22.251 Systems Analysis of the Nuclear Fuel Cycle Fall 2009 PROBLEM SET #8
Problem 1: The purpose of this problem is to appreciate the reactivity
changes as a function of H/HM ratio in the core, and to examine the
implications of the thermal-hydraulic considerations on the H/HM limits in
the core.
1. a) Verify that the PWR 17x17 Westinghouse fuel assembly falls in region (2) in
that attached Figures.
1.b) Explain the behavior of the attached k-H/HM and B1-H/HM plots in terms of
basic reactor physics phenomena and principles. The plots show the initial keffective (i.e. at zero burnp) and the reactivity-limited single batch burnup, B1 as
a function of the ratio H/HM of hydrogen to heavy metal atoms. The curves are
all based on the standard Westinghouse PWR 17x17 fuel geometry and
dimensions. The variations in H/HM were obtained by arbitrarily changing the
water density in CASMO. Address the dominant causes of the trends in each of
the three regions designated, with emphasis on slope, minima and maxima.
1.c) What are the implications for operation in region (3) rather than (2) in
Figure1 for
- Core compactness?
- Reactivity control during a loss of flow and a loss of coolant accident?
1.d) Consider the engineering aspects of the core design, where would you
expect to draw lines in Figure 1 to represent heat transfer limiting lines for steady
state operations?
1.e) Would you want the reactor to be designed at the point of maximum B,
between (2) and (3)? Explain your answer.
1.f) A new design is proposed in which U hydride instead of U oxide is to be used
as fuel. What benefits you think might be derived from such a fuel change?
Problem 2 The purpose of this problem is to examine the effect of Pu and U
recycle on the need for uranium in LWRs, and consequently on the price of
the fuel.
2.a) Solve Problem 7.6 of the Textbook of Cochran and Tsoulfanidis
2.b) Solve Problem 7.7 of the textbook of Cocharan and Tsoulfanidis
1.8
1
2
3
1.7
1.6
k� (t = 0)
1.5
1.4
1.3
1.2
1.1
PWR
1
0.9
0.8
0.7
0.01
1
0.1
10
100
H/HM (atom number ratio)
4.5% U-235
12% U-235
9.75% U-235
19.5% U-235
15% U-235
Fig. 1 Initial k� as a function of hydrogen-to-heavy-metal ratio for uranium fueled lattices.
Image by MIT OpenCourseWare.
1
220
2
3
200
B1 (MWd/kg)
180
PWR
160
140
120
100
80
60
40
20
0.1
1
10
100
H/HM (atom number ratio)
4.5% U-235
12% U-235
9.75% U-235
19.5% U-235
15% U-235
Figure 2. Reactivity-limited burnup as a function of hydrogen-to-heavy­
metal ratio for uranium fueled lattices.
Image by MIT OpenCourseWare.
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http://ocw.mit.edu
22.251 Systems Analysis of the Nuclear Fuel Cycle
Fall 2009
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