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Proceedings of the ASME 2009 International Mechanical Engineering Congress & Exposition IMECE2009

November 13-19, Lake Buena Vista, Florida, USA

IMECE2009-13238

THERMAL-MECHANICAL ANALYSIS OF ANNULAR TARGET DESIGN FOR HIGH VOLUME

PRODUCTION OF MOLYBDENUM-99 USING LOW-ENRICHED URANIUM

Kyler K. Turner University of Missouri-Columbia

Columbia, MO, USA

Gary L. Solbrekken University of Missouri-Columbia

Columbia, MO, USA

Charlie W. Allen University of Missouri Research

Reactor Columbia, MO, USA

ABSTRACT

Techenetium-99m is a diagnostic radioactive medical isotope that is currently used 30,000 times a day in the United States. All supplies of techenetium-99m’s parent isotope molybdenum-99 currently originate from nuclear reactor facilities located in foreign countries and use highly enriched uranium (HEU). In accordance with the Global Threat Reduction Initiative all uranium used in future molybdenum-99 production will use low enriched uranium (LEU). A design approach to using LEU in a cost-effective manner is to use a target that is based on LEU foil. A potential failure mode for the LEU foil based target is temperature excursion during irradiation due to poor thermal contact between the foil and the target cladding. The purpose of this study is to establish the theoretical basis for experimentally measuring the thermal contact resistance.

Replicating in service heating conditions is nearly impossible when testing the thermal contact resistance as part of a study to establish LEU foil warpage tolerances, thus it is necessary to establish an alternate heating configuration that will allow a conservative estimate of the contact resistance. Thermal and mechanical analysis suggests that external heating of an annular target will place the interface into a state that will over-estimate the contact resistance relative to use conditions. Further, the magnitude of the heat load used for testing can be adjusted to control the degree of over-estimation.

NOMENCLATURE a inner cylinder radius b outer cylinder radius E Young’s Modulus h heat transfer coefficient k thermal conductivity L length P pressure q” heat flux R thermal resistance r radius T temperature Greek

coefficient of thermal expansion Poisson's ratio

Subscripts i inner o outer r radius Abbreviations ANL Argonne National Laboratory ANSTO Australian Nuclear Science and

Technology Organization CNEA National Atomic Energy Commission GTRI Global Threat Reduction Initiative HEU high enriched uranium

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LEU low enriched uranium MURR University of Missouri Research Reactor NRC Nuclear Regulatory Commission INTRODUCTION

One of the most commonly practiced radio-medical diagnostic techniques in the world today is technetium-99m diagnostic therapy. Radioactive technetium-99m is the short lived daughter isotope of molybdenum-99 (Mo-99). Currently all Mo-99 production is produced from highly enriched uranium (HEU) or uranium that contains greater than 20% U-235. The high concentration of U-235 in HEU material makes it a great choice for high volume molybdenum-99 production. Unfortunately it also could be used for uranium-based nuclear weapons. The Global Threat Reduction Initiative (GTRI) was created in 2004 and “works to identify, secure, remove and/or facilitate the disposition of high risk vulnerable nuclear and radiological materials (i.e. HEU) around the world, as quickly as possible, that pose a threat to the United States and the international community [1].” The production of Mo-99 using HEU falls within the jurisdiction of this initiative. One alternative to high volume Mo-99 production using HEU material is to use low enriched uranium (LEU). LEU material has a U-235 concentration less than 20%. The focus of this paper is facilitating the development of a high-volume production target design capable of economically producing Mo-99 using LEU while satisfying the safety requirements set forth by the University of Missouri Research Reactor (MURR) and the Nuclear Regulatory Commission (NRC).

BACKGROUND

Current targets use a powder dispersion design. When uranium-aluminide powder is mixed with pure aluminum powder and then hot rolled, a solid monolithic structure results. The solid structure is very attractive from a heat dissipation standpoint. When using LEU a different target strategy is employed in order to increase the yield of Mo-99 and to reduce the amount of liquid waste left behind after dissolving the target to extract the Mo-99. A foil based approach, as illustrated in Figure 1, is utilized. The concept is to place a LEU foil between two pieces of aluminum cladding and seal all edges. The sealing prevents the escape of fission products for later processing. A fission recoil barrier is wrapped around the LEU foil to keep it from bonding with the cladding. This allows the foil to be removed from the cladding for dissolving. This design created by Argonne National Laboratory (ANL) was developed for use with the LEU-Modified Cintichem process, its use has also been demonstrated for alkaline-based processes [2]. Unfortunately the lack of bonding between the LEU foil and cladding creates the potential for heat transfer restricting gaps to form.

