12.1. General considerations about reactor dynamics

Reactor dynamics is concerned with the analysis of the time-dependent behaviour of the reactor in normal operation and during accidents. Also the interpretation of most reactor physics experiments involving reactivity changes requires an analysis of core dynamics.

The kineticst of a nuclear reactor can be described by a set of equations connecting the variables describing the state of the system. The most important variables are the neutron flux and the temperatures of the various reactor components, together with the parameters which can influence these quantities (poison concentrations, cross-sections, coolant mass flow, etc.) and the data defining the causes of the transients. Properly called kinetics equation is the equation connecting the neutron flux to the other variables. As its coefficients are usually temperature-dependent, this equation cannot be solved without considering the reactor heat transfer equations, which in turn can involve the complete power plant system, down to the turbine. Simplifying assumptions will have to be made for each practical case. The feedback of the control system appears in the coefficients of the kinetics equation. Its detailed description would involve treating the control system with its electrical and mechanical parts, and here again simplifications are necessary.

The phenomenon which is in most cases characterizing the reactor dynamic behaviour, is the presence of the delayed neutrons. The /3-decay of a fission product leads in some cases to a highly excited state of the daughter product which can then emit a neutron. Those fission products are commonly referred to as delayed neutron precursors. The neutron emission follows almost immediately (~ КГ14 sec) the /3- radiation, and the delay of the neutron is determined by the /3-decay constants of the parent, which ranges from milliseconds to minutes. The delayed neutrons are usually grouped according to the /3-decay constant of the parent nuclides (the number of groups is often six).

The time variation of the reactor state is the result of various phenomena: fuel burn-up, fission product build-up and decay, temperature variations, reactivity changes due to movement of absorber rods or other geometrical and material changes within the reactor. Each of these phenomena is characterized by a different time constant. The results of reactivity changes are usually rapid transients whose time constant is determined by the lifetime of the prompt and delayed neutrons.

tThe term “kinetics" is generally used to indicate the time-dependence of the neutron population, while reactor "dynamics" includes also beside kinetics, the study of temperature and control feedbacks.

Temperature feedbacks have time constants determined by the heat capacity and conductivity of fuel and moderator. Fuel burn-up and fission product build-up and decay are usually characterized by very long time constants. Most short-lived fission products do not need to be treated explicitly, with the exception of 135Xe because of its enormously high thermal absorption cross-section. The stable nuclide 149Sm gives also rise to transients with short time constant because it has a high cross-section and a short-lived parent. For Xe and Sm transients the time constants vary between 9 and 48 hours.

Each of these phenomena may be mathematically expressed by a set of differential equations. As a general rule it is possible to treat independently transients with widely differing time constants. This means that in solving, for example, the differential equations representing the fuel burn-up and fission product build-up it is possible to assume that Хе, I, Pm, Sm, temperatures and delayed neutrons are in equilibrium condition and the time derivative of these quantities is zero. Thus we can distinguish three independent types of transients: burn-up, Xe and Sm, temperature and delayed neutron transients. The first type of transient does not belong to reactor dynamics and has been treated in Chapter 9. Xenon-135 and 149Sm transients are of the order of some hours and are particularly important for reactor shut-down, start-up, power following, and spatial Xe instability. For these phenomena (long time dynamics) the time derivatives of the neutron flux, delayed neutron precursor concentrations and tempera­tures can be neglected (an exception can be the cases in which the heat capacity of some core component is so big that its time constant approaches the order of magnitude of the 135Xe decay constant).

The other type of transients (short time dynamics) whose time constants vary from fractions of seconds to a few minutes, can be treated assuming constant Xe and Sm concentrations since they hardly change in the short time of the transient. They include all reactivity accidents, temperature stability analysis, and rapid power excursions.