Consistent generalized energy condensation theory

Recently, a method was developed to generalize the multigroup theory to estimate the fine-group angular flux within a coarse-group transport calculation. In the development of that method, the angular dependence of the coarse-group total cross section was neglected. As is well known, this approximation introduces errors in the transport solution making its accuracy dependent on the number of coarse groups and the choice of group structure. This paper extends the generalized energy condensation theory to explicitly account for the angular dependence of the coarse-group total cross section. This is accomplished in a natural way by modifying the treatment of the total cross section to include orthogonal expansions in both energy and angle. As a result, the fine-group flux can be consistently reproduced during the coarse-group calculation. This method paves the way for recondensation of the cross sections on-the-fly thereby eliminating the errors introduced by using simplified problems (e.g. lattice-cells) to estimate the coarse-group cross sections. In this paper, the method is derived in general geometry and implemented and verified with several 1D reactor problems (both LWR and VHTR).

► A new method is presented which explicitly accounts for the energy–angle coupling in multigroup theory. ► Coarse-group solution with full energy–angle coupling correction exactly preserves fine-group physics. ► The new theory is validated via two sets of benchmark problems typical of stylized BWR and HTR core configurations.