The test case

Two hypothetical scenarios are under investigation here: in the first, the helium coolant is lost and the primary loop is in a depressurized state (called Depressurized Conduction Cooldown or DCC); in the other, the helium coolant is retained and the primary loop remains pressurized (called Pressurized Conduction Cooldown or PCC). The key difference for the analysis is that, during PCC, natural convection effects within the primary loop significantly alter the temperature profiles in the core.

Both STAR-CD simulations start at the point when the reactor is operating at full power (600 MW) and all heat sinks are lost except for the Reactor Cavity Cooling System (RCCS, a set of vertical panels along the concrete walls of the cavity containing the reactor vessel, which remove heat from the cavity to the outside). At this point the protection system automatically drops control rods into the core to shut down the reactor. The simulations end one hundred hours (or over four days) of simulated time later, when the energy removed from the reactor exceeds the heat produced by the decay of radionuclides in the core, thereby causing the total energy in the system to decrease.

The main barrier to simulating such long time scales is that time steps in transient calculations are limited by the requirement that the Courant number-a measure of the number of cells that information travels across in one time step-remains below fifty. Here, this corresponds to a maximum time step size of 0.1 seconds. In order to maintain calculation times at feasible magnitudes, a novel method was used. The calculation begins by solving both the momentum and temperature fields for the initial one thousand seconds. Then it alternates between solving both momentum and temperature fields using small time steps and solving the temperature fields alone, with the momentum field frozen, using large time steps.

Running one calculation, in which both the momentum and temperature fields were solved at every time step for ten hours of simulated time, and then comparing the results of this calculation with the results of the method described above validated this approach. Very little difference was found.

The computational domain is a 30º section of the reactor vessel (shown in figure 2). The various materials in the reactor are either modeled explicitly in STAR-CD or homogeneously: i.e., the “mean” physical properties of a particular heterogeneous component are used (an example being the fuel elements, which are composed of fuel compacts and a graphite web containing holes for the compacts and the coolant).

DCC Results

Figure 3 shows the time history of temperatures in the reactor during a DCC transient. With coolant no longer flowing downward through the core, the hottest region moves upward from the bottom of the core to the center. Meanwhile, the upper and lower parts of the reactor vessel interior—which are at the coolant’s inlet temperature during normal operation—become cooler.

The core experiences its highest temperature of 1450 ºC at approximately eighty hours after shutdown. Initially during the transient, the temperature of the pressure vessel decreases as it is cooled by the RCCS. After ten hours, however, some of the heat from the core has passed through the outer graphite blocks and produces a rise in the peak vessel temperature, which reaches a maximum value (of nearly 480ºC) after one hundred hours of simulated time.

PCC Results

Figures 4 and 5 show the temperature profiles in the fluid and solid regions against time for a PCC transient. The natural convection currents develop quickly, with fluid circulating up through the core channels and reflector gaps. The STAR-CD simulation enabled detailed insight into the flow patterns and how they evolve over the cooldown period. A significant change in the flow patterns was observed after approximately ten hours, with the flow currents effectively reversing direction.

An important finding was that, although the peak temperatures are not much higher during PCC than under normal operation, the natural convection currents cause the hot spot to move up the reactor core, exposing the top of the reactor core to high temperatures. Although the DCC case exhibits higher peak fuel temperatures than the PCC case, the thermal stresses on the upper part of the reactor are much greater for the PCC.

Finally, figure 3 shows that, once the initial ten hours of the transient have passed and an offset is established, the behavior in the DCC and PCC scenarios is very similar.