Fuel Rods – Fuel Pins

Nuclear Fuel Assembly
Typical fuel assembly

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. Fuel rods are made of zirconium alloy (e.g. Zr + 1%Nb), which is widely used as a cladding for nuclear reactor fuels. The desired properties of these alloys are a low neutron-capture cross-section and resistance to corrosion under normal service conditions. Zirconium alloys have lower thermal conductivity (about 18 W/m.K) than pure zirconium metal (about 22 W/m.K).

Fuel rods contain fuel pellets, which then loaded and encapsulated within a fuel rod. Aside from the stacked pellets, and cladding tube, the rod comprises two welded endplugs, a plenum (or expansion chamber) to accommodate the fission gases released, and a spring, located inside the plenum, holding the fuel column in position. The fuel rod is filled with helium, at a pressure of about 25 bars, to compensate, in part, for the outside pressure, in the primary circuit (155 bars in PWRs).

A PWR fuel assembly comprises a bottom nozzle into which rods are fixed through the lattice and to finish the whole assembly it is ended by a top nozzle. There are spacing grids between these nozzles. These grids ensure an exact guiding of the fuel rods. The bottom and top nozzles are heavily constructed as they provide much of the mechanical support for the fuel assembly structure. The top nozzle ensures the assembly handling function. Spacing grids are welded onto the guide tubes and ensure, by means of springs and dimples, fuel rod support, and spacing. They may carry vanes, allowing improved mixing of fluid streams, thus enhancing the assembly’s thermal–hydraulic performance.

Western PWRs use a square lattice arrangement and assemblies are characterized by the number of rods they contain, typically, 17×17 in current designs. The enrichment of fuel rods is never uniformed. The enrichment is differentiated in radial direction but also in axial direction. This arrangement improves power distribution and improves fuel economy.

Russian VVER-type reactors use a fuel that is characterized by their hexagonal arrangement, but is otherwise of similar length and structure to other PWR fuel assemblies.

Zirconium Properties

Zirconium is a lustrous, grey-white, strong transition metal that resembles hafnium and, to a lesser extent, titanium. Zirconium is mainly used as a refractory and opacifier, although small amounts are used as an alloying agent for its strong resistance to corrosion. Zirconium alloy (e.g. Zr + 1%Nb) is widely used as a cladding for nuclear reactor fuels. The desired properties of these alloys are a low neutron-capture cross-section and resistance to corrosion under normal service conditions. Commercial non-nuclear grade zirconium typically contains 1–5% of hafnium, whose neutron absorption cross-section is 600x that of zirconium. Hafnium must therefore be almost entirely removed (reduced to < 0.02% of the alloy) for reactor applications. Zirconium alloys have lower thermal conductivity (about 18 W/m.K) than pure zirconium metal (about 22 W/m.K).

Thermal Conductivity of Zirconium

Fuel pellets are 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). 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. Aside from the stacked pellets, and cladding tube, the rod comprises two welded endplugs, a plenum (or expansion chamber) to accommodate the fission gases released, and a spring, located inside the plenum, holding the fuel column in position. The fuel rod is filled with helium, at a pressure of about 25 bars, to compensate, in part, for the outside pressure, in the primary circuit (155 bars in PWRs).

Zirconium Alloy

A typical composition of nuclear-grade zirconium alloys is more than 95 weight percent zirconium and less than 2% of tin, niobium, iron, chromium, nickel and other metals, which are added to improve mechanical properties and corrosion resistance. The most commonly used alloy, to date, in PWRs, has been Zircaloy 4, however currently this is being replaced by new zirconium–niobium-based alloys, exhibiting better corrosion resistance. The maximum temperature, at which zirconium alloys can be used in water cooled reactors, depends on their corrosion resistance. Alloys of type Zircalloy, in which tin is the basic alloying element that provides improvement of their mechanical properties, have a wide distribution in the world. However in this case, the decrease of corrosion resistance in water and steam is taken place that resulted in the need for additional alloying. The improvement brought about by the additive niobium probably involves a different mechanism. High corrosion resistance of niobium alloyed metals in water and steam at temperatures of 400–550°C is caused by their ability to passivation with formation of protective films.

Temperature distribution in Fuel Cladding

Temperature Profile – Fuel Pellets

See also: Temperature Profile – Calculation

See also: Cladding Surface Temperature

Nuclear Fuel - Temperatures

Consider the fuel cladding of inner radius rZr,2 = 0.408 cm and outer radius rZr,1 = 0.465 cm. In comparison to fuel pellet, there is almost no heat generation in the fuel cladding (cladding is slightly heated by radiation). All heat generated in the fuel must be transferred via conduction through the cladding and therefore the inner surface is hotter than the outer surface.

To find the temperature distribution through the cladding we must solve the heat conduction equation. Due to symmetry in z-direction and in azimuthal direction, we can separate of variables and simplify this problem to one-dimensional problem. Thus, we will solve for the temperature as function of radius, T(r), only. In this example, we will assume that there is strictly no heat generation within the cladding. For constant thermal conductivity, k, the appropriate form of the cylindrical heat equation, is:

heat equation - cladding

The general solution of this equation is:

heat equation - cladding - general solution

where C1 and C2 are the constants of integration.

1)

Thermal conduction - fuel pelletCalculate the temperature distribution, T(r), in this fuel cladding, if:

  • the temperature at the inner surface of the cladding is TZr,2 = 360°C
  • the temperature of reactor coolant at this axial coordinate is Tbulk= 300°C
  • the heat transfer coefficient (convection; turbulent flow) is h = 41 kW/m2.K.
  • the averaged material’s conductivity is k = 18 W/m.K
  • the linear heat rate of the fuel is qL = 300 W/cm and thus the volumetric heat rate is qV = 597 x 106 W/m3

From the basic relationship for heat transfer by convection we can calculate the outer surface of the cladding as:

newtons law - cladding

As can be seen, also in this case we have given surface temperatures TZr,1 and TZr,2. This corresponds to the Dirichlet boundary condition. The constants may be evaluated using substitution into the general solution and are of the form:

heat equation - general solution - cladding

Solving for C1 and C2 and substituting into the general solution, we then obtain:

heat equation - cladding - solution

∆T – cladding surface – coolant

Detailed knowledge of geometry, outer radius of cladding, linear heat rate, convective heat transfer coefficient and the coolant temperature determines ∆T between the coolant (Tbulk) and the cladding surface (TZr,1). Therefore we can calculate the cladding surface temperature (TZr,1) simply using the Newton’s Law:

∆T - cladding surface - coolant - newtons law

∆T in fuel cladding

Detailed knowledge of geometry, outer and inner radius of cladding, linear heat rate, and the cladding surface temperature (TZr,1) determines ∆T between outer and inner surfaces of cladding. Therefore we can calculate the inner cladding surface temperature (TZr,2) simply using the Fourier’s Law:

∆T in fuel cladding - fouriers law

References:
Nuclear and Reactor Physics:
      1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
      2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
      3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
      4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
      5. W.S.C. Williams. Nuclear and Particle Physics. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467
      6. G.R.Keepin. Physics of Nuclear Kinetics. Addison-Wesley Pub. Co; 1st edition, 1965
      7. Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.
      8. U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.

Advanced Reactor Physics:

      1. K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2.
      2. K. O. Ott, R. J. Neuhold, Introductory Nuclear Reactor Dynamics, American Nuclear Society, 1985, ISBN: 0-894-48029-4.
      3. D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2. 
      4. E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4.

See above:

Nuclear Fuel