Reactor steady-state spatial distribution

For an actual system having the nuclear and geometric properties assumed above, only one of the solutions (8.283) is physically acceptable. This solution is the fundamental mode o(r). It is clear that, for n > 0, the steady-state spatial distribution would require that i4(r, ) < 0 in certain regions of the reactor. The determination of the neutron-flux spatial distribution in a finite system by means of the integral-equation formulation was demonstrated in Sec. 5.7c for the case of an infinite slab. Those results may be applied directly to the multiplying medium problem. In the case of the infinite-slab reactor, of width 2a, Eq. (8.283) takes the form... 

The aspect ratio effect is seen in Fig. 29. Given a localized source of species (e.g. radicals), the spatial distribution of these species at steady state will depend on the reactor aspect ratio. Low aspect ratio reactors (tall, small radius) yield a distribution that peaks on axis, while large aspect ratio systems (short, large radius) yield a dis-... 

A PFR can be visualized as a tubular reactor for which three conditions must be satisfied (i) the axial velocity profile is flat (ii) there is complete mixing across the tube, so that all the reaction variables are a function of the axial dimension of the reactor (named z) and (iii) there is no mixing in the axial direction. PFRs have spatial variations in concentration and temperature. Such systems are caUed distributed, and analysis of their steady state performance requires the solution of differential equations. 

The CSTR is a fiow reactor, in which the contents are mechanicaUy agitated. If the mixing is adequate, the entering feed will be quickly dispersed through the vessel, and the composition and temperature at any point will approximate the average composition and temperature. Perfect mixers have no spatial distribution of compositions and temperatures. Such systems are called lumped. The steady state performance of lumped systems is determined by algebraic equations rather than differential ones. 

The material buckling of the heavy water, natural uranium subcritical assembly, with a fixed composition and lattice spacing, is determined by measuring the spatial distribution of the neutron flux. The assembly is in a steady-state condition, multiplying neutrons which originate from a neutron source properly placed near the assembly. The buckling determination yields the minimum critical volume of a neutron-chain reactor with the same composition and structure as the exponential assembly. 

---