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Unformatted text preview: KW NEEP 411 Exam #1
October 215‘, 2011 ( 2/5) l. A UOgfuelled LWR has a heterogeneous cylindrical core containing 60,000 fuel rods.
At full power, the maximum thermal neutron ﬂux is 5 x 1013 n/cmZs. The fuel enrichment is 3%. The average moderator temperature is 300 °C. The fuel pellets are 8
mm in diameter. The core is 3.5 m high and 3.5 m in diameter. Neglecting extrapolation
lengths, calculate the total thermal power produced in this reactor in MWth. "ME ML/kthmP sen/demo Tom WMM. mega mm mm:
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k An actual U02 fuel rod experiences some “self—shielding” that is, it is a sufficiently
strong absorber that the neutron ﬂux experiences a small depression as neutrons move
into the fuel. The result of this is that the heat generation rate is not really uniform. Instead, it can be approximated as a parabolic shape: HI m “I L 2
q (r)—qo[1+a[RH Here is the power density in the center of the ﬂiel rod and a is a dimensionless parameter that measures the strength of the self—shielding.
( a») (a) Assuming the rod’s outer surface temperature is known and equal to TS, find an expression for the temperature proﬁle in the rod.
( ’5) (b) What is the temperature difference across the rod if it has a diameter of 1 cm, is 300 MW/m3, a = 0.2 and the rod’s thermal conductivity is 2 W/m°C?
(T) g (c) How much larger or smaller is this than the case without self—shielding, where the power density throughout the rod is uniform and equal to (l ~I— a) ? n, 1
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LL (3D 3. In our pressurized thermal shock problem, the heating from neutron attenuation is
more distributed because not every neutron interaction is an absorption reaction.
Scattering interactions result in deeper penetration than is conveyed in a simple
exponential decay. To model this, let the heat source be represented as follows: d2T
dx2 = j]:— (m) emf—ADC) Here the presence of the linear term, ,ux, results in a less severe attenuation as we move from the inside (x = 0) to the outside (x = t) of the vessel.
(7,0) (a) If the downcomer water temperature is T w and the heat transfer coefﬁcient is h,
ﬁnd an expression for the temperature proﬁle throughout a vessel of thickness t. As with our previous approach, assume the outside of the vessel (x = t) is insulated.
[0) (b) Find an expression for the average temperature through the vessel. (H (c) For t z 20 cm, k = 20 W/m°C, h = 50000 W/m20C, # = 0.2 cm“, = 0.2 MW/m3, and steel material properties E = 200 GPa, v: 0.3 and a = 8 x 10“6 C4, what is the thermally—induced hoop stress on the inner vessel
surface? You may ﬁnd the following integrals useful: Ix exp(—ax)dx = — 3E exp(—ax) ~ ~12— exp(—ax) a a
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\——U (7/0.) 4. A slab—like nuclear fuel element is sandwiched between cladding plates of different
thermal conductivity. Power density is uniform in the nuclear element, and there is
negligible power produced in the cladding. Water ﬂows on either side of the cladding.
The water temperature on either side is the same, but the heat transfer coefﬁcients are different. The geometry of the problem is indicated below: kF
kL kR
t E t
hL hR
Tw Tw
I» x (to) (a) Outline the procedure for ﬁnding the temperature proﬁle in this element,
including the fuel and the cladding. This should include the shapes of the
temperature proﬁles in both the cladding and the nuclear fuel, and any boundary
or interfacial conditions you would use to ﬁnd any undetermined coefﬁcients from the heat conduction equation.
(w) (b) For the case of kp << kL, kR with [Q < [CR and h < m, sketch the expected Shape of the temperature distribution in this element.
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