Thermal contact resistance minimization was a primary driver behind LEU-foil based annular target developed by ANL [3]. Currently this design concept, illustrated in Figure 1, has been demonstrated successfully during irradiation at BATAN in Indonesia, CNEA in Argentina, and ANSTO in Australia with up to 20-g LEU foils [4]. The annular design has not been demonstrated, though, in a high-volume production environment. One of the limiting factors is a lack of thermal contact resistance characterization analysis that defines the required dimensional tolerances for the foil and the aluminum cladding surfaces. The primary objective for this paper is to establish a test methodology that will allow a thermal resistance characterization study to be completed. Analytic and numeric models are utilized to complete the study

Figure 1. Cylindrical Target Diagram [5]

PRELIMINARY CONTACT RESISTANCE ANALYSIS

The annular target design has been evaluated by ANSTO. They evaluated their thermal margin using the CFX numeric code and an experimentally determined thermal contact resistance [6]. There are two significant drawbacks with their thermal analysis that preludes it from being used here. First, the test methodology used to evaluate the thermal contact resistance placed the interface between the LEU foil and cladding in a state that would have reduced the thermal contact resistance relative to the use conditions. Second, their analysis did not provide an envelope for variations in the foil thickness, surface roughness, and material deformations due to manufacturing. This later analysis is required to set the incoming material tolerances needed for high volume production.

A simple 1-D resistor network was used to construct a first order thermal model of the target that allows the maximum possible gap between the LEU foil and cladding to be estimated. The network shown in Figure 2 shows that the heat generated by the LEU conducts

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through either the inner cylinder or the outer cylinder before being convected to the reactor water coolant. It is assumed that there is a uniform air gap between the LEU foil and the aluminum cladding. Figure 2 illustrates the in service geometry that is seen in the ANL annular target. Each of the thermal resistances are calculated using conventional expressions in cylindrical coordinates [7].

(1)

Figure 2. Cartoon of In Service Annular Target Geometry

and Corresponding Thermal Resistance Network In equation (1), the subscript ‘x’ refers to any of the

components shown in the resistance network, and rmin and rmax are the inner and outer radius respectively for each of the resistance components. The length of the target is L and k is the thermal conductivity for each component.

Reactor safety requirements dictate that the water coolant shall not boil. The targets will be irradiated in a pool of water at a depth of 7m where the saturation temperature is about 113 oC. It is assumed that the outer aluminum cladding temperature is then 113 oC. The resulting LEU-foil temperature is shown in Figure 3 for a range of gap thickness and heat load-per-unit target length and a nominal target diameter of about 5 cm. The temperature map illustrates that the LEU temperature increases with increasing gap and heat load. The maximum LEU temperature allowed by MURR is 330 oC. Figure 3 shows that the maximum allowable gap is on the order of 25 µm for LEU heat generation on the order of 35 W/mm.

Figure 3. LEU Temperature Map

The allowed gap size shown in the temperature map

gives an idea of the maximum allowable variation in foil thickness that can be tolerated. A piece of cost-effective LEU foil was obtained and measured to understand the variation in foil thickness. A photograph of the foil is shown in Figure 4 and shows that there are significant processing marks produced during manufacturing. Thickness measurements using a micrometer are plotted in Figure 5. The thickness has a range of about 60 µm. Since the overall variation exceeds the 25 µm allowable gap, further study is required to firmly establish that the LEU temperature will not exceed the allowable limits. An experimental study is planned to establish the impact of such a thickness range on the thermal contact resistance.

Figure 4. Photograph of Cost-Effective LEU Foil

Figure 5. Topographical Map of LEU Foil.

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THERMAL/MECHANICAL ANALYTIC MODELING A thermal/mechanical modeling approach is used to

determine an appropriate experimental strategy. The general idea is to evaluate the thermally induced stress in a cylinder due to the different heating conditions shown in Figure 7. By examining the resulting stress distribution, it can be inferred if the heating condition will increase or decrease the interfacial pressure, and hence the contact resistance relative to the in-service condition where interfacial heating takes place. A plane-stress analytic model for the stress in a long circular cylinder as a function of radius and can be seen in equation (2) [8]

(2)

where r is the location along the radius and / are the constants of integration. Assuming that the cylinder has a central circular hole the boundary conditions

are applied and the constants of integration are

(3)

(4)

Where (a) is the cylinder’s inner radius and (b) is the cylinder’s outer radius.

