9.9. The energy released in the core by fission appears in various forms, but mainly as the kinetic energy of the fission fragments, the fission neu­trons, and the beta particles resulting from radioactive decay of the fission products (see Table 1.2). The fission fragments are usually stopped within the fuel elements themselves; the small fraction that escapes into the clad­ding penetrates only about 0.01 mm. The beta particles of high energy may travel up to 2 mm in a cladding material such as zircaloy (§7.117), and so a large fraction of these particles may escape from the fuel element into the moderator or coolant, but they will not get out of the reactor core.

The fission neutrons lose most of their energy in the first few collisions with moderator atoms, and they travel distances ranging from some cen­timeters to a few feet. It is seem, therefore, that most of the heat from the three sources under consideration, comprising about 90 percent or more of the total energy generated, will be released within the reactor core.

9.10. The remaining 10 percent, or less, of the energy produced in fission appears as gamma rays which are distributed throughout the reactor core and surrounding components in a manner dependent on the specific materials and geometries involved. Thermal stresses as a result of gamma heating of the reactor vessel and surrounding radiation shielding must be considered by the designer (§7.30).

9.11. As we have seen (§2.213), heat generation by radioactive decay of the fission fragments continues after the fission reaction ceases. There­fore, provision must be made for cooling the fuel elements after shutdown. Particularly important are emergency core cooling features to be effective in the case of an accidental loss of normal cooling capability (§12.33). Also, the role of gamma heating affects the after-shutdown spatial distribution somewhat. For example, 1 hour after shutdown, the heat generation rate in the fuel elements will be about 1.5 percent of the operating value, whereas in the reflector and shield it will be approximately 10 percent of the rate during operation.

9.12. It was seen in Chapter 1 that the total energy released in fission, which ultimately appears as heat, is made up of contributions from a num­ber of sources. In general, the total energy, exclusive of the neutrino energy which is lost to the reactor system, may be expressed by

E « 191 + Ec (in MeV),

where Ec is the energy liberated as a result of various parasitic neutron capture processes, e. g., nonfission capture in uranium-235 and uranium — 238, and capture in moderator, coolant, structure, etc.; this includes the energy of the capture gamma radiations and the decay energies, i. e., the energies of the alpha and beta particles and gamma rays, of any radioactive species that are formed by parasitic neutron capture.[1] Since the value of Ec will obviously depend upon the nature of the materials present in the reactor core, it is evident that the total amount of heat produced by fission will vary, to some extent, from one type of reactor to another.

Example 9.1. Determine the total energy release in the core of a pressurized-water reactor (PWR) having volume fractions of uranium oxide (U02), water, and iron of 0.32, 0.58, and 0.10, respectively. The oxide fuel (density = 10.2 x 103kg/m3) has an average enrichment of 2.8 percent 235U, and the average cooling water density is 0.69 x 103 kg/m3. The energy released per neutron captured in uranium, water, and iron may be taken as 6.8, 2.2, and 6.0 MeV, respectively.

The solution requires the calculation of the macroscopic neutron capture cross section for each component (except for the oxygen in U02 which is very small) as well as the 235U macroscopic fission cross section. The final result depends on ratios of cross sections rather than absolute values; hence, the tabulated values for 0.0253-eV neutron microscopic cross sections may be used in the calculations. The capture-to-fission ratios are then as given in the following summary:

The energy released as a result of nonfission captures is

Ec = (6.8 x 0.16) + (6.8 x 0.17) + (2.2 x 0.076) + (6.0 x 0.19) = 3.6 MeV

The total energy released per fission in this core is thus

E = 191 + 3.6 « 195 MeV = 3.1 x 1011 J.