Evaluation of the Paducah Tiger Overpack for Accident Conditions Abstract M. C. Yaksh, Ph.D., PE NAC International T. Chung SAIC An evaluation of the accident conditions for the Paducah Tiger Overpack is performed using ANSYS/LS- DYNA. The accident conditions include the 30-foot drop onto an unyielding surface followed by a 40-inch drop onto a six inch diameter steel pin. The objective is to identify the clearance between the valve at the end of the cylinder and the overpack after both accident conditions. The model is comprised of a foam overpack containing a ferritic steel cylinder. The foam overpack also contains a system of stiffeners. The results indicate that the valve will maintain sufficient clearance to maintain the integrity of the valve at the end of the cylinder. Introduction The transporting of cylinders containing radioactive or fissionable materials are regulated under Code of Federal Regulation, Title 10, Part 71 (Reference 1). The contents of the cylinder in this study is UF 6, which is much less severe than the usual radioactive uranium based contents, is still subject to these regulations. The UF 6 is contained in a 5/8-inch thick ferritic steel cylinder The total weight of the package and contents is approximately 40,000 pounds. The cylinder is protected during transport by a overpack comprised of foam to absorb energy during a 30 foot drop as well as a subsequent 40 inch drop onto a mild steel pin. Stainless steel plates are attached to the sides of the overpack for the protection from a 40-inch drop of the overpack onto a mild steel pin. At one end of the cylinder is a small valve that permits the UF6 to be pumped into and removed from the cylinder. Since the small valve protrudes from the end of the cylinder, it must also be protected during the accident conditions. The design criterion is basically to protect the valve and to limit the accelerations the cylinder will experience during the drop conditions. To further protect the valve, an aluminum plate was added to the design, which was result of the analysis of the drop conditions. Further details on the overpack are contained in Reference 2. Procedure The most severe condition, however, is considered to minimize the clearance between the valve and the deformed structure due to both accident conditions; the 30 foot drop followed by the 40 inch pin puncture drop. A series of orientations is considered ranging from an end drop to an orientation allowing an edge of the overpack to impact. Furthermore, it is essential that the final 40 inch drop condition incorporate the damage associated with the 30 foot drop. The pin orientation is considered to be arbitrary, but the most severe condition is the orientation in which the pin is normal to the bottom surface. While the accelerations are computed they are not considered to be controlling. This evaluation necessitates modeling the foam overpack, the cylinder and the various stiffeners. An overall view of the overpack is shown in Figure 1 and Figure 2. The top end of the overpack is not modeled.
Figure 1 - Overall View of the Half Model of the Paducah Tiger Overpack
Figure 2 - View of the lower section of the overpack without the foam elements Analysis A three-dimensional model of the Paducah Tiger Overpack is constructed in ANSYS and was analyzed using ANSYS/LS-DYNA. The components comprising the model are shown in Figures 1 through 6. Material Models The overpack is comprised of ferritic steel for the shells and tube frame and were modeled using a bilinear stress-strain curve. On the bottom surface of the overpack, a.375 inch thick stainless steel type 304 plate is attached to provide additional puncture resistance and protection for the valve on the bottom surface of the cylinder (See Figure 2). The stainless steel and aluminum plates were also modeled as a piece wise linear material model using stress strain curves for stainless steel type 304 and aluminum 6061, respectively. Strain rate dependent properties were not used.
The overpack contains two types of foam with different densities. The corner region used a foam with an increased density of 20 pcf (see Figure 3), while the remainder of the volume use a low density foam (8 pcf). The material properties require that a compressive stress volumetric strain curve be input, and this data is presented in Figure 6 and Figure 8 for the low density and high density foams respectively. The foam is considered to have a exponential increase in stiffness upon reaching 80% compressive strain. Figure 3 - Triangular Section of the High Density Foam
Figure 4 - Restraint pad Figure 5 - Pin Model for the Pin Puncture
Figure 6 - Model of the Aluminum Plate Finite Element Models There are basically three parts to the model: 1) the ferritic cylinder (containing the payload) 2) the overpack (the steel frame and the foam) 3) the aluminum plate (to add further protection for the valve, see Figure 6) The 5/8 inch thick ferritic cylinder and supporting skirt (see Figure 2) are modeled using shell elements. The weight of the contents of the cylinder was included in the density of the steel comprising the cylinder. Total weight of cylinder and contents is 25,530 pounds. A part to part interface simulates the contact of the cylinder and skirt with the aluminum plate and the inner surface of the overpack. For the overpack, the majority of the model is comprised of the solid elements, which correspond to the foam. Initial considerations were to simplify the foam region at the bottom of the overpack as much as possible to avoid the use of tetrahedral elements. However, with the presence of the tube frame, and the triangular shape of the high-density foam at the edge of the bottom, the use of tetrahedral elements for a small portion of the low density foam was virtually unavoidable. The use of tetrahedral elements was restricted to small regions of low density foam above the high density foam regions and other isolated regions. The high density foam region (see Figure 3) and the low density foam directly under the
cylinder (see Figure 1) were comprised of brick elements. The foam region of the overpack is comprised of 23,265 elements. Since the end of the overpack with the valve was the only end to the simulate an impact, the opposite end of the overpack was not modeled. The total weight of the unmodeled foam was included by adjusting the density of the low-density foam that was modeled. During the various solutions, it was found necessary to select certain tetrahedral elements and define a separate part to increase the modulus for the contact interior to avoid elements developing a negative volume. Additionally, to avoid marked decrease in the time steps, the density of the material was scaled. While mass scaling could have been used, it was performed manually on the selected elements. The additional weight due to mass scaling corresponded to approximately 100 pounds, which is considered to be insignificant when compared to the total 40,000 pound weight of the package. The surfaces of the overpack are comprised of 11-gauge steel, which were modeled with shell elements. The tube steel comprising the interface of the two parts of the overpack were also modeled with shell elements, which were.25 inches thick. In the original model and analysis the aluminum plate (see Figure 6) was not included in the design. After the initial analyses it was determined that such a plate would provide further protection of the valve during the two accident scenario. In this paper only the analyses with the aluminum plate are described. The use of the part to part interface allows the plate to act independent of the overpack and the cylinder. The pin model was also modeled separately using shell elements, which employed a rigid material. (see Figure 5). The pin was moved and reoriented during the different analyses to simulate the most severe conditions. Boundary Conditions The overall analysis encompasses two accident conditions; a 30-foot drop followed by a 40 inch pin puncture. Since a half model was used for this evaluation, symmetry conditions were applied at the plane of symmetry. To simulate the first impact, the initial velocity was specified as the free fall velocity for a 30-foot drop (527.4 inch/sec). The impact surface was represented by a rigid plane. During the first impact the pin was contained in the model, but was essentially made inactive since it was separated from the pack by the rigid plane. The analysis was permitted to continue until the cylinder began its rebound. The efficient restart methodology allows the analysis to continue in an incremental fashion. At this point, a restart was performed. The velocity of all the nodes was reset for a 40-inch drop. The motion option for the rigid plane was used to move the rigid plane out of the path of the package to allow the package to impact the pin. Even though the initial kinetic energy was represented by the initial velocity, the body force was used to ensure that any potential energy associated with the further deformation of the foam would be taken into account. The initial velocity and the body force were altered to represent the drop angle of interest.
