Sample Computation Using Two-group Model

21 Nuclear package power plant (a) actual geometry (b) idealized model. 

Our primary interest in this calculation is the determination of the critical mass of the hot clean reactor and the radial distribution of the fast and thermal flux throughout the core and reflector. An accurate analysis of this system must necessarily take into account the completely reflected cylindrical geometry shown in Fig. 8.216. However, since this would entail a somewhat involved calculation, we will approximate the actual configuration by an equivalent reflected sphere of the same composition. This will reduce our computation appreciably and yet not obscure any of the essential steps in the application of the two-group model. A study of the effect of the corners in the completely reflected cylinder will be deferred until the next section. 

For the purposes of the present calculation we assume that the equivalent spherical system is one which has the same core volume as the actual geometry and a spherical-shell reflector 17.8 cm thick. On this basis the radius of the spherical core is 72 = 31.93 cm, and for convenience we take the extrapolated outer radius of the reflector to be jS = 50 cm. It is important to note that the simplification proposed here, and in particular the selection of the equivalent system, is not to be construed as necessarily representing a good approximation. Its only function is to clarify the presentation. 

The nuclear concentrations of the components listed in the above table are easily computed. These are 

The group constants for this reactor have been computed from the methods described in Sec. 8.4b, using the data (8.200). These are listed in Table 8.5. 

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