Application Of Generalized TTA Based On Backtracking Algorithm In Burn-up Calculation

During the operation of nuclear power plant,the reactor will produce different kinds of nuclear reactions and a lot of nuclide isotopes.The core function of burnup calculation is to solve the point-depletion equation,so as to track the changes of the concentration of different nuclides in the nuclear reaction system and calculate t he related decay heat and reactivity at the same time.With the development of nuclear science and computer hardware and software,a variety of new computational methods have been applied to solve the burnup equation in order to obtain higher accuracy,efficiency and versatility.Transmutation Trajectory analysis(TTA)is an analytic calculation method based on a single linear nuclide chain.It has the advantages of high accuracy,flexible time step and could avoid the stiffness problem of equations.However,due to the complexity of the reaction network of the burnup system,it is hard and tedious to dismantle and establish the sub-chains.Many procedures can deal with the burnup calculation only by using pre-defined nuclide chains which will obviously affect the accuracy and versatility of computation.Based on the traditional Transmutation Trajectory analysis,this paper made it better.The traditional Bateman expression can calculate all the nuclide densities by Laplace transform.But if there are same repeated eigenvalues in a chain,the denominator of the equation will appear to be zero.In this paper,generalized analytic expressions are derived by the use of limit operation which allow repeated eigenvalues.At the same time,by introducing backtracking algorithm,the nuclide chains achieve to be automatic searched,and an adaptive analytic calculation method is formed.Compared with traditional burnup method,the accuracy and versatility have been greatly improved.Then based on this advanced linear sub-chain analysis method and the EAF-2007 database,the burnup calculation program ABURN was developed.In this thesis,ABURN procedure is used to calculate the typical decay,neutron activation and fission reaction problem respectively,and compare the resu lts with the Chebyshev rational approximation method(CRAM).It is shown that the ABURN program can achieve high accuracy and can provide technical support for practical burnup calculation after more tests and verification in the future.