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The parameterization process is an important part to ensure the accuracy of Pin-by-pin calculation. However, the traditional macro-depletion scheme which is based on the base-branch structure will lead to the history effect in the parameterization process. The existing methods to deal with the history effect include the following: 1) The micro-depletion correction which is also based on the base-branch structure but requires the additional lattice output to track the nuclide density in core calculation; 2) The hybrid correction method which is based on the multi-trunk structure. These methods are effective in dealing with homogeneous history problems such as boron concentration variations. However, due to the limitation of the method themselves, they cannot fully describe the instantaneous change process of the off-nominal base to the nominal base. Hence it is difficult for the existing methods to deal with the history when the pin-cell local state parameters are discrete changes, such as the control rod movement history. It might not be so serious in the assembly-homogenization-based two-step scheme. However, due to the refinement of the spatial mesh in the Pin-by-pin calculation, the interference between the pin-cells is stronger, which will worsen the history coming from the discrete changes of pin-cell local state parameters. Therefore, it is necessary to develop an acceptable history effect treatment method for such histories. In this paper, a bi-directional branch correction technique for the strongly heterogeneous operating histories was proposed for the Pin-by-pin calculation. In the traditional multi-base structure, only the depletion histories under the nominal base and the off-nominal base, and the instantaneous change from the nominal base to the off-nominal base can be considered. The bi-directional branch correction technique is a supplement to the traditional multi-base structure. The instantaneous change from off-nominal base to nominal base is further considered for the history of control bar movement, which shows the features of the dramatic changes in pin-cell local state parameters. Theoretically, it is a more comprehensive method to deal with the history effects. The new technique was tested based on a 3×3 multi-pin problem and a single assembly problem. The numerical results show that for the strong spatial heterogeneous history introduced by the control rod movement, the keff deviation obtained by the micro-depletion correction and the multi-base hybrid correction both more than ±1 000 pcm, in contrast, the bi-directional branch correction can keep the keff deviation within ±300 pcm. The numerical results demonstrate that the bi-directional branch correction can effectively handle the control rod movement history in the Pin-by-pin calculation. |