Benchmarking of the Model To provide confidence in the model and the methodology, an analysis was performed using a drop orientation of 20 (measured from the vertical) from the height of 30 feet. The 30-foot distance is measured from the impact plane to the lowest point of the package. This was a single drop analysis in which the pin puncture was not performed following the initial 30-foot drop. This was selected since a test had been previously performed with a full-scale model of the overpack (Reference 2) with this orientation and drop height. The direction of the gravity and the orientation of the rigid plane were adjusted to simulate the impact of the 20 orientation. The initial velocity components were also defined to correspond to this orientation and the rigid plane remained stationary. The deformed shape of the overpack is shown in Figure 9. The cylinder did not exhibit any permanent deformations and the measured deformation at the corner of the overpack from the analysis was 11.8 inches. The test results also determined that the cylinder suffered slight scratching on the cylinder rim without permanent damage, which agreed with the results for the cylinder in the analysis. In the test, the overpack outer skin deformed, crushing the encased foam along 10 inches in the horizontal (radial) direction and about 4 inches longitudinally from the edge of the impact. This corresponds to a magnitude of 10.8 inches or 9% less than the value obtained from the analysis. This difference is considered to be acceptable. While the deformed shape is well defined, the interaction of the dual density foam during the impact is complex, since the compressive strength is strain dependent, and the foam regions are not rectangular in shape. Since the main objective of the analysis was to identify the clearance of the valve with the overpack, the 9% increase in the foam crush was considered as additional conservatism in the end result. Compressive Stress-Strain Curve of Low Density Foam 1000 900 800 700 Compressive Stress, psi 600 500 400 300 200 100 0 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 Volumetric Strain Figure 7 - Stress-Strain Curve for the Low Density Foam
Compressive Stress-Strain Curve of High-Densiy Foam 10,000 9,000 8,000 7,000 Compressive Stress, psi 6,000 5,000 4,000 3,000 2,000 1,000 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Volumetric Strain Figure 8 - Stress-Strain Curve for the High Density Foam Figure 9 - Overpack Post-Drop Damage Graphical Presentation Validation Run, 20 Degree Edge
Analysis Results & Discussion To identify the most severe condition in the axial clearance, a series of analyses were performed using the drop angles of 0 (end drop), 15ºand 27. A summary of the axial clearances is shown in Table 1. During the analyses it became apparent that the size of the slot in the aluminum plate needed to be enlarged due to the motion of the cylinder after the combined drop conditions. The analyses presented below correspond to the enlarged slot condition. For the end drop orientation (0 ), the pin was considered to be at the center of the package or under the pin. The pin at the center condition was considered to the point of weakest resistance with respect to the overpack frame. The pin under the valve was considered to be the point of weakest with respect to proximity of the valve. Figure 10 shows the deformed plot for the end drop condition for both pin locations. In both cases the pin was slightly tilted to maximize the local loading on the stainless steel plate. Pin Under the Valve Pin at Center Figure 10 - Deformation Plots after the 30 foot End drop and the 40 inch Pin Puncture Drop
In considering the off-angle drops, it became apparent that most severe pin puncture would occur for the pin near the valve as opposed to being at the center of the package. For this reason only a single pin puncture position for the 15 and the 27 drops were required. It was determined that the limiting case was for the 27 drop. The deformation for the 27 drop and the subsequent pin puncture is shown in Figure 11. The deformation after the 30 foot drop The deformation after the 40 inch pin puncture drop Figure 11 - Deformation Plots after the 30 foot 27 Drop and the 40 inch Pin Puncture Drop In the cases analyzed above the stainless steel maximum strains remained below the ultimate strain and resisted puncture by the pin. The maximum stress of the aluminum stiffening plate was found to occur during the first 3 milliseconds of the 30-ft end drop. The sudden impact of the overpack square end caused
the center of plate to bulge upward. The maximum stress in the aluminum is 41,300 psi. The corresponding strain is 4.5%. The ultimate stress of the aluminum is 43,000 psi at 7.26% strain. Therefore, the aluminum suffered permanent plastic deformation but without reaching the ultimate stress. Conclusion In this study ANSYS/LS-DYNA was used to simulate a complex loading scenario of a foam overpack subject to two loadings, one being the 30-foot drop followed by a 40 inch pin puncture. A benchmark of a 30 foot drop confirmed that the use of the crushable foam material in ANSYS/LS-DYNA could be used to predict the response of the package. As a result, the methodology was used to enhance the safety of the design of the foam overpack and to confirm that the valve would maintains its integrity during the accident conditions. References 1) Code of Federal Regulations, Packaging and Transportation of Radioactive Materials, Part 71 Title 10, April 1996. 2) Safety Analysis Report for Packaging on the Paducah Tiger Protective Overpack for 10-ton Cylinders of Uranium Hexafluoride, KY-665, June 6, 1975.
Table 1 - Summary of AXIAL Clearances Between Valve and 1/2" End Plate Combined 2 Combined Combined 30 Free Drop (Model No.) Initial Axial Clearance 1 (in) Maximum Differential Displacement (in) Net Minimum Clearance (in) 40 Pin Puncture Drop (Model No.) Maximum Differential Displacement (in) Net Minimum Clearance (in) Minimum Clearance After 3/8 Removed (in) = A B = A - D = E - 0.375 0 on End (A1-1) With 9x8 cutout hole in the stiffener plate 2.375 0.162 2.213 Pin in Center (A1-2) 2.375 0.162 2.213 Pin under Valve (A1-3) 0.419 1.956 1.581 0.364 2.011 1.636 15 on Edge (A2-1) 2.375 0.0 2.375 Pin under Valve (A2-2) 1.080 1.295 0.920 26.7 on Edge (A3-1) 2.375 0.0 2.375 Pin under Valve (A3-2) 2.375 0.0 2.375 Pin under Skirt (A3-3) 1.086 1.289 0.914 0.594 1.781 1.406 Notes for Table 8-1: 1)Initial axial (z-direction) clearance between cylinder valve and 1/2" carbon steel end plate consists of: 2.000 Depth of hole in aluminum stiffening plate + 0.375 Clearance between end of skirt and end of cylinder valve 2.375 Total Initial Axial Clearance Combined maximum differential displacement = Cumulative displacement of 30 drop plus 40 pin puncture drop.