Question 19.1: Calculate the values of the diffusion coefficients for water......
Calculate the values of the diffusion coefficients for water and uranium in a thermal water reactor just prior to start-up.
In this case, the room temperature libraries from BNL-325 (see Appendix C) can be used to find the values for the diffusion coefficient in the fuel and the moderator. The diffusion coefficient D can be thought of as a measure of the physical resistance that a material presents to the flow of neutrons. A large diffusion coefficient implies that it is easy for a neutron to move through a material, and a small diffusion coefficient implies that it is hard. We know from our previous discussion (see Chapter 11) that D = 1/(3Σ_s), and the values of \sum\limits_{s}^{U235} and \sum\limits_{s}^{H_2O} are 0.43 cm^{−1} and 3.44 cm^{−1}, respectively. Hence the values of the diffusion coefficient for the fuel and the moderator are approximately
\mathrm{D}^{\mathrm{FUEL}}=1/\left(3\sum_{S}^{U235}\right)\approx{\frac{1}{3\times0.43}}=0.775\,\mathrm{cm}
\mathrm{D}^{\mathrm{MOD}}=1/\left(3\sum_{S}^{H_2O}\right)\approx\frac{1}{3\times3.44}=0.097\,\mathrm{cm}
This means that the diffusion coefficient for the fuel is approximately eight times larger than the diffusion coefficient for the moderator in a thermal water reactor. This is the behavior we observe in Figure 19.1, wheres the explicit spatial dependence is shown.
