Optimal geometry for fuel solution sloshing based on the boundary perturbation theory

A method which obtains an optimal geometry maximizing keff due to deformation of fuel solution sloshing has been developed. The concept of the ''boundary importance'' has been derived from the ''boundary perturbation theory''. Optimal geometry can be achieved by letting this ''boundary importance'' be constant along the boundary. As a numerical example, this method is applied to a two-dimensional slab fuel solution with and without a water reflector. The neutron diffusion equation on an arbitrary geometry is solved using the boundary-fitted curvilinear coordinate transformation system. Optimal geometry and its maximum reactivity are obtained as a function of the ratio of the solution height (Y) to slab thickness (X). For a bare fuel solution, whose Y/X is less than a certain threshold value, optimal geometry does not exist except for a circle. For a water-reflected fuel solution, whose Y/X is less than its threshold value, optimal geometry can be achieved by using asymmetric deformation. (author)