Assignment for Week 1

B. Rouben

McMasterUniversity

4D03/6D03 Nuclear Reactor Analysis

2015 Sept.-Dec.

2015-11-30

Additional Exercises 1

Solutions

1. A research reactor fuelled with 235U is operated in critical steady state at a power of 40 MW. It is in the shape of a sphere with a diameter of 2.2 m (ignore the extrapolation distance). The average one-group properties are D = 1.1 cm,  = 2.4, and f = 0.0025 cm-1.

(a)Calculate the material buckling.

(b)What is the value of a?

(c)If one fission releases 200 MeV on the average, what is the average value of the flux?

(d)At what rate is 235U fissioningin the entire reactor?

(e)At what rate is 235U being consumed in the entire reactor?

(f)What fraction of neutrons leaks out of the reactor? What fraction is absorbed within the reactor?

Solutions:

2.An experiment is set up to measure the reactivity worth of a control rod by the source multiplication method. The reactor used is a cube of side 4 m, with the bottom parallel to the ground (ignore the extrapolation length). An external neutron source is introduced in the subcritical reactor, and a detector at the centre of the reactor indicates 100. Next, a control rod with a reactivity worth of -10 mk is inserted in the core, and the new reading is 50. Subsequently, the first control rod is removed and a second rod, of unknown worth, is inserted. The new detector reading is also 50. However, it is later determined that the operator making the measurements inadvertently moved the detector before the last reading, so that it was 1 m above the centre of the reactor when the last reading was taken. What is the reactivity worth of the second rod?

Solutions:

3. Consider nuclear material with the following properties in 2 energy groups:

a1 = 0.0012 cm-1, 12 = 0.007 cm-1, a2 = 0.0045 cm-1, f2 = 0.0056 cm-1

f1 = 0 cm-1, D1 = 1.08 cm, D2 = 0.90 cm

(a) Calculate the reactivity of an infinite lattice made of this material. Calculate also the resonance-escape probability in this lattice.

(b) If a homogeneous cylindrical reactor is made with this material, of diameter 5.2 m and height 5 m [neglect the extrapolation distance], calculate the fast and thermal non-leakage probabilities for this reactor, and its reactivity.

(d) Which group flux is higher? By how much?

Solution:

4. A homogeneous solution of 235U and H2O contains 10 g of 235U per litre of solution. Compute:

(a) the atomic density of 235U and the molecular density of H2O

(b) the thermal utilization

(d) the infinite multiplication factor.

Use: a,U-235= 687 b, f,U-235= 587 b, a,H2O= 0.664 b, D = 0.16 cm.

Use235 and 18 for the atomic masses of U-235 and H2O.

Note: You also need  for (d); use = 2.43(forgot to give this in original problem!)

Solution:

5. Suppose a homogeneous reactor has 2-group lattice properties as follows:

D1 / D2 / a1 /  a2 / 12 / f2 / 21 / f1
1.269 cm / 0.937 cm / 0.766E-3
cm-1 / 0.406E-2
cm-1 / 0.740E-2
cm-1 / 0.474E-2
cm-1 / 0 / 0

(a) What is the infinite-lattice multiplication constant of the lattice?

(b) If no reactivity devices are in the reactor, what must the leakage then be (in mk) for criticality?

(c) Use the relationship between the finite-reactor and infinite-lattice multiplication constants to determine the buckling in the critical reactor.

(d) What is the ratio of the thermal flux to the fast flux in the reactor (neglect terms in B4)?

(e) If this critical reactor is in the shape of a sphere, what is its diameter?

Solution: Method very similar to that of Problem 3, I won’t give solution.

6. A reactor is in an approach to critical. Boron (which has a reactivity worth of -8 mk/ppm) is being removed at the rate of 0.015 ppm/minute, and at t = 0 an in-core detector shows a reading of 80 (arbitrary units). At t = 10 minutes, the detector reads 95.

(a)What do you predict the detector reading will be at t = 30 min?

(b)What is the appropriate time to declare the reactor critical?

Solution:

7. A point source of neutrons, of strength S = 108 s-1, is located at point (x1, y1, z1) = (-10 cm, 20 cm, 0). Calculate the neutron flux and current (magnitude and direction) at the point (x, y, z) = (50 cm, 40 cm, 0). Take D = 1 cm and L = 5 cm.

Solution:

8. We want to make a homogeneous critical reactor with nuclear material with the following properties: f = 0.0043 cm-1, a = 0.0095 cm-1,  = 2.43, and D = 1.10 cm. Neglect the extrapolation distance in the following.

a)If we make a cubical reactor, what will be the dimension of the side?

b)If we make a spherical reactor, what will be its diameter?

c)Which of these two reactors would have a smaller value of leakage-to-production, and what will this value be?

Solution:

9. A homogeneous critical cylindrical reactor has a height-to-diameter ratio of 1.5:1. Its nuclear properties in 1 energy group are: a = 0.0078cm-1, f = 0.0085 cm-1, D =1.08 cm. What are the dimensions of the reactor? [Neglect the extrapolation distance.]

Solution: Method similar to that of Problem 8.

10. A research reactor consists of a cubical array of natural-uranium rods in a graphite moderator. Each side of the cube is 6.2 m long. The reactor operates at a steady power of 17 MW. The average value of f is 2.4*10-3 cm-1. Energy per fission Ef = 200 MeV, 1 MeV =1.6*10-19 J. [Neglect the extrapolation distance.]

(a) Calculate the buckling

(b) What is the average value of the neutron flux?

(d) At what rate is U-235 fissioning in the entire reactor (in nuclides/s) and on the average per cm3 per s?

Solution: Method similar to that of previous problems.

11. A CANDU fuel bundle contains 18.8 kg(U). It is introduced in a reactor at a location where its fission power is 450 kW, and it resides 4 months there. It is then moved to a new position, where its fission power is 830 kW. When it is removed from the reactor, its exit burnup is found to be 7,500 MW.d/Mg(U). How long did the bundle reside in the 2nd position?

Solution: