Most of PWRs use the uranium fuel, which is in the form of uranium dioxide. Uranium dioxide is a black semiconducting solid with very low thermal conductivity. On the other hand the uranium dioxide has very high melting point and has well known behavior. The UO2 is pressed into pellets, these pellets are then sintered into the solid cylinder (with a height, and diameter of about 1 centimeter, the height being greater than the diameter). The dimensions of the fuel pellets and other components of the fuel assembly are precisely controlled to ensure consistency in the characteristics of the fuel. These pellets are then loaded and encapsulated within a fuel rod (a metallic cladding tube), which is made of zirconium alloys due to its very low absorption cross-section (unlike the stainless steel). The surface of the tube, which covers the pellets, is called fuel cladding. Fuel rods are base element of a fuel assembly. Fuel rods have the purpose of containing fission products, ensuring mechanical support for the pellets, and allowing the heat removal to the coolant fluid of the heat generated by nuclear reactions. Typical fuel rod, has a length of some 4 m, with a diameter of around 1 cm. An 1100 MWe (3300 MWth) nuclear core may contain 157 fuel assemblies composed of over 45,000 fuel rods and some 15 million fuel pellets.
Temperature Profile – Fuel Pellets
See also: Temperature Profile – Calculation
See also: Cladding Surface Temperature
See also: Thermal Conduction of Uranium Dioxide
Thermal and mechanical behavior of fuel pellets and fuel rods constitute one of three key core design disciplines. Nuclear fuel is operated under very inhospitable conditions (thermal, radiation, mechanical) and must withstand more than normal conditions operation. For example temperatures in the centre of fuel pellets reach more than 1000°C (1832°F) accompanied by fission-gas releases. Therefore detailed knowledge of temperature distribution within a single fuel rod is essential for safe operation of nuclear fuel. In this section we will study heat conduction equation in cylindrical coordinates using Dirichlet boundary condition with given surface temperature (i.e. using Dirichlet boundary condition). Comprehensive analysis of fuel rod temperature profile will be studied in separate section.
Enthalpy of Nuclear Fuel
Enthalpy of nuclear fuel is also used as an acceptance criterion in very specific types of accidents, known as reactivity initiated accidents (RIA), such as Rod Ejection Accidents. RIAs consist of postulated accidents which involve a sudden and rapid insertion of positive reactivity. As a result of rapid power excursion, fuel temperatures rapidly increase, prompting fuel pellet thermal expansion. The power excursion is initially mitigated by the fuel temperature coefficient (or Doppler feedback), which will be the first feedback, that will compensate the inserted positive reactivity.
In these accidents, the large and rapid deposition of energy in the fuel can result in melting, fragmentation, and dispersal of fuel. The mechanical action associated with fuel dispersal can be sufficient to destroy the cladding and the rod-bundle geometry of the fuel and produce pressure pulses in the primary system. The expulsion of hot fuel into water has potential to cause rapid steam generation and these pressure pulses, which could damage nearby fuel assemblies. Limits on specific fuel enthalpy are used, because the experimental tests show that degree of fuel rod damage correlates well with the peak value of fuel pellet specific enthalpy.
Regulatory acceptance criteria vary with country and reactor type, but there are usually two kinds of fuel enthalpy limits:
- CORE COOLABILITY CRITERIA. Reduction of coolability can result from violent expulsion of fuel, which could damage nearby fuel assemblies. In past, the core coolability criteria was revised to specifically address both short-term (e.g., fuel-to-coolant interaction, rod burst) and long-term (e.g., fuel rod ballooning, flow blockage) phenomena which challenge coolable geometry and reactor pressure boundary integrity. A definite limit for core damage, which must not be exceeded at any position in any fuel rod in the core. According to Appendix B of the Standard Review Plan, Section 4.2, these criteria are, for example:
- Peak radial average fuel enthalpy must remain below 230 cal/g. Above this enthalpy, hot fuel particles might be expelled from a fuel rod.
- Peak fuel temperature must remain below incipient fuel melting conditions.
- FUEL CLADDING FAILURE CRITERIA. A fuel rod failure threshold, that define whether a fuel rod should be considered as failed or not in calculations of radioactive release (source term). According to Appendix B of the Standard Review Plan, Section 4.2 fuel rods may fail by several damage mechanisms:
- The high cladding temperature failure criteria for zero power conditions is a peak radial average fuel enthalpy greater than 170 cal/g for fuel rods with an internal rod pressure at or below system pressure and 150 cal/g for fuel rods with an internal rod pressure exceeding system pressure.
