Study On Fission Matrix Acceleration Method And P - CMFD Method In Monte Carlo Critical Computation

Monte Carlo method is widely used to compute the multiplication factor and the fundamental mode eigenfunction of critical systems in reactor physics. The power iteration method is the most important technique for criticality calculation in general Monte Carlo codes. To obtain an accurate multiplication factor and the corresponding flux distribution, the preliminary iteration process has to be done until the source distribution converges. In a loosely coupled system or a large-scale system, the conventional Monte Carlo power iteration method suffers from slow fission source convergence if the initial guess differs significantly from the fundamental mode eigenfunction. To achieve a sufficiently convergent fission source, hundreds or even thousands inactive cycles must be performed before active cycles start. Sometimes, this slow convergence results in unacceptable computational costs, especially for whole core analysis of commercial reactors. Various acceleration methods have been proposed for Monte Carlo criticality calculations. Among these methods, the fission matrix acceleration method and the CMFD acceleration method has many times shown their potential in practical problems.The fission matrix acceleration method accelerates source convergence through adjusting the weights of fission neutrons according to the fundamental mode eigenvector of the fission matrix at each cycle. This method faces instability issue which restricts its wide applications in practice. In this thesis, we have found that the instability of the existing Monte Carlo fission matrix acceleration method is mainly caused by the magnification of the statistical errors during calculating the fundamental mode eigenvector of the fission matrix. Base on this observation, we propose a modified method to improve the stability of the Monte Carlo fission matrix acceleration method. The fundamental mode eigenvector of the fission matrix can be calculated by power iteration. In this thesis, the power iteration procedure to calculate the fundamental mode eigenvector of the fission matrix in each cycle is called as inner iteration to distinguish from the Monte Carlo iteration cycles. In our proposed method, the fission source distribution tallied during the Monte Carlo simulation is taken as the initial vector for the inner iteration. And the weights of the fission neutrons are not adjusted by the fundamental mode eigenvector of the fission matrix, but by the vector obtained with only a few inner iteration steps. We call the proposed method as Monte Carlo fission matrix acceleration method with limited inner iteration. The FM lii method possesses the properties that it is more stable than the existing fission matrix acceleration method as well as preserves considerable acceleration efficiency. Moreover, we analyze the stability property of the proposed method for the case of two weakly coupled fissile arrays. A number of numerical tests for practical large-scale, loosely coupled systems are presented which demonstrate the theoretical analysis and efficiency of this new scheme. The instability of the fission matrix acceleration method may be also caused by imbalanced precisions of elements of the fission matrix. Hence, an improved method in which the space mesh used to compute the fission matrix is defined adaptively based on the fission bank in each cycle is introduced in this thesis. This proposed method ensures balanced precisions of elements of the fission matrix, so is more stable than the existing fission matrix method.The CMFD acceleration method employs standard Monte Carlo thecniques to estimate nonlinear functionals, which are used in low-order CMFD equations to obtain the eigenvalue and discrete representations of the eigenfunction. In a "feedback" procedure, the Monte Carlo fission source is then modified to match the resulting CMFD fission source. In this thesis, the limited inner iteration technique is also applied in the p-CMFD acceleration method to decrease the oscillation of the outcome. Beside the source convergence acceleration, in some cases, the p-CMFD formulation can be utilized for obtaining more accurate MC solutions by applying it to the active cycles. But applying the p-CMFD formulation to the active cycles may also make the ourcomes more oscillatory in many cases. In this thesis, we introduce a step-by-step iteration p-CMFD technique used in the active cycles, the solution of the p-CMFD method is iterate only one step in each Monte carlo cycle. This technique decreases the oscillation of the outcomes efficiently.