**4. A complex example**

## **4.1 EBR-II**

With a comparatively simple application providing excellent comparison results, a more challenging application is warranted. As noted above, the EBR-II design includes numerous fuel assemblies, molten sodium coolant, and a complicated thermal expansion and mechanical interaction process. Detailed characterization of the reactor components and materials along with measurements of control rod critical positions and corresponding bulk coolant temperatures are available [9]. These measured data allow confirmation of the methodology for certain aspects of the reactivity coefficients present in EBR-II such as the thermal expansion of the reactor grid plate. Extrapolation of the methodology can then occur for the more complicated thermal expansion and mechanical interaction of the assembly hexagonal flow ducts.

#### *Finite Element Methods and Their Applications*

While no reliable method of measuring the reactivity coefficient associated with the hexagonal duct expansion and mechanical interactions is known to exist, the methodology described here can be applied and a reliable estimate of the reactivity coefficients can be obtained.
