly, the temperature profile of the fuel assembly with air entering at 400 K [266.33 °F] is presented in Figure 4-14. The fuel assembly attains a maximum temperature of 530 K [494.33 °F] with air inlet temperature at 350 K [170.33 °F]. The maximum fuel assembly temperature increases by approximately 30 K [54 °F] when the incoming air is 50 K [90 °F] warmer; increased airflow driven by warmer air compensates to some degree for the reduced heat removal rate caused by a lower thermal differential between the fuel assembly and air.

The airflow in the gaps between the assemblies is similar to the classical laminar boundary layer in natural convection on a hot vertical flat plate, with a peak in fluid velocity near the hot wall and slower 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 is located 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 of symmetry in the model. Simulations performed with the mixing length turbulence model yield essentially identical results to the laminar-flow model, presumably because the fluid velocities are small. It can be concluded that, due to narrow channel width between fuel assemblies, the fluid flow field is predominately laminar.

(a) (b) Figure 4-13. Steady-State Temperature Distribution of the Fuel Assembly in the Fuel-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.

4-17 (a) (b)

Figure 4-14. Steady-State Temperature Distribution of the Fuel Assembly in the Fuel-Assembly Model for Air Entering at 400 K [266.33 °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.

4-18 5 SUMMARY

Staff is developing capabilities and expertise in thermal modeling in preparation for reviewing potential DOE thermal analyses. Preliminary analyses presented in this report explore heat transfer within a cask system in both open and closed conditions. These analyses provide a basis for assessing the capabilities of commercially available computational fluid dynamics software and enhance understanding of modes of heat transfer (i.e., conduction, natural convection, and radiation) from fuel assemblies under ambient conditions.

This activity started in fiscal year 2005, when DOE-planned operations at Yucca Mountain surface facilities included dry transfer of fuel assemblies (DOE, 2005). The thermal models of the cask systems investigated in these preliminary analyses are based on these DOE-planned activities.

In fiscal year 2006, DOE proposed changes to the design and operations of Yucca Mountain surface facilities (Harrington, 2006) as a result of the newly proposed transport, aging, and disposal canister system. In the new approach, fuel would arrive at the repository loaded into a transportation, aging, and disposal canister, and the fuel assemblies would not be exposed to air under normal operations. Even under the new disposal concept, experience and capabilities gained during this activity will be useful in future thermal analyses.

Based on studies presented in this report, FLUENT can, without modification, effectively simulate the thermal condition of fuel assemblies in a cask system. The off-the-shelf version of FLUENT is capable of modeling conduction, radiation, and natural-convection heat transfer and can specify thermal conductivities for a material as a function of temperature. These capabilities are demonstrated in the cask models developed in this report. The off-the-shelf version of FLOW-3D, on the other hand, does not consider radiation heat transfer and cannot define thermal conductivity of a material as a function of temperature. User-defined modules can be added in FLOW-3D to include radiation heat transfer for simple geometries (Green and Manepally, 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 used as an example cask system for thermal analyses. Three representative models were analyzed to 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 a canister. Energy exchange between the cask system and the ambient environment is analyzed for a dry storage condition using a two-dimensional model in cylindrical coordinates. The individual fuel assemblies and gaps between the assemblies are represented by a cylindrical homogeneous solid fuel region. Model calculations qualitatively match independent calculations by Holtec International (2002), although a different modeling assumption for the decay heat source of fuel region yields somewhat different temperature fields in the two models. Simulated peak temperatures in the closed-cask model is 14.7 K [26.5 °F] less than calculated by Holtec International (2002), in part because the heat source distribution in the fuel region considered by Holtec International (2002) is nonuniform with peak source rate approximately 10 percent higher than the average rate, while the example calculation considers a spatially uniform source for simplicity. The calculated deviation between maximum fuel temperature and ambient

5-1 temperature for the two models differs by approximately 4.2 percent with respect to ambient temperature (299.82 K [80 °F]), suggesting that the models are in reasonable agreement aside from the heat source distribution.

The open-cask system is similar to the closed-cask model, except that the overpack and inner canister lids have been removed, and the helium has been replaced with air. Two representations of the fuel assemblies and fuel basket are considered: (i) the fuel region used for the closed-cask calculation and (ii) three concentric cylindrical solid homogeneous fuel regions with annular gaps between them. The total void volume in the annular gaps is approximately 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 heat production is the same in the two approaches, although the heat source density in the fuel regions is larger in the three separate homogeneous fuel regions to compensate for the annular space. Several observations can be made from the open-cask system:

• Gaps appear to enhance radial energy transfer, evidenced by comparing the no-flow cases for the two representations. Lower peak temperatures are seen in the three fuel regions model without air flow, despite higher heat-source densities.

• Annular spaces between fuel regions greatly increase the efficiency of heat removal and also reduce the influence of radiation transfer. Without flow (three concentric cylindrical solid homogeneous fuel regions), the maximum temperature is about 455 K [819 °F] above the ambient temperature, and almost 93 percent of heat dissipation is by radiation heat transfer. With flow, the maximum 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 total heat dissipation.

• The peak temperature of the fuel regions decreases with turbulent flow models when compared to the laminar-flow model, indicating that turbulence offers significantly greater cooling capability.

• The representation of flow in the annular gaps significantly lowers the maximum temperature of the fuel regions, and neglect of flow in the gaps yields the larger peak temperatures. The fluid flow in the case of three concentric cylindrical homogeneous fuel regions representation may yield a lower-bound estimate, as the annular space imposes unrealistically small amounts of drag and over predicts volumetric air flow.

The fuel-assembly model considers a fuel assembly near the center of an open-cask as well as the gap between two assemblies. The gap has the physical dimensions typical of an actual gap, rather than being the result of a volumetric constraint as in the open-cask model. Thus convection was more closely represented relative to the open-cask model. The fuel-assembly model confirms that internal convection is an important mode of heat transfer for removing decay heat from fuel assemblies, even with apertures representative of the gap between adjacent fuel assemblies and high inlet air temperatures. The fuel-assembly model agrees with the open-cask model in that the location of peak temperature is near the upper part of the fuel assembly. This model indicates that the three separate fuel regions representation in the

5-2 open-cask model may represent a lower bound for fuel temperature. In this model, the narrow gap between assemblies appears to constrain flow velocities sufficiently to make the particular choice 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 the cask system. If necessary, the capabilities acquired in this work can be extended to develop a full-scale three-dimensional heat transfer model of the proposed transportation, aging, and disposal canister. A detailed three-dimensional model would require accurate geometric representation of the canister, temperature-dependent thermophysical properties of component materials, and a flow model that adequately describes the fluid motion of backfilled gas inside the canister. The detailed three-dimentional model could be used to estimate the effect of internal convection on heat transfer from fuel assemblies in a transportation, aging, and disposal canister.

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