B. Rouben
McMaster University
4D03/6D03 Nuclear Reactor Analysis
2015 Sept.-Dec.
Assignment 5
Assigned 2015/10/07
Due by 2015/10/14 11:00 am
4 Problems
Total: 38 marks
1. [12 marks; 2 marks for each part]
A uniform reactor is critical with the following 2-group lattice properties:
D1
D2
a1
 a2
12
f2
21
f1
1.140 1.050 0.595E-3 0.402E-2 0.726E-2 0.443E-2
0
0
-1
-1
-1
-1
cm
cm
cm
cm
cm
cm
(a) Determine the multiplication constant of the infinite lattice.
(b) How can the reactor be critical? Give a quantitative answer.
(c) Determine the buckling in this reactor (neglect terms in B4).
(d) Do you consider that neglecting the terms in B4 was justified? Explain.
(e) What is the ratio of the fast flux to the thermal flux in the reactor?
(f) If this reactor is in the shape of a cube, what is the extrapolated dimension of its
side?
2. [12 marks; 4 for each part]
You want to make a critical assembly by bringing 3 identical uniform cylindrical sections
together end to end. The proportions of each cylindrical section are diameter = 1.3 height.
When the sections are separated from one another, the leakage ensures that the individual
sections are not critical. The material of which the assemblies are made has k = 1.072 and
a migration length of 28 cm. Neglect the extrapolation length in this problem.
(a) What are the dimensions of each section such that the assembly of the 3 sections is
critical?
(b) What is the subcriticality (i.e., how many mk below critical) of each section by itself?
(c) What is the reactivity of an assembly made from 2 sections?
3. [9 marks; 3 for each part]
A reactor is being started up. A detector has been placed in the reactor to follow the
approach to critical
At time t = 0, the detector reading is 225. At that point, the approach to critical is paused,
and a rod of known reactivity, -0.75 mk, is inserted in the core (assume instantaneously).
The detector then reads 206.
(a) What was the system reactivity before the rod was inserted?
(b) The rod is left in the core, and the approach to critical is renewed, with moderator poison
removed at a rate of 0.064 mk per minute. Estimate the reading of the detector at time =
30 min.
(c) When should the reactor be declared critical?
4. [5 marks]
[Refer to the module on solving the diffusion equation numerically.]
In the numerical solution of the diffusion equation by the finite-difference method, you have 2
side-by-side cells:
 Cell L has an x-dimension of 20 cm; its thermal diffusion coefficient is 1.04 cm and
the thermal flux at its centre is 0.97*1013 n.cm-2/s-1
 Cell C has an x-dimension of 30 cm; its thermal diffusion coefficient is 1.12 cm and
the thermal flux at its centre is 1.16*1013 n.cm-2/s-1
The area Ayz of the boundary between the cells (in y and z) is 1,200 cm2.
Calculate the thermal current between the cells in the x-direction, and indicate in which
direction (from which cell to which cell) it is.