Solving the integrals in eqns. (3) and (4) requires knowledge of the radial temperature distribution. The T(r) will differ depending on the heating condition as illustrated in Figure 7. An expression for T(r) was found for the inside heating condition and the outside heating conditions based on the resistance network in Figure 6. It should be noted that this model does not take into account the air gap between the cylinders and only describes the effect of heating on the aluminum cladding. The inside heating condition temperature distribution can be seen in equation (5) and outside heating temperature distribution can be seen in equation (6)

Figure 6. Heat Transfer Resistance Network for the Annular

Target

(5)

(6)

Equations (5) and (6) are then used to evaluate c1 and c2 in eqns. (3) and (4) and integrated using the appropriate limits of integration. The integration of the two equations can be seen below for both the inside heating condition and the outside heating condition.

= (7)

where Q=

= (8)

where Q=

After integration gives = (9)

= (10)

Substituting equation (9) and (10) into equation (2) yields equations (11) and (12), which give the radial stress in the cylinder as function of temperature and radius

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(11)

(12)

The boundary conditions used to complete the

thermal stress analysis can be seen in table 1 and figure 7.

Table 1. Model Surface Boundary Conditions

Inner Surface Interfacial Surface

Outer Surface Cylinder Ends

Inner Heating

Condition

q”=

100 W/cm

N/A

h=

21740 W/m K

h=

0 W/m K

Interfacial Heating

Condition

h=

17522 W/m K

q”=

100 W/cm

h=

17522 W/m K

h=

0 W/m K

Outer Heating

Condition

h=

29305 W/m K

N/A

q”=

100 W/cm

h=

0 W/m K

Interfacial Heating Inner Surface Heating Outer Surface Heating

Figure 7. Cut Away Diagram of the Three Different Heating Situations

The radial temperature distribution as a function of radius for the interior, exterior and interfacial heating cases can be seen in figures 8. The resulting radial thermal stress is shown in figure 9.

Figure 8. Temperature Distribution as a Function of Radius for

the Inner, Interfacial and Outer Heating Conditions

Figure 9. Radial Stress as a Function of Target Thickness for

the Inner, Interfacial and Outer Heating Conditions The results show that the radial stress at the surfaces for the internal and external conditions is zero and that the interior of the cylinder experiences either a compressive or tensile stress depending on the heating direction. A negative radial stress represents a compression force while a positive radial stress implies a tensile force. A compressive force at the interface implies that there will be an increase in the interfacial pressure and a decrease in thermal contact resistance. A tensile force at the interface implies that there will be a decrease in the interfacial pressure and an increase in thermal contact resistance. This latter condition could eventually result in a condition where the cylinders pull apart from one another and create a gap. It should be noted that if a gap were to open at the interface the radial stress at the interface would become zero.

Figure 9 indicates that the inner heating condition causes a compressive thermal stress to develop in the cylinder. This suggests that if a test bed were created that heated a target from the inside, the interface would experience an increase in contact pressure, and hence a

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reduction in thermal contact resistance. Conversely, when the target is heated form the outside, a tensile stress is developed at the interfacial region.

The stress magnitude for the two heating conditions is not symmetric. The results for the external surface heating have an absolute value greater than the absolute value of the internal surface heating condition. The different surface areas of the inner and outer cylinder surfaces are the reason for the asymmetric distribution.

CYLINDIRCAL TARGET NUMERIC MODELING The goal of the numerical model study is to verify

the results obtained with the analytical model and to explore interfacial heating as experienced in the real target. The numerical model was created using Pro-Engineer/Pro-Mechanica. A CAD model was first created in Pro-engineer and then transferred into Pro-Mechanica where it was meshed and analyzed. The mesh contains 12244 elements and was run at a multi-pass adaptive setting with a percent convergence set to 0.01.

Contour plots of the radial stress for the internal and external surface heating conditions can be seen in figures 10 and 11 respectively. As was noted from the analytic model results, the internal surface heating condition put the interface of the cylinders in compression while the external surface heating condition put the interface of the cylinders in tension.

Figure 10. Radial Stress Distribution for Inner Surface Heating

Figure 11. Radial Stress Distribution for Outer Surface Heating A comparison of the radial stress values from the analytic and numeric models is shown in Tables 2 and 3 and Figure 9

The percent difference between all of the compared values is below ten percent and even smaller at the location of the interface. The similar results between the models provide the confidence to use the numerical model to evaluate the stress that is developed when heating at the interface.

