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Abstract
A non linear mathematical model for determining the dynamic response of a pressurized water rector core was developed that incorporates both prompt and delayed temperature feed back.
The problem arising from the stiffness of point reactor kinetics equations has been resolved. The development of the methods therein devised was necessitated by the unavailability of general-purpose numerical integrators capable of efficiently solving stiff systems of ordinary differential equations.
The time dependence of a reactor, taking the Feedback mechanisms into account, is relatively difficult. We will consider a PWR core with a two path Feedback. The reactivity is diminished as the temperature of the Fuel increases due to the Doppler broadening of the resonances. This Feedback is instantaneous since the temperature increase follows the power generated immediately. The second Feedback path is that of the Moderator temperature coefficient. As the Moderator temperature increases, the number density decreases and the neutron mean free path increases so that leakage increases and reactivity decreases.
Also, all of our analysis will be fundamental mode analysis. The physical phenomena are taking place so slowly that the higher harmonics of the flux distribution are all dying out so rapidly that we only need to consider the lowest or fundamental mode.
The thermal analysis really should proceed by the solution of the space-time heat conduction equation. This is a very complicated procedure and would also mean that spatial effects of the kinetics equations should be taken into account. We, therefore, will assume only a lumped parameter model and will obtain the time dependence of a reactor which is really one with the average properties of the reactor under consideration
So, we tried to examine the temperature Feedback mechanism of a PWR, Solve the delayed neutron model with temperature Feedback for a step insertion and a ramp insertion of reactivity and Checkout the Fuel temperature coefficient of reactivity Using Artificial Neural networks.
In doing that we make use of a Standard Runge-Kutta (SRK) method in the solution of the point reactor kinetics equations and to report on its accuracy and efficiency as observed in solving several sample problems. This method is representative of a class of Runge-Kutta methods for the solution of stiff systems. In turn, this class is a member of a set of different approaches developed for that same purpose.
A comparison of the results obtained with ”SRK” and the Hansen’s method oflargest Eigenvalues shows that ”SRK” is fairly moderate.
Finally, we make Use of the up growing technology of artificial neural networks ANNs, So as to predict the Fuel temperature coefficient of reactivity. The results of the ANNs were on the same line with that of both SRK and Hansen’s Method.
THESIS ORGANIZATION
This thesis consists of five chapters and three appendixes.
Chapter I contains a literature review of previous work in the field of simulation then it proceeds with the construction of the basic equations required to derive the point kinetics equations starting from the one group diffusion equation for neutrons.
Chapter 2 contains basic constructions of the equations, assumptions and relaxations used to construct the Feedback model on basis of both thermal and neutronic aspects.
In Chapter 3 the various parameters used in the Feedback model, the Moderator and Fuel temperature coefficients of reactivity, the total heat capacity and the overall heat transfer coefficient were obtained.
Chapter 4 proceeds with the discussion of the ”SRK” method over mathematical view. The Feedback model equations were set and arranged in order to be solved numerically using ”SRK” Method, then the iteration procedures of solution was outlined and the results of calculations was drawn along with that obtained from the Eigenvalue method, a comparison was made between the two methods showing that ”SRK” has the priority.
Chapter 5 includes the prediction of the Fuel temperature coefficient of
reactivity a Fusing ANNs. The results were very good and the predicted values of
aF is nearly the same as the calculated values.
Finally, there are three appendixes. in Appendix A, a list of tables and date used in our calculations, Appendix B contains the flowchart of the program RKFTU and Appendix C is the Use of Eigenvalue method to solve the reactor point kinetic equations.