Reator kinetics. Definition of core reactivity
Core reactivity is, by definition, the reactivity
(36a) calculated from the eigenvalue
λc of the fictitious, stationary, current core state equipped with the current planar reactivities
ρ(z).
This core static reactivity is not explicitly used in the program for solving the kinetic equations but is a parameter of paramount interest for interpreting the transients.
For 1-group model, in terms of planar macro cross sections, planar reactivity ρ(z) is calculated from (36b), where it is reminded that the total removal Σ
does not include axial leakage.
In the stationary form of axial eigen-value diffusion equation (36c), the fission source section F needs to be divided by λc in order to get a stationary solution whose stationary flux η differs from the current dynamic axial flux φ.
Eliminating λc and Σ in (36a:c) leads to the form (36d) of core stationary equation.
Operating (36d), as usual, with the weighted average operator allows to express ρc as a ratio (36e) of two functionals. This ratio provides the exact core reactivity either IF Φ → η OR IF ψ → stationary adjoint flux.
In practice neither η nor ψ are known, unless the eigen value problem is solved at each time step, and Φ and ψ are approximated by the current dynamic flux.
As for the planar reactivity, the error resulting from these approximations will be of second order.
If thermal group model is activated, it is tentatively suggested to add a correction term R21 D2 Δz into the one-group expression.
On an experimental version of the program, we have been able to verfiy that the true ρc is close enough to the approximation (36e) to allow using it for monitoring purpose.
The notation for core reactivity is rc