University of Missouri

Comparison of Uniform and Non-

Uniform Heating in the Plate Type LEU Foil Based Molybdenum-99 Production

Target

2011 ANS Winter Meeting

Washington, D.C.

November 3, 2011

Kyler Turner1, Dr. Gary Solbrekken1, 1University of Missouri, Columbia, MO,

University of Missouri

Outline

• Background/Motivation

– Molybdenum-99 and Technetium-99m

– HEU and LEU production techniques

– Purpose

• Model Benchmarking

– Simply supported plate was compared analytical and numerically.

• Uniform vs. Non-Uniform Modeling

– Examination of uniform and non-uniform heating effects on

deflection and stress.

• Conclusions

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Background / Motivation

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Background: Molybdenum-99 and Technetium-99m

• Relationship

– Technetium-99m (Tc-99m) is Mo-99’s daughter

– Tc-99m is the most widely used diagnostic radio-pharmaceutical

– A stable supply of Mo-99 is critical

TcMo

m9999

TcTcm 9999

• Origins of Molybdenum-99 (Mo-99)

– Mo-99 does not occur naturally

– The uranium-235 fission yield of Mo-99 is six percent

T1/2 = 65.94 hours

T1/2 = 6.02 hours

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Background: Current HEU Fission production

• Current Highly Enriched Uranium (HEU) Method

– Current production techniques are dominated by HEU.

– Nuclear nonproliferation efforts are currently focused on reducing HEU.

• Example of a Traditional HEU Target

– Powder dispersion plate target

Figure 1. HEU powder dispersion method

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Motivation: Uranium Loading/Density

• LEU Foil Approach

– A direct conversion from HEU to LEU would greatly reduce yield

– The uranium loading/density will greatly effect yield

Figure 2. Uranium Loading

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

2750

3000

3250

3500

0 2 4 6 8 10 12 14 16 18 20 22

Mo

.99 A

cti

vit

y (

Ci/cm

^3)

U Density (g/cm^3)

HEU 90% Enriched

LEU 19.75% Enriched

HEU

Dispersion

LEU Dispersion U3Si2 Dispersion

HEU/LEU

Dispersion

Breakeven

LEU Foil

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Background: High Density LEU Techniques

• High Density LEU Target

– The target is a composite structure

– Several different geometries

– Plate is consistent with many current producers designs

Figure 3. LEU Foil Method Figure 4.Possible Geometries

Plate Curved

Plate

Annular

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Purpose of Current Study

• Purpose

– Build on previous uniform heating deflection and stress

study1 and use non-uniform heating to make the heating

profile more realistic.

• Modeling Strategy

– Benchmark the numeric solution

• Examine element type, mesh density, etc.

– Use benchmarked model for non-uniform heating study

• Observe effects on deflection and stress

• Deflection and stress observation will relate directly to the

performance of target

1 G. L. S. Kyler K Turner, Jonathan Morrell " Non-Dimensional Analytical Analysis of a Simply Supported

Molybdenum-99 Production Target," presented at the American Nuclear Society Winter Meeting, Las Vegas,

Nevada, 2010.

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Model Benchmarking: Simply Supported Model Comparison

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Model Benchmarking: Setup

• Model

– A simply supported model with uniform temperature gradient through the thickness

of the plate was developed by Noda, Hetnarski, and Tanigawa2.

– Previous uniform heating study also used this model.

Figure 6. Simply Supported Equations

2 21 1

( , ) sin sinmn

m n

F m x n yx y

a bm n

a b

4 ( )(1 )cos( ) * cos( )mn

T a a b bF m n

ab t m m n n

Figure 5. Simply supported model

2. R. B. H. Naotake Noda, and Yoshinobu Tanigawa, Thermal Stresses, 2nd ed. New York, NY: Taylor &

Francis, 2003.

2 1

1TM

D

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Model Benchmarking: Results

• Benchmarking

– Varying types of elements and mesh densities were examined.

Table 1.Deflection comparison

Figure 7. Deflection results in Abaqus

Figure 8. Simply Supported model created by Noda, Hetnarski, and

Tanigawa

Delta T (K)

Analytic Deflection

(mm)

Numeric Deflection

(mm)

Percent Difference

5 0.06829 0.06864 0.51121

10 0.1366 0.1373 0.51114

50 0.6829 0.6864 0.51121

100 1.366 1.373 0.51114

Thickness = 0.001m

0.06m

0.205m

Figure 9. Plate Dimensions

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Uniform vs. Non-uniform Modeling

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Uniform vs. Non-Uniform Modeling : Setup

• Model

– Two aluminum plates welded at their edges with a uniform and non-uniform heat fluxes.

• Mechanical Boundary Conditions

– The free edge boundary conditions were applied to both models

Figure 10. Visual representation of boundary conditions Figure 11. Data collection points

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Uniform vs. Non-uniform Modeling : Setup

• Thermal Profile

– Uniform heating

• Consistent thermal profile

– Non-uniform heating

• Non-consistent thermal profile

Uniform Thermal Profile Non-Uniform Thermal Profile

LEU Footprint on Cladding

Figure 12. Temperature profiles and LEU footprint

5mm

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Uniform vs. Non-Uniform Modeling : Setup

• Modeling Conditions

– Uranium loading

• Thermal loads and heat fluxes

– Power production

• Assumed a neutron flux of 3.0e14 n/cm2s, 200 hour irradiation time, and 19.75 % enrichment.

Uranium

Loading (g)

Total

Power (W)

Uniform Heat Flux

per Side (W/m2)

Non-uniform Heat

Flux per Side

(W/m2)

Heat Transfer

Coefficient

(W/m2K)

31.6 60,000 2,439,024 3,076,920 20,000/ 5,000/ 500

15.8 30,000 1,219,512 1,538,460 20,000/ 5,000/ 500

0.5 1,000 40,650 51,282 20,000/ 5,000/ 500

Table 2.Uranium Loading and Heat Transfer Coefficients

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Uniform vs. Non-Uniform Heating: Free Edge Central Deflection

Results

Figure 11. Free Edge Deflection

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Uniform vs. Non-Uniform Heating: Free Edge Von Stress Results

Figure 12. Free Edge Von Mises Stress

Al 6061

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Conclusions

• Uniform vs. Non-Uniform Heating

– Established confidence in a numeric modeling tool through benchmarking

– The study indicates that non-uniform heating will produce

greater deflection at the same uranium loading and heat

transfer coefficient in the free edge condition.

– The observed trends illustrate that the deflection can be

controlled by adjusting the LEU footprint or LEU foil

dimensions on the cladding and the holding condition.

• Future Work

– Introduce curvature into the models and assess the effects

on deflection and stress

– Examine the fission gas pressure and uranium growth

– Assess the need for residual stresses

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Acknowledgements

• NNSA: Office of Global Threat Reduction

• Lloyd Jollay: Y-12 National Security Complex

• John Creasy: Y-12 National Security Complex

• Charlie Allen: University of Missouri Research Reactor

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Questions?