(a) Accident analysis

The reactor dynamics calculations for HTRs are often performed with a point model, at least as far as neutron kinetics are concerned. This sort of calculation is often considered sufficient for accident analysis as also the cause of the accident (e. g. the amount of water entering the core) can only be determined with difficulty.

Comparisons performed between space-dependent and point model calculations show that even for the maximum reactivity transients possible for HTRs, there is very little discrepancy in the behaviour of the total reactor power with time. This means that if the flux shape is not altered during the transient (e. g. control-rod movement) the results of the point model are sufficiently accurate as far as neutron kinetics are concerned. This is not valid for the heat-transfer calculation because the shape of the axial temperature profile may change strongly during the power excursion. An example is given in Fig. 12.3 which refers to a hypothetical ejection of a central control rod in the 300-MWe THTR pebble-bed reactor. This distortion in the axial temperature profile gives rise to a considerable discrepancy between the zero and the one-dimensional calculations. This is shown in Fig. 12.4 where the results of the zero-dimensional DYN code’111 are compared with those of a one-dimensional COSTANZA calculation.’81

In the case of big reactivity excursions where the reactor is nearly prompt critical, point model calculations can only give an accurate time behaviour of the reactor power if the proper prompt neutron lifetime is used. The effect of / on point model calculations of power excursion is given in Fig. 12.5. A space-dependent calculation, limited to a few time steps, may be necessary in order to obtain the proper / (see § 12.8).

Still for the case of the central control rod ejection, Fig. 12.6 shows the time behaviour of the flux shape. In order to visualize better the change in shape, all distributions have been renormalized to the initial power level.

One can see that after about 0.05 sec the flux has settled to the new fundamental mode and all higher modes have vanished. As the thermal capacity of THTR fuel elements is about 2 (MW sec/m3°C) even in a pessimistic assumption of no heat release to the coolant (adiabatic assumption in the thermodynamic meaning of this word) one needs an average power density of 400 MW/m3 to have a temperature increase of 10°C in 0.05 sec. In the case of a 0.64% reactivity step the overall power increases in 0.05 sec only by less than a factor of 2, and even in the central region does not increase by more than a factor of 13. As the HTR power density is always in the range 6-8 MW/m3 it does not appear to be possible with foreseeable accidents to reach a power density of the order of 400 MW/m3 in 0.05 sec. This means that the contributions of the higher modes to core temperatures is negligible in HTRs.<12>

Various codes for zero-dimensional or space-dependent reactor dynamics are described in refs. 13 to 18.