Chapter 9. Thermal Performance - mne.psu.edu

1 Light Water Reactor Materials Donald Olander and Arthur Motta 8/30/2009 Chapter 9. Thermal Performance 2 The Fission heat 2 energy Release from 2 Fuel 3 Fission heat 4 heat Conduction in the 4 heat Transfer 7 Gap 7 Axial Temperature 10 Thermal 11 Thermal Conductivity in Porous 12 Conductivity Variation with 13 Thermal Margins and Operational 13 The 14 Departure from nucleate 15 Cladding Temperature 16 Stored 16 17 20 Light Water Reactor Materials Donald Olander and Arthur Motta 8/30/2009 Introduction One of the most important factors in the design of

2 Nuclear power plants is the calculation of power production and the removal of heat from the core that allows energy production during operation. To that end, coolant is circulated through the core and heat flows from the fuel rods to the coolant, which experiences a temperature rise, as explained in Chapter 1. Since the heat is generated inside the fuel rods, temperature gradients are established inside the rods that enable the heat flux to flow out, resulting in a temperature profile within the rods. This temperature profile has a strong influence on the mechanical properties, microstructure evolution under irradiation and corrosion processes occurring in the fuel and the cladding.

3 Thus, a sound understanding of the factors governing the temperature distribution within a reactor fuel element is essential to predicting its Performance during reactor exposure. Both the high temperatures and the steep temperature gradients are important for predicting fuel element Performance . The temperature controls processes such as grain-growth, densification, and fission product diffusion in the fuel and radiation damage accumulation, and corrosion rates in the fuel cladding. The temperature gradients in the fuel cause pore migration and formation of the central void, cause Thermal stresses or fuel cracking, and pellet cladding interaction.

4 In the cladding the temperature gradients causes hydride rim formation and overall hydrogen redistribution. The topic of this Chapter is the Thermal Performance of the fuel rod and the core, including a calculation of the temperature distribution in the fuel rod and its change with reactor exposure and Thermal margins and accident conditions. The Fission heat Generation Nuclear energy is generated in light-water reactors by the fission of uranium induced by absorption of neutrons. The fission of the uranium atom splits it into two smaller parts (the fission products), and releases two to three energetic neutrons (average energy ~ 2 MeV), as well as other particles such as betas, gammas and neutrinos.

5 The neutrons released in the fission reaction cause fissions in other nuclei, a process called fission chain reaction. energy Release from fission The overall energy release in a single fission reaction is 200 MeV, about 90% of which is deposited in the fuel pellet. Although every nuclide in the transuranic region can be fissioned if enough energy is imparted to it, the fission cross-section for certain fissile nuclides (U-233, U-235, Pu-239, Pu-241) is greatly increased if the neutron energy is reduced to values close to the Thermal energy (~ eV at reactor temperature).

6 This energy reduction is done in Thermal reactors (such as the light water reactors considered in this book) by passing the neutron flux through a moderator (water) which causes the neutrons to lose energy by successive collisions until they are in Thermal equilibrium with their surroundings. To ensure that criticality (a fission chain reaction at a constant rate) can occur with Thermal neutrons, natural uranium is enriched to a larger percentage of the isotope U-235 (3-5% in current reactors). In parallel with neutron induced fission, neutron absorption can occur in uranium, causing transuranic (heavier than uranium) elements to be formed.

7 Of chief importance among these is Pu-239, which forms directly by neutron absorption in U-238 followed by beta decay. This creates another fissile isotope which contributes to the fission rate. In parallel with the depletion of U-235, Pu-239 is created from U-238 so that at the end of the fuel residence in the reactor, up to one third of the reactor energy is produced by plutonium fission. Not all the fissile material (U and Pu) is used by the time the fuel is removed from the reactor, so it is also possible to reprocess the spent fuel to extract U and Pu to fabricate mixed-oxide fuel (MOX), which consists of (U,Pu)O2.

8 Thus, there are various sources of heat in a reactor core: fast fission of U-238, Thermal fission of U-235 and Pu-239, and the radioactive decay of fission products. The last term is important in loss-of-coolant accident scenarios, since shutting down the fission chain reaction does not eliminate this heat source and cooling needs to be provided to avoid fuel damage (see Chapter 29). However, during normal operation the most significant heat generation term is Thermal fission in U-235 and Pu-239 (fast fission rate is a few percent of Thermal fission).

9 The first step in calculating the temperature profile is calculating the rate of heat production by nuclear reactions, mostly nuclear fissions. Given the above, we take Thermal fission in U-235 to be the dominant heat production mechanism, and consider a fuel element at the beginning of life, containing enriched uranium. In this case, the fission rate is given by 3(/)fffUfF fission cm sNqN = == ( ) where f is the macroscopic fission cross section (cm-1), is the neutron flux ( ), Nf is the fissile atom density (fissile atom/cm3), f the Thermal fission cross section (barn), q is the enrichment (fissile atom density/uranium density) , and NU is the uranium density (atom/cm3).

10 The theoretical atom density in uranium dioxide is 1022 atom/cm3, while the Thermal fission cross-section for U-235 is ~ 550 barn. Fuel Burnup There are three common measures of the integrated amount of irradiation to which the fuel has been subjected. The first is the fission density given by ( ) 30()[/]tFF t dtFtfission cm= for a constant fission rate. The second is the fractional burnup given by Light Water Reactor Materials Donald Olander and Arthur Motta 8/30/2009 number of fissionsinitial number of uranium atomsUFN == ( ) Finally, the burnup can be given as the number of megawatts days of Thermal energy released by a fuel containing one metric ton of uranium.