CHAPTER 4 – Approximate Solutions of the Point Kinetic Equations without Feedback

Kinetic equations without the thermal feedback are integrated for an arbitrary reactivity variation, assuming that the magnitude of the changes in the excess reactivity is less than one dollar. First and second approximations are obtained. The results are applied to the step, ramp, and periodical reactivity changes. It is found that the logarithm of the flux, in the first approximation, is given by the function which is the solution of the linearized kinetlc equatlons for the flux. Hence, the usual transfer function approach can be used to form the first approximate solution of the nonlinear kinetic equations. The wave form of the flux is obtained for a sinusoidal input, and the second harmonic is calculated. The exponential rise in the average value, as well as in the amplitude, of the oscillations of the flux is given for an alternative reactivity input. The gain of the reactor is defined. It is shown that the relatlve gain of the reactor decreases slightly with the increasing amplitude of the sinusoidal input. The results are compared to a numerical solution obtained by AVIDAC. (auth)

General solution of the reactor kinetic equations without feedback

/pdf/the-b-w-k-approximation-and-hill-s-equation-ii-4t7i5ju99f.pdf

The B. W. K. approximation and Hill’s equation. II

/pdf/a-practical-method-for-solving-hill-s-equation-2r0ir7xkty.pdf

A practical method for solving Hill’s equation

By means of approximate numerical solutions obtained from a first-order correction to the prompt-jump approximation, good agreement is found with exact numerical solutions of the kinetics equations...

Use of the Prompt-Jump Approximation in Fast-Reactor Kinetics

The theory of the P/sub 2/ calculation for a two-region cell in slab geometry is presented. In this treatment the boundary condition of Davison is employed. By this method an upper bound, furnished by the P/sub 2 model, and a lower bound, furnished by a P/sub 1/ model, are obtained on the disadvantage factor. lt is suggested that a single best estimate is normally the average of the two. (auth)

CHAPTER 4 – Approximate Solutions of the Point Kinetic Equations without Feedback

References

General solution of the reactor kinetic equations without feedback

The B. W. K. approximation and Hill’s equation. II

A practical method for solving Hill’s equation

Use of the Prompt-Jump Approximation in Fast-Reactor Kinetics

Disadvantage Factors in Slab Geometry by the P2 Calculation

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