- The PCMI failure criteria is a change in radial average fuel enthalpy greater than the corrosion-dependent limit depicted in Appendix B of the Standard Review Plan, Section 4.2.
See also: Enthalpy of Nuclear Fuel
Fuel – Cladding Gap
There is also one very important phenomenon, which influences the fuel temperature. As the fuel burnup increases the fuel-cladding gap reduces. This reduction is caused by the swelling of the fuel pellets and cladding creep. Fuel pellets swelling occurs because fission gases cause the pellet to swell resulting in a larger volume of the pellet. At the same time, the cladding is distorted by outside pressure (known as the cladding creep). These two effects result in direct fuel-cladding contact (e.g. at burnup of 25 GWd/tU). The direct fuel-cladding contact causes a significant reduction in fuel temperature profile, because the overall thermal conductivity increases due to conductive heat transfer.
Fuel Burnup and High Burnup Structure
In nuclear engineering, fuel burnup (also known as fuel utilization) is a measure of how much energy is extracted from a nuclear fuel and a measure of fuel depletion. Reactor engineers distinguish between:
- Core Burnup. Averaged burnup over entire core (i.e. over all fuel assemblies). For example – BUcore = 25 000 MWd/tHM
- Fuel Assembly Burnup. Averaged burnup over single assembly (i.e. over all fuel pins of a single fuel assembly). For example – BUFA = 40 000 MWd/tHM
- Pin Burnup. Averaged burnup over single fuel pin or fuel rod (over all fuel pellets of a single fuel pin). For example – BUpin = 45 000 MWd/tHM
- Local or Fine Mesh Burnup. Burnup significantly varies also within single fuel pellet. For example, the local burnup at the rim of the UO2 pellet can be 2–3 times higher than the average pellet burnup. This local anomaly causes formation of a structure known as High Burnup Structure.
The distribution of heat generation is not homogeneous across the pellet. Indeed, the generation of Pu 239 by capture, in uranium 238, of epithermal neutrons is quite marked in the pellet rim, by way of the self-shielding effect (for neutrons endowed with an energy corresponding to resonances, the capture cross-section is so large that they are unable to reach the center of the pellet). This overconcentration of plutonium in the rim, gradually building up during irradiation, results in a drop, from rim to center, in radial power distribution. Therefore local burnup significantly varies also within single fuel pellet. For example, the local burnup at the rim of the UO2 pellet can be 2–3 times higher than the average pellet burnup. This local anomaly causes formation of a microstructure known as High Burnup Structure.
Uranium Dioxide – UO2
Uranium dioxide is a ceramic refractory uranium compound, in many cases used as a nuclear fuel. Most of LWRs use the uranium fuel, which is in the form of uranium dioxide (chemically UO2). Uranium dioxide is a black semiconducting solid with very low thermal conductivity. On the other hand the uranium dioxide has very high melting point and has well known behavior.
Uranium dioxide has significantly lower density than uranium in the metal form. Uranium dioxide has a density of 10.97 g/cm3, but this value may vary with fuel burnup, because at low burnup densification of pellets can occurs and at higher burnup swelling occurs.
Thermal Conductivity of Uranium Dioxide
See also: Thermal Conduction of Uranium Dioxide
The thermal conductivity of uranium dioxide is very low when compared with metal uranium, uranium nitride, uranium carbide and zirconium cladding material. The thermal conductivity is one of parameters, which determine the fuel centerline temperature. This low thermal conductivity can result in localised overheating in the fuel centerline and therefore this overheating must be avoided. Overheating of the fuel is prevented by maintaining the steady state peak linear heat rate (LHR) or the Heat Flux Hot Channel Factor – FQ(z) below the level at which fuel centerline melting occurs. Expansion of the fuel pellet upon centerline melting may cause the pellet to stress the cladding to the point of failure.
Thermal conductivity of solid UO2 with a density of 95% is estimated by following correlation [Klimenko; Zorin]:
where τ = T/1000. The uncertainty of this correlation is +10% in the range from 298.15 to 2000 K and +20% in the range from 2000 to 3120 K.
Special reference: Thermal and Nuclear Power Plants/Handbook ed. by A.V. Klimenko and V.M. Zorin. MEI Press, 2003.
Special reference: Thermophysical Properties of Materials For Nuclear Engineering: A Tutorial and Collection of Data. IAEA-THPH, IAEA, Vienna, 2008. ISBN 978–92–0–106508–7.