The previous section has shown how the energy release calculation depends on the equation of state. Figure 4.5 shows several versions of extra­polations from three different sets of basic data.

To understand the importance of this equation in the calculation of total energy and, subsequently, the work energy, it is important to know how it fits into the phase diagram.

Figure 4.11 shows the two-phase diagram for fuel material in terms of the reduced variables pressure pjpc, specific volume vjva, and energy E/Ee. These reduced variables are all unity at the critical point C.

The solid normal configuration fuel exists in a state illustrated by A. When the fuel is overheated it expands, melts, and further expands, all at constant pressure, until all the volume normally occupied by coolant has been filled. Then the fuel state will move along a constant volume line, now with increasing pressures, until some terminal state В is reached, de­fined by the fact that the reactor has shut down due to the dispersion. The constant volume line for the final configuration is usually about vlve of 0.7 as a core has approximately 30% coolant volume.

The path from A to В is the equation of state included in the energy release calculations above. It may pass through the two-phase region in certain cases.

There is very little data available at high temperatures and pressures, even for metal fuels let alone the oxides and carbides; thus the equation of state depends on extrapolations from low temperature data. An alterna­tive method of obtaining the equation of state is to derive it from the generalized tables in terms of the reduced variables.

The law of corresponding states applies for materials with compressibility factors not very different from that of water (0.23). That for uranium oxide defined by Eq. (4.25) is 0.3.

compressibility factor = pcuJRTc (4.25)

The path A to В in Fig. 4.11 is clearly a threshold function and indeed threshold equations of state have been used. Other versions in use are shown in Table 4.3.

In the accident analysis, the true core equation of state should not be that of the oxide or carbide fuel alone, but it should include allowance for the equation of state of the structural steel present as well as the remaining sodium in the core. Difficulty arises since the amount of sodium remaining in the core is generally unknown.

4.3.4 Work Production

The energy release calculations are performed in order to determine the amount of energy that is available to do damage to the structure sur­rounding the core. The ultimate objective is to be able to define the final position and distribution of the core debris, so that this debris can be main­tained subcritical and adequately cooled. Thus we are interested in how much of the total energy release could be converted into damaging work energy.

Some idea of the magnitude of the damage which could be caused by nuclear explosions can be obtained from Fig. 4.12, which shows the energy generated in the destructive tests of the SPERT and BORAX reactors. Also shown is the calculated comparison of the SL-1 excursion (16). The energy ranges up to 200 MW-sec, which, from chemical explosion tests performed on scaled down reactor vessels, is equivalent to approximately 105 lb TNT.

After the power excursion is terminated by a small dispersion of the fuel material, the core will still be in the “constant volume” state assumed in the previous section. The coolant volume is occupied by fuel and structure debris. The center of the core is in a compressed liquid state under high pressures, and there may be some vaporized fuel in the core center while the periphery may be liquid or even solid. There is no sodium within the core, although there will be some sodium surrounding it.

The details of this homogeneous model of the disrupted and collapsed core depend on the severity of the energy release. From this state the core now expands and, in doing so, it does work. There are two basic expansion processes.