Reactivity Due to Deformation of a Thin Plate in a Critical Reactor

Perturbation theory has been used to obtain expressions for the reactivity associated with deformation of a thin plate in a critical reactor. The methodology uses reactivity worth coefficients computed for a homogeneous system to assess the effect of changes in the shape and composition of heterogeneous components such as structural and fuel elements. The resulting expressions are applied to two heuristic sample problems consisting of a uniform plate displacement and a sinusoidal plate bowing deformation. In the former case, the perturbation results agree well with exact analytical calculations. The second case provides useful analytical approximations that illustrate how the deformation reactivity is expected to vary with the fractional plate elongation, the location of the plate in the core, and other parameters.