Calculation of surface power density at bottom of crack between innerwall tiles

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Calculation of surface power density atbottom of
crack between inner-wall tiles

• Steve Scott
• March 4 2005

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qT tan-1(y/D) _at_ y/D y D qT qF tan-1(y/F) _at_
y/F qT(D/F)
qF tan-1(y/F) _at_ y/F
D
Dq qF - qT
Inner wall
y
qT
qF
DNB CL
F
grid
seff
F400 D 450 Þ seff 8s 4.4o
qT
1.02o
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In the limit where the inner wall and the DNB
focal point are co-located the angular
distribution of power is a square wave.
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Power from right min (0.5 (0.5w-x)/dqTmax) Powe
r from left min(0.5 (0.5wx)/dqTmax)
dqTmax
x
d
qTmax
w
If we define a crack angle qc º w/d
then Total power density min(0.5
(qc/qTmax)(0.5-x/w) min(0.5 (qc/qTmax)(0.5-x/w)

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Surprise !!! Power density at center of
bottom of crack is equal to
power density at upper tile surface The power
density is not reduced by a factor like w/d so
the heating problem at the bottom of the tile
will be 30-40 times worse than we thought. Why
Because the angular distribution of incident
power is very narrow it is basically a
square-wave with half-width 8/450 1.02o.
Angular size of crack w/d 0.05/2 1.4o.
Calculation for nominal parameters F 400
cm D 450 cm Crack depth 2.0 cm Crack
witdh 0.05 cm