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					ARGONNE NATIONAL LABORATORY

INTRA-LABORATORY MEMO

July 26, 2000 To: From: Subject: Distribution S. Majumdar Effect of initial crack width on liquid lithium leakage through fatigue cracks in EVOLVE first wall Re:" Slow seepage of liquid lithium through fatigue cracks in EVOLVE first wall" memo dated July 26, 2000. In the above reference, I calculated upper bounds to the mass flow rate of liquid lithium through a 25 mm long fatigue crack in the EVOLVE first wall, assuming viscous and capillary effects to dominate inertia effects. At low pressures, capillary effects were shown to be significant, whereas the MHD pressure drop for planar cracks was shown to be negligible in the range of lithium pressure of interest to EVOLVE. However, these conclusions were based on the assumption that the initial crack width at zero pressure is zero. A closer examination shows that these conclusions are not necessarily valid if the initial crack width is > 0. For example, the mass flow rate as a function of lithium pressure is shown in Fig. 1 for a crack that is initially 10µm wide. Note that in this case, MHD pressure drop effects are greater than capillary effects. Also, the Hartmann numbers are greater for a 10µm wide crack than a crack of zero width (Fig. 2). Thus, at the low pressures of interest, the initial fatigue crack width plays an important role in determining the mass flow rate. It would be helpful if Steve Zinkle could give us some guidance on the typical width of fatigue cracks after initiation.

10 1 Ignoring MHD pressure drop Mass Flow rate (g/s) 10 0

10 -1 Ignoring capillary pressure head Crack length =25 mm Initial crack width=10µm 10 -3 0 0.1 0.2 0.3 p (MPa)
0

10 -2

0.4

0.5

Fig. 1 Variation of liquid lithium mass flow rate with lithium pressure for an initially 10 m wide crack.

10 2 Initial crack width=10µm 10 1 Hartmann Number

10 0 Initial crack width=0

10 -1

10 -2

0

0.1

0.2 0.3 p (MPa)
0

0.4

0.5

Fig. 2 Variation of Hartmann number for 0 and 10 m wide 25 mm long fatigue cracks with pressure.

2


				
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