Critical fuel concentration

We compute the critical fuel concentration Np from Eq. (3.22). If the symbol M denotes the moderator components, then the appropriate form of (3.22) for a homogenized fuel-moderator system is... 

It is proposed that a reactor of pure UFe be constructed, the fluorine to provide the moderation and the U in the uranium to serve as the nuclear fuel. A first estimate of the critical fuel concentration for such a system can be obtained from the one-velocity infinite-medium model. 

Fto. 5.21 Critical fuel concentration and total fuel mass for spherical reactor in the one- velocity model. 

This relationship is the requirement for criticality. The solution of this equation for Np gives the critical fuel concentration [with ly m Fa//[Pg.212]

If the core of this reactor were entirely bare, we could use Eq. (6.80) directly to determine the critical fuel concentration. Since the present configuration is completely reflected, we require a modified relation which will take into account the effect of the reflector. We observed in Chap. 1 that the purpose of the reflector is to decrease the neutron escapes from the core and thereby reduce the critical fuel concentration of the system. Clearly, if we were to ignore the reflector altogether, our estimate of the... 

The refers to the nonfuel components D2O and aluminum and has the value 0.0009762 cm Because of this relatively low nonfuel neutron absorption cross section in the core, it is to be expected that the critical fuel concentration will be low. As a first approximation we take the diffusion coefficient in (6.191) to be that of pure D2O at 49 C. If we assume that the microscopic transport cross section of D2O is independent of temperature around thermal energy, then the only effect on 2tr will be through changes in the density of the material. In that case we may use the relation (see Table 5.1)... 

Equation (8.125) is the criticality equation for a reactor operating at steady state. In its present form, this equation relates the properties of the core (left side of the equation) to the properties of the reflector (right side). Thus, given the properties of the reflector, (8.125) determines the critical fuel concentration (or size) of the core. In making computations with this relation, it will be convenient to call the core term Tc Xj(pc) and the reflector term Tr, (Pr). Note that o) is determined by (PC [according to (8.126)] and that k is determined by (pr (8.127), so that the only variables which remain are x and f, once the s (i.e., cross sections) have been specified. The criticality condition is that... 

Suppose, for example, that the shape and dimensions of the reactor have been specified, and that the composition of the nonfuel components is known. The problem, then, is to determine the critical fuel concentration. The calculation may be carried out by assuming various fuel loadings and finally selecting that loading which satisfies all the system requirements determined above. It should be recognized that, in this procedure, it is necessary to recompute several of the nuclear constants Kif K2y. . . with each assumed value of the fuel concentration. As a rule, only a few of these constants are markedly affected by variations in the fuel concentration, so that as a first approximation one need make adjustments only for these quantities. When a fairly reliable estimate has been obtained for the critical concentration, the entire computation may be repeated, using the corrected values of the less sensitive parameters. 

Computation of critical fuel concentration of system 1. With the... 

Here C denotes all the various factors in (8.389) which are independent of the fuel concentration. If we use these two expressions in (8.392) and solve for the critical fuel concentration Nf, we obtain... 

In all cases, the fuel concentration increases with an increase in fertile material, IF02 (Fig. 24-24). An increase in Vg/Vc increases the thorium c(.)ntcnt, reduces the slowing-down power, increases the average energy of tli( neutron spectrum in the core, and increases the thorium absorptions. -Vs a result of these effects, the critical fuel concentration in the fluid fuel, A 2.5 -Vsi ratio, increases as Fs/Fc increases (Fig. 24-25). 

Fig. 24-24. Critical fuel concentration vs. thorium concentration for single-fluid LMFR.

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