Replacement of reflectors by albedo type boundary conditions

The procedure of representing the effect of a reflector on the behavior of a reactor by using a homogeneous boundary condition at the core-reflector interface has been examined for two-group, two dimensional situations representative of a light water moderated power reactor. In addition the scheme has been extended to the time dependent case. A matrix relating the net neutron currents normal to the surface of the core to the group fluxes on that surface is found. The elements of this matrix are algebraic formulas involving the group cross sections and thickness of the reflector and depending on the instantaneous transverse bucklings and logarithmic time derivatives of the group currents at the core-reflector interface. Comparisons for two dimensional (XY) static problems between flux shapes and eigenvalues determined using these boundary conditions and the analogous quantities determined with the reflector represented explicitly yield agreement of a few tenths of a percent in eigenvalue and a few percent in point flux values. Problem costs are reduced about forty percent. Similar comparisons for one dimensional time-dependent cases are also very encouraging. (6 references) (U.S.)