Hybrid computer simulation of xenon spatial oscillations

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Abstract
This paper is concerned with a hybrid computer simulation of the space-time xenon oscillation problem. Such prob lems are important in large thermal nuclear power reactors. The basic nuclear reaction is modeled by three slightly nonlinear partial differential equations-a diffusion equa tion describing the neutron flux concentration, and two first-order partial differential equations which contain only partials with respect to time and which describe the gen eration and decay of iodine and xenon. The continuous-space discrete-time approximation is used to implement the equations on the hybrid computer. By discretizing the time variable the xenon and iodine equations are reduced to algebraic expressions and the flux equation is reduced to a boundary value problem. The algebraic equations are decoupled from the boundary value problem and, therefore, solvable on the digital computer, by invoking the assumption that the nonlinear flux terms change slowly with respect to the time step. This assump tion also simplifies the boundary value problem which is solved on the analog computer in conjunction with digital function storage. The simulation effectively displays the space-time xenon oscillatory behavior resulting from an initial spatial per turbation of the flux shape. This information is used to study the stability of the local changes in the xenon con centration and, hence, the spatial variations of reactivity in the core.