Flux in a Reflected Thermal Reactor – Two-group Method
It was pointed out, the one-group method may provide reasonable results for the reactor, but this method does not accurately predict the flux. To be more accurate the energy of neutrons must be grouped into at least two groups. The two-group energy model leads to very interesting and important results, that must be considered in the design of nuclear reactors.
In this method, the entire range of neutron energies is divided into 2 intervals (fast group and thermal group). All of neutrons within each interval are lumped into a group and in this group all parameters such as the diffusion coefficients or cross-sections are averaged.
To find solution in a reactor core and in a reflector, it is necessary to solve the following diffusion equations for the fast and thermal energy groups are:
The solution of this system of homogeneous algebraic equations leads to a determinant of the coefficients. Such solution is shown in:
Reference: Ragheb, M. TWO GROUP DIFFUSION THEORY FOR BARE AND REFLECTED REACTORS, University of Illinois, 2006.
One of the striking results of such solution is that the thermal flux reaches local maximum near the core-reflector interface. This behaviour cannot be derived using one-group diffusion method, because it is caused just by thermalisation of fast neutrons. The fast neutrons, which are produced in the core can enter the reflector at high energy, are not absorbed as quickly in the reflector as neutrons thermalizing in the core, because absorption cross-sections in the reflector are much smaller than in the core (due to the absence of fuel). The thermal neutrons accumulates then near the core-reflector interface, resulting in the local maximum, that is usually known as the reflector peak. This also reduces the non-uniformity of the power distribution in the peripheral fuel assemblies and also reduces neutron leakage, i.e. increases keff of the system (or reduces the critical size of the reactor). This effect can be seen in the following figure.
The reflector peak can be seen only in thermal flux within the reflector. It is found that the fast flux does not show recovery peaks in the reflector, but rather drops off sharply inside the reflector (due to thermalization and absorption).