Application And Improvement Of Chebyshev Rational Approximation Method On Burnup Calculation

Burnup refers to the change of nuclide composition and quantity in nuclear fuel with operation time of reactor,involving the depletion,conversion and proliferation of nuclear fuel,and radiation safety.It is significant to reactor physics design,radiation protection and fuel management.The key technology of burnup calculation is to solve the burnup equation.The main calculation methods are the transmutation trajectory analysis method(TTA),time-marching finite-difference method,and matrix exponential method.As a kind of matrix exponential method,Chebyshev rational approximation(CRAM)is widely recommended because it does not need to deal with short-lived nuclides separately and has high computational accuracy.In this paper,we mainly study the 14-order PFD-form CRAM,which is commonly used in burnup calculation at present,and its solution formula in burnup calculation is derivated.Then programming of CRAM is performed,and the inversion calculation of large-scale sparse complex coefficient matrix is completed.As a result,a burnup calculation program is developed,which includes preprocessing module(reading database and input file),solver module(CRAM),and postprocessing module(generating output file).Then,this program is used to test the traditional 14-order PFD-form CRAM,and the results show it is difficult to select suitable time step for decay calcualtion of short-lived nuclides.Through causal analysis of this problem,the necessity of increasing the order of CRAM is clarified.Subsequently,the IPF form of CRAM is introduced,and the order is increased to 36 order.Correspondingly,the selection range of time steps is extended to 10 years.The test results show that the calculation results of high-order CRAM with only 1 time step(i.e.,the time step can be as long as the total depletion/decay time)are highly consistent with the analytic solutions,avoiding the process of time step selection and making the application of CRAM easier.The work of this paper extends the application range of CRAM in burnup calculation through overcoming the difficulty of time step selection,which has certain value on method research.The burnup calculaiton program developed in this paper based on high-order CRAM can be a convenient analytical tool for engineering application.