MATHEMATICAL DESCRIPTIONS OF A NEUTRON POPULATION

Transport theory [58] offers the most accurate description of a reactor’s neutron population in terms of a vector flux, but it has stringent computational demands. However, other than very close to strong absorbers or emitters,[30] neutronic velocity vectors are approximately isotropic and neutron migration can be readily computed when treated like the diffusion of gas molecules. Accordingly, with appropriate boundary conditions neutron conservation is characterized by a scalar neutron flux f as [58]

image037(2.21)

where

f — Scalar neutron flux = Number of neutrons per square centimeter per second D — Diffusion coefficient ^2a — Macroscopic absorption coefficient S — Expected neutron production rate per unit volume V — Neutron speed in each chosen energy band of a simulation

Two — or three-dimensional multigroup[31] diffusion calculations of pro­posed core geometries have been validated by experimental zero-energy assemblies, and they have been proven successful in the United Kingdom for designing AGRs, SGHWR, PFR, and naval PWRs.

The fixed compact core geometries associated with fast reactors and PWRs have normalized neutron flux profiles that are largely governed by the escape of neutrons from the fissile core region, and so are substantially independent of output power. In addition fuel enrichment is deliberately increased toward the core periphery to “flatten” the radial flux profile and thereby enhance economics. These considerations intuitively suggest that the dynamics of these reactor types can be

Table 2.1

Delayed Neutron Data for BWRs and PWRs with Uranium Fuel

Precursor group

1

2

3

4

5

Fraction (bj)

0.00084

0.0024

0.0021

0.0017

0.00026

Decay constant (rj) (s)

0.62

2.19

6.50

31.7

80.2

closely approximated by one-dimensional distributed models [117], and experiments confirm this conjecture. Moreover the point kinetics model in Section 2.3 can also be derived [117] more rigorously by applying the analytical technique of adjoint (conjugate) linear map­pings to these distributed model equations. This further simplification to a point model has proved sufficient for many control and overall plant simulations. However, because steam is a far weaker absorber than its liquid phase, the neutron flux profile in direct cycle systems (e. g., BWRs) changes materially with output power, so these reactor dynam­ics necessarily require the simultaneous solution of the distributed neutron diffusion and thermal-hydraulic equations [145]. Most neutrons (so-called prompt) are released at fission but a very small minority appear somewhat later as various fission products undergo radioactive decay. Table 2.1 lists the pertinent parameters for these delayed neutrons and their precursors. Later in Section 2.5 they are shown to influence reactor dynamics seemingly out of all proportion to their relative concentrations.

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