Table 2. Internal Surface Heating Condition Comparison with

Percent Difference Thickness

Distance (mm) Analytical

Results (Pa) Numerical

Results (Pa) Percent

Difference(%)

0 0 0 0 0.225 -169356 -182036 7.5 0.45 -284604 -285702 0.4

0.675 -349380 -350266 0.3 0.9 -369908 -368026 0.5

1.14 -342367 -338638 1.1 1.38 -367512 -270162 1.0 1.62 -151155 -154787 2.4 1.87 0 0 0

Table 3. External Surface Heating Condition Comparison with

Percent Difference Thickness

Distance (mm) Analytical

Results (Pa) Numerical

Results (Pa) Percent

Difference (%)

0 0 0 0 0.225 207736 193556 7.3 0.45 326037 325107 0.3

0.675 399716 398889 0.2 0.9 419984 422121 0.5

1.14 386447 388771 0.6 1.38 308303 303592 1.6 1.62 176640 172328 2.5 1.87 0 0 0

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INTERFACIAL HEATING CONDITION Recall that the primary goal of the numerical study is

to provide direction in establishing a measurement methodology for the next phase of the target development. This means the interfacial heating which is impossible to replicate in lab, must be compared to the internal and external surface heating experimental configurations. Figure 8 compares the temperature distributions of the inner, interfacial and outer heating conditions. The plot shows that for the same heating load the overall temperature drops. More importantly from a thermal stress standpoint, the qualitative temperature distribution within the cylinder is parabolic as opposed to linear in the case of heating from one of the exposed surfaces. A plot of the radial stresses as a function of the target thickness compared to the inner and outer surface heating can be seen in Figure 9.

Figure 9 shows that the interfacial radial stress is zero at the inner and outer surfaces. However, unlike the inner and outer heating cases, there is an interior point at which the stress is zero. The stress located between the inner surface and the zero point is a positive tensile stress and the stress from this point to the outer surface is a negative compressive stress. Overall the stress level is also much smaller than interior or exterior heating held at the same heat load level.

From a metrology perspective, it is clear that heating from the external surface will tend to increase the thermal contact resistance while internal surface heating will decrease the thermal contact resistance. To ensure that the measurements provide conservative results with respect to evaluating the interface contact resistance, external heating will be preferred. In other words, if the thermal contact resistance measured when the interface is put in tension still meets performance requirements, then there will be a low risk that the target will fail due to thermal contact resistance while being irradiated. Further, it can be seen that the total heat load for testing can be significantly reduced to achieve a stress field that will be closer in magnitude to the internal heating case.

CONCLUSIONS The purpose of the analysis presented in this paper

is to evaluate the thermal mechanical behavior of a LEU based annular target to establish a thermal contact resistance test method. The results show that an internally applied heat flux would put the target into a compressive state leading to a lower thermal contact resistance. An externally applied heat flux creates a tensile force at the cylinder’s interface. The tensile force at the interface will increase the thermal contact resistance by decreasing the contact pressure. To ensure that the state of the interface is evaluated conservatively, the externally applied heat flux should be used to characterize the thermal contact resistance. Further, the heat load can be reduced to develop a

stress field that more closely matches the stress field that develops when heat is generated at the interface.

ACKNOWLEDGMENTS We would like to thank Dr. George Vandegrift and

Argonne National Laboratory for supporting this activity.

REFERENCES

1. NNSA Office of Global Threat Reduction, http://nnsa.energy.gov/nuclear_nonproliferation/1550.htm

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4. Mutalib, A., B. Purwadi, Adang H. G., Hotman L., M. Kadarisman, A. Sukmana, Sriyono, A. Suripto, H. Nasution, D. L. Amin, A. Basiran, A. Gogo, D. Sunaryadi, T. Taryo, G. F. Vandegrift ,G. Hofman, C. Conner, J. Sedlet, D. Walker, ,R. A. Leonard, E. L. Wood, T. C. Wiencek, and J. L. Snelgrove, “Full-scale Demonstration of the Cinithem Process for the Production of Mo-99 Using A Low-Enriched Target,” Argonne National Laboratory Report ANL/CMT/CP-97560, 1999.

5. Solbrekken, G.L., El-Gizawy, S., “Moly-99 Production at MURR: LEU Target Design,” Argonne National lab, 24 April 2008.

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