The Thermal Utilization in Noncylindrical Reactor Cells Containing a Cylindrical Fuel Rod

A new analytical method is presented for computing the thermal utilization of a noncylindrical unit cell containing a cylindrical fuel rod. No cylindrization of the cell is required. The boundary condition at the outer edge of the cell is formulated in terms of a procedure that minimizes the square of the neutron current at a number of unspecified points along the edge. This leads to rapid convergence in computations of the thermal utilization, even with tightly packed lattices for which previous methods may not converge. The method is used to derive specific formulas for the thermal utilization using diffusion theory; the method of Amouyal, Benoist, and Horowitz; and, finally, the P_N method with anisotropic scattering. Sample computations using these models are also presented.